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3 years ago

Given a regular decagon, find the measures of the angles formed by (

1 answer:

3 0

A decagon has 10 sides (think decade and decathlon). From the center of the decagon we draw the radii and in doing so we take the area of the decagon and divide it into 10 congruent Triangles.

The angles around the center add up to 360 because they form a circle and since there are 10, they each measure 36 degrees. So the answer to the first part (the angle between the radii) is 36 degrees.

Each of these triangles has two equal sides (both radii) so is Isosceles. That means that the base angles are congruent. So the two angles that are left in each triangle must measure the same. Since the angles in a triangle add up to 180 degrees, we know that the two remaining angles are together equal to 180-36=144 degrees. Since they are equal in measure they each measure 72 degrees.

Thus the answer to the second part, trhe measure of the angle between a radius and the side of the polygon is 72 degrees.

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The Nellie Mae organization conducts an extensive annual study of credit card usage by college students. For their 2004 study, t

Masja [62]

Answer:

1. Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1=p_2$

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$

2. Test statistics = 4.63

P-value = 0.00001

3. We conclude that the proportion of undergraduate students who held a credit card differed between these two years.

Step-by-step explanation:

We are given that the Nellie Mae organization conducts an extensive annual study of credit card usage by college students.

For their 2004 study, they analyzed credit bureau data for a random sample of 1,413 undergraduate students between the ages of 18 and 24. They found that 76% of the students sampled held a credit card. Three years earlier they had found that 83% of undergraduates sampled held a credit card.

Let $p_1$ = population proportion of undergraduate students who held a credit card in year 2001

$p_2$ = population proportion of undergraduate students who held a credit card in year 2004

1. Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1=p_2$ {means that the proportion of undergraduate students who held a credit card does not differed between these two years}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$ {means that the proportion of undergraduate students who held a credit card differed between these two years}

The test statistics that will be used here is Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of undergraduate students who held a credit card in 2001 = 83%

$\hat p_2$ = sample proportion of undergraduate students who held a credit card in 2004 = 76%

$n_1$ = sample of students surveyed in 2001 = 1,413

$n_2$ = sample of students surveyed in 2004 = 1,413

So, test statistics = $\frac{(0.83-0.76)-(0)}{\sqrt{\frac{0.83(1-0.83)}{1,413} +\frac{0.76(1-0.76)}{1,413}} }$

= 4.63

2. Hence, the value of test statistics is 4.63.

Also, P-value is given by the following formula;

P-value = P(Z > 4.63) = 1 - P(Z $\leq$ 4.63)

= 1 - 0.99999 = 0.00001

3. Since in the question we are not given the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics is does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the proportion of undergraduate students who held a credit card differed between these two years.

6 0

3 years ago

Credit cards are 0.76 mm thick. How thick is a stack of 10thirds credit cards piled one on top of the other???

natima [27]

You are correct its A

3 0

3 years ago

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Which graph is the solution of the following systems HELP ON ON GRADPOINT

makkiz [27]

I think it is the second one but I’m not for sure I’m really just doing this for points

6 0

3 years ago

What is the equation of the line which has a gradient of 2 and passes through the point (1,4)

timofeeve [1]

Answer:

Y= 2x+2

Step-by-step explanation:

line equation is y=mx +c

m is the gradient = 2

We are given an x and y value

X= 1
y= 4

substitute that into the equation:

4= 2(1) +c

2=c

Put all the equation together:

Y= 2x+2

5 0

2 years ago

A new amusement park presold discounted tickets for the opening day as well as upon arrival at the park the opening day ticket s

julia-pushkina [17]

Answer:

-64 tickets per hour

Step-by-step explanation:

4 0

3 years ago

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