Question

7.5b

1. the clock has a diameter of 7.5 inches

and a circumference of 24 inches.
what expression represents π?
a. \\( \frac { 7.5 } { 24 } \\) c.\\( \frac { 24 } { 7.5 } \\)
b. \\( \frac { 15 } { 24 } \\) d. \\( \frac { 24 } { 3.25 } \\)
7.5a

1. two rectangles are similar. which

proportion could you solve to find the
missing side length?
a. \\( \frac { 4 } { 15 } = \frac { 22.5 } { x } \\)
b. \\( \frac { 4 } { x } = \frac { 22.5 } { 15 } \\)
c. \\( \frac { x } { 15 } = \frac { 22.5 } { 4 } \\)
d. \\( \frac { 4 } { 15 } = \frac { x } { 22.5 } \\)
7.13b
34.use joelles budget below to determine
if each statement is true or false.
a. more than \\( \frac { 1 } { 3 } \\) of joelles income is
allocated toward rent.
b. joelle is saving less than 10% of her
monthly income
c. joelles car payment and other spending
account for less than 25% of her monthly
budget.

Explanation:

30.

Step1: Recall the formula for circumference

The formula for the circumference of a circle is \(C=\pi d\), where \(C\) is the circumference and \(d\) is the diameter.

Step2: Solve for \(\pi\)

Given \(C = 24\) inches and \(d=7.5\) inches. From \(C=\pi d\), we can solve for \(\pi\) by dividing both sides of the equation by \(d\). So \(\pi=\frac{C}{d}\). Substituting the values, we get \(\pi=\frac{24}{7.5}\).

Step1: Use the property of similar rectangles

For similar rectangles, the ratios of corresponding sides are equal. If one rectangle has sides \(4\) cm and \(15\) cm, and the other has sides \(x\) cm and \(22.5\) cm, then the proportion should be \(\frac{4}{x}=\frac{15}{22.5}\) (cross - multiply gives \(4\times22.5 = 15x\)) or \(\frac{4}{15}=\frac{x}{22.5}\) (by the property of proportion \(\frac{a}{b}=\frac{c}{d}\) is equivalent to \(\frac{a}{c}=\frac{b}{d}\)).

Step1: Calculate total income

First, find the total income. \(850 + 150+100 + 400+350+250+200=\$2300\)

Step2: Analyze statement a

For rent: \(\frac{850}{2300}\approx0.37\), and \(\frac{1}{3}\approx0.33\). Since \(0.37>0.33\), more than \(\frac{1}{3}\) of income is for rent.

Step3: Analyze statement b

For savings: \(\frac{200}{2300}\approx0.087<0.1\) (since \(10\% = 0.1\)), so saving less than \(10\%\) of income.

Step4: Analyze statement c

Car payment and other spending: \(350 + 250=\$600\). \(\frac{600}{2300}\approx0.26>0.25\) (since \(25\%=0.25\))

Answer:

C. \(\frac{24}{7.5}\)

32.