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3 years ago

Find the circumference of the circle with the given radius or diameter. (Use 3.14 for it) r=20

Mathematics

2 answers:

Margarita [4]3 years ago

6 0

Answer:

$\huge\boxed{C\approx125.6}$

Step-by-step explanation:

The formula of a circumference of a circle:

$C=d\pi=2\pi r$

d - diameter

r - radius

We have the radius r = 20.

Substitute:

$C=2\pi(20)=40\pi$

use π ≈ 3.14

$C\approx(40)(3.14)=125.6$

iogann1982 [59]3 years ago

4 0

Answer:

C = 2πr = 2 * 3.14 * 20 = 125.6

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A journalist reported that the average amount of time that a French person spends eating lunch at a restaurant is 22 minutes. Pe

maw [93]

Answer:

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

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

$t=\frac{19 -22)-(0)}{4.095\sqrt{\frac{1}{8}+\frac{1}{7}}}=-1.416$

Step-by-step explanation:

Data given

American: 21,17,17,20,25,16,20,16 (Sample 1)

French: 24,18,20,28,18,29,17 (Sample 2)

When we have two independent samples from two normal distributions with equal variances we are assuming that

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

And the statistic is given by this formula:

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

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

This last one is an unbiased estimator of the common variance $\sigma^2$

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2 \neq 0$

Our notation on this case :

$n_1 =8$ represent the sample size for group 1

$n_2 =7$ represent the sample size for group 2

$\bar X_1 =19$ represent the sample mean for the group 1

$\bar X_2 =22$ represent the sample mean for the group 2

$s_1=3.117$ represent the sample standard deviation for group 1

$s_2=5.0$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$S^2_p =\frac{(8-1)(3.117)^2 +(7 -1)(5.0)^2}{8 +7 -2}=16.770$

And the deviation would be just the square root of the variance:

$S_p=4.095$

And now we can calculate the statistic:

$t=\frac{19 -22)-(0)}{4.095\sqrt{\frac{1}{8}+\frac{1}{7}}}=-1.416$

Now we can calculate the degrees of freedom given by:

$df=8+7-2=13$

And now we can calculate the p value using the altenative hypothesis:

$p_v =2*P(t_{13}$

So with the p value obtained and using the significance level assumed $\alpha=0.1$ 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 10% of significance we don't have significant differences between the two means.

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3 years ago

What does it mean when is says write a sequence hat plots the ordered pair if you start at the origin when you are plotting ??

RideAnS [48]

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3 years ago

Which of the following is part of a line that has two endpoints?

yarga [219]

The answer is C.) line segment

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4 years ago

A particle, initially 15 m from the origin and travelling at -2 ms), accelerates at a constant rate and ends up -20 m from the o

tigry1 [53]

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3 years ago

For a production of sweeney todd in las vegas, orchestra seats cost $42 and mezzanine seats cost $25. if a group of 14 people sh

Lesechka [4]

Answer: 8 orchestra seats and 6 mezzanine seats.

Step-by-step explanation:

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Set up a system of equations:

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