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8090 [49]
3 years ago
15

A circle has an area of 200.96 units2 and a circumference of 50.24 units. If the radius is 8 units, what can be said about the r

elationship between the area and the circumference? (Use 3.14 for pi.)
A.

The ratio of the area to the circumference is equal to the square root of the radius.


B.

The ratio of the area to the circumference is equal to the radius squared.


C.

The ratio of the area to the circumference is equal to half the radius.


D.

The ratio of the area to the circumference is equal to twice the radius.
Mathematics
1 answer:
AleksandrR [38]3 years ago
6 0

Answer:

C. The ratio of the area to the circumference is equal to half the radius.

Step-by-step explanation:

The area of a circle can be written as;

Area A = πr^2

The circumference of a circle is;

Circumference C = 2πr

Using the formula, w can derive the relationship between the two variables.

A = kC

k = A/C

Substituting the two formulas;

k = (πr^2)/(2πr) = r/2

So,

A = (r/2)C

A/C = r/2

The ratio of the area to the circumference is equal to half the radius.

Given;

Area = 200.96

Circumference = 50.24

Radius = 8

To confirm;

k = r/2 = 8/2 = 4

Also,

A/C = 200.96/50.24

A/C = 4

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A) x^2-2x-8

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The total points by Washington High School =  162 points

The total points by  Johnson High School   =  159 points

The total points by  Roosevelt High School =  108 points

The total points by  Lewis High School =  196 points

Washington High School  has WON the meet.

Johnson High School came second.

The difference in the points= 2 points

Step-by-step explanation:

Points awarded for first place = 10 points

Points awarded for second place = 8 points

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About Washington High School

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2 first places  = 2 x ( 7) = 14 points

So, the total points by  Washington High School  = Sum of all points  

=  100 + 48 + 14   =  162 points     .............. (1)

About Johnson High School

8 first places  = 8 x ( 10) = 80 points

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4 first places  = 4 x ( 10) = 40 points

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3 second places  = 3 x ( 8) = 24 points

6 first places  = 6 x ( 7) = 42 points

So, the total points by  Lewis High School  = Sum of all points  

=  30 + 42 + 24   =  96 points      .............. (4)

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Washington High School  has WON the meet.

Johnson High School came second.

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3 years ago
Assume that you have a sample of n 1 equals 6​, with the sample mean Upper X overbar 1 equals 50​, and a sample standard deviati
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Answer:

t=\frac{(50 -38)-(0)}{7.46\sqrt{\frac{1}{6}+\frac{1}{5}}}=2.656

df=6+5-2=9

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Step-by-step explanation:

Data given

n_1 =6 represent the sample size for group 1

n_2 =5 represent the sample size for group 2

\bar X_1 =50 represent the sample mean for the group 1

\bar X_2 =38 represent the sample mean for the group 2

s_1=7 represent the sample standard deviation for group 1

s_2=8 represent the sample standard deviation for group 2

System of hypothesis

The system of hypothesis on this case are:

Null hypothesis: \mu_1 \leq \mu_2

Alternative hypothesis: \mu_1 > \mu_2

We are assuming that the population variances for each group are the same

\sigma^2_1 =\sigma^2_2 =\sigma^2

The statistic for this case is given by:

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}

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And the pooled deviation is:

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The statistic is given by:

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The degrees of freedom are given by:

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Since the p value is higher than the significance level given of 0.01 we don't have enough evidence to conclude that the true mean for group 1 is significantly higher thn the true mean for the group 2.

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