What is the sum of the geometric sequence 1, 3, 9, ... if there are 11 terms?

Answers

Answer 1

The sum of the geometric sequence 1, 3, 9, ... with 11 terms is 88,573.

To find the sum of a geometric sequence, we can use the formula:

S = [tex]a * (r^n - 1) / (r - 1)[/tex]

where:

S is the sum of the sequence

a is the first term

r is the common ratio

n is the number of terms

In this case, the first term (a) is 1, the common ratio (r) is 3, and the number of terms (n) is 11.

Plugging these values into the formula, we get:

S = [tex]1 * (3^11 - 1) / (3 - 1)[/tex]

S = [tex]1 * (177147 - 1) / 2[/tex]

S = [tex]177146 / 2[/tex]

S = [tex]88573[/tex]

Therefore, the sum of the geometric sequence 1, 3, 9, ... with 11 terms is 88,573.

For more questions on sequence

https://brainly.com/question/7882626

#SPJ8


Related Questions

given the equation 4x^2 − 8x + 20 = 0, what are the values of h and k when the equation is written in vertex form a(x − h)^2 + k = 0? a. h = 4, k = −16 b. h = 4, k = −1 c. h = 1, k = −24 d. h = 1, k = 16

Answers

the values of h and k when the equation is written in vertex form a(x − h)^2 + k = 0  is (d) h = 1, k = 16.

To write the given quadratic equation [tex]4x^2 - 8x + 20 = 0[/tex] in vertex form, [tex]a(x - h)^2 + k = 0[/tex], we need to complete the square. The vertex form allows us to easily identify the vertex of the quadratic function.

First, let's factor out the common factor of 4 from the equation:

[tex]4(x^2 - 2x) + 20 = 0[/tex]

Next, we want to complete the square for the expression inside the parentheses, x^2 - 2x. To do this, we take half of the coefficient of x (-2), square it, and add it inside the parentheses. However, since we added an extra term inside the parentheses, we need to subtract it outside the parentheses to maintain the equality:

[tex]4(x^2 - 2x + (-2/2)^2) - 4(1)^2 + 20 = 0[/tex]

Simplifying further:

[tex]4(x^2 - 2x + 1) - 4 + 20 = 0[/tex]

[tex]4(x - 1)^2 + 16 = 0[/tex]

Comparing this to the vertex form, [tex]a(x - h)^2 + k[/tex], we can identify the values of h and k. The vertex form tells us that the vertex of the parabola is at the point (h, k).

From the equation, we can see that h = 1 and k = 16.

Therefore, the correct answer is (d) h = 1, k = 16.

To know more about equation visit:

brainly.com/question/649785

#SPJ11

Please check within the next 20 minutes, Thanks!
Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum = 21, maximum 122, 8 classes The class w

Answers

For a given minimum of 21, maximum of 122, and eight classes, the class width is approximately 13. The lower class limits are 21-33, 34-46, 47-59, 60-72, 73-85, 86-98, 99-111, and 112-124. The upper class limits are 33, 46, 59, 72, 85, 98, 111, and 124.

To find the class width, we need to subtract the minimum value from the maximum value and divide it by the number of classes.

Class width = (maximum - minimum) / number of classes

Class width = (122 - 21) / 8

Class width = 101 / 8

Class width = 12.625

We round up the class width to 13 to make it easier to work with.

Next, we need to determine the lower class limits for each class. We start with the minimum value and add the class width repeatedly until we have all the lower class limits.

Lower class limits:

Class 1: 21-33

Class 2: 34-46

Class 3: 47-59

Class 4: 60-72

Class 5: 73-85

Class 6: 86-98

Class 7: 99-111

Class 8: 112-124

Finally, we can find the upper class limits by adding the class width to each lower class limit and subtracting one.

Upper class limits:

Class 1: 33

Class 2: 46

Class 3: 59

Class 4: 72

Class 5: 85

Class 6: 98

Class 7: 111

Class 8: 124

To know more about lower class limits refer here:

https://brainly.com/question/31059294#

#SPJ11

Which of these is NOT an assumption underlying independent samples t-tests? a. Independence of observations b. Homogeneity of the population variance c. Normality of the independent variable d. All of these are assumptions underlying independent samples t-tests

Answers

The assumption that is NOT underlying independent samples t-tests is: c. Normality of the independent lines  variable.

An independent samples t-test is a hypothesis test that compares the means of two unrelated groups to see if there is a significant difference between them. This test is used when we have two separate groups of individuals or objects, and we want to compare their means on a continuous variable. It is also referred to as a two-sample t-test.The underlying assumptions of independent samples t-tests are as follows:1. Independence of observations: The observations in each group must be independent of each other. This means that the scores of one group should not influence the scores of the other group.2.

Homogeneity of the population variance: The variance of scores in each group should be equal. This means that the spread of scores in one group should be the same as the spread of scores in the other group.3. Normality of the dependent variable: The distribution of scores in each group should be normal. This means that the scores in each group should be distributed symmetrically around the mean, with most of the scores falling close to the mean value. The assumption that is NOT underlying independent samples t-tests is normality of the independent variable.

To know more about parallel lines visit:

https://brainly.com/question/16701300

#SPJ11

A spring has a natural length of 16 cm. Suppose a 21 N force is required to keep it stretched to a length of 20 cm. (a) What is the exact value of the spring constant (in N/m)? k= N/m (b) How much work w lin 1) is required to stretch it from 16 cm to 18 cm? (Round your answer to two decimal places.)

Answers

The work done in stretching the spring from 16 cm to 18 cm is 0.10 J.

Calculation of spring constant The given spring has a natural length of 16 cm. When it is stretched to 20 cm, a force of 21 N is required. We know that the spring constant is given by the force required to stretch a spring per unit of extension. It can be calculated as follows; k = F / x where k is the spring constant F is the force required to stretch the spring x is the extension produced by the force Substituting the given values in the above formula, we get; k = 21 N / (20 cm - 16 cm) = 5 N/cm = 500 N/m Therefore, the exact value of the spring constant is 500 N/m.(b) Calculation of work done in stretching the spring from 16 cm to 18 cm The work done in stretching a spring from x1 to x2 is given by the area under the force-extension graph from x1 to x2.

The force-extension graph for a spring is a straight line passing through the origin with a slope equal to the spring constant. As we know that W = 1/2kx²The extension produced in stretching the spring from 16 cm to 18 cm is:x2 - x1 = 18 cm - 16 cm = 2 cm The work done in stretching the spring from 16 cm to 18 cm is given by:W = (1/2)k(x2² - x1²) = (1/2)(500 N/m)(0.02 m)² = 0.10 J.

