AnswersAlgebra 2 with ProbabilityMathematical Modeling

Mathematical Modeling — Test Answers

24 verified answers
1
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If all city buses carry the same number of passengers, what is the least number of buses needed to carry 710 passengers?

A
11
B
5
C
12
D
10
2
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What is the range of f of x ?

A
start set f of x such that 0 is less than or equal to f of x comma f of x is less than infinity end set
B
start set f of x such that negative infinity is less than f of x comma f of x is less than infinity end set
C
start set f of x such that negative infinity is less than f of x comma f of x is less than or equal to 4 end set
D
start set f of x such that 4 is less than f of x comma f of x is less than infinity end set
4

What is the domain for the piece of the function represented by f of x is equal to x plus 1 ?

A
negative 1 is less than or equal to x comma x is less than or equal to 1
B
1 is less than or equal to x comma x is less than 2
C
x is less than negative 1
D
x is greater than 1
5

Which function is represented by the graph?

A
f of x is equal to x plus 3 when x is less than 0; f of x is equal to 3 when x is greater than or equal to 0
B
f of x is equal to x minus 3 when x is less than 0; f of x is equal to 3 when x is greater than or equal to 0
C
f of x is equal to negative x minus 3 when x is less than or equal to 0; f of x is equal to 3 when x is greater than 0
D
f of x is equal to negative x plus 3 when x is less than or equal to 0; f of x is equal to 3 when x is greater than 0
6

The function f of x is to be graphed on a coordinate plane. f of x is equal to negative x when x is less than 0; f of x is equal to 1 when x is greater than or equal to 0 At what point should an open circle be drawn?

A
negative 1 comma 0
B
0 comma 1
C
1 comma 0
D
0 comma 0
7

Edmundo used a number line to show the solution for the inequality start absolute value 2 x minus 6 end absolute value is less than 4 Which number line shows the solution?

A
Image with description A horizontal number line shows two separate intervals. One interval begins with an open circle at negative 5 and extends indefinitely to the left. The other interval begins with an open circle at negative 1 and extends indefinitely to the right. Arrowheads indicate both rays continue beyond the number line.
B
Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Open circles are on 1 and 5 and are connected.
C
Image with description A horizontal number line shows two separate intervals. One interval begins with an open circle at 1 and extends indefinitely to the left. The other interval begins with an open circle at 5 and extends indefinitely to the right. Arrowheads indicate both rays continue beyond the number line.
D
Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Open circles are on negative 5 and negative 1 and are connected.
8

Which of the following represents the solution to the inequality 2 start absolute value 5 minus 2 x end absolute value minus 3 is less than or equal to 15 ?

A
left bracket 1 point 5 comma 7 point 5 right bracket
B
the union of open paren infinity close paren and open paren 7.5 close paren
C
the union of open paren infinity close paren and open paren 7 close paren
D
left bracket negative 2 comma 7 right bracket
9

What are the domain and range of the step function with the equation? f of x is equal to negative 3 lceil x rceil

A
The domain is all real numbers, and the range is all integers that are multiples of 3 .
B
The domain is all integers, and the range is all integers that are multiples of 3 .
C
The domain is all real numbers, and the range is all real numbers.
D
The domain is all integers, and the range is all real numbers.
10

If f of x is equal to 3 lfloor x minus 2 rfloor , what is f of 5 point 9 ?

A
11
B
10
C
12
D
9
11

Aaron solved an inequality and then graphed the solution as shown. Open image in full-screen view Which inequality did Aaron solve?

A
start absolute value x plus 2 end absolute value is less than 3
B
start absolute value x plus 2 end absolute value is greater than 3
C
start absolute value x plus 3 end absolute value is greater than 2
D
start absolute value x plus 3 end absolute value is less than 2
12

Jamilla solved the inequality start absolute value x plus b end absolute value square 2 and graphed the solution as shown. Open image in full-screen view What is the value of b and the missing symbol in Jamilla’s inequality?

A
b is equal to 1 , is greater than or equal to
B
b is equal to negative 1 , is greater than or equal to
C
b is equal to 1 , is less than or equal to
D
b is equal to negative 1 , is less than or equal to
13

Used books cost 2 point 2 5 dollars each. Which expression represents the total number of books that can be purchased for 10 dollars ?

A
the fraction with numerator 10 and denominator lfloor 2 point 2 5 rfloor
B
the fraction with numerator 10 and denominator lceil 2 point 2 5 rceil
C
lceil 10 over 2 point 2 5 rceil
D
lfloor 10 over 2 point 2 5 rfloor
14

A shipping company charges 6 dollars to ship a package that weighs up to 1 pound and 2 dollars for each additional pound or portion of a pound. Which equation represents the cost, in dollars, of shipping a package that weighs x pounds?

A
f of x is equal to 6 plus 2 lceil x plus 1 rceil , where x is greater than 0
B
f of x is equal to 6 plus 2 lfloor x minus 1 rfloor , where x is greater than 0
C
f of x is equal to 6 plus 2 lfloor x plus 1 rfloor , where x is greater than 0
D
f of x is equal to 6 plus 2 lceil x minus 1 rceil , where x is greater than 0
15

In the function y is equal to lfloor x rfloor minus 1 , which values of the function are equivalent?

