49

4

B) multiply the binomials; minimum value;

49

4

C) set each factor equal to zero and solve for x; minimum value;

−2

5

D) set each factor equal to zero and solve for x; maximum value;

−7

2

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.

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.

The lengths of two sides of a triangle are 9 and 15. What can be said about the length of the third side? A. It must be greater than or equal to 6 and less than 24. B. It must be greater than or equal to 6 and at most 24. C. It must be greater than 6 and less than 24. D. It must be greater than 6 and at most 24.

Sand poured from a beach pail forms a cone with a height of 32 centimeters and a volume of 3351.0 cubic centimeters. What is the radius of the sand poured from a beach pail in the shape of a cone?

I don’t get this can someone plz help fast

What is the solution to this system?

By what factor is z multiplied to get z1?

Sand poured from a beach pail forms a cone with a height of 32 centimeters and a volume of 3351.0 cubic centimeters. What is the radius of the sand poured from a beach pail in the shape of a cone?

I don’t get this can someone plz help fast

What is the solution to this system?

By what factor is z multiplied to get z1?

which equals 120 seconds.

raal

**Answer:**

**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**

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.

To know more about **Average **visit:

#SPJ1

**Answer:**

yes

**Step-by-step explanation:**

Because the point lie on the plane they are coplanar

**Answer: 4 1/6 **

**Step-by-step explanation:**

**Answer:**

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.

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).

- 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.
- 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.
- 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.

#SPJ3

**Answer:**

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.