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yKpoI14uk [10]
3 years ago
11

The width of a rectangular prism is six times its length. The height is five times its length. If its length is m units, what is

m units; what is the volume of the prism?
Mathematics
1 answer:
I am Lyosha [343]3 years ago
8 0

Answer:

30m^3 cubic units.

Step-by-step explanation:

Let m represent length of the rectangular prism.

We have been given that the width of a rectangular prism is six times its length, so width of the prism would be 6m.

We are also told that the height is five times its length, so height of the prism would be 5m.

We know that volume of rectangular prism is height times width times length.

\text{Volume of rectangular prism}=lwh

\text{Volume of rectangular prism}=m\cdot 6m\cdot 5m

\text{Volume of rectangular prism}=30m^3

Therefore, the volume of the given rectangular prism would be 30m^3 cubic units.

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selim is ordering concrete spheres to place as barriers in the city park. the spheres cost $2 per square foot, and selim can spe
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The maximum diameter of the spheres he can purchase is  1. 78 ft. Option C

<h3>How to determine the diameter</h3>

The formula for area of a sphere is expressed as;

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If Selim paid $2 per square foot and have a maximum of $20 per square

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Substitute the value into the formula

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A maker of a certain brand of low-fat cereal barsclaims that the average saturated fat content is 0.5gram. In a random sample of
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Answer:

t=\frac{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386    

p_v =2*P(t_{(7)}  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance.  So then the claim makes sense

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

In order to calculate the mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}} (3)  

The mean calculated for this case is \bar X=0.475

The sample deviation calculated s=0.183

We need to conduct a hypothesis in order to check if the true mean is 0.5 or no, the system of hypothesis would be:  

Null hypothesis:\mu = 0.5  

Alternative hypothesis:\mu \neq 0.5  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

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

t=\frac{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=8-1=7  

Since is a two sided test the p value would be:  

p_v =2*P(t_{(7)}  

Conclusion  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance.  So then the claim makes sense

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3 years ago
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