Victory for the ACT Student Text 15e

V ICTORY P RACTICE T EST A NSWERS AND E XPLANATIONS • 463

Set up a direct proportion:

47. (C) (p. 389) Mathematics/Number and Quantity/Rates and Proportions .

320

miles

8

hours

x

miles

2 hours

miles 2 hours :

320

x

miles

8

hours

80 miles Or, calculate the rate: r t miles per hour hours

d g ‘ǡ –”ƒ˜‡Ž‹‰ ƒ– ƒ ”ƒ–‡ ‘ˆ ͶͲ ’Š ˆ‘” ʹ Š‘—”• ‡“—ƒŽ• miles. 48. (H) (p. 389) Mathematics/Geometry/Trigonometry/Trigonometric Relationships . r 40 8 miles per hour hours r 320 miles miles miles per hour ] ] g 80 40 hour miles hours e eo o 2 2

Use the common denominator, , to simplify the expression and apply the Pythagorean trigonometric identity ( sin cos x x 1 2 2 + = ): cos cos

(sin ) (cos ) x x

x x

x x

x

x

d

n

d

n

sin

sin

x

x

sin

cos

cos

sin

x

x

2

2

cos

sin

=

+

x

x

x

x

(sin ) (cos )

(sin ) (cos )

+

x

x

2

2

sin cos

=

x

x

(sin ) (cos )

1

=

x

x

(sin ) (cos )

49. (E) (p. 390) Mathematics/Statistics and Probability/Measures of Center . ‰”‡ƒ–‡•– ˆ”‡“—‡…›ǣ ͻͳι Ǥ 50. (F) (p. 390) Mathematics/Number and Quantity/Percentages . ‹’Ž‹ˆ› –Š‡ •–‡ǣ Dzͻ ‹• ™Šƒ– ’‡”…‡– ‘ˆ ͵Ͳǫdz ‡– —’ –Š‡ “is-over-of” equation and solve for the missing value: % is The mode is the data element with the

of

100

x

9

30

100

9(100)

x

30

%30

51. (B) (p. 390) Mathematics/Algebra and Functions/Manipulating Algebraic Expressions/Factoring Expressions . Rearrange the expression and then factor: − + − = − − 2 2

t t

t

t

( t 7 6 3 6 7 3 = + − ) ( 3 1 2 3 t

)