if it takes 3/4 of an hour to fill 3/5 of a pool how many hours will it take to fill the pool completely

a) The expected value is 75, the standard deviation is 3 and the shape is approximately normal.

b) 0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.

c) 0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68.

d) 0.8907 = 89.07% probability that the average aptitude test in the sample will be less than 78.69.

e) The value of C = 81.51.

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]$\mu$[/tex] and standard deviation [tex]$\sigma$[/tex], the z-score of a measure X is given by:

[tex]$Z=\frac{X-\mu}{\sigma}$[/tex]

The Z-score calculates the deviation of the measure from the mean in standard deviations. We glance at the z-score table after determining the Z-score to determine the p-value connected to it. The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the p-value.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]$\mu$[/tex] and standard deviation [tex]$\sigma$[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]$\mu$[/tex] and standard deviation [tex]$s=\frac{\sigma}{\sqrt{n}}$[/tex].

The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15.

This means that [tex]$\mu=75, \sigma=15$[/tex]

a. By the Central Limit Theorem, it will be approximately normal, with expected value [tex]$\mu=75$[/tex] and standard deviation [tex]$s=\frac{15}{\sqrt{25}}=3$[/tex]

b. The p-value of Z when X = 82.14 subtracted by the p-value of Z when X = 70.14.

X = 82.14

[tex]$Z=\frac{X-\mu}{\sigma}$[/tex]

By the Central Limit Theorem

[tex]$Z=\frac{X-\mu}{s}$[/tex]

[tex]$Z=\frac{82.14-75}{3}$[/tex]

Z = 2.38

Z = 2.38 has a p-value of 0.9913.

[tex]$Z=\frac{X-\mu}{s}$[/tex]

substitute the values in the above equation, we get

[tex]$Z=\frac{70.14-75}{3}$[/tex]

Z = -1.62 has a p-value of 0.0526

0.9913 - 0.0526 = 0.9387

0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.

c. This is 1 subtracted by the p-value of Z when X=82.68.

[tex]$Z=\frac{X-\mu}{s}[/tex]

substitute the values in the above equation, we get

[tex]$&Z=\frac{82.68-75}{3} \\[/tex]

Z = 2.56 has a p-value of 0.9948.

1 - 0.9948 = 0.0052

0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68

d. This is the p-value of Z when X=78.69. So

[tex]$&Z=\frac{X-\mu}{s} \\[/tex]

substitute the values in the above equation, we get

[tex]$&Z=\frac{78.69-75}{3} \\[/tex]

Z = 1.23 has a p-value of 0.8907

0.8907 = 89.07 % probability that the average aptitude test in the sample will be less than 78.69.

e. Find a value, C, such that P((x>C) = 0.015.

This is X when Z has a p-value of 1 - 0.015 = 0.985.

So X when Z = 2.17.

[tex]$Z=\frac{X-\mu}{s}$[/tex]

substitute the values in the above equation, we get

[tex]$2.17=\frac{X-75}{3}$[/tex]

X - 75 = 3 × 2.17

X = 81.51

Therefore, the value of C = 81.51

The complete question is:

MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 25 is taken from a population of 500.

a. What are the expected value, the standard deviation, and the shape of the sampling distribution of?

b. What is the probability that the average aptitude test in the sample will be between 70.14 and 82.14?

c. What is the probability that the average aptitude test in the sample will be greater than 82.68?

d. What is the probability that the average aptitude test in the sample will be less than 78.69?

e. Find a value, C, such that P(( x>C) = .015.

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Answer:

Angle YVX = 59°

Angle Y = 85°

x = 3

Step-by-step explanation:

You got the first two correct.

The last bit, use the fact that the shape is a parallelogram, the opposite sides are equal.

2x = 6

x = 3

Answer:

Step-by-step explanation:

The linear line interacts with the y-axis at 0. Meaning that the y-int is 0. This represents that the original amount of gasoline was 0.

If car has 1/x part in cleaning the house in 1 hour 1/x-5 must be part of Jose if he also clean the house for 1 hr.