To know more about spring visit:-

https://brainly.com/question/29975736

#SPJ11

Let X be the standard uniform random variable and let Y = 20X + 10. Then, Y~ Uniform(20, 30) Y is Triangular with a peak (mode) at 20 Y~ Uniform(0, 20) Y~ Uniform(10, 20) Y ~ Uniform(10, 30)

Answers

"Let X be the standard uniform random variable and let Y = 20X + 10. Then, Y~ Uniform(20, 30)." is True and the correct answer is :

D. Y ~ Uniform(10, 30).

X is a standard uniform random variable, this means that X has a range from 0 to 1, which can be expressed as:

X ~ Uniform(0, 1)

Then, using the formula for a linear transformation of a uniform random variable, we get:

Y = 20X + 10

Also, we know that the range of X is from 0 to 1. We can substitute this to get the range of Y:

When X = 0,

Y = 20(0) + 10

Y = 10

When X = 1,

Y = 20(1) + 10

Y = 30

Therefore, Y ~ Uniform(10, 30).

Thus, the correct option is (d).

To learn more about standard uniform random variable visit : https://brainly.com/question/20815963

#SPJ11

The additional growth of plants in one week are recorded for 11 plants with a sample standard deviation of 2 inches and sample mean of 10 inches. t at the 0.10 significance level = Ex 1,234 Margin of error = Ex: 1.234 Confidence interval = [ Ex: 12.345 1 Ex: 12345 [smaller value, larger value]

Answers

Answer :  The confidence interval is [9.18, 10.82].

Explanation :

Given:Sample mean, x = 10

Sample standard deviation, s = 2

Sample size, n = 11

Significance level = 0.10

We can find the standard error of the mean, SE using the below formula:

SE = s/√n where, s is the sample standard deviation, and n is the sample size.

Substituting the values,SE = 2/√11 SE ≈ 0.6

Using the t-distribution table, with 10 degrees of freedom at a 0.10 significance level, we can find the t-value.

t = 1.372 Margin of error (ME) can be calculated using the formula,ME = t × SE

Substituting the values,ME = 1.372 × 0.6 ME ≈ 0.82

Confidence interval (CI) can be calculated using the formula,CI = (x - ME, x + ME)

Substituting the values,CI = (10 - 0.82, 10 + 0.82)CI ≈ (9.18, 10.82)

Therefore, the confidence interval is [9.18, 10.82].

Learn more about standard deviation here https://brainly.com/question/13498201

#SPJ11

jenna is redoing her bathroom floor with tiles measuring 6 in. by 14 in. the floor has an area of 8,900 in2. what is the least number of tiles she will need?

Answers

The area of the bathroom floor = 8,900 square inchesArea of one tile = Length × Width= 6 × 14= 84 square inchesTo determine the least number of tiles needed, divide the area of the bathroom floor by the area of one tile.

That is:Number of tiles = Area of bathroom floor/Area of one tile= 8,900/84= 105.95SPSince she can't use a fractional tile, the least number of tiles Jenna needs is the next whole number after 105.95. That is 106 tiles.Jenna will need 106 tiles to redo her bathroom floor.

To know more about fractional visit:

brainly.com/question/10354322

#SPJ11

You measure 49 turtles' weights, and find they have a mean weight of 68 ounces. Assume the population standard deviation is 4.3 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight.Give your answer as a decimal, to two places±

Answers

The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 1.0091 ounces.

Given that: Mean weight of 49 turtles = 68 ounces, Population standard deviation = 4.3 ounces, Confidence level = 90% Formula to calculate the maximal margin of error is:

Maximal margin of error = z * (σ/√n), where z is the z-score of the confidence level σ is the population standard deviation and n is the sample size. Here, the z-score corresponding to the 90% confidence level is 1.645. Using the formula mentioned above, we can find the maximal margin of error. Substituting the given values, we get:

Maximal margin of error = 1.645 * (4.3/√49)

Maximal margin of error = 1.645 * (4.3/7)

Maximal margin of error = 1.645 * 0.61429

Maximal margin of error = 1.0091

Thus, the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 1.0091 ounces.

Learn more about margin of error visit:

brainly.com/question/29100795

#SPJ11

The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 0.1346.

The formula for the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is shown below:

Maximum margin of error = (z-score) * (standard deviation / square root of sample size)

whereas for the 90% confidence level, the z-score is 1.645, given that 0.05 is divided into two tails. We must first convert ounces to decimal form, so 4.3 ounces will become 0.2709 after being converted to a decimal standard deviation. In addition, since there are 49 turtle weights in the sample, the sample size (n) is equal to 49. By plugging these values into the above formula, we can find the maximal margin of error as follows:

Maximal margin of error = 1.645 * (0.2709 / √49) = 0.1346.

Therefore, the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 0.1346.

Learn more about margin of error visit:

brainly.com/question/29100795

#SPJ11

Question 8 6 pts In roulette, there is a 1/38 chance of having a ball land on the number 7. If you bet $5 on 7 and a 7 comes up, you win $175. Otherwise you lose the $5 bet. a. The probability of losing the $5 is b. The expected value for the casino is to (type "win" or "lose") $ (2 decimal places) per $5 bet.

Answers

a. The probability of losing the $5 is 37/38. b. The expected value for the casino is to lose $0.13 per $5 bet. (Rounded to 2 decimal places)

Probability of landing the ball on number 7 is 1/38.

The probability of not landing the ball on number 7 is 1 - 1/38 = 37/38.

The probability of losing the $5 is 37/38.

Expected value for the player = probability of winning × win amount + probability of losing × loss amount.

Here,

probability of winning = 1/38

win amount = $175

probability of losing = 37/38

loss amount = $5

Therefore,

Expected value for the player = 1/38 × 175 + 37/38 × (-5)= -1.32/38= -0.0347 ≈ -$0.13

The expected value for the casino is the negative of the expected value for the player.

Therefore, the expected value for the casino is to lose $0.13 per $5 bet. 37/38 is the probability of losing $5.

To learn more about Expected value refer here

https://brainly.com/question/28197299#

#SPJ11

Suppose a, b, c, n are positive integers such that a+b+c=n. Show that n-1 (a,b,c) = (a-1.b,c) + (a,b=1,c) + (a,b,c - 1) (a) (3 points) by an algebraic proof; (b) (3 points) by a combinatorial proof.

Answers

a) We have shown that n-1 (a, b, c) = (a-1, b, c) + (a, b-1, c) + (a, b, c-1) algebraically. b) Both sides of the equation represent the same combinatorial counting, which proves the equation.

(a) Algebraic Proof:

Starting with the left-hand side, n-1 (a, b, c):

Expanding it, we have n-1 (a, b, c) = (n-1)a + (n-1)b + (n-1)c.

