solve each proportion.
16. $\frac{x}{13} = \frac{18}{39}$ $x = $
(work shown: $x \cdot 39 = 13 \cdot 18$, $39x = 234$, $\frac{39x}{39} = \frac{234}{39}$, $x = 6$)
17. $\frac{6}{25} = \frac{d}{30}$ $d = $
18. $\frac{2.5}{6} = \frac{h}{9}$ $h = $
assume the situations are proportional. write and solve by using a proportion.
19. for every person who has the flu, there are 6 people who have only flu-like symptoms. if a doctor sees 40 patients, determine approximately how many patients you would expect to have only flu-like symptoms.
20. for every left-handed person, there are about 4 right-handed people. if there are 30 students in a class, predict the number of students who are right-handed.
21. jeremiah is saving money from a tutoring job. after the first three weeks, he saved $135. assume the situation is proportional. use the unit rate to write an equation relating the amount saved $s$ to the number of weeks $w$ worked. at this rate, how much will jeremiah save after eight weeks?
22. make a prediction a speed limit of 100 kilometers per hour (kph) is approximately equal to 62 miles per hour (mph). write an equation relating kilometers per hour $k$ to miles per hour $m$. then predict the following measures. round to the nearest tenth.
a. a speed limit in mph for a speed limit of 75 kph
b. a speed limit in kph for a speed limit of 20 mph

Question

Accepted Answer

### Problem 16
# Explanation:
## Step1: Cross - multiply the proportion
Given $\frac{x}{13}=\frac{18}{39}$, cross - multiplying gives $x\times39 = 13\times18$
## Step2: Simplify the right - hand side
$13\times18 = 234$, so the equation becomes $39x=234$
## Step3: Solve for $x$
Divide both sides of the equation by 39: $\frac{39x}{39}=\frac{234}{39}$, which simplifies to $x = 6$
# Answer:
$x = 6$

### Problem 17
# Explanation:
## Step1: Cross - multiply the proportion
Given $\frac{6}{25}=\frac{d}{30}$, cross - multiplying gives $6\times30=25\times d$
## Step2: Simplify the left - hand side
$6\times30 = 180$, so the equation becomes $25d = 180$
## Step3: Solve for $d$
Divide both sides of the equation by 25: $d=\frac{180}{25}=\frac{36}{5}=7.2$
# Answer:
$d = 7.2$

### Problem 18
# Explanation:
## Step1: Cross - multiply the proportion
Given $\frac{2.5}{6}=\frac{h}{9}$, cross - multiplying gives $2.5\times9 = 6\times h$
## Step2: Simplify the left - hand side
$2.5\times9=22.5$, so the equation becomes $6h = 22.5$
## Step3: Solve for $h$
Divide both sides of the equation by 6: $h=\frac{22.5}{6}=3.75$
# Answer:
$h = 3.75$

### Problem 19
# Explanation:
## Step1: Set up the proportion
Let $x$ be the number of patients with only flu - like symptoms. The ratio of people with flu to people with flu - like symptoms is $1:6$. The total number of parts in the ratio is $1 + 6=7$. The proportion is $\frac{6}{7}=\frac{x}{40}$ (since the number of people with flu - like symptoms is 6 parts out of 7 total parts, and the total number of patients is 40)
## Step2: Cross - multiply and solve
Cross - multiplying gives $7x=6\times40$, $7x = 240$, $x=\frac{240}{7}\approx34.3$ (or we can think of it as for every 1 person with flu, 6 with flu - like, so the number of flu - like is $\frac{6}{1 + 6}\times40=\frac{6}{7}\times40\approx34.3$)
# Answer:
Approximately 34 patients (or $\frac{240}{7}\approx34.3$)

### Problem 20
# Explanation:
## Step1: Set up the proportion
Let $x$ be the number of right - handed students. The ratio of left - handed to right - handed is $1:4$, so the total number of parts is $1 + 4 = 5$. The proportion is $\frac{4}{5}=\frac{x}{30}$ (since right - handed is 4 parts out of 5 total parts, and total students is 30)
## Step2: Cross - multiply and solve
Cross - multiplying gives $5x=4\times30$, $5x = 120$, $x = 24$
# Answer:
24 students

### Problem 21
# Explanation:
## Step1: Find the unit rate
The unit rate (amount saved per week) $r=\frac{135}{3}=45$ dollars per week.
## Step2: Write the equation
The equation relating the amount saved $s$ to the number of weeks $w$ is $s = 45w$ (since it's a proportional relationship, $s=rw$ where $r = 45$)
## Step3: Find the amount saved in 8 weeks
Substitute $w = 8$ into the equation: $s=45\times8 = 360$
# Answer:
The equation is $s = 45w$ and Jeremiah will save \$360 after 8 weeks.

### Problem 22
## Part (a)
# Explanation:
## Step1: Find the conversion factor
We know that $100$ kph $= 62$ mph, so the conversion factor from kph to mph is $\frac{62}{100}=0.62$ mph per kph. The equation relating $k$ (kph) and $m$ (mph) is $m = 0.62k$
## Step2: Predict for 75 kph
Substitute $k = 75$ into the equation: $m=0.62\times75 = 46.5$
# Answer:
The equation is $m = 0.62k$ and the speed limit in mph for 75 kph is 46.5 mph.

## Part (b)
# Explanation:
## Step1: Rewrite the conversion equation
From $100$ kph $= 62$ mph, we can solve for $k$ in terms of $m$: $k=\frac{100}{62}m\approx1.6129m$
## Step2: Predict for 20 mph
Substitute $m = 20$ into the equation: $k=\frac{100}{62}\times20=\frac{2000}{62}\approx32.3$
# Answer:
The equation is $k=\frac{100}{62}m$ (or $k\approx1.61m$) and the speed limit in kph for 20 mph is approximately 32.3 kph.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 16

Step1: Cross - multiply the proportion

Step2: Simplify the right - hand side

Step3: Solve for \(x\)

Step1: Cross - multiply the proportion

Step2: Simplify the left - hand side

Step3: Solve for \(d\)

Step1: Cross - multiply the proportion

Step2: Simplify the left - hand side

Step3: Solve for \(h\)

Answer:

Problem 17