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3 years ago

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Brian is having a baseball-shaped piñata at his birthday party. If the piñata has a diameter of 12 inches, approximately how man

y cubic inches of candy can it hold? (Use 3.14 for π.)
A. 150.72
B. 602.88
C. 7,234.56
D. 904.32

1 answer:

den301095 [7]3 years ago

7 0

Answer:

Option D. $904.32\ in^{3}$

Step-by-step explanation:

we know that

The volume of the sphere (a baseball-shaped piñata ) is equal to

$V=\frac{4}{3}\pi r^{3}$

we have

$r=12/2=6\ in$ -----> the radius is half the diameter

$\pi=3.14$

substitute the values

$V=\frac{4}{3}(3.14)(6)^{3}=904.32\ in^{3}$

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The table shows the height, in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a

Paha777 [63]

Hello! For ease of calculations, we can identify the time it took for the weight to bounce back to the other direction, then the other, and then back to its original position by looking at the time it took for the weight to change from 0 to 25 to 0 to -25 then back to 0. This is one whole cycle of the weight.

By the time the weight first reached zero, 1.5 seconds has passed. By the third time it got to zero again, 7.5 seconds has passed. Therefore, one whole cycle of the weight is 7.5-1.5 = 6.0 seconds.

ANSWER: One whole cycle of the weight took 6 seconds.

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3 years ago

8. Solve the system using elimination.<br> 3x - 4y = 9<br> - 3x + 2y = 9

olga nikolaevna [1]

Answer:

3x−4y=9 −3x+2y=9

Add these equations to eliminate x: −2y=18

Then solve−2y=18

for y: −2y=18 −2y −2 = 18 −2 (Divide both sides by -2)

y=−9

Now that we've found y let's plug it back in to solve for x.

Write down an original equation: 3x−4y=9

Substitute−9for y in 3x−4y=9: 3x−(4)(−9)=9

3x+36=9(Simplify both sides of the equation)

3x+36+−36=9+−36(Add -36 to both sides)

3x=−27 3x 3 = −27 3 (Divide both sides by 3) x=−9

Answer: x=−9 and y=−9

Hope This Helps!!!

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3 years ago

Write the coordinates of the vertices after a reflection over the y-axis.

vampirchik [111]

Answer:

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1 year ago

In 2002, the mean age of an inmate on death row was 40.7 years with a standard deviation of 9.6 years according to the U.S. Depa

marissa [1.9K]

Answer:

The <em>95% confidence interval</em> for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

Step-by-step explanation:

The <em>confidence interval</em> of the mean is given by the next formula:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$ [1]

We already know (according to the U.S. Department of Justice):

The (population) standard deviation for this case (mean age of an inmate on death row) has a standard deviation of 9.6 years ( $\\ \sigma = 9.6$ years).
The number of observations for the sample taken is $\\ n = 32$ .
The sample mean, $\\ \overline{x} = 38.9$ years.

For $\\ z_{1-\frac{\alpha}{2}}$ , we have that $\\ \alpha = 0.05$ . That is, the <em>level of significance</em> $\\ \alpha$ is 1 - 0.95 = 0.05. In this case, then, we have that the <em>z-score</em> corresponding to this case is:

$\\ z_{1-\frac{\alpha}{2}} = z_{1-\frac{0.05}{2}} = z_{1-0.025} = z_{0.975}$

Consulting a cumulative <em>standard normal table</em>, available on the Internet or in Statistics books, to find the z-score associated to the probability of, $\\ P(z$ , we have that $\\ z = 1.96$ .

Notice that we supposed that the sample is from a population that follows a <em>normal distribution</em>. However, we also have a value for n > 30, and we already know that for this result the sampling distribution for the sample means follows, approximately, a normal distribution with mean, $\\ \mu$ , and standard deviation, $\\ \sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$ .

Having all this information, we can proceed to answer the question.

Constructing the 95% confidence interval for the current mean age of death-row inmates

To construct the 95% confidence interval, we already know that this interval is given by [1]:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

That is, we have:

$\\ \overline{x} = 38.9$ years.

$\\ z_{1-\frac{\alpha}{2}} = 1.96$

$\\ \sigma = 9.6$ years.

$\\ n = 32$

Then

$\\ 38.9 \pm 1.96*\frac{9.6}{\sqrt{32}}$

$\\ 38.9 \pm 1.96*\frac{9.6}{5.656854}$

$\\ 38.9 \pm 1.96*1.697056$

$\\ 38.9 \pm 3.326229$

Therefore, the Upper and Lower limits of the interval are:

Upper limit:

$\\ 38.9 + 3.326229$

$\\ 42.226229 \approx 42.23$ years.

Lower limit:

$\\ 38.9 - 3.326229$

$\\ 35.573771 \approx 35.57$ years.

In sum, the 95% confidence interval for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

Notice that the "mean age of an inmate on death row was 40.7 years in 2002", and this value is between the limits of the 95% confidence interval obtained. So, according to the random sample under study, it seems that this mean age has not changed.

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3 years ago

How do I simplify (6x-10x^2+3)-(5x^2+3x-4) ???

Neporo4naja [7]

Answer:

Step-by-step explanation:

6x-10x^2+3-(5x^2+3x-4)

when there is a - in front of an expression in (), change the sign of each term in the expression

6x-10x^2+3-5x^2-3x+4

now collect like terms

3x-10x^2+3-5x^2+4

3x-15x^2+3+4

3x-15x^2+7

now use the commutative property to reorder the terms

-15x^2+3x+7

=-15x^2+3x+7

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3 years ago