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4 years ago

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A rectangular prism has a volume of 160 cm. The height of the prism is 5 cm. The length is twice the width. What are the dimensi

ons of the base?

1 answer:

Y_Kistochka [10]4 years ago

4 0

The answer to your question id 8*5*4.
8*5=40 40*4=160 8 is twice of 4. the length is twice the width.

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The rate of change (dP/dt), of the number of people on an ocean beach is modeled by a logistic differential equation. The maximu

Kazeer [188]

Answer:

$\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})$

Step-by-step explanation:

The logistic differential equation is as follows:

$\frac{dP}{dt} = rP(1 - \frac{P}{K})$

In this problem, we have that:

$K = 1200$ , which is the carring capacity of the population, that is, the maximum number of people allowed on the beach.

At 10 A.M., the number of people on the beach is 200 and is increasing at the rate of 400 per hour.

This means that $\frac{dP}{dt} = 400$ when $P = 200$ . With this, we can find r, that is, the growth rate,

So

$\frac{dP}{dt} = rP(1 - \frac{P}{K})$

$400 = 200r(1 - \frac{200}{1200})$

$166.67r = 400$

$r = 2.4$

So the differential equation is:

$\frac{dP}{dt} = rP(1 - \frac{P}{K})$

$\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})$

3 0

3 years ago

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on con

AlladinOne [14]

Using the z-distribution, a sample size of 180 is needed for the estimate.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

The margin of error is given by:

$M = z\frac{\sigma}{\sqrt{n}}$

In which:

$\overline{x}$ is the sample mean.

z is the critical value.

n is the sample size.

$\sigma$ is the standard deviation for the population.

In this problem, we have a 98% confidence level, hence $\alpha = 0.98$ , z is the value of Z that has a p-value of $\frac{1+0.98}{2} = 0.99$ , so the critical value is z = 2.327.

The population standard deviation is of $\sigma = 23$ , and to find the sample size, we have to solve for n when M = 4.

Hence:

$M = z\frac{\sigma}{\sqrt{n}}$

$4 = 2.327\frac{23}{\sqrt{n}}$

$4\sqrt{n} = 2.327 \times 23$

$\sqrt{n} = \frac{2.327 \times 23}{4}$

$(\sqrt{n}) = \left(\frac{2.327 \times 23}{4}\right)^2$

n = 179.03.

Rounding up, as a sample size of 179 would result in an error slightly above 4, a sample of 180 is needed.

More can be learned about the z-distribution at brainly.com/question/25890103

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2 years ago

Please help with this math problem! The intersection of GK and HL is point P. Which triangle must be an isosceles triangle? *loo

Whitepunk [10]

None of the triangles listed has two equal base angles or two equal side lengths, therefore: D. No triangle is isosceles.

<h3>Properties of an Isosceles Triangle</h3>

An isosceles triangle has two base angles having equal angle measure.
The side lengths that are opposite each of the equal base angles are also congruent to each other.

Thus, none of the triangles listed has two equal base angles or two equal side lengths, therefore: D. No triangle is isosceles.

Learn more about isosceles triangle on:

brainly.com/question/11884412

5 0

3 years ago

if an amount of $100 in a savings account increases by 10% , then increases by 10% again, is that the same as increasing by 20%

Elina [12.6K]

100 + 100 * 10/100 = 110

NOW 110 INCREASES BY 10 %, 110 + 110*10/100 = 110+ 11 = 121

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SO IT IS NOT SAME

5 0

4 years ago

Read 2 more answers

There are 5/7 as many barrettes as hair ties in Sasha's hair supplies. There are 5/8 barrettes as hair bands in her supplies. Wh

motikmotik

Answer:

1/3

Step-by-step explanation:

We are given ...

barrettes : hair ties = 5 : 7

barrettes : hair bands = 5 : 8

Then the combined ratios are ...

barrettes : hair ties : hair bands = 5 : 7 : 8

For every 5 barrettes, there are 7+8 = 15 hair ties and bands, so their ratio is ...

barrettes/(hair ties and bands) = 5/15 = 1/3

7 0

3 years ago

Read 2 more answers