An instructor is administering a final examination. She tells her class that she with give an A grade to the 10% of the students who earns the highest marks. Past experience with the same examination has yielded grades that are normally distributed with a mean of 70 and a standard deviation of 10. If present class runs true to form, what numerical score would a student need to earn an A grade?

Step-by-step explanation:

Theoretical probabilities can be calculated using the concept of probability. Each student has a 0.5 chance of selecting either List A or List B. Therefore, the probability of getting 27 heads and 33 tails can be calculated as:

P(27 heads and 33 tails) = (60 choose 27) * (0.5)^27 * (0.5)^33 where (60 choose 27) is the number of ways to select 27 students out of 60.

Using a calculator, we can compute the above probability as approximately 0.109. This means that if we were to repeat this experiment many times, we would expect to get 27 heads and 33 tails about 10.9% of the time.

Comparing this theoretical probability to the experimental results, we see that the observed proportion of heads (27/60 = 0.45) is lower than the expected proportion of heads (0.5) and the observed proportion of tails (33/60 = 0.55) is higher than the expected proportion of tails (0.5).

However, it is important to note that due to the random nature of the experiment, we would not expect the exact theoretical probabilities to match the experimental results exactly. In other words, there is always some amount of variation expected in the results. Nonetheless, the experimental results are consistent with the theoretical probabilities, and we can conclude that there is no significant deviation from what we would expect by chance.

Answer: A positive whole number multiplied by any whole number will remain positive. In the case of the squares of 4, it will always end in a 6 which is a positive number.

Step-by-step explanation:

4^2= 16

16^2 = 256

256^2= 65,536

etc.

The first limit,  [tex]\lim_{x\to \→-2^- } -3(x+2)/x²+4x+4[/tex]  , evaluates to negative infinity, while the second limit, [tex]\lim_{ x\to \-2^+}-3(x+2)/x²+4x+4[/tex] , evaluates to positive infinity.

Function in maths is a relation between two sets of values. It is a type of mathematical equation in which each input value has a unique output value. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.

This indicates that the function has a vertical asymptote at x=-2.

In order to understand why this is the case, we can first rewrite the function as follows:

f(x) = -3(x+2)/(x+2)(x+2)

The denominator of the function is (x+2)(x+2), which has a double root at x=-2. This means that the denominator is equal to zero when x=-2. As a result, the function f(x) will have a vertical asymptote at x=-2, since the denominator will be equal to zero and the function will approach negative or positive infinity. This is why the two limits mentioned above both evaluate to either negative or positive infinity.

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The limit of the given functions are:

[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = positive infinity

[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = negative infinity

[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined

Function is a relation between two sets of values. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.

[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4

= -3(-2+2)/(-2)²+4(-2)+4

= -3/0 + 8 + 4

= +∞  (infinity)

[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4

= -3(-2+2)/(-2+2)²+4(-2+2)+4

= -3/4 + 0 + 4

= -∞

[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4

= -3(-2+2)/(-2+2)²+4(-2+2)+4

= -3/0 + 0 + 4

= Undefined

Therefore, the limit of the functions given are:

[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = +∞

[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = -∞

[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined

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Important points to conduct a survey are; to gather information, make informed decisions, evaluate programs or services, identify trends, assess needs.

Surveys are conducted for a variety of reasons, including gathering information, making informed decisions, evaluating programs or services, identifying trends, and assessing needs. By using surveys, organizations can collect valuable data that can be used to inform decisions, improve programs or services, and better understand their target audience.

Surveys, also known as questionnaires, are used to gather information from a targeted group of individuals or a population. Surveys are an important tool for collecting data in a structured manner and can be used for a variety of reasons. Here are some of the reasons why surveys are conducted:

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Answer:

The value could be any length between 3 and 15

Step-by-step explanation:

9 - 6 = 3

and

9 + 6 = 15

The conditional relative frequency that a student rides the bus, given that the student is in middle school is 0.16 / 0.96 ≈ 0.17.

