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A school board has determined that there should be 3 teachers for every 50 students. How many teachers are needed for an enrollment of 2,650 students?


A) 134 teachers
B) 148 teachers
C) 159 teachers
D) 143 teachers
E) 216 teachers

F) B) and C)
G) All of the above

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Kent drives his Mazda 270 miles in the same time that Dave drives his Nissan 250 miles. If Kent averages 4 miles per hour faster than Dave, find their rates.


A) 46 mph for Dave and 50 mph for Kent
B) 45 mph for Dave and 49 mph for Kent
C) 60 mph for Dave and 64 mph for Kent
D) 50 mph for Dave and 54 mph for Kent
E) 54 mph for Dave and 46 mph for Kent

F) A) and E)
G) B) and D)

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Express the rational number in reduced form. −4050- \frac { 40 } { 50 }


A) 12\frac { 1 } { 2 }
B) −45- \frac { 4 } { 5 }
C) 15\frac { 1 } { 5 }
D) 45\frac { 4 } { 5 }
E) −56- \frac { 5 } { 6 }

F) All of the above
G) B) and C)

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Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero. x+79(x+7) \frac { x + 7 } { 9 ( x + 7 ) }


A) x7\frac { x } { 7 }
B) 19\frac { 1 } { 9 }
C) 9x+7\frac { 9 } { x + 7 }
D) x+79\frac { x + 7 } { 9 }
E) in lowest terms

F) B) and E)
G) C) and D)

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Perform the indicated division and express your answer in simplest form. 12sa3s2−3sa÷sa+a2s−2a\frac { 12 s a } { 3 s ^ { 2 } - 3 s a } \div \frac { s a + a } { 2 s - 2 a }


A) 8(s+1) (s−a) 2\frac { 8 ( s + 1 ) } { ( s - a ) ^ { 2 } }
B) 8s+1\frac { 8 } { s + 1 }
C) 5+a8\frac { 5 + a } { 8 }
D) 8s+a\frac { 8 } { s + a }
E) s+18\frac { s + 1 } { 8 }

F) C) and D)
G) A) and B)

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Perform the multiplication. Simplify the answer, if possible. 4sa7z⋅7za3s\frac { 4 s a } { 7 z } \cdot \frac { 7 z a } { 3 s }


A) 27\frac { 2 } { 7 }
B) 4s3\frac { 4 s } { 3 }
C) 43a2\frac { 4 } { 3 } a ^ { 2 }
D) 47z\frac { 4 } { 7 z }
E) a24\frac { a ^ { 2 } } { 4 }

F) A) and B)
G) A) and C)

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Do the addition. Simplify the result when possible. 19+127\frac { 1 } { 9 } + \frac { 1 } { 27 }


A) 43\frac { 4 } { 3 }
B) 227\frac { 2 } { 27 }
C) 427\frac { 4 } { 27 }
D) 49\frac { 4 } { 9 }
E) 727\frac { 7 } { 27 }

F) C) and D)
G) A) and B)

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Solve the proportion for the variable. 6y=930\frac { 6 } { y } = \frac { 9 } { 30 }


A) 22
B) 23
C) 16
D) 25
E) 20

F) A) and E)
G) A) and D)

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Perform the multiplication. Simplify the answer, if possible. 2s5y⋅5y3s\frac { 2 s } { 5 y } \cdot \frac { 5 y } { 3 s }


A) 2s3y\frac { 2 s } { 3 y }
B) 25y\frac { 2 } { 5 y }
C) 87\frac { 8 } { 7 }
D) 2s3\frac { 2 s } { 3 }
E) 53y\frac { 5 } { 3 y }

F) A) and E)
G) None of the above

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Express the rational number in reduced form. 2530\frac { 25 } { 30 }


A) 56\frac { 5 } { 6 }
B) 67\frac { 6 } { 7 }
C) 66
D) 16\frac { 1 } { 6 }
E) 12\frac { 1 } { 2 }

