Question

if 50 one - cent coins were stacked on top of each other in a column, the column would be approximately $3\frac{7}{8}$ inches tall. at this rate, which of the following is closest to the number of one - cent coins it would take to make an 8 - inch - tall column?\
a) 75\
b) 100\
c) 200\
d) 390\
\
29\
a motor powers a model car so that after starting from rest, the car travels $s$ inches in $t$ seconds, where $s = 16t\sqrt{t}$. which of the following gives the average speed of the car, in inches per second, over the first $t$ seconds after it starts?\
a) $4\sqrt{t}$\
b) $16\sqrt{t}$\
c) $\frac{16}{\sqrt{t}}$\
d) $16t$\
\
37\
one morning, ms. simon drove directly from her home to her workplace in 24 minutes. what was her average speed, in miles per hour, during her drive that morning?

Explanation:

First Question (Coin Stacking)

Step1: Convert mixed number to improper fraction

The height of 50 coins is \( 3\frac{7}{8} \) inches. Convert \( 3\frac{7}{8} \) to an improper fraction: \( 3\frac{7}{8}=\frac{3\times8 + 7}{8}=\frac{31}{8} \) inches.

Step2: Find the number of coins per inch

Let \( x \) be the number of coins per inch. We know that 50 coins correspond to \( \frac{31}{8} \) inches. So, \( x=\frac{50}{\frac{31}{8}} = 50\times\frac{8}{31}=\frac{400}{31}\approx12.9 \) coins per inch.

Step3: Calculate coins for 8 - inch column

To find the number of coins for an 8 - inch column, multiply the number of coins per inch by 8. Let \( n \) be the number of coins. Then \( n=\frac{400}{31}\times8=\frac{3200}{31}\approx103.2 \). The closest option to 103.2 is 100.

Step1: Recall the formula for average speed

The formula for average speed \( v \) is \( v=\frac{\text{distance}}{\text{time}} \).

Step2: Substitute the given distance and time

The distance \( s = 16t\sqrt{t} \) and the time is \( t \) seconds. So, \( v=\frac{16t\sqrt{t}}{t} \).

Step3: Simplify the expression

Cancel out the \( t \) terms: \( v = 16\sqrt{t} \).

Answer:

B) 100

Second Question (Model Car Speed)