Conditional relative frequency is a statistical measure that describes the proportion or percentage of a specific group or category within a subset of data. It is calculated by dividing the frequency of the specific category in the subset by the frequency of the total subset.

To find the conditional relative frequency that a student rides the bus, given that the student is in middle school, we need to divide the frequency of middle school students who ride the bus by the total number of middle school students.

From the table, we see that the frequency of middle school students who ride the bus is 0.16. The total number of middle school students is the sum of the frequencies in the first row, which is 0.20 + 0.16 + 0.12 + 0.48 = 0.96.

So, the conditional relative frequency that a student rides the bus, given that the student is in middle school is:

0.16 / 0.96 ≈ 0.17

Rounded to the nearest hundredth, the answer is 0.17. Therefore, about 17% of middle school students ride the bus.

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The median salary of the workers is P11,000.

In statistics, the median is a measure of central tendency that represents the middle value of a data set when the data set is ordered from least to greatest (or vice versa). If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values. The median is used as a measure of central tendency when the data set has outliers or is not normally distributed.

To calculate the median of a set of numbers:

In the given question,

To find the median salary of the workers, we need to arrange the salaries in order from lowest to highest.

The salaries are:

P9,000, P9,000, P10,500, P10,500, P11,000, P11,000, P11,000, P11,000, P12,500, P12,500, P12,500, P12,500

There are 12 workers, so the median salary will be the average of the 6th and 7th salaries when arranged in order.

Median salary = (P11,000 + P11,000)/2

= P11,000

Therefore, the median salary of the workers is P11,000.

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The area of the right triangle given in this problem is given as follows:

21 units squared -> Option A.

To calculate the area of a triangle, you can use the formula presented as follows:

Area = (1/2) x base x height

In which the parameters are given as follows:

For a right triangle, we can consider one side to be the base and the other side to be the height, hence the parameters are given as follows:

Hence the area of the triangle is given as follows:

A = 0.5 x 7 x 6 = 21 units squared.

The complete problem is defined as follows:

"Calculate the area of the given triangle".

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Step-by-step explanation:

7eh8heusvush0wio0w92726 2is 3the world ydgugd8jd8djkd0jd9jd8hd7hd

If 2 books are chosen at random, then the probability that both are statistics books is (a) 1/21.

The number of statistics book in bookcase is = 2;

The number of biology books in bookcase is = 5;

So, the total number of books is = 7;

The Probability of choosing a statistics book on the first draw is 2/7, since there are 2 statistics books out of a total of 7 books.

After the first book is chosen, there will be 6 books left, including 1 statistics book out of a total of 6 books.

So, the probability of choosing another statistics book on the second draw is 1/6.

In order to find the probability of both events happening together (i.e. choosing 2 statistics books in a row), we multiply the probabilities of each event:

So, P(choosing 2 statistics books) = P(1st book is statistics) × P(2nd book is statistics given that the 1st book was statistics);

⇒ (2/7) × (1/6)

⇒ 1/21

Therefore, the required probability is (a) 1/21.

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The given question is incomplete, the complete question is

A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is

(a) 1/21

(b) 10/21

(c) 11

(d) 21/11

Answer: 62°

Step-by-step explanation:

All angles of a triangle add up to 180°.

So, add up all the other angles.

15 + 25 + 39 = 79

180 - 79 = 101

Then, to find x, subtract 39 from 101, to get 62!

Hi Martin,

To calculate the total purchase price of your items, you'll need to apply the state, county, and city taxes to the total purchase cost of all three items.

The total purchase cost of all three items is:

Snow shovel: $28.61

Winter coat: $23.27

Rock salt: $7.96

Total purchase cost: $59.84

Now, we apply the applicable taxes:

State tax: 5% of $59.84 = $2.99

County tax: 0.5% of $59.84 = $0.30

City tax: 2.5% of $59.84 = $1.49

Total taxes: $2.99 + $0.30 + $1.49 = $4.78

Therefore, the total purchase price is:

Total purchase cost + Total taxes = $59.84 + $4.78 = $64.62

Answer:

True.