F) B) and E)
G) A) and E)

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Perform the indicated division. (2x−1) 2200x−100÷10x2+3x−410x+5\frac { ( 2 x - 1 ) ^ { 2 } } { 200 x - 100 } \div \frac { 10 x ^ { 2 } + 3 x - 4 } { 10 x + 5 }


A) 12\frac { 1 } { 2 }
B) 2
C) 2x+14x+8\frac { 2 x + 1 } { 4 x + 8 }
D) 2x+110x+8\frac { 2 x + 1 } { 10 x + 8 }
E) 10x+82x+1\frac { 10 x + 8 } { 2 x + 1 }

F) A) and B)
G) B) and C)

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Simplify the rational expression. 8x2y+24xy2−32y348x3y−36x2y2−12xy3\frac { 8 x ^ { 2 } y + 24 x y ^ { 2 } - 32 y ^ { 3 } } { 48 x ^ { 3 } y - 36 x ^ { 2 } y ^ { 2 } - 12 x y ^ { 3 } }


A) 2(x−4y) 3x(4x+y) \frac { 2 ( x - 4 y ) } { 3 x ( 4 x + y ) }
B) 2y(x+4y) 3x(x−4y) \frac { 2 y ( x + 4 y ) } { 3 x ( x - 4 y ) }
C) 23x\frac { 2 } { 3 x }
D) 2(x+4y) 3x(4x+y) \frac { 2 ( x + 4 y ) } { 3 x ( 4 x + y ) }
E) 2(x−4y) 3xy(4x−y) \frac { 2 ( x - 4 y ) } { 3 x y ( 4 x - y ) }

F) None of the above
G) B) and D)

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Perform the division. 12x−3y+36z12xy\frac { 12 x - 3 y + 36 z } { 12 x y }


A) 34+3zxy\frac { 3 } { 4 } + \frac { 3 z } { x y }
B) 1y+14x+1xy\frac { 1 } { y } + \frac { 1 } { 4 x } + \frac { 1 } { x y }
C) 1y−14x+3xy\frac { 1 } { y } - \frac { 1 } { 4 x } + \frac { 3 } { x y }
D) 1y−14x+3zxy\frac { 1 } { y } - \frac { 1 } { 4 x } + \frac { 3 z } { x y }
E) 4y−45x+3zxy\frac { 4 } { y } - \frac { 4 } { 5 x } + \frac { 3 z } { x y }

F) A) and C)
G) A) and D)

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Find the quotient. (−35) ÷(−1310) \left( - \frac { 3 } { 5 } \right) \div \left( - \frac { 13 } { 10 } \right)


A) 665\frac { 6 } { 65 }
B) −613- \frac { 6 } { 13 }
C) 613\frac { 6 } { 13 }
D) −213- \frac { 2 } { 13 }
E) 213\frac { 2 } { 13 }

F) B) and D)
G) C) and D)

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Perform the operation. 133(−1813) \frac { 13 } { 3 } \left( - \frac { 18 } { 13 } \right)


A) 1313
B) −6- 6
C) −13- 13
D) 66
E) none of these

F) A) and B)
G) A) and D)

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Perform the multiplication. Simplify the answer, if possible. tz2t2z⋅9z2a2tza÷tza2t3a2\frac { t z ^ { 2 } } { t ^ { 2 } z } \cdot \frac { 9 z ^ { 2 } a ^ { 2 } } { t z a } \div \frac { t z a ^ { 2 } } { t ^ { 3 } a ^ { 2 } }


A) 9z2at3\frac { 9 z ^ { 2 } a } { t ^ { 3 } }
B) 2t3az4\frac { 2 t ^ { 3 } a } { z ^ { 4 } }
C) 2z3a2 z ^ { 3 } a
D) 9z3at4\frac { 9 z ^ { 3 } a } { t ^ { 4 } }
E) 9za9 z a

F) A) and E)
G) D) and E)

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