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2 years ago

The area of a rectangular trampoline is 135 ft. The length of the trampoline is 6 ft

Mathematics

1 answer:

sammy [17]2 years ago

4 0

Step-by-step explanation:

let width be x

length = 6+x

x times 6+x=135

2x+6=135

2x=135-6

129/2=x

64.5

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Below are the data collected from two random samples of 500 American adults on the number of hours they spend doing leisure and

ElenaW [278]

From the question we are told that:

Total Sample size n=500

Dan's mean \=x_D= 3hr

Bret's mean \=x_D= 4hr

Generally, the Total hours spent doing leisure and sports activities is mathematically given by

For Sample A

$T_a=(1*70)+(2*90)+(3*135)+(4*140)+(5*65)\\\\$

$T_a=1540 hours$

For Sample B

$T_b=(1*80)+(2*80)+(3*130)+(4*135)+(5*75)$

$T_b=1545$

Therefore

Average Time spent doing leisure and sports activities by an American Adult

For Sample A

$T_A=\frac{T_a}{n}$

$T_A=\frac{1540}{500}$

$T_A=3.08$

$T_A \approx 3$

For Sample B

$T_A'=\frac{T_b}{n}$

$T_A'=\frac{1545}{500}$

$T_A'=3.09$

$T_A' \approx 3$

Therefore

Dan is Correct because 3.08 or 3.09 is approximately equal to 3

7 0

2 years ago

A population has a mean, μ = 89 and a standard deviation,σ = 24.

Cloud [144]

Answer:

$\bar X \sim N(\mu=89, \frac{24}{\sqrt{64}}=3)$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

Let X the random variable of interest for a population. We know from the problem that the distribution for the random variable X is given by:

$X\sim N(\mu =89,\sigma =24)$

We take a sample of n=64 . That represent the sample size.

The sample mean is defined as:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And if we find the expected value and variance for the sample mean we got:

$E(\bar X) = \mu$

Var(\bar X) = \frac{\sigma^2}{n}[/tex]

The distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar X \sim N(\mu=89, \frac{24}{\sqrt{64}}=3)$

3 0

2 years ago

(h(1) = 14<br> h(n)<br> 28<br> hin - 1)<br> h(2) =

Serhud [2]

Answer:

Y=ax2

Step-by-ste:

Y=ax28(n)

5 0

2 years ago

Ten more than 6 times a number is 4 less than 4 times the number

Marta_Voda [28]

10 + 6n = 4 - 4n

I'm just guessing but I'm pretty sure that's it.

4 0

2 years ago

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The di

lawyer [7]

Answer:

0.0063 ft / min

Step-by-step explanation:

From the problem statement we have that the variation in volume with respect to time is equal 10, like this:

dV / dt = 10 ft ^ 3 / min

We know that the volume of the cone is given by the equation:

V = (1/3) * Pi * r ^ 2 * h

Now, we are mentioned that the diameter of the base of the cone is approximately three times the altitude, therefore:

2r = 3h, solving for r we have:

r = (3/2) * h, replacing the volume equation:

V = (1/3) * Pi * [(3h / 2) ^ 2] * h, solving we have:

V = (3/4) * Pi * h ^ 3

They ask us to calculate the change in height with respect to time, that is dh / dt

Therefore we derive both sides with respect to time, we have to:

dV / dt = (3/4) * Pi [3 * (h ^ 2) dh / dt] = (9/4) * pi * (h ^ 2) * dh / dt

reorganizing for dh / dt, we have:

dh / dt = [4/9 * pi * (h ^ 2)] * dV / dt

Knowing that h is 15 and dV / dt is 10, we replace these values:

dh / dt = [4/9 * 3.14 * (15 ^ 2)] * 10 = 0.0063 ft / min

0.0063 ft / min would be the change in height with respect to time.

4 0

2 years ago