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3 years ago

Write the absolute value equation that has two solutions x=5 and x=11

Mathematics

1 answer:

Gelneren [198K]3 years ago

4 0

Answer:

|8-x|=3

Step-by-step explanation:

Find the average

11+5=16

16*1/2=8

8-5=3

8-11=-3

|3|=|-3|

|8-x|=3

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The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown popula

ryzh [129]

Answer:

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

Step-by-step explanation:

We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.8}{2} = 0.1$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.5 = 0.9$ , so $z = 1.282$

Now, find the margin of error M as such

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

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.282*\frac{6}{\sqrt{21}} = 1.68$

The lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.

The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

6 0

3 years ago

Can anybody help me figure out the area of simple composite figure?

zvonat [6]

Given:

The length of the rectangle = 16 ft

The width of the rectangle = 12 ft

The diameter of the semicircle = 12 ft

To find the area of the given figure.

Formula

$A=A_{1} +A_{2}$

where,

$A$ be the area of the given figure

$A_{1}$ be the area of the rectangle

$A_{2}$ be the area of the semicircle.

The area of the rectangle = $lb$ where, l be the length and b be the width
Area of the semicircle = $\frac{1}{2} \pi r^{2}$ , r be the radius of the semicircle.

Now,

The radius of the semicircle r = 6 ft

Putting, r=6, l=16 and b= 12 we get,

$A_{1} = (16)(12)$ sq ft

or, $A_{1} = 192$ sq ft

$A_{2} = \frac{1}{2} (3.14)(6^{2} )$ sq ft

or, $A_{2}=56.52$ sq ft

So,

$A = 56.52+192$ sq ft

$A$ = 248.52 sq ft

Rounding off to the nearest tenth, we get;

A=248.5 sq ft.

Hence,

The area of the composite figure is 248.5 sq ft.

7 0

3 years ago

Two figures are similar with a scale factor of 5/2.

aev [14]

Answer:

If we have two figures, F and F'

Such that if we start with F, and dilate it with a scale factor K, we get F'.

We will have:

All the measures of F', are K times the correspondent measures of F.

Then if F has s₁, s₂, ..., sₙ sides, the sides of F' will be:

K*s₁, K*s₂, ..., K*sₙ

The ratio between correspondent sides will be equal to K

The ratio between perimeters will also be equal to K (because the perimeter is the sum of all the sides of each figure, so we can just take K as a common factor)

In the case of the area, because we usually multiply a measure by another, a factor K^2 will appear, and the quotient between the areas is K^2

And finally, for the volumes, the ratio will be K^3

a) The ratio of corresponding lengths is K, in this case is 5/2

b) The ratio of the perimeters is K, in this case is 5/2

c) The ratio of the areas is K^2, in this case is (5/2)^2 = 25/4

d) The ratio of the areas is K^3, in this case is (5/2)^3 = 125/8

e) Two figures are similar if the figures have the same shape, then the corresponding angles are exactly the same, then the ratio of corresponding angle measures is 1.

6 0

3 years ago

What is the image of (2,-2) after a dilation by a scale factor of 5 centered at the<br> origin?

ss7ja [257]

Answer:

(10, -10)

Step-by-step explanation:

since the point is at the origin, simply multiply.

2 * 5 = 10

-2 * 5 = -10

3 0

4 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=y%20%20%3D%202%20x%20%2B%205" id="TexFormula1" title="y = 2 x + 5" alt="y = 2 x + 5" align="

stealth61 [152]

Yes. The lines would insert in quadrant 1. At (1,7)

4 0

3 years ago