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Practice Exam Answers

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21
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The vertices of a triangle are given in the columns of the matrix cap t is equal to the 2 by 3 matrix row 1, 0 4 0 row 2, 0 0 5 If the 2 by 2 matrix, row 1, column 1, negative 1 column 2, 0 row 2, column 1, 0 column 2, negative 1 times cap t is found to perform a transformation, what are the coordinates of the transformed triangle?

A
open paren 0 comma 0 close paren comma open paren negative 4 comma 0 close paren comma open paren 0 comma negative 5 close paren
B
(0, 0), (4, 0), (0,−5).
C
open paren 0 comma 0 close paren comma open paren negative 4 comma 0 close paren comma open paren 0 comma 5 close paren
D
(0, 0), (4, 0), (0, 5).
22
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Haji rows his canoe 10 mph in still water. He noticed one day that he could row 4 miles upstream in the same amount of time he could row 6 miles downstream. What was the approximate speed of the current that day?

A
2 point 0 mph
B
3 point 3 mph
C
5 point 0 mph
D
10 point 0 mph
23

What are the values of x and y in the matrix equation? the 2 by 1 column matrix row 1 x plus 4 row 2 y squared plus 1 plus the 2 by 1 column matrix row 1 negative 9 x row 2 negative 17 is equal to the 2 by 1 column matrix 28 0

A
x is equal to 3 y is equal to plus 4 comma negative 4
B
x is equal to 3 y is equal to plus 8 comma negative 8
C
x is equal to negative 3 y is equal to plus 4 comma negative 4
D
x is equal to negative 3 y is equal to 4
24

An initial investment of 200 dollars is now valued at 350 dollars The annual interest rate is 8 percent compounded continuously. The equation 200 e raised to the 0 point 0 8 t power is equal to 350 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

A
19 years
B
7 years
C
22 years
D
5 years
25

The first term of a geometric sequence is negative 2 and the common ratio is negative 1 fourth What are the next three terms of the sequence?

A
1 half comma 1 eighth comma 1 over 32
B
1 half comma negative 1 eighth comma 1 over 32
C
negative 1 half comma 1 eighth comma negative 1 over 32
D
negative 1 half comma negative 1 eighth comma negative 1 over 32
26

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach negative infinity. To which family of functions might the described function belong?

A
square root
B
exponential
C
absolute value
D
cube root
27

Which expression is equivalent to open paren the fraction with numerator x to the negative 6 power and denominator x squared close paren cubed ?

A
the fraction with numerator 1 and denominator x to the 24th power
B
1 over x
C
the fraction with numerator 1 and denominator x to the 9th power
D
the fraction with numerator 1 and denominator x to the 5th power
28

Jerome solved the equation by graphing. the log base 2 of x plus log sub 2 of open paren x minus 2 close paren is equal to 3 Which of the following shows the correct system of equations and solution?

A
y sub 1 is equal to the fraction with numerator log x and denominator log 2 plus the fraction with numerator the log of open paren x minus 2 close paren and denominator log 2 , y sub 2 is equal to 3 ; x is equal to 4
B
y sub 1 is equal to log x plus the log of open paren x minus 2 close paren , y sub 2 is equal to 3 ; x is equal to 44
C
y sub 1 is equal to the fraction with numerator log x and denominator log 2 plus the fraction with numerator the log of open paren x minus 2 close paren and denominator log 2 , y sub 2 is equal to 3 ; x is equal to 3
D
y sub 1 is equal to log x plus the log of open paren x minus 2 close paren , y sub 2 is equal to 3 ; x is equal to 33
29

What values are excluded from the domain and range of the function f of x is equal to the fraction with numerator x plus 3 and denominator 2 x plus 5 ?

A
domain: x is not equal to 1 half range: y is not equal to negative 5 halves
B
domain: x is not equal to negative 3 range: y is not equal to 2
C
domain: x is not equal to negative 5 halves range: y is not equal to 2
D
domain: x is not equal to negative 5 halves range: y is not equal to 1 half
30

Which expression is equivalent to the following complex fraction? the fraction with numerator 1 over x minus 1 over y and denominator 1 over x plus 1 over y

A
the fraction with numerator open paren y minus x close paren times open paren y plus x close paren and denominator x squared y squared
B
the fraction with numerator y plus x and denominator y minus x
C
the fraction with numerator x squared y squared and denominator open paren y plus x close paren times open paren y plus x close paren
D
the fraction with numerator y minus x and denominator y plus x
31

The equation of the piecewise defined function f of x is shown. What is the value of f of negative 2 ? f of x equals enlarged left-brace first row negative x squared comma x less than negative 2. Second row 3 comma negative 2 less than or equal to x less than 0. Third row 3 x plus 2 comma x greater than or equal to 0.

A
f of negative 2 is equal to 0
B
f of negative 2 is equal to negative 4
C
f of negative 2 is equal to negative 6
D
f of negative 2 is equal to 3
32

A student would like to estimate the average number of text messages sent by cell-phone users in a day. Which of the following methods would provide a voluntary response sample?

A
a survey of all students in a statistics class
B
a text poll provided during a nightly news broadcast
C
a survey of adults leaving a movie theater
D
a survey of every 10th person leaving a large shopping mall
33

Which of the following is the graph of y is equal to negative square root of x plus 1 ?

A
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve opens up and to the right in quadrant 4. The origin of the curve is at (0 comma 1). The curve passes through the points (1 comma 0) and (8 comma negative 2).
B
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve originates from (0 negative 1) and passes through the points (4 comma negative 3) and (9 comma negative 4) in the 4th quadrant.
C
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve opens down and to the left in quadrants 1 and 3. The origin of the curve is at (0 comma negative 1). The curve passes through the points (negative 1 comma 0) and (negative 8 comma 2).
D
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve originates from (0 comma 1) and passes through the points (negative 4 comma 3) and (negative 8 comma 4) in the 2nd quadrant.
34

An equation for the depreciation of a car is given by y is equal to cap A times open paren 1 minus r close paren to the t th power , where y is equal to current value of the car, cap A is equal to original cost, r is equal to rate of depreciation, and t is equal to time, in years. The current value of a car is 12 dollars comma 282 point 5 0 The car originally cost 20 dollars comma 000 and depreciates at a rate of 15 percent per year. How old is the car?

A
1 fourth years
B
4 years
C
1 third years
D
3 years
35

Which statement describes the candle?

A
The candle starts at a height of 25 centimeters and burns at a rate of 0 point 6 2 5 centimeters per hour.
B
The candle starts at a height of 22 point 5 centimeters and burns at a rate of 0 point 6 2 5 centimeters per hour.
C
The candle starts at a height of 25 centimeters and burns at a rate of 2 point 5 centimeters per hour.
D
The candle starts at a height of 22 point 5 centimeters and burns at a rate of 2 point 5 centimeters per hour.
36

Which statement best describes the explanatory and response variables in the regression model?

A
In the logarithmic regression model, the explanatory variable is time and the response variable is the remaining mass.
B
In the exponential regression model, the explanatory variable is time and the response variable is the remaining mass.
C
In the exponential regression model, the explanatory variable is the remaining mass and the response variable is time.
D
In the logarithmic regression model, the explanatory variable is the remaining mass and the response variable is time.

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