Allowance bank received a deposit of 28,000 and is free to lend out 25,480 what is the reserve rate?

Answers

Answer 1

Answer:

Reserve rate = 9%

Step-by-step explanation:

Reserve ratio/rate is the percentage of deposits which commercial banks are required to keep as cash, as directed by the central banks.

first, let us calculate the reserve amount as follows:

Reserve = Deposit - (free amount to lend out)

Reserve = 28,000 - 25,480 = $2,520

[tex]Reserve\ rate = \frac{Reserves}{Deposits} \times100\\Reserve\ rate = \frac{2520}{28000} \times100\\=\frac{252000}{28000} =9\%[/tex]

Therefore the reserve rate = 9%


Related Questions

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 5x − 4 x(x2 + 7)2

Answers

Answer:

[tex]\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}[/tex]

Step-by-step explanation:

Given the expression [tex]\frac{5x-4}{x(x^2+7)^2}[/tex], we are to re-write the expression in form of a partial fraction.

Before we write in form of a partial fraction, we need to note the expression at the denominator. Since the expression in parenthesis is a quadratic equation, the equivalent numerator must be a linear expression.

Also the quadratic equation is a repeated form since it is squared. This means that we are to repeat the quadratic equation twice when writing as a partial fraction.

[tex]\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}[/tex]

From the above partial fraction, it can be seen that x² + 7 in parenthesis was repeated twice and their equivalent expressions at the numerator are  both linear i.e Bx+E and Dx+ E where A, B, C, D and E are the unknown constant.

heeeeeeeeelpppppppppppp

Answers

Answer:

1). x = 2.67 units

2). x = 4.80 units

3). x = 6.00 units

Step-by-step explanation:

1). By applying Pythagoras theorem,

 Hypotenuse² = [Leg(1)]² + [leg(2)]²

  12² = x² + b² [Let the base of both the triangles = b units]

  144 = x² + b² ------(1)

  Similarly, 13² = (x + 3)² + b²

  169 = x² + 6x + 9 + b²

  169 - 9 - 6x = x² + b²

  160 - 6x = x² + b² ------(2)

  From equation (1) and (2)

  144 = 160 - 6x

  6x = 160 - 144

  x = [tex]\frac{16}{6}[/tex]

  x = 2.67 units

2). By applying Pythagoras theorem,

  10² = x² + h² [Let the height of the triangle = h]

  100 = x² + h² ------(1)

  13² = (2x)² + h²

  169 = 4x² + h² -----(2)

  By substituting equation (1) from equation (2),

  169 - 100 = (4x² + h²) - (x² + h²)

  69 = 3x²

  x² = 23

  x = √23

  x = 4.795

  x ≈ 4.80 units

3). By applying Pythagoras theorem,

  9² = x² + h² [Let the height of the triangle = h units]

  81 = x² + h² ------(1)

  7² = (x - 4)² + h²

  49 = x² + 16 - 8x + h²

  49 - 16 = x² + h² - 8x

  33 + 8x = x² + h² -------(2)

  From equation (1) and (2)

  81 = 33 + 8x

  8x = 48

   x = 6.00 units

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,999. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $574. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,550 per year on reading and entertainment?

Answers

Answer:

The probability is  [tex]P(X > x ) = 0.19215[/tex]

Step-by-step explanation:

From the question we are told that

   Th The population mean [tex]\mu = \$ 1,999[/tex]

    The  standard deviation is  [tex]\sigma = \$ 574[/tex]

    The  values considered is  [tex]x = \$ 2,500[/tex]

Given that the distribution of the amounts spent follows the normal distribution then the  percent of the adults spend more than $2,550 per year on reading and entertainment is mathematically represented as

    [tex]P(X > x ) = P(\frac{ X - \mu}{\sigma } > \frac{ x - \mu}{\sigma } )[/tex]

Generally  

            [tex]X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

So

      [tex]P(X > x ) = P(Z > \frac{ x - \mu}{\sigma } )[/tex]

substituting values

      [tex]P(X > 2500 ) = P(Z > \frac{ 2500 - 1999}{574 } )[/tex]

      [tex]P(X > 2500 ) = P(Z >0.87 )[/tex]

From the normal distribution table the value of [tex]P(Z >0.87 )[/tex] is  

       [tex]P(Z >0.87 ) = 0.19215[/tex]

Thus  

       [tex]P(X > x ) = 0.19215[/tex]

Which part of an I-statement involves a description of your needs or feelings?​

Answers

Answer:

the answer is c

Step-by-step explanation:

A football team starts on the 10 yard line moving toward the 50 yard line so they can score on the other side of the field. In three plays they gain 14 yards, lose 12 yards, and gain 4 more yards. What yard line do they start their fourth play?

