Question

real numbers day 4
show all work for credit
monday september 29
all year:
al runs 8 miles per hour. bob runs 1 mile in 8 minutes. carl runs 2 miles in 15 minutes. dan runs $\frac{1}{2}$ mile in 3.5 minutes. who runs at the fastest rate?
yesterday:
set a represents the set of integers. set b represents the set of whole numbers. which venn diagram shows the correct placement of numbers in the sets?
released staar questions:
triangle hjk is similar to triangle lmn.
which proportion can be used to calculate the length of lm in centimeters?

Explanation:

Step1: Convert Bob's speed to miles per hour

1 hour has 60 minutes. If Bob runs 1 mile in 8 minutes, then in 60 minutes (1 hour), the number of miles he runs is $\frac{60}{8}= 7.5$ miles per hour.

Step2: Convert Carl's speed to miles per hour

Carl runs 2 miles in 15 minutes. In 1 hour (60 minutes), the number of 15 - minute intervals is $\frac{60}{15}=4$. So Carl runs $2\times4 = 8$ miles per hour.

Step3: Convert Dan's speed to miles per hour

Dan runs $\frac{1}{2}$ mile in 3.5 minutes. In 1 hour (60 minutes), the number of 3.5 - minute intervals is $\frac{60}{3.5}=\frac{600}{35}=\frac{120}{7}\approx17.14$. So Dan runs $\frac{1}{2}\times\frac{120}{7}=\frac{60}{7}\approx8.57$ miles per hour.

Step4: Compare speeds

Al runs 8 miles per hour, Bob runs 7.5 miles per hour, Carl runs 8 miles per hour, and Dan runs approximately 8.57 miles per hour.

for Venn - diagram question:
Whole numbers are non - negative integers (0, 1, 2, 3,...). Integers include positive and negative whole numbers and 0. So set B (whole numbers) is a subset of set A (integers). In option D, set A contains negative integers (-20, - 7) and non - negative integers, and set B (a subset of A) contains only non - negative integers (0, 9, 81).

for similar - triangles question:
For similar triangles $\triangle HJK$ and $\triangle LMN$, the ratios of corresponding sides are equal. The side of length 6 in $\triangle HJK$ corresponds to the side of length 9 in $\triangle LMN$, and the side of length 7.5 in $\triangle HJK$ corresponds to the side of length $LM$ in $\triangle LMN$. So the proportion is $\frac{6}{9}=\frac{7.5}{LM}$, which can be rewritten as $\frac{6}{7.5}=\frac{9}{LM}$.

Answer:

Dan