Which expressions are equivalent to (4⋅a)⋅2 ?

Natali [406]

Answer:

Geometric proof in explanation.

Step-by-step explanation:

Draw an equilateral triangle.

A equilateral triangle has it's sides all congruent and all it's angles measures 60 degrees.

We are going to draw a line segment to cut the equilateral triangles into two congruent right triangles. I will do this in the attachment with p being positive.

You can see we will get 30-60-90 triangles.

We don't need to find the adjacent measurement to the angle whose measurement is 30 degrees since sine is opposite over hypotenuse.

$\sin(30^\circ)=\frac{\frac{p}{2}}{p}=\frac{p}{2} \cdot \frac{1}{p}=\frac{1}{2}$

$\sin(30^\circ)=\frac{1}{2}$

7 0

3 years ago

A church group is interested in estimating the true proportion of Americans who attend weekly religious services. How large a sa

artcher [175]

Answer:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can use an estimatior for the population proportion as $\hat p=0.5$ since we don't know previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

Step-by-step explanation:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since the confidence level is 99%, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.03$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can use an estimatior for the population proportion as $\hat p=0.5$ since we don't know previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

8 0

3 years ago

The sum of two consecutive odd integers is at most 166. What are the greatest consecutive odd integers?

bagirrra123 [75]

. x + (x + 2)≤166
. 2x+2≤166
. x≤83 - 1
. x≤82
. x=81
. 81+(81+2)=164; 164<166
answer: 81 and 83

4 0

4 years ago

A tree is 15 meters tall. A seedling next to it is 7 centimeters tall. What is the ratio of the height of the seedling to the he

tiny-mole [99]

Answer:

7/15

Step-by-step explanation:

it right i think if not srry :)

4 0

3 years ago

He mean potassium content of a popular sports drink is listed as 140 mg in a 32-oz bottle. Analysis of 20 bottles indicates a sa

mezya [45]

Answer: (A) H0: μ = 140 mg vs. H1: μ ≠ 140 mg

Step-by-step explanation:

Usually null hypothesis represents the claim that the values associated to the groups being tested have no statistical difference but alternative hypothesis supports the claim that there is statistical difference.

Let $\mu$ be the population mean .

We are given that the mean potassium content of a popular sports drink is listed as 140 mg in a 32-oz bottle.

i.e. Null hypothesis : $H_0:\mu=140$

Alternative hypothesis for two tail hypothesis has sign (≠).

i.e. Alternative hypothesis : $H_1 : \mu\neq140$

∴ The hypotheses for a two-tailed test of the claimed potassium content:

H0: μ = 140 mg vs. H1: μ ≠ 140 mg

3 0

4 years ago