Now, let's look at the right-hand side:

(a-1, b, c) + (a, b-1, c) + (a, b, c-1)

Expanding each term, we have:

(a-1)a + (a-1)b + (a-1)c + a(b-1) + b(b-1) + (b-1)c + ac + bc + (c-1)c

Combining like terms, we get:

a² - a + ab - b + ac - c + ab - b² + bc - b + ac + bc - c² + c

Simplifying further:

a² + ab + ac - a - b - c - b² - c² + 2ab + 2ac - 2b - 2c

Rearranging the terms:

a² + 2ab + ac - a - b - c - b² + 2ac - 2b - c² - 2c

Combining like terms again:

(a² + 2ab + ac - a - b - c) + (-b² + 2ac - 2b) + (-c² - 2c)

Notice that the first term is equal to (a, b, c) since it represents the sum of the original numbers a, b, c.

The second term is equal to (a-1, b, c) since we have subtracted 1 from b.

The third term is equal to (a, b, c-1) since we have subtracted 1 from c.

Therefore, the right-hand side simplifies to:

(a, b, c) + (a-1, b, c) + (a, b, c-1)

(b) Combinatorial Proof:

Let's consider a combinatorial interpretation of the equation a+b+c=n. Suppose we have n distinct objects and we want to partition them into three groups: Group A with a objects, Group B with b objects, and Group C with c objects.

On the left-hand side, n-1 (a, b, c), we are selecting n-1 objects to distribute among the groups. This means we have n-1 objects to distribute among a+b+c-1 spots (since we have a+b+c total objects and we are leaving one spot empty).

Now, let's look at the right-hand side:

(a-1, b, c) + (a, b-1, c) + (a, b, c-1)

For (a-1, b, c), we are selecting a-1 objects to distribute among a+b+c-1 spots, leaving one spot empty in Group A.

For (a, b-1, c), we are selecting b-1 objects to distribute among a+b+c-1 spots, leaving one spot empty in Group B.

For (a, b, c-1), we are selecting c-1 objects to distribute among a+b+c-1 spots, leaving one spot empty in Group C.

The sum of these three expressions represents selecting n-1 objects to distribute among a+b+c-1 spots, leaving one spot empty.

Hence, we have shown that n-1 (a, b, c) = (a-1, b, c) + (a, b-1, c) + (a, b, c-1) by a combinatorial proof.

To know more about equation:

https://brainly.com/question/10724260

#SPJ4

Chi Square Crash Course Quiz Part A: We conduct a similar study
using the same two groups we used for the t-Test. Recall
that in this clothing study, the boys were randomly assigned to
wear either sup
You get the following data: I Clothing Condition (1= Superhero, 2= Street Clothes) When do superheroes work harder? Crosstabulation When do superheroes work harder? in their street clothes Total Count

Answers

In this problem, we are given that we conduct a similar study using the same two groups we used for the t-Test. Also, recall that in this clothing study, the boys were randomly assigned to wear either superhero or street clothes.

We have been given the following data for Chi Square Crash Course Quiz Part A: Clothing Condition Street Clothes Superhero Total

When superheroes are loaded with content 832212.

When superheroes are not loaded with content 822224.

Total 165444.

According to the given data, we can construct a contingency table to carry out a Chi Square test.

The formula for Chi Square is: [tex]$$χ^2=\sum\frac{(O-E)^2}{E}$$[/tex].

Here,O represents observed frequency, E represents expected frequency.

After substituting all the values, we get,[tex]$$χ^2=\frac{(8-6.5)^2}{6.5}+\frac{(3-4.5)^2}{4.5}+\frac{(2-3.5)^2}{3.5}+\frac{(2-0.5)^2}{0.5}=7.98$$[/tex].

The critical value of Chi Square for α = 0.05 and degree of freedom 1 is 3.84 and our calculated value of Chi Square is 7.98 which is greater than the critical value of Chi Square.

Therefore, we reject the null hypothesis and conclude that there is a statistically significant relationship between the superhero's clothing condition and working hard. Hence, the given data is loaded with Chi Square.

To know more about Chi Square, visit:

https://brainly.com/question/31871685

#SPJ11

We can conclude that there is not enough evidence to suggest that the clothing type has an effect on how hard the boys work.

Given,Chi Square Crash Course Quiz Part A:

We conduct a similar study using the same two groups we used for the t-Test.

Recall that in this clothing study, the boys were randomly assigned to wear either superhero or street clothes.

in their street clothes Total Count.

Using the data given in the question, let's construct a contingency table for the given data.

The contingency table is as follows:

Superhero Street Clothes Total Hard Work

30                 20                         50

Less Hard Work

20 30 50

Total 50 50 100

The total count of the contingency table is 100.

In order to find when superheroes work harder, we need to perform the chi-squared test.

Therefore, we calculate the expected frequencies under the null hypothesis that the clothing type (superhero or street clothes) has no effect on how hard the boys work, using the formula

E = (Row total × Column total)/n, where n is the total count.

The expected values are as follows:

Superhero Street Clothes TotalHard Work

25                  25                          50

Less Hard Work 25 25 50

Total 50 50 100

The chi-squared statistic is given by the formula χ² = ∑(O - E)² / E

where O is the observed frequency and E is the expected frequency.

The calculated value of chi-squared is as follows:

χ² = [(30 - 25)²/25 + (20 - 25)²/25 + (20 - 25)²/25 + (30 - 25)²/25]χ²

= 2.0

The degrees of freedom for the test is df = (r - 1)(c - 1) where r is the number of rows and c is the number of columns in the contingency table.

Here, we have df = (2 - 1)(2 - 1) = 1.

At a 0.05 level of significance, the critical value of chi-squared with 1 degree of freedom is 3.84. Since our calculated value of chi-squared (2.0) is less than the critical value of chi-squared (3.84), we fail to reject the null hypothesis.

Therefore, we can conclude that there is not enough evidence to suggest that the clothing type has an effect on how hard the boys work.

To know more about contingency table, visit:

https://brainly.com/question/30920745

#SPJ11

please help
Given a normal distribution with µ =4 and a -2, what is the probability that Question: Between what two X values (symmetrically distributed around the mean) are 95 % of the values? Instructions Pleas

Answers

Approximately 95% of the values in a normal distribution with a mean of 4 and a standard deviation of 2 fall between X ≈ 0.08 and X ≈ 7.92.

