All categories

2 years ago

In degree measure, the angles pie/3, pie/4, and pie/2 are respectively

Mathematics

1 answer:

strojnjashka [21]2 years ago

3 0

Answers:

pi/3 radians = 60 degrees
pi/4 radians = 45 degrees
pi/2 radians = 90 degrees

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

Explanation:

To apply the conversion, we use the idea that pi radians is equivalent to 180 degrees

pi radians = 180 degrees

To convert from radians to degrees, we'll multiply by the conversion factor (180/pi)

This leads us to the following:

(pi/3 radians)*(180/pi) = (pi*180)/(3*pi) = 180/3 = 60. So pi/3 radians converts to 60 degrees
(pi/4 radians)*(180/pi) = (pi*180)/(4*pi) = 180/4 = 45. So pi/4 radians converts to 45 degrees
(pi/2 radians)*(180/pi) = (pi*180)/(2*pi) = 180/2 = 90. So pi/2 radians converts to 90 degrees

You might be interested in

What is (-4,9) as an inequality

Allisa [31]

The answer is [4,9)!

4 0

2 years ago

Archeologists found a previously unknown pyramid in Central America, shown in the figure. The media is interested in the volume

german

Answer: height of the pyramid is 52 m.

4 0

2 years ago

Raul crosses Main Street when he walks home from school. The graph of the function d(t)=4|t-0.75) shows Raul's distance, in mile

lina2011 [118]

Answer: does someone have it cause I’m stuck to

Step-by-step explanation:

7 0

2 years ago

A sample of 200 observations from the first population indicated that x1 is 170. A sample of 150 observations from the second po

igor_vitrenko [27]

Answer:

a) For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b) Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c) $z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d) Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

Step-by-step explanation:

Data given and notation

$X_{1}=170$ represent the number of people with the characteristic 1

$X_{2}=110$ represent the number of people with the characteristic 2

$n_{1}=200$ sample 1 selected

$n_{2}=150$ sample 2 selected

$p_{1}=\frac{170}{200}=0.85$ represent the proportion estimated for the sample 1

$p_{2}=\frac{110}{150}=0.733$ represent the proportion estimated for the sample 2

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

a.State the decision rule.

For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b. Compute the pooled proportion.

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c. Compute the value of the test statistic.

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d. What is your decision regarding the null hypothesis?

Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

5 0

3 years ago

98.75 + 5% sales tax

jolli1 [7]

Answer:

103.69

Step-by-step explanation:

5% of 98.75 is about 4.94. So if you were to do money, it'd be 98.75 + 4.94, which equals about 103.69.

5 0

3 years ago