Adam built a toy box for his children’s wooden blocks.
A. If the inside dimensions of the box are 18 inches by 12 inches by 6 inches, what is the maximum number of 2-inch wooden cubes that will fit in the toy box?

B. What if Adam had built the box 16 inches by 9 inches by 9 inches? What is the maximum number of 2-inch wooden cubes that would fit in this size box?

A. 162

B. 128

Step-by-step explanation:

We have wooden cubes of 2 in of side.

A. If the box is 18 x 12 x 6 in., in the base (18 x 12), we can fit 54 cubes:

As the height is 6 in, we can fit 6/2=3 layers of 54 cubes in the box, se we can fit 162 cubes:

B. If we have a box with measures 16 x 9 x 9 in., and the base is 16x9 in, we can fit (16/2)*(9/2)=8*4=32 cubes per layer.

Note that in the 9 in side we can only put 4, as we need 10 in to fit 5 cubes (we can not cut them).

In the same way, as we have 9 in of height, we can fit 4 layers of 32 cubes, so this is a total of 128 cubes:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

first one because it can't have a fraction in it

step-by-step explanation: