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Eva8 [605]
3 years ago
5

The circumference of Circle K is $\pi$ . The circumference of Circle L is $4\pi$ . Two circles, one labeled "Circle K" and the o

ther as "Circle L." What is the value of ratio of their circumferences? Of their radii? Of their areas? Write the ratios as fractions in simplest form.
Mathematics
1 answer:
timurjin [86]3 years ago
3 0

Answer:

Step-by-step explanation:

Given the circumference of Circle K = π

circumference of Circle L = 4π

Ratio of their circumferences = Ck/Cl

Ratio of their circumferences = π/4π

Ratio of their circumferences = 1/4 = 1:4

For their radii

C = 2πr

for circle k with circumference π

π = 2πrk

1 = 2rk

rk = 1/2

for circle l with circumference 4π

4π = 2πr

4 = 2r

r = 4/2

rl = 2

ratio

rk/rl = 1/2/2

rk/rl = 1/4 = 1:4

for the areas

Area of a circle = πr²

for circle k

Ak = π(1/2)²

Ak = π(1/4)

Ak = π/4

for circle l

Al = π(2)²

Al = 4π

Ratio of their areas

Ak/Al = π/4/(4π)

Ak/Al = π/16π

Ak/Al = 1/16 = 1:16

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If we solve any such equation and get the answer as 0 = 0 so this means that system of equations has infinite solutions.

Step-by-step explanation:

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The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 1000 voters in th
garri49 [273]

Answer:

z=\frac{0.42 -0.39}{\sqrt{\frac{0.39(1-0.39)}{1000}}}=1.945  

p_v =P(Z>1.945)=0.0259  

If we compare the p value obtained with the significance level given \alpha=0.02 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 2% of significance the proportion of residents who favored annexation is not significantly higher than 0.39.  

Step-by-step explanation:

1) Data given and notation  

n=1000 represent the random sample taken

\hat p=0.42 estimated proportion of residents who favored annexation

p_o=0.39 is the value that we want to test

\alpha=0.02 represent the significance level

Confidence=98% or 0.98

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion is higher than 0.39:  

Null hypothesis:p\leq 0.39  

Alternative hypothesis:p > 0.39  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.42 -0.39}{\sqrt{\frac{0.39(1-0.39)}{1000}}}=1.945  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.02. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

p_v =P(Z>1.945)=0.0259  

If we compare the p value obtained with the significance level given \alpha=0.02 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 2% of significance the proportion of residents who favored annexation is not significantly higher than 0.39.  

4 0
3 years ago
The average person in the United States drinks 767 cups of coffee annually. How many quarts of coffee is that? Show your work. (
My name is Ann [436]

Answer: 191.75 quarts.

Step-by-step explanation:

We know that:

1 quart = 4 cups.

Then:

1 cup = 1/4 quarts.

this means that 1 cup, is equal to 1/4 quarts.

Then 767 cups is equal to 767 times 1/4 quarts.

The change of units is simply:

767 cups = 767*( 1/4 quarts) = 191.75 quarts.

7 0
3 years ago
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