Let's follow the instructions step by step:

1. Draw the normal curve:

                            _

                           /   \

                          /     \

2. Insert the mean and standard deviation:

  Mean (µ) = 4

 

Standard Deviation (σ) = -2 (assuming you meant 2 instead of "a -2")

                    _

                   /   \

                  /  4  \

3. Label the area of 95% under the curve:

                     _

                   /   \

                  /  4  \

                 _________________

                |                 |

                |                 |

                |                 |

                |                 |

                |                 |

                |                 |

                |                 |

                |_________________|

4. Use Z to solve the unknown X values (lower X and Upper X):

We need to find the Z-scores that correspond to the cumulative probability of 0.025 on each tail of the distribution. This is because 95% of the values fall within the central region, leaving 2.5% in each tail.

Using a standard normal distribution table or calculator, we can find that the Z-score corresponding to a cumulative probability of 0.025 is approximately -1.96.

To find the X values, we can use the formula:

X = µ + Z * σ

Lower X value:

X = 4 + (-1.96) * 2

X = 4 - 3.92

X ≈ 0.08

Upper X value:

X = 4 + 1.96 * 2

X = 4 + 3.92

X ≈ 7.92

Therefore, between X ≈ 0.08 and X ≈ 7.92, approximately 95% of the values will fall within this range in a normal distribution with a mean of 4 and a standard deviation of 2.

To know more about the Z-scores refer here :

https://brainly.com/question/30557336#

#SPJ11

Complete question :

Given a normal distribution with µ =4 and a -2, what is the probability that Question: Between what two X values (symmetrically distributed around the mean) are 95 % of the values? Instructions Please don't simply state the results. 1. Draw the normal curve 2. Insert the mean and standard deviation 3. Label the area of 95% under the curve 4. Use Z to solve the unknown X values (lower X and Upper X)

Please show work clearly and graph.
2. A report claims that 65% of full-time college students are employed while attending college. A recent survey of 110 full-time students at a state university found that 80 were employed. Use a 0.10

Answers

1. Null Hypothesis (H0): The proportion of employed students is equal to 65%.

Alternative Hypothesis (HA): The proportion of employed students is not equal to 65%.

2. We can use the z-test for proportions to test these hypotheses. The test statistic formula is:

 [tex]\[ z = \frac{{p - p_0}}{{\sqrt{\frac{{p_0(1-p_0)}}{n}}}} \][/tex]

  where:

  - p is the observed proportion

  - p0 is the claimed proportion under the null hypothesis

  - n is the sample size

3. Given the data, we have:

  - p = 80/110 = 0.7273 (observed proportion)

  - p0 = 0.65 (claimed proportion under null hypothesis)

  - n = 110 (sample size)

4. Calculating the test statistic:

[tex]\[ z = \frac{{0.7273 - 0.65}}{{\sqrt{\frac{{0.65 \cdot (1-0.65)}}{110}}}} \][/tex]

 [tex]\[ z \approx \frac{{0.0773}}{{\sqrt{\frac{{0.65 \cdot 0.35}}{110}}}} \][/tex]

 [tex]\[ z \approx \frac{{0.0773}}{{\sqrt{\frac{{0.2275}}{110}}}} \][/tex]

[tex]\[ z \approx \frac{{0.0773}}{{0.01512}} \][/tex]

[tex]\[ z \approx 5.11 \][/tex]

5. The critical z-value for a two-tailed test at a 10% significance level is approximately ±1.645.

6. Since our calculated z-value of 5.11 is greater than the critical z-value of 1.645, we reject the null hypothesis. This means that the observed proportion of employed students differs significantly from the claimed proportion of 65% at a 10% significance level.

7. Graphically, the critical region can be represented as follows:

[tex]\[ | | \\ | | \\ | \text{Critical} | \\ | \text{Region} | \\ | | \\ -------|---------------------|------- \\ -1.645 1.645 \\ \][/tex]

  The calculated z-value of 5.11 falls far into the critical region, indicating a significant difference between the observed proportion and the claimed proportion.

To know more about statistic visit-

brainly.com/question/32758775

#SPJ11

Given f(x)=x^2-6x+8 and g(x)=x^2-x-12, find the y intercept of (g/f)(x)
a. 0
b. -2/3
c. -3/2
d. -1/2

Answers

The y-intercept of [tex]\((g/f)(x)\)[/tex]is (c) -3/2.

What is the y-intercept of the quotient function (g/f)(x)?

To find the y-intercept of ((g/f)(x)), we first need to determine the expression for this quotient function.

Given the functions [tex]\(f(x) = x^2 - 6x + 8\)[/tex] and [tex]\(g(x) = x^2 - x - 12\)[/tex] , the quotient function [tex]\((g/f)(x)\)[/tex]can be written as [tex]\(\frac{g(x)}{f(x)}\).[/tex]

To find the y-intercept of ((g/f)(x)), we need to evaluate the function at (x = 0) and determine the corresponding y-value.

First, let's find the expression for ((g/f)(x)):

[tex]\((g/f)(x) = \frac{g(x)}{f(x)}\)[/tex]

[tex]\(f(x) = x^2 - 6x + 8\) and \(g(x) = x^2 - x - 12\)[/tex]

Now, let's substitute (x = 0) into (g(x)) and (f(x)) to find the y-intercept.

For [tex]\(g(x)\):[/tex]

[tex]\(g(0) = (0)^2 - (0) - 12 = -12\)[/tex]

For (f(x)):

[tex]\(f(0) = (0)^2 - 6(0) + 8 = 8\)[/tex]

Finally, we can find the y-intercept of ((g/f)(x)) by dividing the y-intercept of (g(x)) by the y-intercept of (f(x)):

[tex]\((g/f)(0) = \frac{g(0)}{f(0)} = \frac{-12}{8} = -\frac{3}{2}\)[/tex]

Therefore, the y-intercept of [tex]\((g/f)(x)\)[/tex] is [tex]\(-\frac{3}{2}\)[/tex], which corresponds to option (c).