Step-by-step explanation:

Alternate interior angles are congruent, meaning they have equal measure. When we have two parallel lines that are intersected by a transversal, and again my parallel lines are identified by using the same number of arrows, then two special angles are congruent and that is alternate interior angles.

The particular solution of Differential equation y" – 2y' + 2y = et sin x is yp = (1/2et - 1/2et cos(x))sin(x).

We assume the particular solution is of the form of given differential equation is

yp = (Aet + Bcos(t))sin(x) + (Cet + Dsin(t))cos(x)

where A, B, C, and D are constants to be determined.

Taking the first and second derivative of yp with respect to t:

yp' = Aet sin(x) - Bsin(t)sin(x) + Cet cos(x) + Dcos(t)cos(x)

yp'' = Aet sin(x) - Bcos(t)sin(x) - Cet sin(x) + Dsin(x)cos(t)

Substituting these into the differential equation and simplifying, we get:

(et sin x) = (A - C)et sin(x) + (B - D)cos(x)sin(t)

Since et sin x is not a solution to the homogeneous equation, the coefficients of et sin x and cos(x)sin(t) on both sides of the equation must be equal. Therefore:

A - C = 1 and B - D = 0

Solving for A, B, C, and D, we get:

A = 1/2, B = 0, C = -1/2, D = 0

So the particular solution is:

yp = (1/2et - 1/2et cos(x))sin(x)

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Answer:

Step-by-step explanation:

1st find v solving 3v + 1 = 7

3v + 1 = 7

3v = 7 - 1

3v = 6

v = 6 : 3

v = 2

v + 8 =

replace v with 2

2 + 8 = 10

Answer:

10

Step-by-step explanation:

Solve for the value of the variable, v, in the given equation of 3v + 1 = 7, by isolating the variable. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 1 from both sides of the equation:

[tex]3v + 1 = 7\\3v + 1 (-1) = 7 (-1)\\3v = 7 - 1\\3v = 6[/tex]

Next, divide 3 from both sides of the equation:

[tex]3v = 6\\\frac{3v}{3} = \frac{6}{3} \\v = \frac{6}{3} \\v = 2[/tex]

Then, plug in 2 for v in the first given expression:

[tex]v + 8\\=(2) + 8\\=10[/tex]

10 is your answer for v + 8 when 3v + 1 = 7.

~

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The decimal number 555 is written as 4210 in base-5.

Answer:  [tex]555_{10} =4210_{5}[/tex]

Step-by-step explanation:

Decimal to base five conversion

here

                                    D   Q            Remainders

                                    5  |555               0

                                     5  |111                   1

                                      5  |22                  2

                                       5  |4                     4

                                             0  

Answer:5

Step-by-step explanation:5555555

Yes, the apparent under representation of Hispanics on the jury duty calls into question the fairness of the jury selection system, as the results of the hypothesis test suggest that the system may be systematically excluding Hispanics.

To determine whether the apparent underrepresentation of Hispanics on the jury selection system is statistically significant and calls into question its fairness, we need to perform a hypothesis test.

First, we set up the null hypothesis, which is the assumption that there is no difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool. That is, the proportion of Hispanics in the jury pool is expected to be equal to 19%.

The alternative hypothesis is that there is a difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool.

We can use a one-tailed z-test to test the null hypothesis, where the test statistic is calculated as:

z = (p - P) / sqrt(P(1-P)/n)

where p is the proportion of Hispanics in the jury pool, P is the proportion of Hispanics in the county population (0.19), and n is the sample size (72).

Plugging in the values, we get

z = (9/72 - 0.19) / sqrt(0.19*(1-0.19)/72) = -2.39

Assuming a significance level of 0.05, we compare the calculated z-value with the critical z-value of -1.645 (obtained from a standard normal distribution table). Since the calculated z-value is less than the critical z-value, we reject the null hypothesis and conclude that the proportion of Hispanics in the jury pool is significantly different from the proportion of Hispanics in the county population.

