Can someone please explain what I did wrong here? Thank you!

The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

for more such questions on probability visit:

https://brainly.com/question/251701

#SPJ8

In order for f(x) to be a linear function, determine the value of k in the data set.

x = {-7, -2, 2, 5}

f(x) = {-15, k, 3, 9}

The value of k is {-5}.

Given that to find the value of k in the data set such that the data set represents a linear function.

Linear Function is a straight line on the coordinate plane is represented by a linear function. The formula for a linear function is f(x) = mx + b, where m and b are real values.

Here, f(x) or y is the dependent variable, m is a slope of the line, x is the independent variable and b is the y-intercept.

Here,(x,f(x)) are {(-7,-15),(-2,k),(2,3),(5,9)}

The slope of the function,

(x, f(x)) = (2,3) and (5,9)

Slope formula is m=\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\).

Slope m= \(\frac{9-3 }{5-2}\)

Slope m=\(\frac{6}{3}\)

Slope m=2.

Using the point slope form, determine the linear function's equation.

\(y-y_{1} =m(x-x_{1})\)

Here, \((x_{1},y_{1})=(-7,-15)\) and m=2

We get

y + 15 = 2 (x + 7)

y = 2x - 1

Now at x = -2 and f(x) = k

k = 2(-2) - 1

k = -4-1

k=-5

Therefore, the value of k is -5.

To learn more about linear function visit: https://brainly.com/question/21107621

#SPJ9

Joel has 3/8 gallon of paint left after painting the ceiling and the wall.

How to calculate this?

To answer the question, we have to follow the below steps:

Step 1: Joel used 1/4 gallon of paint to paint a ceiling.

Step 2: Joel used 3/8 gallon of paint to paint a wall.

Step 3: We have to find out how much paint is left with Joel.

Step 4: Let's find the paint used by Joel in total to paint a ceiling and a wall.

Pint used to paint ceiling = 1/4

Pint used to paint wall = 3/8

Total paint used = 1/4 + 3/8

Common denominator = 8Paint used = 2/8 + 3/8 = 5/8 of a gallon

Step 5: Let's find out the remaining paint with Joel.

Pint of paint = 1

Pint used to paint the ceiling and wall = 5/8

Remaining paint = 1 - 5/8= 3/8

Learn more about Common Denominator.

brainly.com/question/29775115

#SPJ11

To multiply -1(x^2-4x+8), we need to distribute the -1 to each term inside the parentheses:

-1(x^2-4x+8) = -x^2 + 4x - 8

So, the product of -1 and the expression (x^2-4x+8) is -x^2 + 4x - 8.

Answer:

126th

Step-by-step explanation:

16 = |x - 7|

First solution Second solution

16 = x - 7 -16 = x - 7

16 + 7 = x -16 + 7 = x

23 = x x = 9

Answer:

1. -4x + 2 > 0

-4x>-2

2x<1

x<0.5

2. 5x > x + 4

4x>4

x>1

3. 3x + 4 < 10

3x<6x<2

4. -10x + 5 -4 > 4x + 3 -1

4x>27

x<1

x<1/7

5. 6x + 3 < 7x - 10

-x<-13

x>13

6. 2x - 4 < 8x + 2

-6x>-6

x<1

7. -3s + 3 > 3

-3s>0

s<0

8. 4s + 2s > 6

6s>6

s>1

9. 6t < 12

t<2

10. 11x < 12

1x<11

11. 3x > 36

x>12

12. 25x < 500

x<20

13. 16r < 8 (10)? U wanted to right

16r < 8*10?

If yes, then

16r < 80

r < 5

14. 6s > 216

s>36

15. 8x < 64

x<8

Answer:

i think you will make it into smaller pices

Step-by-step explanation:

Answer:

OG slope is 1, perpendicular slope is -1

Step-by-step explanation:

rise over run is 1/1, perpendicular slopes are the reciprocoal, or opposite slope, so -1

The intended population in this study is all members who received physical therapy in the past 12 months. The sample is the 212 members who returned the questionnaire.

The health care provider wants information about the satisfaction of its members who received physical therapy in the past 12 months. Therefore, the intended population in this study is all members who received physical therapy in that time period. This includes both the members who returned the questionnaire and those who did not.

On the other hand, the sample refers to the group from which the health care provider actually obtains information. In this case, the sample consists of the 212 members who returned the questionnaire. These are the individuals who voluntarily participated in the survey and provided their feedback on the satisfaction with physical therapy services. The sample represents a subset of the intended population.

