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3 years ago

Find the radius of sphere with a volume of 1372π/3 cubic feet.

Mathematics

1 answer:

Arisa [49]3 years ago

4 0

Answer:

The radius of the sphere is 7m

Step-by-step explanation:

Given

Volume of a sphere = 1372π/3 m³

Required

The radius.

The volume of a sphere is calculated using the following formula.

V = 4/3 πr³

Where V = volume of the sphere and r represents it's radius.

By substitution;

1372π/3 = 4/3 πr³

Multiply both sides by 3

1372π = 4πr³

Divide through by 4

343π = πr³

Divide through by π

343 = r³

Take cube root of both sides.

r = 7.

Hence, the radius of the sphere is 7m

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The following function represents the production cost f(x), in dollars, for x number of units produced by company 1: f(x) = 0.15

dsp73

Answer: g(x) at (70, 55)

Step-by-step explanation:

The minimum of g(x) is lower than f(x) which is (20, 340) and thats obviously higher than (70, 55) so :)

5 0

3 years ago

Find the cost of 12 items if the cost function is C(x) = 2x +12

pantera1 [17]

Answer:

$36

Step-by-step explanation:

we need to find the cost of 12 items, and the function of determining the cost is C(x)=2x+12, where x is the number of items (the input value of the function)

we know that there are 12 items, so in this function, x=12

substitute x as 12 in the function; the x in C(x) also gets substituted as 12, as 12 is the input value and the value of C(x) is the output

C(12)=2(12)+12

multiply

C(12)=24+12

add

C(12)=36

that means, for 12 items, the cost will be $36

7 0

3 years ago

31/25x=−62 find the value of x

Rainbow [258]

The answer to the question is -50

6 0

3 years ago

A local police chief claims that 31% of all drug-related arrests are never prosecuted. A sample of 500 arrests shows that 27% of

Elis [28]

Answer:

$z=\frac{0.27 -0.31}{\sqrt{\frac{0.31(1-0.31)}{500}}}=-1.933$

$p_v =P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.02$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.

Step-by-step explanation:

1) Data given and notation

n=500 represent the random sample taken

X represent the number of arrests that were not prosecuted.

$\hat p=0.27$ estimated proportion of arrests that were not prosecuted

$p_o=0.31$ 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 true proportion is less than 0.31.:

Null hypothesis: $p\geq 0.31$

Alternative hypothesis: $p < 0.31$

When we conduct a proportion test we need to use the z statisitc, 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:

$z=\frac{0.27 -0.31}{\sqrt{\frac{0.31(1-0.31)}{500}}}=-1.933$

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 left tailed test the p value would be:

$p_v =P(Z$

3 0

3 years ago

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nekit [7.7K]

Answer:

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Step-by-step explanation:

3 0

3 years ago