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Answer:

What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←​

Step-by-step explanation:

To map the point (4, -7) to (7, 4) by a rotation centered about the origin, we need to find the angle of rotation and direction.

We can start by finding the vector from the origin to (4, -7), which is <4, -7>. We want to rotate this vector to the vector from the origin to (7, 4), which is <7, 4>.

To do this, we need to find the angle between these two vectors. Using the dot product, we have:

<4, -7> · <7, 4> = (4)(7) + (-7)(4) = 0

Since the dot product is zero, we know that the two vectors are orthogonal, and the angle between them is 90 degrees.

To map (4, -7) to (7, 4) with a 90-degree rotation counterclockwise, we can use the matrix:

[0 -1]

[1 0]

Multiplying this matrix by the vector <4, -7>, we get:

[0 -1] [4] = [-7]

[1 0] [-7] [ 4]

which corresponds to the point (-7, 4). This matches our desired endpoint, so the answer is 90° counterclockwise.

Answer:

90° counterclockwise

Step-by-step explanation:

I am not sure if the picture helps or not.  I am trying to show that I traced the point (4,-7).  Then I have a plus sign at (0,0).  I start rotating the tracing paper counterclockwise until  I get to the point (7,4).  I needed to turn one turn of the plus sign.  That would be 90°

Helping in the name of Jesus.

Conversely, as the confidence level decreases, the margin of error becomes smaller, and the confidence interval becomes narrower.

In statistics, a confidence interval is a range of values that is likely to contain the true value of a population parameter (such as a mean or a proportion), based on a sample from that population. The confidence interval is typically expressed as an interval around a sample statistic, such as a mean or a proportion, and is calculated using a specified level of confidence, typically 90%, 95%, or 99%.

Here,

To develop a confidence interval, we need to use the following formula:

Confidence Interval = sample mean ± margin of error

where the margin of error is calculated as:

Margin of Error = z* (sample standard deviation/ √n)

where z* is the critical value from the standard normal distribution table based on the chosen confidence level.

a. For a 90% confidence interval, the critical value (z*) is 1.645. Thus, the margin of error is:

Margin of Error = 1.645 * (4 / √25) = 1.317

So, the 90% confidence interval for the population mean is:

30 ± 1.317, or (28.683, 31.317)

b. For a 95% confidence interval, the critical value (z*) is 1.96. Thus, the margin of error is:

Margin of Error = 1.96 * (4 / √25) = 1.568

So, the 95% confidence interval for the population mean is:

30 ± 1.568, or (28.432, 31.568)

c. For a 99% confidence interval, the critical value (z*) is 2.576. Thus, the margin of error is:

Margin of Error = 2.576 * (4 / √25) = 2.0656

So, the 99% confidence interval for the population mean is:

30 ± 2.0656, or (27.9344, 32.0656)

d. As the confidence level increases, the margin of error also increases, because we need to be more certain that our interval includes the true population mean. This means that the confidence interval becomes wider as the confidence level increases.

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if we  that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:

100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.

If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.

So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:

On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.

However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.

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Answer:

Step-by-step explanation:

The three inequalities that x and y must satisfy because of the package's requirements for protein, fat, and carbohydrate are:

Protein: 1x + 1y ≥ 8 (at least 8 units of protein)

Carbohydrates: 2x + 1y ≥ 11 (at least 11 units of carbohydrates)

Fat: 1x + 1y ≤ 10 (no more than 10 units of fat)

The inequalities that x and y must satisfy because they cannot be negative are:

x ≥ 0

y ≥ 0

Step-by-step explanation:

To satisfy the requirements for protein, fat, and carbohydrates, the following three inequalities must be satisfied:

1. 1x + 1y ≥ 8 (At least 8 units of protein)

2. 2x + 1y ≥ 11 (At least 11 units of carbohydrates)

3. 1x + 1y ≤ 10 (No more than 10 units of fat)

To ensure that x and y are non-negative, the following inequalities must be satisfied:

x ≥ 0y ≥ 0

Therefore, the complete set of inequalities for x and y are:

x + y ≥ 82x + y ≥ 11x + y ≤ 10x ≥ 0y ≥ 0

Answer:

X=18

Step-by-step explanation:

Answer:

x = 3.5 units (nearest tenth)

Step-by-step explanation:

The given triangle has a one right angle and two angles each measuring 45°. Therefore, it is a 45-45-90 triangle.