Answers

Answer:

16 yard line

Step-by-step explanation:

The football team is starting on the 10 yard line. In the first play, they move up to the 24 yard line. Then in the second play, they go back to the 12 yard line since they lost 12 yards. Then in the third play, they gain 4 yards so you add 4 to 12. They end up at the 16 yard line after the third play. This means that they're going to start their fourth play at the 16 yard line.

Answer:

16 yards.

Step-by-step explanation:

They start at 10 yards. They are moving towards the 50 yard line, so gaining yards will add to the 10 yards instead of subtract from the 10 yards.

In the first play, they gain 14 yards. 10 + 14 = 24 yards.

In the second play, they lose 12 yards. 24 - 12 = 12 yards.

In the third play, they gain 4 yards. 12 + 4 = 16 yards, which is where they start their fourth play.

Hope this helps!

Assume the triangular prism has a base area of 49cm^2 and a volume of 588cm^3. What side length does the rectangular prism need to have the same volume?

Answers

Answer:

Length = Width = 7 cm

Step-by-step explanation:

Volume of a triangular prism is represented by the formula,

Volume = (Area of the triangular base) × height

588 = 49 × h

h = [tex]\frac{588}{49}[/tex]

h = 12 cm

We have to find the side length of a rectangular prism having same volume.

Volume = Area of the rectangular base × height

588 = (l × b) × h [l = length and b = width ]

588 = (l × b) × 12

l × b = 49 = 7 × 7

Therefore, length = width = 7 cm may be the side lengths of the rectangular prism to have the same volume.              

Given below are descriptions of two lines. Line 1: Goes through (-2,10) and (1,1) Line 2: Goes through (-2,8) and (2,-4)

Answers

Answer:

Option (2)

Step-by-step explanation:

1). If two lines have the same slope, lines are defined as parallel.

m₁ = m₂

2). If the multiplication of the slopes of two lines is (-1), lines will be perpendicular.

m₁ × m₂ = (-1)

Line 1 : It passes through two points (-2, 10) and (1, 1).

Slope of the line 1 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                              = [tex]\frac{1+2}{10-1}[/tex]

                              = [tex]\frac{3}{9}[/tex]

                         m₁ = [tex]\frac{1}{3}[/tex]

Line 2 : It passes through two points (-2, 8) and (2, -4).

Slope of the line 2 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                               = [tex]\frac{8+4}{-2-2}[/tex]

                               = [tex]-\frac{12}{4}[/tex]

                         m₂ = -3

Since, m₁ × m₂ = [tex]\frac{1}{3}\times (-3)[/tex]

                        = (-1)

Therefore, given lines are perpendicular to each other.

Option (2) is the correct option.

Let A and B be events. The symmetric difference A?B is defined to be the set of all elements that are in A or B but not both.
In logic and engineering, this event is also called the XOR (exclusive or) of A and B.
Show that P(AUB) = P(A) + P(B)-2P(AnB), directly using the axioms of probability.

Answers

Correction:

P(AΔB) = P(A) + P(B) - 2P(AnB)

is what could be proven using the axioms of probability, and considering the case of symmetric difference given.

Answer:

P(AΔB) = P(A) + P(B) - 2P(AnB)

Has been shown.

Step-by-step explanation:

We are required to show that

P(AUB) = P(A) + P(B) - 2P(AnB)

directly using the axioms of probability.

Note the following:

AUB = (AΔB) U (AnB)

Because (AΔB) U (AnB) is disjoint, we have:

P(AUB) = P(AΔB) + P(AnB)..................(1)

But again,

P(AUB) = P(A) + P(B) - P(AnB)...............(2)

Comparing (1) with (2), we have

P(AΔB) + P(AnB) = P(A) + P(B) - P(AnB)

P(AΔB) = P(A) + P(B) - 2P(AnB)

Where AΔB is the symmetric difference of A and B.

A research center poll showed that % of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief? 78 The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)

Answers

Question:

A research center poll showed that 78% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?

