MATHEMATICS HIGH SCHOOL

A family of 5 is going on a cross-country vacation. For a bit of variety, the family of 5 decides that they will frequently change the seating arrangement in their 5-seated vehicle. How many seating arrangements can they make if ALL of them have their driver's license.

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

This questions bothers permutation since permutation talks about arrangement.

The number of ways n objects can be arranged is n! ways

n! = n(n-1)(n-2)!

If a family of 5 is going on a cross-country vacation, and decided to change their seating arrangement. The total seating arrangement that they can have is;

5! = 5*4*3*2*1

5! = 20*6

5! = 120 different arrangements

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A rain barrel is a right circular cylinder. If 1ft^3 =7.5 gallons, how many gallons of rainwater can the barrel hold? Use 3.14
Barrel is 1.35ft left to right.... And 5ft top to bottom.

Answers

Find volume of right circular cylinder
V = pie * r * r * h
= 3.14 * 1.35/2 * 1.35/2 * 5 ft^3
= 7.153 ft^3

Since 1ft^3 = 7.5 gallons
7.153 ft^3 = 7.5 * 7.153 gallons
i.e equal to 53.65 gallons

If an object is dropped from a height of 85 feet, the function h(t)=-16t^2+85 gives the height of the object after t seconds. Approximately, when will the object hit the ground?a. 85.00 seconds
b. 69.00 seconds
c. 0.33 seconds
d. 2.30 seconds

Answers

We are given the function of the situation. The function is given as h(t) = -16t^2 + 85 where h(t) signifies that height is a function of time. For this case, our height would be zero and we find the time it hits the ground. Thus,

0 = -16t^2 + 85
t = 2.30 seconds

The answer is d.

What is the value of x in the equation −x = 6 − 3x + 8?−14
−7
14
7

Answers

Answer:

x = 7

Step-by-step explanation:

Add 3x to both sides of the equation.

2x = 6+8

Divide both sides by 2.

x = 7

Answer:

Step-by-step explanation:

Find the diameter of the circle that has a circumference equal to its area.2
4
8
10

Answers

Circumference may have the same numerical magnitude as area, but they will never be "equal". Circumference is a length or distance, and area is an area.
So they can never have the same units, and quantities can't be equal without
the same units.

You might say that   π D (circumference) = π (D/2)² (area) .

Then D = (D/2)²

   D = D² / 4

   1 = D / 4

   D = 4 .

But this is no more than a parlor trick. In order to do it, you need to
ignore units completely, and that's unacceptable in math.

The formula for circumference of a circle:
$C=2 \pi r$

The formula for area of a circle:
$A=\pi r^2$
r - radius

The circumference is equal to the area.
$C=A \n2 \pi r=\pi r^2 \ \ \ |/ \pi r, \ r>0 \n2=r \nr=2$

The diameter is two times the radius.
$d=2r=2 * 2=4 \n \n\boxed{d=4}$

A population has a mean of 300 and a standard deviation of 70. Suppose a sample of size 125 is selected and is used to estimate . Use z-table. What is the probability that the sample mean will be within +/- 8 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.) What is the probability that the sample mean will be within +/- 17 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

Answers

Following are the calculation to the given points:

Using central limit theorem:

$\to \mu_{\bar{x}}= \mu = 300\n\n\to \sigma_{\bar{x}}=(\sigma)/(√(n))=(70)/(√(125))= 6.261\n\n$

For point a)

Within $\pm 8$ population mean: $\to P(\mu-8<\bar{x}<\mu+8)=P\left ( (\mu-8-\mu)/(6.261)Within [tex]\pm 17$

For point b)

Within $\pm 17$ population mean:

[tex]\to P(\mu-17<\bar{x}<\mu+17)=P\left ( \frac{\mu-17-\mu}{6.261}

Learn more:

brainly.com/question/6096474

Final answer:

To find the probability that the sample mean will be within a certain range, we need to calculate the z-scores and look them up in the z-table.

Explanation:

To find the probability that the sample mean will be within +/- 8 of the population mean, we need to convert this range to z-scores. The z-score formula is calculated by subtracting the population mean from the sample mean and dividing by the standard deviation divided by the square root of the sample size.

For +/- 8, the z-score will be (8 - 0) / (70 / sqrt(125)) = 2.09.

Using the z-table, we can find the probability associated with a z-score of 2.09, which is approximately 0.9828. Therefore, the probability that the sample mean will be within +/- 8 of the population mean is 0.9828.

Similarly, for +/- 17, the z-score will be (17 - 0) / (70 / sqrt(125)) = 4.18. Using the z-table, the probability associated with a z-score of 4.18 is nearly 1.0000. Hence, the probability that the sample mean will be within +/- 17 of the population mean is 1.0000.