A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.  

Therefore, the formula for the ratio of the sides is x : x : x√2 where:

As the hypotenuse of the given right triangle is 5 units:

[tex]\implies x\sqrt{2} = 5[/tex]

To find the measure of x, solve for x:

[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{5}{\sqrt{2}}[/tex]

[tex]\implies x = \dfrac{5}{\sqrt{2}}[/tex]

[tex]\implies x =3.5355339...[/tex]

[tex]\implies x=3.5\; \sf units\;(nearest\;tenth)[/tex]

Therefore, the length of side x to the nearest tenth is 3.5 units.

Answer:

1 cubic meter = 1000000 cm cubed

Step-by-step explanation:

[tex]1m^3*10^6=1000000cm^3[/tex]

Answer:

1 cubic meter = 10000000 cm cube

A positive semi-definite operator's rayleigh quotient must have a minimum value of zero to be considered positive.

Let A be a non-positive definite positive semi-definite operator. This proves that a non-zero vector x exists such that Ax = 0. The Rayleigh quotient of A with regard to x may thus be defined as follows:

[tex]R(x) = (x^T)Ax / (x^T)x[/tex]

A is positive semidefinite, hence for each vector x, (xT)Ax >= 0 is true. However, there is a non-zero vector x such that Ax = 0 if A is not a positive definite. In this instance, the Rayleigh quotient's numerator is 0, and as a result, the Rayleigh quotient is also 0. Since there is always a non-zero vector x such that Ax = 0, we may infer that the Rayleigh quotient's lowest value for a positive semi-definite but not positive definite operator is 0.

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Answer:

Let's call the unknown number "x".

According to the problem:

x - (-17) = 25x

Simplifying:

x + 17 = 25x

Subtracting x from both sides:

17 = 24x

Dividing by 24:

x = 17/24

Therefore, the unknown number is 17/24.

As the triangles are similar to each other, using congruent theorem, we get the value of side JK = 63.8.

Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.

This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".

As per the triangles,

Let JK be = x.

GF/GH = JI/JK

⇒ 11/18 = 36 /x

⇒ x = 36 × 18/11

⇒ x = 63.8.

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Answer:

1.Neither

2.Perpendicular

3.Perpendicular

4.Neither

5.Perpendicular

6.Perpendicular

7.Neither

8.Neither

9.Perpendicular

10.Neither

11. Perpendicular

12.Perpendicular

13.Neither

14.Neither

15.Neither

16.Neither

17.Parallel

18.Neither

here are the answers in order from top to bottom

The composite function is obtained applying the inner function as the input to the outer function.

The functions for this problem are defined as follows:

Hence the composite function is obtained replacing the two instances of T on the function N(t) by the definition of T(t), hence:

N(T(t)) = 20(6t + 1.2)² - 128(6t + 1.2) + 77

N(T(t)) =  720t² + 288t + 28.8 - 768t - 204.6.

N(T(t)) = 720t² - 480t - 175.8.

For a population of 18413 bacteria, we have that N(T(t)) = 18413, hence:

720t² - 480t - 175.8 = 18413

720t² - 480t - 18588.8 = 0.

The coefficients of the quadratic function are given as follows:

a = 720, b = 480, c = -18.588.8.

Using a quadratic function calculator, the positive solution is given as follows:

t = 4.76 hours.

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Answer:

Hence, factors are 3x,(x−4y).

Step-by-step explanation:

We need to factorise 3x 2 −12xy

Here we can take 3x common.

Thus we have 3x 2−12xy=3x(x−4y)

Hence, factors are 3x,(x−4y).

Answer: 3x ( x - 4y )

Step-by-step explanation:

Factorizing 3x²-12xy

3x ( x - 4y )