The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)

Answer:

[tex]q = 0.22[/tex]

Step-by-step explanation:

Given

Let p represent the given proportion

p = 78%

Required

Determine the probability that someone holds a contrary belief

Start by converting the given proportion to decimal

[tex]p = 78\%[/tex]

[tex]p = \frac{78}{100}[/tex]

[tex]p = 0.78[/tex]

In probability, the sum of opposite probability is equal to 1

Represent the probability that someone holds a contrary belief with q

So;

[tex]p + q = 1[/tex]

Make q the subject of formula

[tex]q = 1 - p[/tex]

Substitute 0.78 for p

[tex]q = 1 - 0.78[/tex]

[tex]q = 0.22[/tex]

Hence, the probability that someone does not believe is 0.22

The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations on x = TOST time hr and y = RBOT time min for 12 oil specimens.TOST 4200 3575 3750 3700 4050 2770 4870 4500 3450 2675 3750 3300RBOT 370 340 375 310 350 200 400 380 285 220 345 280Required:Calculate the value of the sample correlation coefficient. Round your answer to four decimal places. r = _____

Answers

Answer:

0.9259

Step-by-step explanation:

Given the following data :

TOST(x) :4200 3575 3750 3700 4050 2770 4870 4500 3450 2675 3750 3300

RBOT(y) : 370 340 375 310 350 200 400 380 285 220 345 280

The correlation Coefficient tells about the strength of the statistical relationship which exists between two variables. The value of correlation Coefficient ranges from - 1 to +1.

The closer the value of correlation Coefficient is to ±1 , the stronger the correlation Coefficient with a negative and positive values signifying a negative and positive relationship respectively. Value of 1 depicts a perfect correlation while 0 means no relationship exists between them. Values close to zero denotes weak relationship.

Using the online Coefficient of correlation calculator ;

The r value of the data above is 0.9259 which signifies a very strong positive relationship between the variables.

In this exercise we have to calculate the value of the coefficient which can be descriptive statistics as:

0.9259

Given the following data :

[tex]TOST(x) :\\4200\\ 3575\\ 3750 \\3700\\ 4050\\ 2770\\ 4870\\ 4500\\ 3450\\ 2675\\ 3750\\ 3300[/tex][tex]RBOT(y) : \\370 \\340 \\375\\ 310\\ 350\\ 200\\ 400\\ 380\\ 285\\ 220\\ 345\\ 280[/tex]

The correlation Coefficient tells about the strength of the statistical relationship which exists between two variables. The value of correlation Coefficient ranges from - 1 to +1.

The closer the value of correlation Coefficient is to ±1 , the stronger the correlation Coefficient with a negative and positive values signifying a negative and positive relationship respectively. Value of 1 depicts a perfect correlation while 0 means no relationship exists between them. Values close to zero denotes weak relationship.

Using the online Coefficient of correlation calculator, the r value of the data above is 0.9259 which signifies a very strong positive relationship between the variables.

See more about descriptive statistics at  brainly.com/question/11532972

Consider a bag of jelly beans that has 30 red, 30 blue, and 30 green jelly beans. a) How many color combinations of 15 beans have at least 6 green beans

Answers

Answer:

680

Step-by-step explanation:

Number of red beans = 30

Number of Blue beans = 30

Number of green beans = 30

How many color combinations of 15 beans have at least 6 green beans?

Since at least 6 of the beans must be green,

Then (15 - 6) = 9

Then, the remaining 9 could be either red, blue or green.

Therefore, C(9 + (9 - 1), 3)

C(17, 3) = 17C3

nCr = n! ÷ (n-r)! r!

17C3 = 17! ÷ (17 - 3)! 3!

17C3 = 17! ÷ 14!3!

17C3 = (17 * 16 * 15) / (3 * 2)

17C3 = 4080 / 6

17C3 = 680 ways

Using the combination formula, it is found that there are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.

