Question

1. to the nearest percent, what is the probability of rolling a 4 on a number cube? 4) identify the constant of proportionality (unit rate) using the table below. give the rate in feet per second.

seconds	feet
15	360
20	480

Explanation:

3)

Step1: Determine total outcomes

A number - cube has 6 faces numbered 1 - 6, so the total number of possible outcomes when rolling it is $n = 6$.

Step2: Determine favorable outcomes

The event of rolling a 4 is a single outcome, so the number of favorable outcomes $m = 1$.

Step3: Calculate probability

The probability $P$ of an event is given by the formula $P=\frac{m}{n}$. Substituting $m = 1$ and $n = 6$, we get $P=\frac{1}{6}\approx0.1667$.

Step4: Convert to percentage

To convert the decimal to a percentage, we multiply by 100. So $0.1667\times100 = 16.67\%$. Rounding to the nearest percent, we get $17\%$.

Step1: Recall the formula for constant of proportionality

The constant of proportionality (unit - rate) $k$ in a relationship between two variables $y$ (distance in feet) and $x$ (time in seconds) is given by $k=\frac{y}{x}$.

Step2: Choose a row from the table

Let's take the first row where $x = 5$ seconds and $y = 120$ feet. Then $k=\frac{120}{5}=24$ feet per second.
We can check with other rows. For the second row, $x = 15$ seconds and $y = 360$ feet, and $\frac{360}{15}=24$ feet per second. For the third row, $x = 20$ seconds and $y = 480$ feet, and $\frac{480}{20}=24$ feet per second.

Answer:

$17\%$

4)