115 students choose to attend one of three after school activities: football, tennis or running.
There are 51 boys.
32 students choose football, of which 25 are girls.
47 students choose tennis.
12 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.

thanks!

Answer:

86.65% probability that the mean monitor life would be greater than 74.4 months in a sample of 85 monitors

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Population: \(\mu = 75, \sigma = 5\)

Sample of 85: \(n = 85, s = \frac{5}{\sqrt{85}} = 0.5423\)

If the claim is true, what is the probability that the mean monitor life would be greater than 74.4 months in a sample of 85 monitors

This is 1 subtracted by the pvalue of Z when X = 74.4. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{74.4 - 75}{0.5423}\)

\(Z = -1.11\)

\(Z = -1.11\) has a pvalue of 0.1335

1 - 0.1335 = 0.8665

86.65% probability that the mean monitor life would be greater than 74.4 months in a sample of 85 monitors

The area of this composite figure made from placing a sector of a circle on a triangle is 95.55 square cm

The sector area

The area of the sector is calculated as

Area = x/360 * πr²

Where

r² = 8² + 6²

So, we have

r² = 100

This means that

Area = 82/360 * π * 100

Evaluate

Area = 71.55

The triangle area

This is calculated as

Area = 0.5bh

So, we have

Area = 0.5 * 8 * 6

Evaluate

Area = 24

So, the area of the figure is

Figure = 24 + 71.55

Figure = 95.55

Hence, the area is 95.55

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The statements that are true are:

A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).

C. f(-1) = 6

To determine the truth of each statement, we need to analyze the given table of values for the function f(x).

A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).

The x-values listed in the table are -2, -1, 0, 1, 2, 3, 4, 5, and 6. These are the inputs for the function, and therefore, they represent the domain of f(x). Thus, statement A is true.

B. The range for f(x) is all real numbers.

Looking at the y-values listed in the table for f(x), we can see that the range of f(x) is from 5 to 13. It does not include all real numbers, so statement B is false.

C. f(-1) = 6

From the table, we can see that when x = -1, f(x) = 6. Thus, statement C is true.

D. f(5) = -2

There is no entry in the table for f(5), so we cannot determine the value of f(5) from the given information. Therefore, statement D is false.

In conclusion, the true statements are A and C.

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Answer:

Step-by-step explanation:

d = 13.416408

For:

(X1, Y1) = (-4, -5)

(X2, Y2) = (8, 1)

Answer:

L = 9.49 units

Step-by-step explanation:

From the 1st point to the 2nd, x changes by 12; from the 1st to the 2nd, y changes (increases) by 6.  These results (12 and 6) represent the leg length of a right triangle whose diagonal length we wish to calculate using the Pythagorean Theorem:

12^2 = 144 and 6^2 = 36.

Combining these results in the length of the diagonal:

L = √(144 + 36) = √180 = 13.42 units using the Pythagorean Theorem

Rounding off, we get L = 9.49 units

Answer:

dang with what

Step-by-step explanation:

Answer:

Learn how to do it

Step-by-step explanation:

if you learn how to do it you won't have trouble

Answer:

Second graph with straight diagonal lines

Step-by-step explanation:

The second graph with straight diagonal lines represents the direct variation

The X and Y axis represents two variables A and B  and these two variables in case of second graph with straight lines are directly proportional to each other.

Hence, If value of variable A increases, then value of variable B will also increase

Answer:

I believe it's the third one

explanation:

its one of the only graphs that the line passes through the orgin, and its linear.

Hope it helps and plase forgive me if I'm wrong

Answer:  h = -(16t + 3)(t - 2)

               h(0) = 6

               h(1) = 19

               h(2) = 0

Step-by-step explanation:

Factor the equation by finding two numbers whose

product = a×c and sum = b, then replace the b value with those two numbers and factor the equation.

h = -16t² + 29t + 6      

 a=-16   b=29   c=6           a×c = -96      b = 29      

                                      32 × -3 = 96          32 + (-3) = 29

h = -16t² + 32t    -3t + 6

h = -16t(t - 2)      -3(t - 2)

h = (-16t - 3) (t - 2)

h = -(16t + 3)(t - 2)

h(0) = -[16(0) + 3] [0 - 2]

      = -(3)(-2)

      = 6  

h(1) = -[16(1) + 3] [1 - 2]

      = -(19)(-1)

      = 19  

h(2) = -[16(2) + 3] [2 - 2]

      = -(35)(0)

      = 0  

Answer:

work is shown and pictured

Answer:

\(0.5\sqrt{16a^2}=-2a \quad \text{if}\;\;a < 0\)