The order in which the beans are chosen is not important, hence, the combination formula is used to solve this question.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Th total number of combinations of 15 beans from a set of 30 + 30 + 30 = 90 is:

[tex]C_{90,15} = \frac{90!}{15!75!} = 45795674000000000[/tex]

With less than 6 green, we have:

0 green:

[tex]C_{30,0}C_{60,15} = \frac{60!}{15!45!} = 53194089000000[/tex]

1 green:

[tex]C_{30,1}C_{60,14} = \frac{30!}{1!29!} \times \frac{60!}{14!46!} = 520376960000000[/tex]

2 green:

[tex]C_{30,2}C_{60,13} = \frac{30!}{2!28!} \times \frac{60!}{13!47!} = 2247585600000000[/tex]

3 green:

[tex]C_{30,3}C_{60,12} = \frac{30!}{3!27!} \times \frac{60!}{12!48!} = 5681396900000000[/tex]

4 green:

[tex]C_{30,4}C_{60,11} = \frac{30!}{4!26!} \times \frac{60!}{11!49!} = 9391696900000000[/tex]

5 green:

[tex]C_{30,5}C_{60,10} = \frac{30!}{5!25!} \times \frac{60!}{10!50!} = 10744101000000000[/tex]

Hence, the total for the number of combinations with less than 5 green is:

[tex]53194089000000 + 520376960000000 + 2247585600000000 + 5681396900000000 + 9391696900000000 + 10744101000000000 = 28638351000000000[/tex]

Subtracting the total amount of combinations from the number with less than 5 green, the number of combinations with at least 6 green is:

[tex]T = 45795674000000000 - 28638351000000000 = 17157323000000000[/tex]

There are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.

A similar problem is given at https://brainly.com/question/24437717

find the sum 7+7(2)+7(2^2)+...+7(2^9)​

Answers

Answer:

7161

Step-by-step explanation:

7 + 7(2) + 7(2)² + ... + 7(2)⁹

= ∑₁¹⁰ 7(2)ⁿ⁻¹

= 7 (1 − 2¹⁰) / (1 − 2)

= 7161

A potato chip company makes potato chips in two flavors, Regular and Salt & Vinegar. Riley is a production manager for the company who is trying to ensure that each bag contains about the same number of chips, regardless of flavor. He collects two random samples of 10 bags of chips of each flavor and counts the number of chips in each bag. Assume that the population variances of the number of chips per bag for both flavors are equal and that the number of chips per bag for both flavors are normally distributed. Let the Regular chips be the first sample, and let the Salt & Vinegar chips be the second sample. Riley conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence that both flavors have the same number of chips in each bag. (a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test. (b) t≈1.44 , p-value is approximately 0.167 (c) Which of the following are appropriate conclusions for this hypothesis test?
A. There is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.B. There is sufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.C. Reject H0.D. Fail to reject H0.

Answers

Answer:

A. There is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.

D. Fail to reject H0.

Step-by-step explanation:

From the summary of the given test statistics.

The null and the alternative hypothesis are:

[tex]H_0:\mu_1=\mu_2 \\ \\ Ha:\mu_1 \neq \mu_2[/tex]

This test is also a two tailed test.

Similarly, the t value for the test statistics = 1.44

The p- value - 0.167

The level of significance ∝ = 0.05

The objective we are meant to achieve here is to determine which of the following from the given options are appropriate conclusions for this hypothesis test.

From what we have above:

Decision Rule: We fail to reject the null hypothesis since the p-value is greater than the level of significance at 0.05

CONCLUSION: Therefore, we can conclude that  there is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag as we fail to reject H0.

a westward moving motorcycle slows down from 24.0 m/a to 12.0 m/s in 3.0 seconds. what is the magnitude and direction of the acceleration

Answers

Answer:

0

Step-by-step explanation:

Let R be a system consisting of rational expressions. Which operations are closed for R?

Answers

Answer:

D

Step-by-step explanation:A set is said to be closed under an operation when the application of the operation between any two elements of the set leads to an element that belongs to the same set. If a set is closed under an operation, it is said to have the closure property of that operation. When we combine two rational expressions by adding, subtracting, multiplying, or dividing, we get a rational expression. This pattern indicates that rational expressions are closed for all four operations.

How to graph the line y=4/3x

Answers

Answer:

make a table of values

Step-by-step explanation:

then plot using those values

The required graph has been attached which represents the line y = 4/3x

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

We have been given the equation of a line below as:

y = 4/3x

Rewrite in slope-intercept form.

y = (4/3)x

Use the slope-intercept form to discover the slope and y-intercept.

Here the slope is 4/3 and  y-intercept = (0, 0)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.

When substitute the value of x = 0, then the value of y = 0, and When substitute the value of x = 3, then the value of y = -4,

Hence, the graph represents the line y = 4/3x

Therefore, the required graph of the line y=4/3x will be shown in the as attached file.

Learn more about the graphs here:

brainly.com/question/16608196

#SPJ2

An airline claims that the proportion of no-shows for passengers who booked on its flights is less than 0.06. In a random sample of 380 reservations, 19 were no-shows. A hypothesis test is to be performed to test the airline's claim that the proportion of no-shows on its flights is less than 0.06. Calculate the test statistic associated with this sample. An airline claims that the proportion of no-shows for passengers who booked on its flights is less than 0.06. In a random sample of 380 reservations, 19 were no-shows. A hypothesis test is to be performed to test the airline's claim that the proportion of no-shows on its flights is less than 0.06. Calculate the test statistic associated with this sample.

Answers

Answer:

≈ -0.821

Step-by-step explanation:

Given:

n= 380, samplex= 19, no-shows countp = 0.06, proportion of no-shows

Then, the sample proportion is:

p' = x/n = 19/ 380 = 0.05

Hypothesis test:

H₀: p = 0.06H₁: p< 0.06

Test statistics:

z = (p' - p) /[tex]\sqrt{p(1-p)/n}[/tex] z = (0.05 - 0.06)/[tex]\sqrt{006(1-0.06)/380}[/tex] ≈ -0.821


What is an equation of the line that passes through the points (2, -7) and (8, -4)?

Answers

Answer:

The answer is

[tex]y = \frac{1}{2} x - 8[/tex]

Step-by-step explanation:

To find the equation of the line that passes through two points , first find the slope and then use the formula

y - y1 = m(x - x1)

where m is the slope

(x1 , y1) are any of the points

To find the slope of the line using two points we use the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Slope of the line using points

(2, -7) and (8, -4) is

[tex] \frac{ - 4 + 7}{8 - 2} = \frac{3}{6} = \frac{1}{2} [/tex]

Now the equation of the line using point (2 , - 7) and slope 1/2 is

[tex] y + 7 = \frac{1}{2} (x - 2)[/tex][tex]y + 7 = \frac{1}{2} x - 1[/tex][tex]y = \frac{1}{2} x - 1 - 7[/tex]

We have the final answer as

[tex]y = \frac{1}{2} x - 8[/tex]

Hope this helps you

Sharvay spends $15 to buy 17 pieces of candy. M&M’s cost $0.75 and candy bars cost $1. How many M&M’s and candy bars did Sharvay buy?

Answers

Answer:

8 M&Ms and 9 Candy Bars

Step-by-step explanation:

$15 dollars could buy 15 candy bars, and there are 17 pieces of candy total.

Prioritizing the number of bars:

0.75 * 2 = 1.50

1.50 * 2 = 3

At least $3 were spend on M&Ms, meaning 4 M&Ms and 12 candy bars, which is only 16 candy pieces...

8 M&Ms and 9 candy bars is equivalent to 17 total candy pieces.

If possible, find AB. & State the dimension of the result.

Answers

Answer:

The answer is "[tex]AB= \left[\begin{array}{cc} -2 &51 \\-8&33\\0&27&\end{array}\right][/tex]"

Step-by-step explanation:

If the value of A and B is:

[tex]A= \left[\begin{array}{cc}-1&6\\-4&5\\0&3\end{array}\right][/tex]

[tex]B=\left[\begin{array}{cc}2&3\\0&9\end{array}\right][/tex]

Find the value of A[tex]\times[/tex]B:

[tex]AB =\left[\begin{array}{cc}-1 \times 2+6 \times 0 &-1 \times 3+6 \times 9\\ -4 \times 2+5 \times 0& -4 \times 3+5 \times 9\\ 0 \times 2+3 \times 0&-1 \times 2+3\times 9\end{array}\right] \\ \\\\AB =\left[\begin{array}{cc}-2+0 &- 3+54\\ -8+0& -12+45\\ 0+ 0&-2 +27\end{array}\right] \\ \\[/tex]

[tex]AB= \left[\begin{array}{cc} -2 &51 \\-8&33\\0&27&\end{array}\right][/tex]

Choose the correct ray whose endpoint is B.

Answers

Answer:

The second option.

Step-by-step explanation:

The first option consists of a line that extends at both opposite sides to infinity, with no precise end.

The third option is a ray that has an endpoint of A, and extends to infinity towards B.

The fourth option is a line segment. It has two endpoints, B and A.

The second portion is a ray that has an endpoint B, and extends towards A in one direction, to infinity.

The answer is the 2nd option.

In a study of academic procrastination, researchers reported that for a random sample of 41 undergraduate students preparing for a psychology exam, the mean time spent studying was 11.9 hours with a standard deviation of 4.5 hours. Compute a 95% confidence interval for μ, the mean time spent studying for the exam among all students taking this course.

Answers

Answer:

The 95% confidence interval is  [tex]10.5 < \mu <13.3[/tex]

Step-by-step explanation:

From the question we are told that

     The  sample size is  [tex]n = 41[/tex]

      The  sample mean is  [tex]\= x = 11.9 \ hr[/tex]

       The standard deviation is  [tex]\sigma = 4.5[/tex]

For  a  95% confidence interval the confidence level is  95%

Given that the confidence level is 95% then the level of significance can be mathematically represented as

                  [tex]\alpha = 100 - 95[/tex]

                  [tex]\alpha = 5 \%[/tex]

                  [tex]\alpha = 0.05[/tex]

Next we obtain the critical values of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table

     The values is

                             [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

                             [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]

substituting values

                           [tex]E = 1.96 * \frac{ 4.5 }{ \sqrt{41} }[/tex]  

                           [tex]E = 1.377[/tex]

The 95% confidence interval is mathematically represented as

          [tex]\= x - E < \mu < \= x - E[/tex]

substituting values

         [tex]11.9 - 1.377 < \mu <11.9 + 1.377[/tex]

         [tex]10.5 < \mu <13.3[/tex]

Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product by first multiplying the coefficients...then adding your "like term" angles...for instance, cos (2pi/5) + cos (-pi/2) = cos (2pi/5 + -pi/2)...then use the calculator in RADIAN mode to evaluate." Doing those steps, I got the correct constant but a coefficient that was completely off. For the second one, I was told "Good effort...express the quotient by first dividing the coefficients...then subtract your "like term" angles...for instance, cos (2pi/5) - cos (-pi/2) = cos (pi/6 - pi/3)...Finally, use the calculator (in radian MODE) to evaluate."

Answers

Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

[tex]6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) [tex]\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}[/tex]

( 2 ) [tex]\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}[/tex]

These two identities makes sin(π / 10) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and cos(π / 10) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex].

Therefore cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]. Substitute,

[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex]

And now simplify this expression to receive our answer,

[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex] = [tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i[/tex],

[tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}[/tex] = [tex]-2.01749\dots[/tex] and [tex]\:\frac{3\sqrt{3-\sqrt{5}}}{4}[/tex] = [tex]0.65552\dots[/tex]

= [tex]-2.01749+0.65552i[/tex]

As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.

________________________________________

First Attachment : We know from the previous problem that cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex], cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,

[tex]6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}[/tex]

We know that [tex]6\sqrt{5+\sqrt{5}} = 16.13996\dots[/tex] and [tex]-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots[/tex] . Therefore,

Solution : [tex]16.13996 - 5.24419i[/tex]

Which rounds to about option b.

The first step in a mathematical induction proof is to divide by n. (True or False).

Answers

Answer:

Step-by-step explanation:

Hello, this is false.

The first step of a mathematical induction proof is to prove the statement for the initial value, which is most of the time for n = 0 or n = 1.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

What is the image of point (8,-4) under the rotation R90° about the origin?

A) (8,4)
B) (4,8)
C) (-4,8)
D) (-4,-8)​

Answers

Answer:

D). (-4,-8)​

Step-by-step explanation:

An image at (8,-4) if rotated at an angle of 90° wipl have another location.

First of all, an image at (8,-4) is in the fourth quadrant, and if it's to rotate clockwise at 90° iths supposed to be in the third quadrant.

And in the third quadrant both x and y is negative.

So the new position is at (-4,-8)​

A box contain 12 balls in which 4 are white 3 are blue and 5 are red.3 balls are drawn at random from the box.find the chance that all three are selected​

Answers

Answer:

3/11

Step-by-step explanation:

In the above question, we have the following information

Total number of balls = 12

White balls = 4

Blue balls = 3

Red balls = 5

We are to find the chance of probability that if we select 3 balls, all the three are selected.

