Which relation is a function.

Using central limit theorem, the probability that the class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test is 0.00017332

We can use the Central Limit Theorem (CLT) to approximate the distribution of the sample mean completion time for the class. According to CLT, the distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the population mean is given as 48 minutes, the population standard deviation is given as 15 minutes, and the sample size is 20. Therefore, the mean of the sample mean completion time is also 48 minutes, and the standard deviation of the sample mean completion time is 15/√20 ≈ 3.3541 minutes.

To find the probability that the class mean completion time is greater than 60 minutes, we can standardize the distribution of the sample mean completion time using the z-score formula:

z = (x - μ) / (σ / √n)

where x is the value we want to find the probability for (in this case, x = 60), μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we get:

z = (60 - 48) / (15 / √20) = 3.5777

Using a standard normal distribution table (or calculator), we can find the probability that a z-score is greater than 3.5777.

P = 0.00017332

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A sample size of 5 is required to estimate the population mean with a 98% confidence level and a margin of error of 5.

To determine the sample size required to estimate a population mean with a 98% confidence level and a margin of error of 5, we need to use the formula:

n = (z^2 * σ^2) / E^2

where:
- n is the sample size
- z is the z-score associated with the confidence level (in this case, 2.33 for a 98% confidence level)
- σ is the population standard deviation (0. given in the question)
- E is the margin of error (5 in this case)

Plugging in the values, we get:

n = (2.33^2 * 0.^2) / 5^2
n = 4.8556

Since we cannot have a fraction of a sample, we round up to the nearest whole number. Therefore, a sample size of 5 is required to estimate the population mean with a 98% confidence level and a margin of error of 5.

It is important to note that this formula assumes that the population is normally distributed. If this assumption is not met, the sample size calculation may need to be adjusted. Additionally, this formula only estimates the minimum sample size required and does not take into account factors such as cost and feasibility of obtaining the sample.

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Given:

Two cards are drawn with replacementss in succession.

Required:

We need to find the probability that both cards are drawn is Queen.

Explanation:

The sample space = The number of cards.

Let A be the event of drawing a queen.

The favourable outcomes =The number of queen cards.

The probability of drawing the first card, which is queen.

The card is replaced.

Let B be the event of drawing the second card after replacement.

The probability of drawing the second card, which is queen is equal to the probability of drawing the first card, which is queen.

The probability that both cards drawn are Queen.

Final answer:

Answer:

a) To calculate the percent markup, we need to divide the profit by the original cost and multiply by 100 to express it as a percentage:

Markup = (Selling price - Cost) / Cost * 100

Markup = (8.50 - 5) / 5 * 100 = 70%

So the markup on the item was 70%.

b) To find the total profit, we need to subtract the original cost from the selling price:

Profit = Selling price - Cost

Profit = 8.50 - 5 = 3.50

So the total profit on the item was $3.50.

7 × 5 is used to find the total number of squares.

Each has 7 small squares.

There are 5 parts,

So we can write:

7+7+7+7+7

That is adding 7 five times. By this we get the total number of square.

So by multiplying 7 by 5 we get the total number of square.

= 7× 5

Therefore the expression 7×5 is used to find the total number of squares.

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Answer:

k = 1

Step-by-step explanation:

since the polynomial is divisible by (x + 1) then x = - 1 is a root and will make the polynomial equal to zero.

substitute x = - 1 and equate to zero

\((-1)^{100}\) + 2\((-1)^{99}\) + k = 0 , that is

1 + 2(- 1) + k = 0

1 - 2 + k = 0

- 1 + k = 0 ( add 1 to both sides )

k = 1

Answer:

14

Step-by-step explanation:

35÷5=7

2×7=14

hope this helps

Answer:

14

Step-by-step explanation:

35÷5=7

7×2= 14

ya welcome

Answer:

01 V READING / VOCABULARY The Prophecy of the Frogs: Write a paragraph (3-4 sentences) in your notebook to explain why this animated film is a tragicomic social fable.  (Why is it a fable, why is it a social fable, why is it tragicomic).  Submit a photo of your work in TEAMS.  

Answer:

x = 1 y = 2

Step-by-step explanation:

hard to explain but try it pretty sure its correct.

Answer:

What the other person said

Answer:

Step-by-step explanation:

When an inequality is graphed, the solutions will be shaded in a color. \

On this graph, it is shaded blue.

First we want to put all the points on the graph. During this step, it does not mater if the point is in the blue or not.

Now that we have all 8 points plotted, we can begin elimination.