Learn more about y-intercept of quotient function

brainly.com/question/30973944

#SPJ11

3. Calculating the mean when adding or subtracting a constant A professor gives a statistics exam. The exam has 50 possible points. The s 42 40 38 26 42 46 42 50 44 Calculate the sample size, n, and t

Answers

The sample consists of 9 exam scores: 42, 40, 38, 26, 42, 46, 42, 50, and 44. The mean when adding or subtracting a constant A professor gives a statistics exam is √44.1115 ≈ 6.6419

To calculate the sample size, n, and t, we need to follow the steps below:

Find the sum of the scores:

42 + 40 + 38 + 26 + 42 + 46 + 42 + 50 + 44 = 370

Calculate the sample size, n, which is the number of scores in the sample:

n = 9

Calculate the mean, μ, by dividing the sum of the scores by the sample size:

μ = 370 / 9 = 41.11 (rounded to two decimal places)

Calculate the deviations of each score from the mean:

42 - 41.11 = 0.89

40 - 41.11 = -1.11

38 - 41.11 = -3.11

26 - 41.11 = -15.11

42 - 41.11 = 0.89

46 - 41.11 = 4.89

42 - 41.11 = 0.89

50 - 41.11 = 8.89

44 - 41.11 = 2.89

Square each deviation:

[tex](0.89)^2[/tex] = 0.7921

[tex](-1.11)^2[/tex] = 1.2321

[tex](-3.11)^2[/tex] = 9.6721

[tex](-15.11)^2[/tex] = 228.6721

[tex](0.89)^2[/tex] = 0.7921

[tex](4.89)^2[/tex] = 23.8761

[tex](0.89)^2[/tex] = 0.7921

[tex](8.89)^2[/tex] = 78.9121

[tex](2.89)^2[/tex] = 8.3521

Find the sum of the squared deviations:

0.7921 + 1.2321 + 9.6721 + 228.6721 + 0.7921 + 23.8761 + 0.7921 + 78.9121 + 8.3521 = 352.8918

Calculate the sample variance, [tex]s^2[/tex], by dividing the sum of squared deviations by (n-1):

[tex]s^2[/tex] = 352.8918 / (9 - 1) = 44.1115 (rounded to four decimal places)

Calculate the sample standard deviation, s, by taking the square root of the sample variance:

s = √44.1115 ≈ 6.6419 (rounded to four decimal places)

To know more about mean refer here:

https://brainly.com/question/31101410#

#SPJ11

how is the variable manufacturing overhead efficiency variance calculated?

Answers

Variable Manufacturing Overhead Efficiency can be calculated by comparing the standard cost of actual production at the standard number of hours required to produce the actual output, which is multiplied by the standard variable overhead rate per hour, with the actual variable overhead cost incurred in producing the actual output.

Variance is calculated by comparing the standard cost of actual production at the standard number of hours required to produce the actual output, which is multiplied by the standard variable overhead rate per hour, with the actual variable overhead cost incurred in producing the actual output.

The following formula can be used to calculate the Variable Manufacturing Overhead Efficiency Variance:

Variable Manufacturing Overhead Efficiency

Variance = (Standard Hours for Actual Output x Standard Variable Overhead Rate) - Actual Variable Overhead Cost

Where,

Standard Hours for Actual Output = Standard time required to produce the actual output at the standard variable overhead rate per hour

Standard Variable Overhead Rate = Budgeted Variable Manufacturing Overhead / Budgeted Hours

Actual Variable Overhead Cost = Actual Hours x Actual Variable Overhead Rate

The above formula can also be represented as follows:

Variable Manufacturing Overhead Efficiency Variance = (Standard Hours for Actual Output - Actual Hours) x Standard Variable Overhead Rate

Therefore, the Variable Manufacturing Overhead Efficiency Variance can be calculated by comparing the standard cost of actual production at the standard number of hours required to produce the actual output, which is multiplied by the standard variable overhead rate per hour, with the actual variable overhead cost incurred in producing the actual output. It is an essential tool that helps companies measure their actual productivity versus the estimated productivity.

To know more about standard variable visit:

https://brainly.com/question/30693267

#SPJ11

how to find the coordinates of the center and length of the radius of the cricle.
The equation of a circle is x^2+y^2-2x+6y+3=0.

Answers

To find the coordinates of the center and the length of the radius of a circle given its equation, we need to rewrite the equation in the standard form (x - h)^2 + (y - k)^2 = r^2.

Where (h, k) represents the center of the circle and r represents the radius.

In the given equation x^2 + y^2 - 2x + 6y + 3 = 0, we can complete the square for both the x and y terms. Let's start with the x terms:

x^2 - 2x + y^2 + 6y + 3 = 0

(x^2 - 2x + 1) + (y^2 + 6y + 9) = 1 + 9

(x - 1)^2 + (y + 3)^2 = 10

Comparing this with the standard form, we can see that the center of the circle is at (1, -3) and the radius is √10.

Therefore, the coordinates of the center of the circle are (1, -3), and the length of the radius is √10.

To know more about coordinates click here: brainly.com/question/22261383

#SPJ11

please help me :( i don't understand how to do this problem
-5-(10 points) Let X be a binomial random variable with n=4 and p=0.45. Compute the following probabilities. -a-P(X=0)= -b-P(x-1)- -c-P(X=2)- -d-P(X ≤2)- -e-P(X23) - W

Answers

The probability of X = 0 for a binomial random variable with n = 4 and p = 0.45 is approximately 0.0897.

To compute the probability of X = 0 for a binomial random variable, we can use the probability mass function (PMF) formula:

[tex]P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)[/tex]

Where:

- P(X = k) is the probability of X taking the value k.

- C(n, k) is the binomial coefficient, given by C(n, k) = n! / (k! * (n - k)!).

- n is the number of trials.

- p is the probability of success on each trial.

- k is the desired number of successes.

In this case, we have n = 4 and p = 0.45. We want to find P(X = 0), so k = 0. Plugging in these values, we get:

[tex]P(X = 0) = C(4, 0) * 0.45^0 * (1 - 0.45)^(4 - 0)[/tex]

The binomial coefficient C(4, 0) is equal to 1, and any number raised to the power of 0 is 1. Thus, the calculation simplifies to:

[tex]P(X = 0) = 1 * 1 * (1 - 0.45)^4P(X = 0) = 1 * 1 * 0.55^4P(X = 0) = 0.55^4[/tex]

Calculating this expression, we find:

P(X = 0) ≈ 0.0897

Therefore, the probability of X = 0 for the binomial random variable is approximately 0.0897.

To know more about binomial random variable refer here:

https://brainly.com/question/31311574#

#SPJ11

3 Taylor, Passion Last Saved: 1:33 PM The perimeter of the triangle shown is 17x units. The dimensions of the triangle are given in units. Which equation can be used to find the value of x ? (A) 17x=30+7x

Answers

The equation that can be used to find the value of x is (A) 17x = 30 + 7x.

To find the value of x in the given triangle, we can use the equation that represents the perimeter of the triangle. The perimeter of a triangle is the sum of the lengths of its three sides.

Let's assume that the lengths of the three sides of the triangle are a, b, and c. According to the given information, the perimeter of the triangle is 17x units.

Therefore, we can write the equation as:

a + b + c = 17x

Now, if we look at the options provided, option (A) states that 17x is equal to 30 + 7x. This equation simplifies to:

17x = 30 + 7x

By solving this equation, we can determine the value of x.

