Question

1. one side of square abcd has a length of 12 meters. a certain rectangle whose area is equal to the area of abcd has a width of 8 meters. what is the length, in meters, of the rectangle?

a. 12
b. 16
c. 18
d. 20
e. 24

1. the average of a list of 4 numbers is 92.0. a new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 40, and the fourth number in the new list is 48. what is the average of this new list of numbers?

f. 81.0
g. 92.0
h. 94.0
j. 94.4
k. 96.6

1. the vector i represents 1 mile per hour east, and the vector j represents 1 mile per hour north. maria is jogging south at 12 miles per hour. one of the following vectors represents marias velocity, in miles per hour. which one?

a. - 12i
b. - 12j
c. 12i
d. 12j
e. 12i + 12j

Explanation:

Step1: Calculate area of square

The area formula for a square is $A = s^2$, where $s$ is the side - length. Given $s = 12$ meters, so $A=12^2=144$ square meters.

Step2: Calculate length of rectangle

The area formula for a rectangle is $A = lw$, where $l$ is the length and $w$ is the width. We know $A = 144$ square meters and $w = 8$ meters. Then $l=\frac{A}{w}=\frac{144}{8}=18$ meters.

Step1: Find sum of original 4 - number list

The average formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Given $n = 4$ and $\bar{x}=92.0$, then the sum of the original 4 - number list, $S_1=92\times4 = 368$.

Step2: Find sum of new 4 - number list

The sum of the first 3 numbers in the original list is $S_{1 - 3}=S_1 - 40=368 - 40 = 328$. The fourth number in the new list is 48. So the sum of the new 4 - number list, $S_2=328 + 48=376$.

Step3: Calculate average of new list

The average of the new list, $\bar{y}=\frac{S_2}{4}=\frac{376}{4}=94.0$.

Since $\vec{j}$ represents 1 mile per hour north and Maria is jogging south (opposite direction of north) at 12 miles per hour, her velocity vector is $- 12\vec{j}$.

Answer:

C. 18