The scientific definition of work is different in many ways from its everyday meaning. The definition of work in physics reveals its relationship to energy – whenever work is done, energy is transferred.

For a work to be done, in a scientific sense, a force must be exerted, and there must be displacement in the direction of the force. With this said, we can say that Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.

Mathematically, the above statement is expressed as follows:

W = (F cos θ) d = F. d

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Answer:

Explanation:

Here, we want to get the right triangles

Mathematically, for us to have a right triangle, the square of the hypotenuse (which is the longest side) equals the sum of the squares of the two other sides. This is Pythagoras' theorem

We shall be testing this principle out on the given options

We proceed as follows:

What this means is that only options A and B is correct

In a bar graph the length of the bar need not be in proportion to the information being False.

Bar graph. A bar chart is frequently used to compare values of different things at a specific time. It presents information visually using rectangles (bars). It generally serves as a visual aid for proportions, patterns, comparisons, and contrasts.

To represent value, it makes use of bars that stretch to various heights. Vertical bars, horizontal bars, grouped bars (several bars that compare values in a category), and stacked bars can all be used to construct bar graphs (bars containing multiple types of information).

A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.

comparisons of several variables that are simple. clarity in the presentation of data trends. Simple value determination.

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Answer:

6.39 and 100.8

Step-by-step explanation:

To find a certain percent of a number, convert the percent to a decimal and multiply them together

0.09 * 71 = 6.39

1.26 * 80 = 100.8

Answer:

The time take for the journey can be calculated by dividing the total distance by the distance travelled in an hour.

Which is 2171 (Total distance) / 520 (Distance travelled in a hour)

[tex]2171/520 = 4.175[/tex]

Which can be rounded of to 4.2

It takes 4.2 hours for the flight between Los Angeles and Toronto

We get that the expected temperature is

Step 1: Distributive property:

Step 2: Subtraction Property of Equality

Step 3: Simplifying

Step 4: Division property of equality

Step 5: Simplifying

Given the expression

9(u + 2) = -45

Step 1: Expand using the Distributive property:

9u + 9(2) = -45

9u + 18 = -45

Step 2: Subtract 18 from both sides (Subtraction property of equality)

9u + 18 - 18 = -45 - 18

Step 3: Simplifying

9u = -63

Step 4: Divide both sides by 9 (Division property of equality)

9u/9 = -63/9

Step 5: Simplifying

u = -7

Answer: D

Step-by-step explanation:

as when 3746 is rounded to the nearest hundred t is 4000

whereas when 3746 is rounded to the nearest ten it is 3800.

4000 is larger than 3800 so the answer is D.

Since the school district will allow parents to decide whether they want their children to be in the tracked or non-tracked group, the type of design that the school district has implemented is  a. matched design.

A matched group design is an experimental layout where the study subjects are selected because their variables match.

Therefore, In a matched pairs design, study participants are matched according to important variables or shared traits that are pertinent to the study's subject. The second step involves assigning one member of each pair to the control group and the other to the experimental group.

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See full question below

Parents have raised major concerns over a school district's proposed experiment to examine the effectiveness of removing math tracks and instead placing all students into one open math class. In response, the school district has decided not to randomly assign students to be placed in tracked or non-tracked math classes. Instead, the school district will allow parents to decide whether they want their children to be in the tracked or non-tracked group.

which methodological problem is very likely under this scenario

Select one:

a. matched design

b. pre-post design

c. nonequivalent comparison design

d. multiple time-series design

Step-by-step explanation:

Hope it helps you ..

MATHEMATICS IS OUR OWN LANGUAGE,LETS TALK TOGETHER

The value of the function c(75) for  c(p) = 0.15p is c(75) = $11.25

From the question, the function definition is given as

c(p) = 0.15p

The above function is a linear function

This is so because it is represented as  y = mx where m is the slope

The function value to calculate is given as

c(75)

This means that we calculate c(p) when p = 75

So, we have

c(75) = 0.15(75)

This gives

c(75) = 0.15 x (75)

Evaluate the product

c(75) = 11.25

Hence, the function value is c(75) = 11.25

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Hello!