Learn more about subset here:

https://brainly.com/question/31569950

#SPJ11

The maximal amount of medically unsupervised weight loss that an adult should aim for in one week is generally 1-2 pounds (0.5-1 kg). This is because losing weight too quickly can be harmful to your health and lead to a number of negative side effects, such as muscle loss, fatigue, dehydration, and gallstones.

It's important to note that the amount of weight an individual can lose in a week can vary depending on factors such as their starting weight, body composition, and overall health. In some cases, a doctor or other medical professional may recommend a faster rate of weight loss under close supervision, but this is generally reserved for people who are severely overweight or have medical conditions that require rapid weight loss.

Ultimately, it's important to approach weight loss in a healthy and sustainable way, with a focus on making long-term lifestyle changes rather than relying on quick fixes or fad diets. A balanced diet, regular exercise, and a consistent sleep schedule are all important components of a healthy weight loss plan.

for such more question on  weight

https://brainly.com/question/17562784

#SPJ11

Answer:

3628800 ways if the women are always required to stand together.

To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.

First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).

Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.

Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.

Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.

There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.

To know more about arrangement visit

https://brainly.com/question/1427391

#SPJ11

The value of the variables as identified from the reciprocal function are;

a = 5

h = -6

k = 7

2. The correct option is Option A

A reciprocal function is a mathematical function that can be represented as f(x) = 1/x, where x ≠ 0.

The graph of a reciprocal function is a hyperbola with two branches that approach the x and y axes, but never touch them.

From the information given, we have the function as;

y = a/x - h + k

Given that the function with numbers is written as;

y = 5/x + 6 + 7

To determine the values of a, h and k, we get;

The variable, a = 5

The variable, k = 7

The variable, h = -(6) = -6

Learn more about reciprocal functions at: https://brainly.com/question/12621604

#SPJ1

Answer:

24

Step-by-step explanation:

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

To know more about equation of the curve refer here:

https://brainly.com/question/31467851#

#SPJ11

The number of ways to split the array nums into three non-empty parts is (n-2) × (n-1) ÷ 2.

To split the array nums into three non-empty parts, we can choose the indices of the first two splits. We can choose the first split in (n-2) ways, since we cannot choose the first or last element as the split point.

We can choose the second split in (n-1) ways, since we cannot choose the last element as the split point. However, since the order of the first two splits does not matter, we must divide by 2 to avoid over counting. Therefore, the total number of ways to split the array nums into three non-empty parts is:

(n-2) × (n-1) ÷ 2

if nums = [1, 2, 3, 4, 5], then the number of ways to split nums into three non-empty parts is:

(5-2) × (5-1) ÷ 2 = 3 × 4 / 2 = 6

The possible splits are [1], [2, 3], [4, 5]; [1], [2, 3, 4], [5]; [1, 2], [3, 4], [5]; [1, 2], [3], [4, 5]; [1, 2, 3], [4], [5]; and [1, 2, 3], [4, 5], [ ].

Learn more about Splitting array

brainly.com/question/14124291

#SPJ11

Answer:

would slow down

I am nt sure

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

k12 test

The simplified form of \(B C+\overline{B C D}+B\) is \(B+C\bar{D}+1\)

Boolean Algebra and DeMorgan’s theorems are used to simplify the given logic expressions.

The following are the solutions:i. \(\overline{A B C}+\overline{\bar{D}+E)}\)\(\overline{A B C}+\bar{\bar{D}.E}\)

Using DeMorgan’s theorem, \(\bar{(\bar{D}+E)}=\bar{\bar{D}.\bar{E}}\)= \(D+E\bar{E}\) = \(D+0\) = \(D\)

∴ \(\overline{A B C}+\overline{\bar{D}+E)}\) = \(\overline{A B C}+D\).ii. \(B C+\overline{B C D}+B\) = \(B+C(\bar{B D}+1)\)

Using DeMorgan’s theorem, \(\overline{B C D}=\bar{B}+\bar{C}+\bar{D}\)∴ \(B C+\overline{B C D}+B\) = \(B+C(\bar{B}+\bar{C}+\bar{D}+1)+B\)= \(B+C\bar{B}+C\bar{C}+C\bar{D}+C+B\)= \(B+C\bar{D}+1\)

Thus, the simplified form of \(B C+\overline{B C D}+B\) is \(B+C\bar{D}+1\).

therefore the solution is explained using DeMorgan’s theorem and Boolean Algebra.

Learn more about: Boolean Algebra

https://brainly.com/question/31647098

#SPJ11

Answer:

A

Step-by-step explanation:

it passes the vertical line test.<3

Answer:

Step-by-step explanation:

Area is the space that is contained in a two-dimensional figure.