A
f of 2 and f of 1 point 9
B
f of negative 3 and f of negative 2 point 1
C
f of 1 and f of 0
D
f of negative 1 and f of negative 2
16

In a certain country, a letter up to 1 ounce requires postage in the amount of 0 point 4 2 dollars , and each additional ounce (or fraction of an ounce) has an additional cost. The function represents the cost of mailing one letter with a weight of x ounces in this country. f of x is equal to 0 point 4 2 plus 0 point 2 0 lceil x minus 1 rceil Josiah has two letters. The first weighs 2 point 9 ounces, and the second weighs 4 point 1 ounces. What is the total amount Josiah can expect to pay for postage?

A
1 point 6 2 dollars
B
1 point 8 4 dollars
C
1 point 6 4 dollars
D
2 point 0 4 dollars
17

A student found the solution for the given inequality. start absolute value x minus 9 end absolute value is less than negative 4 x minus 9 is greater than 4 and x minus 9 is less than negative 4 x is greater than 13 and x is less than 5 Which of the following explains whether the student is correct?

A
The student is completely correct because the student correctly wrote and solved the compound inequality.
B
The student is partially correct because only one part of the compound inequality is written correctly.
C
The student is partially correct because the student should have written the statements using “or” instead of “and”.
D
The student is completely incorrect because there is “no solution” to this inequality.
18

A function, h of x , is defined as shown. h of x is equal to 1 fourth x minus 4 when x is less than or equal to 0; h of x is equal to 1 third x minus when 0 is less than x and x is less than or equal to 3; h of x is equal to 1 half x minus 2 when x is greater than or equal to 4 Which graph represents h of x ?

A
Image with description A coordinate plane showing a piecewise function labeled h of x across all 4 quadrants. The horizontal x axis is labeled from negative 4 to 6, and the vertical y axis is labeled from negative 5 to 5. The function consists of three distinct line segments. The first segment starts at the second quadrant at negative 4 comma 3 and extends upward to the right, ending at the y axis with a solid circle at 0 comma 4. The second segment begins directly below at 0 comma 3 with an open circle and extends upward to the right, ending with a solid circle at 3 comma 4. The third segment starts at 4 comma 4 with a solid circle and extends upward to the right, ending in the first quadrant at 6 comma 5.
B
Image with description A coordinate plane showing a piecewise function labeled h of x across all 4 quadrants. The horizontal x axis is labeled from negative 4 to 6, and the vertical y axis is labeled from negative 5 to 5. The function consists of three distinct line segments. The first segment starts on the x axis at negative 4 comma 0 and extends upward to the right, ending at the y axis with a solid circle at 0 comma 1. The second segment begins directly below at 0 comma negative 3 with an open circle and extends upward to the right, ending with a solid circle at 3 comma negative 2. The third segment starts at 4 comma negative 2 with a solid circle and extends upward to the right, ending at 6 comma negative 1.
C
Image with description A coordinate plane showing a piecewise function labeled h of x across all 4 quadrants. The horizontal x axis is labeled from negative 4 to 6, and the vertical y axis is labeled from negative 5 to 5. The function consists of three distinct line segments. The first segment starts at the fourth quadrant near negative 4 comma negative 5 and extends upward to the right, ending at the y axis with a solid circle at 0 comma negative 4. The second segment begins directly above at 0 comma negative 3 with an open circle and extends upward to the right, ending with a solid circle at 3 comma negative 2. The third segment starts at 4 comma 0 with a solid circle and extends upward to the right, ending at 6 comma 1.
D
Image with description A coordinate plane showing a piecewise function labeled h of x across all 4 quadrants. The horizontal x axis is labeled from negative 4 to 6, and the vertical y axis is labeled from negative 5 to 5. The function consists of three distinct line segments. The first segment starts on the x axis at negative 4 comma 0 and extends upward to the right, ending at the y axis with a solid circle at 0 comma 1. The second segment begins directly below at 0 comma negative 1 with an open circle and extends upward to the right, ending with a solid circle at 3 comma 0. The third segment starts at 4 comma negative 2 with a solid circle and extends upward to the right, ending at 6 comma negative 1.
19

What is the solution to the inequality start absolute value 2 n plus 5 end absolute value is greater than 1 ?

A
n is less than negative 3 or n is greater than negative 2
B
negative 3 is greater than n comma n is greater than negative 2
C
2 is less than n comma n is less than 3
D
n is less than 2 or n is greater than 3
20

Whose work is correct?

A
Elise’s work
B
Xiao’s work
C
Malik’s work
D
Jake’s work
21

What are the domain and range of the step function?

A
domain is equal to dot dot dot minus 5 comma negative 2 comma 1 comma 4 comma dot dot dot , range is equal to dot dot dot minus 4 comma negative 1 comma 2 comma 5 comma dot dot dot
B
domain = {all real numbers}, range is equal to dot dot dot minus 4 comma negative 1 comma 2 comma 5 comma dot dot dot
C
domain = {all real numbers}, range = {all real numbers}
D
domain = {all integers}, range = {all real numbers}

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