\(-5\sqrt{y^2}=-5y \quad \text{if}\;\;y > 0\)

\(3\sqrt{c^2}=3c \quad \text{if}\;\;c \geq 0\)

\(-\sqrt{9y^2}=3y \quad \text{if}\;\;y < 0\)

Step-by-step explanation:

\(0.5\sqrt{16a^2}\;\; \text{if}\;\;a < 0\)

\(\implies 0.5\sqrt{16}\sqrt{a^2}\)

\(\implies 0.5\cdot 4\sqrt{a^2}\)

\(\implies 2\sqrt{a^2}\)

\(\implies 2 \cdot -a\)

\(\implies -2a\)

\(-5\sqrt{y^2}\;\; \text{if}\;\;y > 0\)

\(\implies -5y\)

\(3\sqrt{c^2}\;\; \text{if}\;\;c \geq 0\)

\(\implies 3c\)

\(-\sqrt{9y^2}\;\; \text{if}\;\;y < 0\)

\(\implies -\sqrt{9}\sqrt{y^2}\)

\(\implies -3\sqrt{y^2}\)

\(\implies -3 \cdot -y\)

\(\implies 3y\)

We have to solve the system of equations for x. The equations are:

In this case, we can replace y using the second equation and then solving for x in the first equation.

We find y as:

Then, we replace y in the first equation and we wlll obtain:

Answer: x = 28 [Option A]

Step-by-step explanation:

Just till the number 9 upside down to make it 6 then

6+11+13=30

The sum of three odd numbers can never be even. so I did it in that way.

I HOPE THIS WILL HELP U

STAY SAFE, STAY HAPPY

Answer:

14 units

Step-by-step explanation:

I graphed it on a website look at screen shot

Answer:

The answer is 14 units.

Step-by-step explanation:

Answer:

240 tickets

Step-by-step explanation:

1200/5=240

btw the "/" means divide

Answer:

9

Step-by-step explanation:

15 / 5/3 = 15 x 3/5=9

Because a negative numebr divided by a negative number is always positive.

Answer:

9

Step-by-step explanation:

Answer:

Her brother has $15

Step-by-step explanation:

How come Molly has $45 which is as 3 times as much money as her brother has, we divide 45 by 3 which gives us $15.

(I don't really know what your question is but I hope this helped.)

Find the amount of the markup by subtracting:

76-39 = $37

Divide the amount of the mark up by the purchase price:

37/39 = 0.948 x 100 = 94.8%

Answer: 94.8 %. Round the answer as needed.

C. The point estimate of the difference between the two population means is 2.

D. The 90% confidence interval estimate of the difference between the two population means is (1.748, 0.867)

Given that:

Sample 1 mean (x1) = 9

Sample 2 mean (x2) = 7

Sample 1 standard deviation (σ1^2) = 2.28

Sample 2 standard deviation (σ2^2) = 1.79

C. To find point estimate of the difference between the two population   means.

sample mean(x1) - sample mean(x 2)

 = 9 - 7

= 2

Therefore, point estimate = 2

D. To find 90% confidence interval estimate of the difference between the two population means

90% confidence for 't'

df = (n1 + n2) - 2

   = 12-2

   = 10

90%  confidence with df = 10 is t

t = 1.812

point estimate + 1 - t * \(\sqrt{\frac{s^2_{1} }{n_{1} } + \frac{s^2_{2} }{n_{2} } }\)

2 + 1 - 1.812*\(\sqrt{\frac{2.28^2}{6} + \frac{1.79^2}{6} }\)

3 - 1.812 *\(\sqrt{0.866 + 0.534}\)

1.188 * 0.9305 + 0.7307

(1.748, 0.867)

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Answer:

Going from bottom to top, left to right:

3804

5005

8118

15094

13391

28485

27422

Step-by-step explanation:

Answer:

23° and 157°

Step-by-step explanation:

Let n represent the smaller angle then the larger angle would be...

n+134

Supplementary angles add up to 180 degrees. We can use this information to set up an equation...

n+n+134=180

Combine like terms

2n+134=180

Subtract 134 from both sides

2n=46

Divide both sides by 2

n=23

n+134=157

23° and 157°

Answer:

10 11/15

Step-by-step explanation:

the improper fraction you would use is 23/5 and 7/3

to convert improper fractions you would take the whole number multiply by the denominator and then add the numerator so 4*5 which is 20 + 3

do that to both fractions then multiply

23     7    and you will get 161/15 which simplifies to 10 11/15

5       3

Answer:

Hi there!!

