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3 years ago

A sphere has a radius of 16 in. Which statements about the sphere are true? Check all that apply.

Mathematics

2 answers:

mr_godi [17]3 years ago

7 0

Answer:

The True statements are:

The sphere has a diameter of 32 in.

The radius’s length is one-half the length of the diameter.

The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed.

Step-by-step explanation:

The sphere has a diameter of 8 in. False

This is false because a radius is half of a diameter. Half of the given diameter of 8 in is 4 in whereas the radius in the question is 16 in.

The volume of the sphere is StartFraction 2,048 Over 3 EndFraction pi inches cubed. False

This is false because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.

The sphere has a diameter of 32 in. True

This is True because a radius is half of a diameter. Half of the given diameter of 32 in is 16 in and the radius in the question is also 16 in.

The radius’s length is one-half the length of the diameter. True

This is True because a radius is half of a diameter

The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed. True

This is True because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.

The diameter’s length is one-half the length of the radius. False

It is the radius’s length that is one-half the length of the diameter

Wewaii [24]3 years ago

6 0

Answer:

The sphere has a diameter of 32 in. CORRECT: the diameter of a sphere doubles its radio, so if the radio equals 16,the diameter measures the double, in this case, 32.
The radius' lenght is one half the length of the diameter. CORRECT: , by definition, the diameter is the maximum distance between two opposite points on the surface of the sphere, and its lenght equals twice the radius because the radius is the distance between the center of the sphere and any point of the frontier of the sphere (then, one colud imagine that the distance between two opposite points in a sphere can be united by two radius, or a diameter).
The volume (V) of a sphere can be calculated as $\frac{4\pi r^3}{3}$ , where r is the radio. In this case, the volume of the sphere will be $\frac{4\pi\times16^3}{3}=\frac{4\pi\times4096}{3}$ , which is also equal to $\frac{16384\times\pi}{3}$ .

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3 years ago

The following 5 questions are based on this information: An economist claims that average weekly food expenditure of households

liq [111]

Answer:

Null hypothesis: $\mu_{1}-\mu_{0}\leq 0$

Alternative hypothesis: $\mu_{1}-\mu_{2}>0$

$SE=\sqrt{\frac{12.5^2}{35}+\frac{9.25^2}{30}}=2.705$

b) 2.70

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b. 0.03

a. We can reject H(0) in favor of H(a)

Step-by-step explanation:

Data given and notation

$\bar X_{1}=164$ represent the mean for the sample 1

$\bar X_{2}=159$ represent the mean for the sample 2

$\sigma_{1}=12.5$ represent the population standard deviation for the sample 1

$s_{2}=9.25$ represent the population standard deviation for the sample B2

$n_{1}=35$ sample size selected 1

$n_{2}=30$ sample size selected 2

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the expenditure of households in City 1 is more than that of households in City 2, the system of hypothesis would be:

Null hypothesis: $\mu_{1}-\mu_{0}\leq 0$

Alternative hypothesis: $\mu_{1}-\mu_{2}>0$

We know the population deviations, so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{(\bar X_{1}-\bar X_{2})-0}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Standard error

The standard error on this case is given by:

$SE=\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}$

Replacing the values that we have we got:

$SE=\sqrt{\frac{12.5^2}{35}+\frac{9.25^2}{30}}=2.705$

b. 2.70

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{(164-159)-0}{\sqrt{\frac{12.5^2}{35}+\frac{9.25^2}{30}}}=1.850$

P-value

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

$p_v =P(Z>1.85)=0.032$

b. 0.03

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

a. We can reject H(0) in favor of H(a)

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3 years ago

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2 years ago

Read 2 more answers

Miguel spent a total of $60 at the grocery store. Of this amount , he spent $18 on fruit. What percentage of the total did he sp

Paraphin [41]

Answer:

30%

Step-by-step explanation:

A percent can be found by dividing the part by the whole, or

part/whole

In this case, the part is the amount he spent on fruit. The whole is the total amount he spent.

amount spent on fruit/ total amount spent

He spent $18 on fruit, and $60 in total.

$18/ $60

Divide 18 by 60

18/60

0.3

Convert 0.3 to a decimal by multiplying by 100 or moving the deicaml place two spots to the right.

0.3*100=30

0.3--> 3.0 --> 30

30%

He spent 30% on fruit.

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3 years ago