So, we are given the following to solve.

Solve for v.

[tex]\frac{v}{8}-3.1=-15.9[/tex]

To solve for v, we to do as follows:

1. Add 3.1 to both sides.

2. Simplify.

3. Multiply both sides by 8.

4. Simplify.

Hope this helps!

Answer:

5% of 40 = 20

Step-by-step explanation:

To find 5% of 40, you can turn the 5% to 0.5, and the "of" means multiplication.

So, in turn you would have:

0.5 x 40 = 20

x is each friend

3x + 28 > 200

3x > 172

x > $57.33

if right can a i get brainliest pls

Answer:

Step-by-step explanation: $200-$28= $172

                                                $172÷3=$57.33

(a) The probability that the next page you read contain zero is 0.8187.

(b) The probability that the next page you read contains  or more typographical errors is 0.0175.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes

The probability that the next page you read contains zero. The expected number of typographical errors on a page of a certain magazine is  

That is, y = 0.2

Let  is a random variable representing the number of typos per page.

Since, we have a large number of letters per page, and the number of errors in one page will be small, we use Poisson distribution. The probability function of the Poisson distribution is defined as,

[tex]P(x = i) = e^-^y\frac{y^i}{i!},..... i = 0, 1, 2, ...[/tex]          ...(1)

Here, y is a parameter.

Find the probability that the next page you read contains zero.

That is, find P(y = 0)

plug y = 0 in equation (1), we get

P(x = 0) = 0.8187

The probability that the next page you read contain zero is 0.8187

Given the question that the probability that the next page you read contains  more typographical errors. The expected number of typographical errors on a page of a certain magazine is 0.2

That is y = 0.2

Let is a random variable representing the number of typos per page.

Find the probability that the next page you read contains more typographical errors.

That is find P(x ≥ 2)

P(x ≥ 2) = 1 - P(x ≤ 1)

= 1 - (P(x = 0) + P(x = 1))

= 1 - 0.982477

= 0.0175

The probability that the next page you read contains  or more typographical errors is 0.0175.

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Answer:x=    1/4=0.250

Step-by-step explanation:

letter A = C

letter B = B

Letter C= B

Answer:

(a) Figure C

(b) Figures B and C

(c) Figures B and C

Step-by-step explanation:

Figure A does not apply to any of the 3 questions

Hope this helps

SOLUTION

We want to find which of the following values make the inequality

x ≤ 16.3 to be true.

This inequality means that x is equal to 16.3 or less than 16.3. So the numbers that fall under this are numbers smaller than 16.3 and also 16.3.

The numbers that fall under here are 8, 1/4, -3 and 16.3

Hence the answer b, c, e and f

Answer:

78

Step-by-step explanation:

80-2+78 soo,

78+2 +80 with means 102+78 =180

Answer:

102 + 78 = 180

Step-by-step explanation:

SOLUTION

From the question

Cross multiplying you have that

Hence, the answer is 70

corresponding (option D)

Since the lines are parallel and a tranversal line cuts the two lines:

The angle 2 at the top of the first line correspods to angle 6 at the top of the second line.

Angle 2 and angle 6 are equal.

Hence. we say angle 2 and angle 6 are corresponding angles (option D)

Answer

Graph 1 = 1/3 slope

Graph 2 = -1/3 slope

Graph 3 = 3 slope

Graph 4 = -3 slope

I found these by counting rise over run,

or y/x to points on the line that cross the x or y axis.

The graphs that have a line that go up from left to right are positive slopes

The graphs that have a line that go down from left to right are negative slopes

Problems solved!

Answer:

Step-by-step explanation:

    2

3x + y =-12x

Answer:

Step-by-step explanation:

y= 2

45−6x

2−3 y=

2− 45−6x

2 −3 , ∣x∣≤ 2

30

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