Learn more about triangle

brainly.com/question/29083884

#SPJ11

Question 6 of 12 View Policies Current Attempt in Progress Solve the given triangle. Round your answers to the nearest integer. Ax Y≈ b= eTextbook and Media Sve for Later 72 a = 3, c = 5, B = 56°

Answers

The angles A, B, and C are approximately 65°, 56° and 59°, respectively.

Given data:

a = 3, c = 5, B = 56°

In a triangle ABC, we have the relation:

a/sin(A) = b/sin(B) = c/sin(C)

The given angle B = 56°

Thus, sin B = sin 56° = b/sin(B)

On solving, we get b = c sin B/ sin C= 5 sin 56°/ sin C

Now, we need to find the value of angle A using the law of cosines:

cos A = (b² + c² - a²)/2bc

Putting the values of a, b and c in the above formula, we get:

cos A = (25 sin² 56° + 9 - 25)/(2 × 3 × 5)

cos A = (25 × 0.5543² - 16)/(30)

cos A = 0.4185

cos⁻¹ 0.4185 = 65.47°

We can find angle C by subtracting the sum of angles A and B from 180°.

C = 180° - (A + B)C = 180° - (65.47° + 56°)C = 58.53°

Thus, the angles A, B, and C are approximately 65°, 56° and 59°, respectively.

To know more about angles visit:

https://brainly.com/question/31818999

#SPJ11

Suppose we did a regression analysis that resulted in the following regression model: yhat = 11.5+0.9x. Further suppose that the actual value of y when x=14 is 25. What would the value of the residual be at that point? Give your answer to 1 decimal place.

Answers

The value of the residual at that point is 0.9.

The regression model is yhat = 11.5+0.9x. Given that the actual value of y when x = 14 is 25. We want to find the residual at that point. Residuals represent the difference between the actual value of y and the predicted value of y. To find the residual, we first need to find the predicted value of y (yhat) when x = 14. Substitute x = 14 into the regression model: yhat = 11.5 + 0.9x= 11.5 + 0.9(14)= 11.5 + 12.6= 24.1.

Therefore, the predicted value of y (yhat) when x = 14 is 24.1.The residual at that point is the difference between the actual value of y and the predicted value of y: Residual = Actual value of y - Predicted value of y= 25 - 24.1= 0.9.

To know more about residual visit:-

https://brainly.com/question/19131352

#SPJ11

What does a linear model look like? Explain what all of the pieces are? 2) What does an exponential model look like? Explain what all of the pieces are? 3) What is the defining characteristic of a linear model? 4) What is the defining characteristic of an exponential model?

Answers

A linear model is that it represents a constant Rate of change between the two variables.

1) A linear model is a mathematical representation of a relationship between two variables that forms a straight line when graphed. The equation of a linear model is typically of the form y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope of the line, and b represents the y-intercept. The slope (m) determines the steepness of the line, and the y-intercept (b) represents the point where the line intersects the y-axis.

2) An exponential model is a mathematical representation of a relationship between two variables where one variable grows or decays exponentially with respect to the other. The equation of an exponential model is typically of the form y = a * b^x, where y represents the dependent variable, x represents the independent variable, a represents the initial value or starting point, and b represents the growth or decay factor. The growth or decay factor (b) determines the rate at which the variable changes, and the initial value (a) represents the value of the dependent variable when the independent variable is zero.

3) The defining characteristic of a linear model is that it represents a constant rate of change between the two variables. In other words, as the independent variable increases or decreases by a certain amount, the dependent variable changes by a consistent amount determined by the slope. This results in a straight line when the data points are plotted on a graph.

4) The defining characteristic of an exponential model is that it represents a constant multiplicative rate of change between the two variables. As the independent variable increases or decreases by a certain amount, the dependent variable changes by a consistent multiple determined by the growth or decay factor. This leads to a curve that either grows exponentially or decays exponentially, depending on the value of the growth or decay factor.

For more questions on Rate .

https://brainly.com/question/25720319

#SPJ8

Find the area of the surface.
The helicoid (or spiral ramp) with vector equation r(u, v) = u cos v i + u sin v j + v k, 0 ≤ u ≤ 1, 0 ≤ v ≤ π

Answers

To find the area of the surface, we can use the surface area formula for a parametric surface given by r(u, v):

A = ∬√[ (∂r/∂u)² + (∂r/∂v)² + 1 ] dA

where ∂r/∂u and ∂r/∂v are the partial derivatives of the vector function r(u, v) with respect to u and v, and dA is the area element in the u-v coordinate system.

In this case, the vector equation of the helicoid is r(u, v) = u cos(v) i + u sin(v) j + v k, with the given parameter ranges 0 ≤ u ≤ 1 and 0 ≤ v ≤ π.

Taking the partial derivatives, we have:

∂r/∂u = cos(v) i + sin(v) j + 0 k

∂r/∂v = -u sin(v) i + u cos(v) j + 1 k

Plugging these values into the surface area formula and integrating over the given ranges, we can calculate the surface area of the helicoid. However, this process involves numerical calculations and may not yield a simple closed-form expression.

Hence, the exact value of the surface area of the helicoid in this case would require numerical evaluation using appropriate numerical methods or software.

To know more about derivatives visit-

brainly.com/question/31952261

#SPJ11

Three candidates, A, B and C, participate in an election in which eight voters will cast their votes. The candidate who receives the absolute majority, that is at least five, of the votes will win the

Answers

The total number of possible outcomes, we get 3^8 - 2^8 = 6,305. Therefore, there are 6,305 possible outcomes in this scenario.

A, B, and C are the three up-and-comers in an eight-vote political decision. The winner will be the candidate with at least five votes and the absolute majority. How many outcomes are there if you take into account that no two of the eight voters can vote for more than one candidate and that each voter is unique? 3,8 minus 2,8 equals 6,305 less than 256.

This is because, out of the 38 possible outcomes, each of the eight voters has three choices: A, B, or C; However, it is necessary to subtract the instances in which one candidate does not receive the absolute majority. A candidate needs at least five votes to win the political race. Without this, there are two possible outcomes: 1. Situation: Each newcomer requires five votes. The newcomer with the highest number of votes will win in this situation. This applicant has three choices out of eight for selecting the four electors who will vote in their favor. The other applicant will win the vote of the remaining citizens.

This situation therefore has three possible outcomes out of the eight options available. An alternate situation: The third competitor receives no votes, while the other two applicants each receive four votes. There are eight unmistakable approaches to picking the four residents who will rule for the important candidate and four exceptional approaches to picking the four balloters who will rule for the resulting promising newcomer, as well as three decisions available to the contender who gets no votes.

