Question

1. circle every true relationship?

a. ( 14% = 0.14 )
b. ( 80%=\frac{8}{100} )
c. ( 65 = 65% )
d. ( \frac{21}{100}=0.21 )
e. ( 0.90 = 90% )
f. ( 76%=\frac{76}{100} )
g. ( \frac{40}{100}=0.04 )

1. last year, a state university received 3,560 applications from boys. of those applications, 35% were from boys who lived in other states.

a. how many applications did the university receive from boys who lived in other states? show your work.
b. applications to the university from boys represented 40% of all applications. how many applications did the university receive in all? explain how you found your answer.

Explanation:

Step1: Convert percentage to decimal or fraction

• For A: \(14\%=\frac{14}{100}=0.14\), so A is correct.
• For B: \(80\%=\frac{80}{100}

eq\frac{8}{100}\), so B is incorrect.

• For C: \(65

eq65\%\) (\(65\% = 0.65\)), so C is incorrect.

• For D: \(\frac{21}{100}=0.21\), so D is correct.
• For E: \(0.90 = 90\%\), so E is correct.
• For F: \(76\%=\frac{76}{100}\), so F is correct.
• For G: \(\frac{40}{100}=0.4

eq0.04\), so G is incorrect.

Step2: Solve part 5A

The number of applications from boys who lived in other states is \(3560\times35\%=3560\times0.35 = 1246\).

Step3: Solve part 5B

Let the total number of applications be \(x\). Since applications from boys (\(3560\)) represent \(40\%\) of all applications, we have the equation \(0.4x=3560\). Solving for \(x\), we get \(x=\frac{3560}{0.4}=8900\).

Answer:

1. A, D, E, F are correct relationships.

5A) 1246 applications.
5B) 8900 applications.