Question

Question 1
A) For the direct variation equation
y =38x
The constant of proportionality is .
Question 2
x
, what is the constant of proportionality? (1 point)
A) Donte is told that for a particular math problem, the value of is always 8 times the value of
. Donte writes the equation
y
y =8x
constant of proportionality? (1 point)
to show the relationship between and . What is the
The constant of proportionality is .
Question 3
x
y
A) A group of hikers is packing trail mix. The direct variation equation shows the
relationship between number of hikers, , and number of cups of trail mix, . What is the
constant of proportionality in this situation? (1 point)
y = x
3
4
x
The constant of proportionality is
Question 4
A) A hummingbird flaps its wings 5,000 times a minute when hovering in place. How many
times will it flap its wing in 15 seconds? (1 point)
The hummingbird will flap its wings times.
Question 5
A) In 2 days, Quinesha exercises 50 minutes. At this rate, how many minutes does she
exercise in 4 weeks? (1 point)
Quinesha exercises minutes in 4 weeks

Answer 1

Here are the answers to your questions:

**Question 1:**
The direct variation equation is \( y = 38x \). The constant of proportionality is **38**.

**Question 2:**
The equation written by Donte is \( y = 8x \). The constant of proportionality is **8**.

**Question 3:**
The equation given is \( y = \frac{3}{4}x \). The constant of proportionality is **\(\frac{3}{4}\)**.

**Question 4:**
To find out how many times the hummingbird will flap its wings in 15 seconds, first calculate how many seconds are in a minute and then find the number of flaps in 15 seconds:
- \( 5,000 \) flaps/minute.
- \( 1 \) minute = \( 60 \) seconds.
- In \( 15 \) seconds:
\[
\text{Flaps in 15 seconds} = \frac{5,000 \text{ flaps}}{60 \text{ seconds}} \times 15 \text{ seconds} = \frac{5,000 \times 15}{60} = 1,250.
\]
The hummingbird will flap its wings **1,250** times.

**Question 5:**
Quinesha exercises **50 minutes** in **2 days**. First, find her daily exercise in minutes:
- Daily exercise:
\[
50 \text{ minutes}/2 \text{ days} = 25 \text{ minutes/day}.
\]
Now, calculate how many minutes she exercises in **4 weeks** (which is **28 days**):
\[
25 \text{ minutes/day} \times 28 \text{ days} = 700 \text{ minutes}.
\]
Quinesha exercises **700** minutes in 4 weeks.