For this step, we will cross out or eliminate any points in the white.

Any points in the blue, will be correct

After doing this step, you should have the answers (0,0), (4,9), (-1,5), (-4,-8)

So those are the correct answers

Answer:

D. 4

Step-by-step explanation:

I just did this, it's in the instruction and I got it right.

Answer:

The width is 10 inches

The length is 30 inches

Step-by-step explanation:

Perimeter of a Rectangle

The perimeter of a rectangle of length L and width W is calculated as follows:

P = 2L + 2W

It's given the length of a rectangle is 10 more than twice the width:

L = 2W + 10

Substituting into the formula of the perimeter:

P = 2(2W + 10) + 2W

Operating:

P = 4W + 20 + 2W

P = 6W + 20

It's given this perimeter is 80 inches, thus

6W + 20 = 80

Subtracting 20:

6W = 80 - 20 = 60

Dividing by 6:

W = 60 /6 = 10

Since :

L = 2W + 10

L = 2*10 + 10

L = 30

The width is 10 inches

The length is 30 inches

Answer:

\( {3x}^{2} + 5x + 2 \\ = {3x}^{2} + 3x + 2x + 2 \\ = 3x(x + 1) + 2(x + 1) \\ = (3x +2)(x + 1)\)

Answer:

x=-2/3 and x=-1

factored form

(3x+2)(x+1)

[Let me know if there is another method your instructor wanted you to use]

Step-by-step explanation:

Given:

\(3x^2+5x+2=0\)

Factor using the quadratic formula:

\(x=\frac{-b+-\sqrt{b^2-4(a)(c)} }{2a}\)

\(x=\frac{-5+-\sqrt{(5)^2-4(3)(2)} }{2(3)}\)

\(x=\frac{-5+-\sqrt{25-24} }{6}\)

\(x=\frac{-5+-\sqrt{1} }{6}\)

\(x=\frac{-5+1}{6}\) and \(x=\frac{-5-1}{6}\)

Finally:

\(x=-2/3\) and \(x=-1\)

Written in factored form would be:

\((3x+2)(x+1)\)

Answer:

-14x-48

Step-by-step explanation:

Answer: the error is in the second part 0.12 it should be 1.2 for the answer to be 1.44

Step-by-step explanation:

1.2x0.12 = 0.144

0.12x0.12=0.0144

1.2x 1.2 = 1.44

We can get the exact value of a using the vertex and one point on the parabola.

This means h = 2, k = -7, x = 0, and y = -3. We use this value in the vertex form

Now, we solve for a

The image above shows the vertex point of the given parabola. Also shows the point we used.

Answer:

Child = $ 10.00

Adult = $ 14.00

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number of cucumber = x

And the cost of the cucumber = y

Cost of the cucumber will be directly proportional to the number of cucumbers.

y ∝ x

y = kx [Here, k = proportionality constant]

Since, market sells 3 cucumbers for $1.2

1.2 = k(3)

k = 0.4

Therefore, equation for this situation will be,

y = 0.4x

Part A

If x = 1,

y = 0.4(1)

  = 0.4

For x = 2,

y = 0.4(2)

  = 0.8

For x = 3,

y = 0.4(3)

  = 1.2

Number of cucumbers            Cost($)

          1                                          0.4

          2                                         0.8

          3                                          1.2

Part B

Equation representing relation between number of cucumbers and the cost will be,

y = 0.40x [Option A]

Answer:

mathe meitics

Step-by-step explanation:

Answer:

3 goals

Step-by-step explanation:

Lets say the 12 goals is 100%

Luke scored 25% of those goals

So to find 25 percent of 12 multiply 12 by the percent 25

25 times 12 is 300

divided by 100 is 3

Luke scored 3 goals

Tell me if this is wrong if not

Hope I helped :]

Answer:

1/4

Step-by-step explanation:

there are 4 colors meaning each one has a 1/4 chance

Answer:

b

Step-by-step explanation:

Therefore, the maximum blood pressure of 200 mmHg occurs at approximately 0.524 seconds, and the minimum blood pressure of 120 mmHg occurs at approximately 1.571 seconds within the time interval 0 ≤ t ≤ 0.75.

To find the maximum and minimum values of the blood pressure function p(t), we need to examine the behavior of the sinusoidal term, -40sin(3t), within the given time interval. The function is a sine wave with an amplitude of 40 and a period of 2π/3. This means that the maximum value occurs at the peak of the sine wave (amplitude + offset), and the minimum value occurs at the trough (amplitude - offset).