Hence,

Probability ( all the three balls are selected) = P(White ball) × P(Blue ball) × P( Red ball)

Probability ( all the three balls are selected) = 4/12 × 3/11 × 5/10

= 60/1320

= 1/22

The number of ways by which we can selected all the three balls is a total of 6 ways:

WBR = White, Blue, Red

WRB = White, Red, Blue

RBW = Red, Blue, White

RWB = Red, White, Blue

BRW = Blue, Red, White

BWR = Blue, White, Red

Therefore, the chance that all three are selected :

1/22 × 6 ways = 6/22 = 3/11

Rewrite the expression as an equivalent ratio of logs using the indicated base.log17(52.875) to base 10.

Answers

Answer:

[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Step-by-step explanation:

Given

[tex]log_{17}(52.875)[/tex]

Required

Convert to base 10

To do this, we make use of the following logarithm laws;

[tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]

In the given parameters;

[tex]a = 52.875[/tex]

[tex]b = 17[/tex]

Substitute these values in [tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]

[tex]log_{17}52.875 = \frac{log_{10}52.875}{log_{10}17}[/tex]

Represent as a ratio

[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Hence;

[tex]log_{17}(52.875)[/tex] is represented as [tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Expression  [tex]log_{17} 52.875[/tex] can be written as in form of ratio of log  [tex]\frac{log_{10} 52.875}{log_{10} 17}[/tex] .

Any logarithmic expression [tex]log_{a} b[/tex] can we written as in form of ratio of log on base 10.

                   [tex]log_{a} b=\frac{log_{10} b}{log_{10} a}[/tex]

Here logarithmic expression is,  [tex]log_{17} 52.875[/tex] comparing with above expression.

We get,    [tex]b=52.875,a=17[/tex]

Substitute values of a and b in above expression.

 We get,      [tex]log_{17} 52.875=\frac{log_{10} 52.875}{log_{10} 17}[/tex]

Learn more:

https://brainly.com/question/12049968                                            

You know only the given information about
the measures of the angles of a triangle. Find the probability that the triangle is equiangular.
39. Each is a multiple of 12.

Answers

Since they are multiples if 12

The possibilities are

12, 12, 156

12,24,144

12,36,132

12,48,120

12,60,108

12,72,96

12,84,84

24,24,132

24,36,120

24,48,108

24,60,96

24,72,84

36,36,108

36,48,96

36,60,84

36,72,72

48,48,84

48,60,72

60,60,60

Hence the probability is 1/19 or 0.0526

Activity 12-4: A large monohybrid crossa corn ear with purple and yellow kernels The total number of purple and yellow kernels on 8 different corn ears were counted: Purple kernels 3593 Yellow kernels 1102 What is the ratio of purple kernels to yellow kernels

Answers

Complete Question

The  complete question is shown on the first uploaded image

Answer:

  The correct option is C

Step-by-step explanation:

From the question we are told that

      The  number of purple  kernel is  [tex]n_k = 3593[/tex]

        The number of  yellow kernel is  [tex]n_y = 1102[/tex]

Generally the ration of the purple to the yellow kernels is mathematically evaluated as

              [tex]r = \frac{n_k}{n_y}[/tex]

substituting values

              [tex]r = \frac{3593}{1102}[/tex]

              [tex]r = 3.3[/tex]      

              [tex]r \approx 3[/tex]

Therefore the ratio is  

               [tex]1 \ Yellow : 3 \ Purple[/tex]

A man saves 4% of his monthly
income of $19,540, the percentage
Savings is increased in the ratio
3:2 Calculate the savings from
the monthly
income.​

Answers

Answer:

Although the question is not clear, It most likely looks like you were asking for the calculation of the savings for the month after increase.

savings for the month after increase = $1172.4

Step-by-step explanation:

First, let us calculate how much was saved before the increase in savings:

monthly income = $19,540

Percentage saved = 4% of monthly income

= 4/100 × 19,540 = 0.04 × 19,540 = $781.6

Next, we are given the ratio of increase in savings as 3:2

Let the new savings amount be x

3 : 2 = x : 781.6

[tex]\frac{3}{2} = \frac{x}{781.6} \\781.6\ \times 3\ =2x\\2344.8 = 2x\\x =\frac{2344.8}{2} \\x = \$1172.4[/tex]

therefore savings for the month after increase = $1172.4

Just incase you were looking for the savings before the increase, the answer is $781.6 (as calculated above)

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