Surface area is the total area of all of the sides and faces of a three-dimensional figure.  

To find the surface area, the area of each face is calculated and then add these areas together.

To find the area of a rectangle, multiply the length by the width .

From the graph the length of the rectangle is 10 m and the width is 8 m. Therefore, the area of the bottom face is

From the graph the length of the rectangle is 10 m and the width is 5 m. Therefore, the area of one of the rectangular side faces is

To find the area of a triangle use the following formula  where b is the base and h is the height.

From the graph the base of the triangle is 8 m and the height is 3 m. Therefore, the area of one of the triangular faces is

The surface area of the prism is the sum of the area of the bottom face, the area of the two rectangular side faces, and the area of the two triangular faces

Answer:

740

Step-by-step explanation:

Let the AP be a, a+d, a+2d, a+3d, ...

The  term of AP is given by:

\(t n =a+(n-1)d\)

We are given that the third term is 7.

\(t 3=7\)

⇒  \(a+(3-1)d=7\)

⇒\(a+2d=7 ---(1)\)

Also, the seventh term is 2 more than three times the third term.

\(t7=3t3+2\)

⇒\(a+ (7-1)d=3(a+(3-1)d)+2\)

⇒\(a+6d=3(a+2d)+2\)

⇒\(a+6d=3a+6d+2\)

⇒\(-2a=2\)

⇒\(a=-1\)

We can put it in (1)

\(a+2d=7\)

⇒\((-1)+2d=7\)

⇒\(2d=8\)

⇒d=4

Now, the Sum of n terms of an AP is given by the formula:

\(sn=\frac{n}{2}(2a+(n-1)d)\)

So, Sum of first 20 terms would be:

\(s 20=\frac{20}{2}(2(-1) +(20-1) x 4)\)

⇒\(s20=10(-2+19 x 4)\)

⇒\(s 20=10 x(-2+76)\)

⇒\(s 20= 10 x 74\)

⇒\(s 20=740\)

Thus, The Sum of first 20 terms of the AP is 740.

Answer:

whatever is higher than 1.5 is higher than r

Step-by-step explanation:

-1.2 ≤ -0.8r

-1.2/0.8 ≤ -0.8r/0.8

-1.5 ≤ -r

-1.5/-1 ≤ -r/-1

1.5 ≥ r

1.5 is equal to or bigger than r

Answer: -0.8r is bigger

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

4/6x1/2

4x1=4

6x2=12

Answer will be 4/12 or 1/3

So A is the answer because it shows 4/12

Answer:

multiply 6x10then by 20

Using the probability concept, we have that the probabilities are:

P(red, red):

Hence:

\(p = \frac{6}{20} \times \frac{6}{20} = \frac{36}{400} = 0.09 = 9\%\)

P(not white, green):

Hence:

\(p = \frac{17}{20} \times \frac{7}{20} = 0.2975 = 29.75\%\)

P(blue or white, red):

Hence:

\(p = \frac{7}{20} \times \frac{6}{20} = 0.105 = 10.5\%\)

P(red, red), without replacement:

Then:

\(p = \frac{6}{20} \times \frac{5}{19} = 0.0789 = 7.89\%\)

You can learn more about the probability concept at https://brainly.com/question/15536019

Answer:

graph C

Step-by-step explanation:

when X= 0

Y ---> -5

so , answer is graph C

Answer:

c

Step-by-step explanation:

the graph of | x | has its vertex at the origin and has shape V

the graph of | x | - 5 is the graph of | x | translated 5 units vertically down.

That is graph c represents | x | - 5

The mean should be set to 12.07 ounces, so that 1% of the cups will overfill.

12 + (0.07 * 2) = 12.14; 12.14 - (12.14 * 0.01) = 12.07

The mean amount of coffee to be dispensed should be set to 12.07 ounces in order to allow 1% of the cups to overfill. This is calculated by taking the normal value of 12 ounces, and adding the standard deviation of 0.07 ounce, resulting in 12.14 ounces. Then, 1% of that value is subtracted, giving 12.07 ounces. This amount will ensure that 1% of the cups will overfill, while the other 99% will be filled to the normal value of 12 ounces. This is beneficial for the customer, as it guarantees that no cup will be underfilled. It also ensures that the vending machine will not waste any coffee by overfilling the cups too much. Setting the mean to 12.07 ounces is the best solution for both the customer and the vending machine.

Learn more about mean here

https://brainly.com/question/15323584

#SPJ4