The maximum blood pressure corresponds to the peak of the sine wave, which is 40 + 160 = 200 mmHg. To find the time at which this occurs, we set the argument of the sine function, 3t, equal to π/2 (since the peak of the sine wave is π/2 radians). Solving for t gives t = (π/2) / 3 = π/6 ≈ 0.524 seconds.

Similarly, the minimum blood pressure corresponds to the trough of the sine wave, which is -40 + 160 = 120 mmHg. Setting the argument of the sine function equal to 3π/2 (the trough of the sine wave), we find t = (3π/2) / 3 = π/2 ≈ 1.571 seconds.

Therefore, the maximum blood pressure of 200 mmHg occurs at approximately 0.524 seconds, and the minimum blood pressure of 120 mmHg occurs at approximately 1.571 seconds within the time interval 0 ≤ t ≤ 0.75.

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both directions can be chosen as positive in this example. The right-hand rule solves these ambiguities. The resultant remains the same at 3.2 *10^4 Tm

It is possible for the line integral to go around the loop in either direction (clockwise or counterclockwise), the vector area dS to point in either of the two normal directions and Ienc, which is the net current passing through the surface S, to be positive in either direction—but both directions can be chosen as positive in this example. The right-hand rule solves these ambiguities.

The resultant remains the same at 3.2 *10^4 Tm

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The total yearly salary for a major league baseball team with a mean salary of $1.2 million and 25 players on the active roster would be $30 million.

The mean yearly salary for a major league baseball team's players is $1.2 million. With 25 players on the active roster, we can calculate the total salary for the team.

To find the total salary, we multiply the mean salary by the number of players on the roster. In this case, we multiply $1.2 million by 25:

$1.2 million x 25 = $30 million

Therefore, the total yearly salary for the team would be $30 million.

In baseball, salaries can vary greatly between players. Some players may earn more than the mean salary, while others may earn less. The mean salary gives us an average value to understand the overall salary distribution of the team.

It's important to note that this calculation does not take into account additional factors such as signing bonuses, incentive bonuses, or other contract terms that may affect individual player salaries. This calculation simply provides an estimation of the total salary based on the given mean salary and number of players on the roster.

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The direction of the cross product is perpendicular to both of the vectors being multiplied. So, the answer to the question of what is the direction of the cross product could be any of the six options provided (x direction, -x direction, y direction, -y direction, z direction, -z direction), depending on the orientation of the vectors being multiplied.

The direction of the cross product is determined by the right-hand rule. When you have two vectors, A and B, the cross product (A x B) will be perpendicular to both A and B in a third direction. To find this direction, point your fingers in the direction of vector A, and then curl them towards vector B. Your thumb will point in the direction of the cross product. The options you provided (x, -x, y, -y, z, -z) depend on the specific vectors you are working with. In general, the cross product direction will be in the z direction or -z direction for vectors lying in the xy plane.

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Interpreting the scatterplot, it is found that the correct option is:

Springside weakens the correlation shown in the scatterplot.

Springside weakens the correlation shown in the scatterplot.

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Raphael could finish the job in 3/2 hr = 90 min. Matilde could finish the job in 3 hr.

Let M denote for matilde

R for Raphael.

I assume they worked on the task together to finish it in 1 hr.

M does 1/M of the job per hr.

R does 1/R of the job per hr.

(1/M + 1/R) * x hr = 1 whole job completed

We are told x = 1 hr, so that's done.

We are told M's rate of work is 1/2 of R's

R's rate of work is 1/R

1/2 * 1/R = 1/2R

substitute 1/2R for 1/M

(1/2R + 1/R) * 1 hr = 1 whole job completed

solve

(R+ 2R)/ 2R^2 = 1

3R /2R^2 = 1

3R = 2R^2

2R^2 -3R = 0

R(2R-3) = 0

R = 0 or 2R = 3

However, if R could do the work in 0 hours, then his rate of work would be undefined.

Therefore, we select 2R = 3, which means R= 3/2.

R can do the whole job in 3/2 hr working alone.

M can do the whole job in 2*3/2 = 3 hr working alone.

We can check this solution to be sure it is correct.

In 1 hr, R can do 2/3 of the job.

In 1 hr, M can do 1/3 of the job

2/3+1/3 = 1.

We also can substitute in the original equation as double-check.

(1/3 + 1/(3/2))*1 = 1 ??

(1/3 + 2/3) = 1

Answer: R could finish the job in 3/2 hr = 90 min. M could finish the job in 3 hr.

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