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3 years ago

14

Farmer Dave builds a create to hold vegetables. The volume of the create is 48 cubic feet. The base area of the create is 16 squ

are feet. What is the height of the create?

1 answer:

Veronika [31]3 years ago

5 0

16 sq ft = 2 ft x 8 ft
4 ft x 4 ft

but..
4 ft x 4 ft x 4 ft = 64 cubic ft

So 4 cannot be the height of this crate.

h represents the height of the crate (defined variable)
2 ft x 8 ft x h = 48 cubic ft
16h = 48
h = 3 ft

The height of the crate is 3 feet.

Check:
2 ft x 8 ft x 3 ft = 48 ft ³

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An insurance company states that it settles 85% of all life insurance claims within 30 days. A consumer group asks the state ins

BlackZzzverrR [31]

Using the z-distribution, it is found that since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, it is tested if there is not enough evidence that the proportion is below 85%, that is:

$H_0: p \geq 0.85$

At the alternative hypothesis, it is tested if there is enough evidence that the proportion is below 85%, that is:

$H_0: p < 0.85$

<h3>What is the test statistic?</h3>

The test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

In which:

$\overline{p}$ is the sample proportion.

p is the proportion tested at the null hypothesis.

n is the sample size.

For this problem, the parameters are:

$p = 0.85, n = 250, \overline{p} = \frac{203}{250} = 0.812$

Hence the test statistic is:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

$z = \frac{0.812 - 0.85}{\sqrt{\frac{0.85(0.15)}{250}}}$

z = -1.68

<h3>What is the p-value and the conclusion</h3>

Using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -1.68, the p-value is of 0.0465.

Since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.

More can be learned about the z-distribution at brainly.com/question/16313918

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4 0

1 year ago

On a coordinate plane, a circle has a center at (0, 0). Point (3, 0) lies on the circle.

9966 [12]

Answer:

The correct option is;

No, the distance from (0, 0) to (2, √6) is not 3 units

Step-by-step explanation:

The given parameters of the question are as follows;

Circle center (h, k) = (0, 0)

Point on the circle (x, y) = (3, 0)

We are required to verify whether point (2, √6) lie on the circle

We note that the radius of the circle is given by the equation of the circle as follows;

$Distance \, formula = \sqrt{\left (x_{2}-x_{1} \right )^{2} + \left (y_{2}-y_{1} \right )^{2}}$

Distance² = (x - h)² + (y - k)² = r² which gives;

(3 - 0)² + (0 - 0)² = 3²

Hence r² = 3² and r = 3 units

We check the distance of the point (2, √6) from the center of the circle (0, 0) as follows;

$\sqrt{\left (x_{2}-x_{1} \right )^{2} + \left (y_{2}-y_{1} \right )^{2}} = Distance$

Therefore;

(2 - 0)² + (√6 - 0)² = 2² + √6² = 4 + 6 = 10 = √10²

$\sqrt{\left (2-0 \right )^{2} + \left (\sqrt{6} -0 \right )^{2}} = 10$

Which gives the distance of the point (2, √6) from the center of the circle (0, 0) = √10

Hence the distance from the circle center (0, 0) to (2, √6) is not √10 which s more than 3 units hence the point (2, √6), does not lie on the circle.

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3 years ago

Read 2 more answers

A catering company loses $110 as a result of a delay. The 5 owners of the company must share the loss equally. Which quotient re

nasty-shy [4]

They all loss $22.00

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2 years ago

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Which statement describes the inverse of m(x) = x^2 – 17x?

DochEvi [55]

Given:

The function is

$m(x)=x^2-17x$

To find:

The inverse of the given function.

Solution:

We have,

$m(x)=x^2-17x$

Substitute m(x)=y.

$y=x^2-17x$

Interchange x and y.

$x=y^2-17y$

Add square of half of coefficient of y , i.e., $\left(\dfrac{-17}{2}\right)^2$ on both sides,

$x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2$

$x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2$

$x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2$ $[\because (a-b)^2=a^2-2ab+b^2]$

Taking square root on both sides.

$\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}$

Add $\dfrac{17}{2}$ on both sides.

$\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y$

Substitute $y=m^{-1}(x)$ .

$m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}$

We know that, negative term inside the root is not real number. So,

$x+\left(\dfrac{17}{2}\right)^2\geq 0$

$x\geq -\left(\dfrac{17}{2}\right)^2$

Therefore, the restricted domain is $x\geq -\left(\dfrac{17}{2}\right)^2$ and the inverse function is $m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}$ .

Hence, option D is correct.

Note: In all the options square of $\dfrac{17}{2}$ is missing in restricted domain.

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3 years ago

Write a word problem that can be solved by ordering 3 decimals to thousand include a solution

IrinaK [193]

Answer:

I have no clue but this was two years ago so hopefully you know the answer by now

Step-by-step explanation:

yes

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3 years ago