# Sara is completing the square to find the maximum or minimum value of the function f(x) = (2 - x) (5 + x). What is the first step that Sara must take? Does the function have a maximum or minimum value? What is that value?A) multiply the binomials; maximum value; 494B) multiply the binomials; minimum value; 494C) set each factor equal to zero and solve for x; minimum value; −25D) set each factor equal to zero and solve for x; maximum value; −72

Answer: Definitely multiply out the given factors:

f(x) = 10 + 2x - 5x - x^2, or  f(x) = -x^2 - 3x + 10
Find the derivative:  f '(x) = -2x - 3
Set the deriv. = to 0 and solve for x:  -2x = 3, and x = -3/2
This x = -3/2 is the x-coordinate of the max value.  The y-coord. is

f(-3/2) = (-3/2)^2 - 3(-3/2) + 10 = 21.25

I realize that this result does not agree with any of the four possible answers.  Please ensure that y ou have copied down this problem completely and correctly.

## Related Questions

The picture shows a carousel. The carousel spins while the horses move up and down. A student determines toeach horse completes one up-down cycle in 30 seconds. The student rides a horse on the carousel for 2 minute
which equals 120 seconds.
raal

4 times

Step-by-step explanation:

Note,

• 60 seconds = 1 minute
• 120 seconds = 2 minutes (60*2).

Since the student rode a horse for 120 seconds, to find the number of times the student riding the carousel completed the up-down cycle, we divide it by 30 seconds (which is the duration for the horse to complete one up-down cycle) because the student would be having the same duration as the horse because he was on top the horse.

Hence, we have;

120/30 = 4

HELP!!!!!In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.

What is the average number of siblings for this group? Enter your answer as a decimal, rounded to the nearest tenth,
_______

The average number of siblings for the group is 1.3.

We must compute the total number of siblings and divide it by the total number of children in the group to determine the average number of siblings for the group.

There are a total of: siblings in the bunch.

3 + 8 + 9 = 20 (1 sibling times 3 children) + (2 siblings times 4 children) + (3 siblings times 3 children)

The total number of kids in the group is: 5 + 3 + 4 + 3 = 15

As a result, the group as a whole has an average of:

20/15 = 1.33 (rounded to the nearest tenth) (rounded to the nearest tenth)

So, the group as a whole has 1.3 siblings on average.

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Are the points B, F, and W coplanar?​

yes

Step-by-step explanation:

Because the point lie on the plane they are coplanar

-2 1/2 x (-1 2/3) what is the answer for this question

Step-by-step explanation:

Suppose that a random sample of size 36 is to be selected from a population with mean 50 and standard deviation 7. What is the approximate probability that will be within 0.5 of the population mean?

The probability that the sample mean will be within 0.5 of the population mean is 0.3328.

Step-by-step explanation:

It is provided that a random variable X has mean, μ = 50 andstandard deviation, σ = 7.

A  random sample of size, n = 36 is selected.

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

And the standard deviation of the distribution of sample mean is given by,

So, the distribution of the sample mean of X is N (50, 1.167²).

Compute the probability that the sample mean will be within 0.5 of the population mean as follows:

Thus, the probability that the sample mean will be within 0.5 of the population mean is 0.3328.

To approximate the probability that the sample mean will be within 0.5 of the population mean, we can use the Central Limit Theorem. This theorem states that the sampling distribution of the sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough. To calculate the probability, we need to find the standard error of the mean (SE), calculate the z-score for the upper bound of 0.5 deviations above the mean, and then find the cumulative probability corresponding to that z-score using a z-table or calculator.

### Explanation:

To find the approximate probability that the sample mean will be within 0.5 of the population mean, we can use the Central Limit Theorem. According to the Central Limit Theorem, the sampling distribution of the sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough (typically n ≥ 30).

1. Calculate the standard error of the mean (SE) using the formula SE = σ/√n, where σ is the standard deviation of the population and n is the sample size. In this case, σ = 7 and n = 36, so SE = 7/√36 = 7/6 = 1.1667.
2. Next, calculate the z-score corresponding to the upper bound of 0.5 deviations from the mean by using the formula z = (X - μ)/SE, where X is the value 0.5 deviations above the mean (50 + 0.5 = 50.5 in this case), μ is the mean of the population, and SE is the standard error of the mean. The z-score for 0.5 deviations above the mean can be calculated as z = (50.5 - 50)/1.1667 ≈ 0.4292.
3. Finally, use a z-table or a calculator to find the probability corresponding to the z-score found in the previous step. The probability can be determined by subtracting the cumulative probability of the lower bound (z = -0.4292) from the cumulative probability of the upper bound (z = 0.4292). This can be expressed as p = P(Z < 0.4292) - P(Z < -0.4292).

Using a standard normal distribution table or a calculator, the approximate probability that the sample mean will be within 0.5 of the population mean is the difference between the cumulative probabilities of the upper and lower bounds found in step 3.

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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.

D. F(x) = 2(x-3)^2 + 3

Step-by-step explanation:

We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)

We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.

The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.

Our two equations left are:

B. F(x) = 2(x+3)^2 + 3

D. F(x) = 2(x-3)^2 + 3

Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.

y = 2(3+3)^2 + 3 =

2(6)^2 + 3 =

2·36 + 3 =

72 + 3 =

75

That one didn't give us a y value of 3.

y = 2(3-3)^2 + 3 =

2(0)^2 + 3 =

2·0 + 3 =

0 + 3 =

3

This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:

D. F(x) = 2(x-3)^2 + 3

Hopefully this helps you to understand parabolas better.