Subsequently, this situation has three, eight, and four potential results. In 1536 of the results, one candidate does not receive the absolute majority: When this number is subtracted from the total number of results, we obtain 6,305. 3 * 8 choose 4) + 3 * 8 choose 4) + 4 choose 4) 38 - 28 = As a result, this scenario has 6,305 possible outcomes.

To know more about possible outcomes refer to

https://brainly.com/question/29181724

#SPJ11

find the absolute maximum and minimum, if either exists, for f(x)=x^2-2x 5

Answers

Given that f(x) = x² - 2x + 5. We need to find the absolute maximum and minimum of the function.Let us differentiate the function to find critical points, that is, f '(x) = 2x - 2.We know that f(x) is maximum or minimum at critical points. So, f '(x) = 0 or f '(x) does not exist.

Let's solve for x.2x - 2 = 0⇒ 2x = 2⇒ x = 1Therefore, f '(1) = 2(1) - 2 = 0The critical point is x = 1.Now, we need to test if this critical point gives an absolute maximum or minimum.To do this, we can check the value of f(x) at this point as well as the values of f(x) at the endpoints of the domain of x. Here, the domain is -∞ < x < ∞.Let's begin by calculating f(x) at the critical point.x = 1⇒ f(1) = (1)² - 2(1) + 5= 4Therefore, the function has a maximum at x = 1.

Now, let's check the values of f(x) at the endpoints of the domain.x → -∞⇒ f(x) → ∞x → ∞⇒ f(x) → ∞Therefore, there are no minimum values of the function.To summarize, the absolute maximum of the function f(x) = x² - 2x + 5 is 4 and there is no absolute minimum value of the function as f(x) approaches infinity for both positive and negative values of x.

To know more about domain visit :

brainly.com/question/30133157

#SPJ11

A swim team has 75 members and there is a 12% absentee rate per
team meeting.
Find the probability that at a given meeting, exactly 10 members
are absent.

Answers

To find the probability that exactly 10 members are absent at a given meeting, we can use the binomial probability formula. In this case, we have a fixed number of trials (the number of team members, which is 75) and a fixed probability of success (the absentee rate, which is 12%).

The binomial probability formula is given by:

[tex]\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \][/tex]

where:

- [tex]\( P(X = k) \)[/tex] is the probability of exactly k successes

- [tex]\( n \)[/tex] is the number of trials

- [tex]\( k \)[/tex] is the number of successes

- [tex]\( p \)[/tex] is the probability of success

In this case, [tex]\( n = 75 \), \( k = 10 \), and \( p = 0.12 \).[/tex]

Using the formula, we can calculate the probability:

[tex]\[ P(X = 10) = \binom{75}{10} \cdot 0.12^{10} \cdot (1-0.12)^{75-10} \][/tex]

The binomial coefficient [tex]\( \binom{75}{10} \)[/tex] can be calculated as:

[tex]\[ \binom{75}{10} = \frac{75!}{10! \cdot (75-10)!} \][/tex]

Calculating these values may require a calculator or software with factorial and combination functions.

After substituting the values and evaluating the expression, you will find the probability that exactly 10 members are absent at a given meeting.

To know more about probability visit-

brainly.com/question/31198163

#SPJ11

(1 point) let f and g be functions such that f(0)=2,g(0)=5, f′(0)=9,g′(0)=−8. find h′(0) for the function h(x)=g(x)f(x).

Answers

The given problem requires us to find h′(0) for the function h(x) = g(x)f(x), where f and g are functions such that f(0) = 2, g(0) = 5, f′(0) = 9, and g′(0) = −8.In order to find h′(0), we can use the product rule of differentiation.

The product rule states that the derivative of the product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.In other words, if we have h(x) = f(x)g(x), thenh′(x) = f(x)g′(x) + f′(x)g(x).Applying this rule to our problem, we geth′(x) = f(x)g′(x) + f′(x)g(x)h′(0) = f(0)g′(0) + f′(0)g(0)h′(0) = 2(-8) + 9(5)h′(0) = -16 + 45h′(0) = 29Therefore, h′(0) = 29.

To know more about functions visit :-

https://brainly.com/question/31062578

#SPJ11

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Points A and B are the endpoints of an arc of a circle. Chords are drawn from the two endpoints to a third point, C, on the circle. Given m AB =64° and ABC=73° , mACB=.......° and mAC=....°

Answers

Measures of angles ACB and AC are is m(ACB) = 64°, m(AC) = 146°

What is the measure of angle ACB?

Given that m(AB) = 64° and m(ABC) = 73°, we can find the measures of m(ACB) and m(AC) using the properties of angles in a circle.

First, we know that the measure of a central angle is equal to the measure of the intercepted arc. In this case, m(ACB) is the central angle, and the intercepted arc is AB. Therefore, m(ACB) = m(AB) = 64°.

Next, we can use the property that an inscribed angle is half the measure of its intercepted arc. The angle ABC is an inscribed angle, and it intercepts the arc AC. Therefore, m(AC) = 2 * m(ABC) = 2 * 73° = 146°.

To summarize:

m(ACB) = 64°

m(AC) = 146°

These are the measures of angles ACB and AC, respectively, based on the given information.

Learn more about angles in circles

brainly.com/question/23247585

#SPJ11

If you are testing hypotheses and you find p-value which gives you an acceptance of the alternative hypotheses for a 1% significance level, then all other things being the same you would also get an acceptance of the alternative hypothesis for a 5% significance level.

True

False

Answers

The statement give '' If you are testing hypotheses and you find p-value which gives you an acceptance of the alternative hypotheses for a 1% significance level, then all other things being the same you would also get an acceptance of the alternative hypothesis for a 5% significance level '' is False.

The significance level, also known as the alpha level, is the threshold at which we reject the null hypothesis. A lower significance level indicates a stricter criteria for rejecting the null hypothesis.

If we find a p-value that leads to accepting the alternative hypothesis at a 1% significance level, it does not necessarily mean that we will also accept the alternative hypothesis at a 5% significance level.

If the p-value is below the 1% significance level, it means that the observed data is very unlikely to have occurred by chance under the null hypothesis. However, this does not automatically imply that it will also be unlikely under the 5% significance level.

Accepting the alternative hypothesis at a 1% significance level does not guarantee acceptance at a 5% significance level. The decision to accept or reject the alternative hypothesis depends on the specific p-value and the chosen significance level.

To know more about p-value, refer here :

https://brainly.com/question/30078820#

#SPJ11

Find the average rate of change of the function f ( x ) = 9 3 x - 1 , on the interval x ∈ [-1,5]. Average rate of change = Give an exact answer.

Answers

The average rate of change of the function f(x) = (9/3)x - 1 on the interval x ∈ [-1, 5] is 3.