Your answer is:

\(10 \times \frac{11}{15} \)

Step-by-step explanation:

\(4 \times \frac{3}{5} \)

Multiply 4 by the denominator and add to the numerator!

4×5+3

20+3

23

23/5 ×

\(2 \times \frac{1}{3} \)

2×3+1

6+1

7

7/3×

7/3 × 23/5

7× 23 = 161

3×5= 15

161/15

SIMPLIFY!

10 & 11/15

Hope this helps

Answers:

A, B, D, E

Nearly everything except choice C is true.

====================================================

Explanation:

Answer:

\(x=-10\)

Step-by-step explanation:

\(\frac{x}{2}=-5\\\mathrm{Multiply\:both\:sides\:by\:}2\\\frac{2x}{2}=2\left(-5\right)\\Simplify\\x=-10\)

Answer:

m-15

Step-by-step explanation:

(a) This utility function represents a person who has equal preferences for both goods x and y. (b) This utility function represents a person who has a budget constraint and can only afford to buy either x or y, but not both. (c) This utility function represents a person who has a preference for either x or y but not both.

(a) U(x, y) = x + 2y

This utility function represents a person who has equal preferences for both goods x and y. To sketch the indifference curves, we will keep the total utility constant and increase the quantity of one good while decreasing the quantity of the other good.

For example, the first indifference curve can be represented by the equation x + 2y = 10. As we increase x by 1 unit, we decrease y by 0.5 units to keep the total utility constant.

Similarly, we can create a second indifference curve by keeping the total utility constant at a higher value, such as x + 2y = 20. The graph would show that as the total utility increases, the person is willing to have more of both goods x and y.

(b) U(x, y) = min{2x, y}

This utility function represents a person who has a budget constraint and can only afford to buy either x or y, but not both. To sketch the indifference curves, we will keep the minimum of 2x and y constant and show the different combinations of x and y that the person finds equally desirable.

For example, the first indifference curve can be represented by the equation min{2x, y} = 2. This means that the person can either buy 2 units of x or 2 units of y, but not both. As x increases, y decreases and vice versa.

Similarly, we can create a second indifference curve by keeping the minimum of 2x and y constant at a higher value, such as min{2x, y} = 4. The graph would show that as the minimum value increases, the person is willing to have more of both goods x and y.

(c) U(x, y) = max{2x, 3y}

This utility function represents a person who has a preference for either x or y but not both. To sketch the indifference curves, we will keep the maximum of 2x and 3y constant and show the different combinations of x and y that the person finds equally desirable.

For example, the first indifference curve can be represented by the equation max{2x, 3y} = 6. This means that the person either has 6 units of x or 6 units of y, but not both. As x increases, y decreases and vice versa.

Similarly, we can create a second indifference curve by keeping the maximum of 2x and 3y constant at a higher value, such as max{2x, 3y} = 9. The graph would show that as the maximum value increases, the person is willing to have more of both goods x and y.

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Hey, there are no numbers added to this problem but if you were to add them as I did down below that is how you solve this question!

Step-by-step explanation:

Suppose s and h are the mileage numbers for the SUV and Hybrid, respectively. Then if each vehicle drives 1 mile, the total gas consumption is

.. 1/s +1/h

Then the combined mileage is

.. 2/(1/s +1/h) = 2sh/(s+h)

Option 1: s=12, h=60

.. mpg = 2*12*60/(12+60) = 20

Option 2: s=11, h=75

.. mpg = 2*11*75/(11 +75) = 1650/86 ≈ 19.2

In summary,

.. Option 1: 20.0 mpg

.. Option 2: 19.2 mpg

The median of the given data set is 26.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

Given the data set, we need to find the median.

So, let's arrange the numbers from smallest to largest in order to find the median.

\(\sf 15,20,22,26,28,35,36.\)

\(\text{Median}=\sf 26\)

Therefore, the median of the data set is 26.

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Answer:

ooga booga ooga booga ooga booga ooga booga ooga booga

Step-by-step explanation:

Answer:

P(5,6) = 63

Step-by-step explanation:

Test each point to see which ordered pair maximizes the objective function:

(0,0): p = 3(0) + 8(0) = 0

(2,7): p = 3(2) + 8(7) = 6 + 56 = 62

(5,6): p = 3(5) + 8(6) = 15 + 48 = 63

(8,1): p = 3(8) + 8(1) = 24 + 8 = 32

Hence, (5,6) is the ordered pair that maximizes the objective function.

Answer:

Step-by-step explanation:

a = x

b = 2x^2

ab = x * 2x^2

ab = 2 x^3

2ab = 4 * x^3