Every year, people in the US buy 2.7 billion boxes of breakfast cereal. A “typical” cereal box has dimensions of 2.5 inches by 7.75 inches by 11.75 inches. Imagine a warehouse that has a rectangular floor and that contains all the boxes of breakfast cereal bought in the US in one year. If the warehouse is 10 feet tall, what could the side lengths be? Is is possible to design a different sized cereal box to increase the amount of cereal in this warehouse?

A possible pair of values for length and width of the warehouse are:

Length = 10^4 ft, Width = 3.5571 * 10^3 ft.

It is not possible to redesign the cereal box to increase the amount of cereal in this warehouse, because the total volume occupied inside the warehouse will be the same (limited by the warehouse volume).

Step-by-step explanation:

First we need to find the volume of one box. The volume of the box can be calculated multiplying all the three dimensions:

V_box = 2.5 * 7.75 * 11.75 = 227.6563 in3

We know that the warehouse can store 2.7 billion boxes, so we can find the volume of the warehouse by multiplying this amount by the volume of each box:

V_warehouse = 227.6563 * 2.7 * 10^9 = 614.6719 * 10^9 in3

Converting from cubic inches to cubic feet (1 ft3 = 12^3 in3), we have:

V_warehouse = 614.6719 * 10^9 / 12^3 = 3.5571 * 10^8 ft3

If we know that the height of the warehouse is 10 feet, we have that the base area is:

Area = V_warehouse / height = 3.5571 * 10^7 ft3

A possible pair of values for length and width of the warehouse are:

Length = 10^4 ft, Width = 3.5571 * 10^3 ft

(We just need to choose value that makes the relation Length * Width = Area be true)

It is not possible to redesign the cereal box to increase the amount of cereal in this warehouse, because the total volume occupied inside the warehouse will be the same (limited by the warehouse volume)

rounding to the nearest thousandth would be 452,000

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.