To find the average rate of change, we need to determine the difference in the function values at the endpoints of the interval and divide it by the difference in the corresponding x-values.

The function values at the endpoints are:

f(-1) = (9/3)(-1) - 1 = -3 - 1 = -4

f(5) = (9/3)(5) - 1 = 15 - 1 = 14

The corresponding x-values are -1 and 5.

The difference in function values is 14 - (-4) = 18, and the difference in x-values is 5 - (-1) = 6.

Hence, the average rate of change is:

Average rate of change = (f(5) - f(-1)) / (5 - (-1)) = 18 / 6 = 3.

Therefore, the exact average rate of change of the function f(x) = (9/3)x - 1 on the interval x ∈ [-1, 5] is 3.

To learn more about average rate visit:

brainly.com/question/32208982

#SPJ11

Other Questions
a lens has a refractive power of -1.50. what is its focal length? Question 1 An assumption of non parametric tests is that the distribution must be normal O True O False Question 2 One characteristic of the chi-square tests is that they can be used when the data are measured on a nominal scale. True O False Question 3 Which of the following accurately describes the observed frequencies for a chi-square test? They are always the same value. They are always whole numbers. O They can contain both positive and negative values. They can contain fractions or decimal values. Question 4 The term expected frequencies refers to the frequencies computed from the null hypothesis found in the population being examined found in the sample data O that are hypothesized for the population being examined Concord Guitar Company makes high-quality customized guitars. Concord uses a job order costing system. Because the guitars are handmade, the company applies overhead based on direct labor hours. At the beginning of the year, the company estimated that total manufacturing overhead costs would be $303,000 and that 20,200 direct labor hours would be worked. At year-end, Kenneth, the company's founder and CEO, gives you the following information regarding Concord's operations. 1. The beginning balances in the inventory accounts were: Raw Materials Inventory $7.900 Work in Process Inventory $26,400 Finished Goods Inventory $32,300 2. During the year, the company purchased raw materials costing $104,000. All purchases were made on account. 3. The production department requisitioned $96,000 of raw materials for use in production. Of those, 70% were direct materials and 30% were indirect materials. 4. The company used 21,400 direct labor hours at a cost of $13 per hour during the year (credit Wages Payable). 5. The company used 6,900 indirect labor hours at a cost of $10 per hour (credit Wages Payable). 6. The company paid $178,000 for insurance, utilities, and property taxes on the factory. 7. The company recorded factory depreciation of $40,500. 8. The company applied manufacturing overhead to inventory based on the 21,400 labor hours actually worked during the year. 9. Products costing $663,000 were completed during the year and transferred to the Finished Goods Inventory. 10. During the year, the company sold products costing a total of $671,000. 11. The company closes under- and overapplied overhead to Cost of Goods Sold. pay Prepare journal entries for each of the transactions just listed. (Credit account titles are automatically indented when the amount is entered. Do not indent manually. Post entries in order presented in the problem. If no entry is required, select "No Entry" for the account titles and enter O for the amounts.) No. Account Titles and Explanation 1. 2. 3. 4. (To record raw materials purchases) (To record use of direct and indirect materials in production) Debit DO Credit 5. 6. 7. 8. 9. (To record direct labor payroll) (To record indirect labor payroll) (To record other manufacturing overhead incurred) (To record factory depreciation) (To apply manufacturing overhead) 00 00 00 00 00 10. 11. (To record transfer of completed products to finished goods) (To record cost of sales) (To dispose of overapplied overhead) eTextbook and Media List of Accounts Save for Later Attempts: 0 of 3 used Submit Answer How did learning about what happened in ap calculus class with MR Escalante impact you? jill is offered a choice between receiving $50 with certainty or possibly receiving the proceeds from a gamble. in the gamble a fair coin is tossed, and if it comes up heads, jill will receive $100; if the coin comes up tails, she will receive nothing. jill chooses the $50 instead of the gamble. jill's behavior indicates . Diversification Start with asset A which has an expected return of 10% and a volatility of 30%.1. Suppose that we introduce asset B with an expected return of 10% and a volatility of 30%. The correlation between the two asset returns is 0.9. What is the optimal combination of A and B? What is the volatility of this portfolio? [Hint: The expected return of any combination is 10%, so you want to minimize the portfolio volatility.]2. Now suppose that we introduce asset C with an expected return of 10% and a volatility of 30%. The returns of asset C are uncorrelated with both the returns of asset A and of asset B. What is the optimal combination of A, B, and C? What is the volatility of this portfolio?3. Did the introduction of B or C have a greater effect in decreasing the portfolio volatility? Why is this the case? ________blank is the most localized approach and is appropriate when, for perhaps cultural reasons, the product that sells well in one country will not transfer to another or does so for quite a different set of purposes.Multiple ChoiceA global product with a local brandA global product with a global brandA local product with a global brandA local product with a local brand Bond Z is a 12% annual coupon bond maturing in 5 years with aface value of $1,000. The interest rate for all maturities is 10%.What is Bond Zs Macaulay duration? All are, example of Sexual reproduction in plant except. a.cutting B.tissues culture c.Sporoulation d. cloning for example, we have a job scheduling task, here job weights resemble job priority. if all job weights are identical, should we schedule shorter or longer jobs earlier? an atom's configuration based on its number of electrons ends at 3p2. another atom has eight more electrons. starting at 3p, what would be the remaining configuration? draw a ppf that represents the tradeoffs for producing bicycles or motorcycles. use the drop box to upload an image or file containing your ppf. A positive differentiation factor based on a product's experience or credence characteristics typically presents sellers with less of communication challenge compared with search characteristics. Select one: O True O False for a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is race records and hillbilly music have the following in common, except: A municipal bond has a coupon rate of 6.04 percent and a YTM of 5.67 percent. If an investor has a marginal tax rate of 39 percent, what is the equivalent pretax yield on a taxable bond? A) 3.46% B) 9.90% C) 3.68% D) 6.49% E) 9.30% Which of the following diversity issues is true in the U.S. workforce?Among the top 500 U.S. companies, most currently do not yet offer domestic partner benefits forsame-sex couples.Unemployment among the disabled has dropped sharply since the introduction of the Americans withDisabilities Act.The median age of the American worker is increasing. Which of the following measures of retention is the least sensitive in triggering retrieval?A. recallB. recognitionC. relearningD. they are equally sensitive in the chinese culture priests made these to communicate with the gods. (True or False) Choose one of the leaders from the "Leaders with values" video. I choose Barack ObamaDescribe the leadership obstacles this person faced.Describe the actions or behaviors that he/she did that showed leadership attributes.What showed that this person was a leader?Explain what stood out to you that made you choose this individual?