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3 years ago

The length of a rectangle is 10m more than twice the width. The

Mathematics

1 answer:

ipn [44]3 years ago

3 0

Answer:

5.6, 21.3

Step-by-step explanation:

Let x be the width.

We know that the length is 10+2x. The area of a rectangle is length times width, so substitute the values.

x*(10+2x)=120

10x+2x^2=120

Divide both sides by 2.

x^2+5x=60

Add 25/4 to both sides so we can make a square.

x^2+5x+ 25/4= 60+25/4=265 /4

Factor the left side.

(x+ 5 /2 )^2= 265 /4

x+2.5=(positive or negative) sqrt(265/4)

x=(positive or negative) sqrt(265/4)-2.5

But, we know that if the equation is negative, the width of the rectangle would be negative. Therefore, x=positive sqrt(265/4)-2.5

Then, we will find the sides.

sqrt66.25-2.5=5.63941, or about 5.6

10+(2(sqrt66.25-2.5))= 21.278821, or about 21.3

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Find the value of x and y.

Oxana [17]

Answer:

x = 4

y = 12°

Step-by-step explanation:

Since each angles are equal ,

So each angle is 60°.

=> 5y = 60°

=> y = 60/5°

=> y = 12°

Again all sides will be equal ,

=> 5x - 6 = 3x + 2

=> 5x - 3x = 6+2

=> 2x = 8

=> x = 4

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2 years ago

Nick volunteers at the library shelving books.

ch4aika [34]

Answer:

B: A

He earns $90 in 3 weeks.

He shelves 90 books in 3 hours.

Step-by-step explanation:

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3 years ago

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How is the process of finding the surface area of a rectangular prism the same as finding the surface area of a triangular prism

harina [27]

Answer:

see the explanation

Step-by-step explanation:

we know that

The surface area of a prism is given by the formula

$SA=2B+PH$

where

B is the area of the base

P is the perimeter of the base

H is the height of the prism

For both prism the formula is the same

How is it different?

Rectangular prism

The area of the base is given by the formula

$A=LW$ -----> is the area of rectangle

where

L is the length and W is the width of rectangle

The perimeter of the base is given by

$P=2(L+W)$ ---> is the perimeter of rectangle

The height H is the same in both cases

Triangular prism

The area of the base is given by the formula

$A=\frac{1}{2} (b)(h)$ -----> is the area of the triangular base

where

b is the base of triangle and h is the height of triangle

The perimeter of the base is given by

$P=(a+b+c)$ ---> is the perimeter of triangle

where

a, b and c are the length sides of triangle

The height H is the same in both cases

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3 years ago

Read 2 more answers

If g(x) = 2x2 + 6x + 5, use synthetic division to find g(-5).

diamong [38]

<h3>Answer: 25</h3>

=================================================

Explanation:

Check out the image below. I've posted the synthetic division table. The value at the very end of the bottom row is the remainder. By the remainder theorem, this is exactly the value of g(-5).

Recall the remainder theorem says: If you divide p(x) by (x-k), then the remainder is p(k). In this case, k = -5 is our test root which is the value placed in the box on the left.

As a way to check the answer, we can say

g(x) = 2x^2 + 6x + 5

g(-5) = 2(-5)^2 + 6(-5) + 5

g(-5) = 25

So the answer is confirmed.

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2 years ago

A government report gives a 99% confidence interval for the proportion of welfare recipients who have been receiving welfare ben

juin [17]

Answer:

The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

$ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

$ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

5 0

3 years ago