Arectangular pyramid has a volume of 90 cubic feet. what is the volume of a rectangular prism with the same size base and same height?

30 cubic feet

Step-by-step explanation:

Here we are given the volume of rectangular pyramid as 90 cubic feet as we are required to find the volume of rectangular prism.

For that we need to use the theorem which says that

the volume prism is always one third of the volume of the pyramid . Whether it is rectangular of triangular base. Hence in this case also the volume of the rectangular prism will be one third of the volume of the rectangular pyramid.

Volume of Rectangular prism = * Volume of rectangular pyramid

=   * 90

= 30

We conclude that the percentage of residents attending college in that age-group is greater than 23.8%.

Step-by-step explanation:

We are given that in 1990, 23.8% of 18-24 year-old in Biddeford, Maine were attending college. About 10 years later, a random sample of 610 18-24 year-old showed 178 were attending college.

Let p = % of 18-24 year-old in Biddeford, Maine who were attending college = 23.8%

Let Null Hypothesis, : p 0.238  {means that the percentage of residents attending college in that age-group is less than or equal to 23.8%}

Alternate Hypothesis, : p > 0.238  {means that the percentage of residents attending college in that age-group is greater than 23.8%}

The test statistics will be used here is One-sample proportion test;

                T.S. =  ~ N(0,1)

where, = % of 18-24 year-old in Biddeford, Maine who were attending college in a sample of 610 people = = 0.292

           n = sample size = 610

So, test statistics  =

                             = 2.933

Now, at 1% significance level the z table gives critical value of 2.5758. Since our test statistics is more than the critical value so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the percentage of residents attending college in that age-group is greater than 23.8%.