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## Question Explanations For

##
*Practice Test 4 (Math Calculator)*

## 1.

## 2.

*x*+ 2.5

*x*+ 3.5

*x*+ 4

*x*= 11

*x*. Since he edits 33 manuscripts in total, 11

*x*= 33, so

*x*= 3.

## 3.

## 4.

## 5.

*x*

^{2}+ 13

*x*– 6, you can use FOIL to expand each factored expression. Option I gives 5

*x*

^{2}+ 15

*x*– 2

*x*– 6 = 5

*x*

^{2}+ 13

*x*– 6. Option II gives 5

*x*

^{2}+ 3

*x*– 10

*x*– 6 ≠ 5

*x*

^{2}– 7

*x*– 6. Option III gives 5(

*x*

^{2}+ 3

*x*- 2

*x*– 6) ≠ 5

*x*

^{2}+ 5

*x*– 30. So, the only option which is equivalent to 5

*x*

^{2}+ 13

*x*– 6 is option I.

## 6.

## 7.

*y*, you can set the right sides equal to each other:

This means that *x* = 3 or *x* = -2. Plugging these values of *x* into either equation shows you that the two solutions are (3, 20) and (–2, –10). This gives two possible values of *xy*: 60 and 20. Since only 60 is an answer choice, (D) is correct.

## 8.

*x*,

*y*), then its equation is true for those values of

*x*and

*y*. Plugging in 3 for

*x*and 6 for

*y*gives

*k*(3) – 6(6) = 24. Solving for

*k*gives

*k*= 20.

## 9.

*x*as follows:

## 10.

*x*– 4 ≤ 6 and –(

*x*– 4) ≤ 6. Solving for

*x*gives

*x*≤ 10 and –2 ≤

*x*, which can be rewritten as –2 ≤

*x*≤ 10.

## 11.

*y*=

*mx*+

*b*. You can see in the table that when

*x*= 0,

*f*(

*x*) = 2. Therefore, the

*y*-intercept (the constant

*b*) is 2. You can also calculate the slope

*m*using the slope formula: . Plugging in two points, (

*x*

_{1},

*y*

_{1}) and (

*x*

_{2},

*y*

_{2}), from the frequency table will give you the slope; for example, . Since and

*b*= 2, .

## 12.

*x*

^{2}term would be negative, not positive. However, a hot air balloon would increase in height, so (C) is correct.

## 13.

## 14.

*T*= 200,

*S*is about 40, and when

*T*= 400,

*S*is about 80. Since , this yields a slope of 0.2. If the line of best fit were extended, it would intersect the

*y*-axis at about 0, meaning the equation of the line is

*S*= 0.2

*T*+ 0, or

*S*= 0.2

*T*. You could have also found the

*y*-intercept by setting up the equation

*y*= 0.2

*x*+

*b*, substituting a point on the line for (

*x*,

*y*), and solving for

*b*.

## 15.

*x*

^{2}+ 2

*x*- 2)(3

*x*

^{2}-

*x*- 1) = (

*x*

^{2})(3

*x*

^{2}-

*x*- 1) + 2

*x*(3

*x*

^{2}-

*x*- 1) - 2(3

*x*

^{2}-

*x*- 1) = 3

*x*

^{4}-

*x*

^{3}-

*x*

^{2}+ 6

*x*

^{3}- 2

*x*

^{2}- 2

*x*- (6

*x*

^{2}- 2

*x*- 2) = 3

*x*

^{4}+ 5

*x*

^{3}- 9

*x*

^{2}+ 2.

## 16.

## 17.

## 18.

*y*-axis at (0, 1), so

*b*= 1.

## 19.

(A) and (B) are incorrect because the means are the same. (C) is incorrect because Data Set A has a larger standard deviation that Data Set (B), not smaller.

## 20.

*x*is the total number of students. Solving for

*x*shows that there are 700 students in total. If 7% of the students are affected indirectly, as shown in the diagram, then (0.07)(700) = 49 students are affected indirectly.

## 21.

## 22.

*y*in the first equation into the second equation to get . Multiplying both sides by 30 to cancel the denominators gives 20

*x*+ 80 = 3

*x*– 15, which we can simplify to 17

*x*= –95, so

*x*= –95/17. Plugging this into either equation gives

*y*= –18/17.

## 23.

^{3}; the volume of package 2 is (6 in)(6 in)(4 in) = 144 in

^{3}. The efficiency of package 1 is 120/184 = 0.65; the efficiency of package 2 is 144/168 = 0.86. So, Package 2 is more efficient than Package 1 by approximately 0.20 cubic inches per square inch.

## 24.

## 25.

(A) is incorrect because sharing goals showed a greater increase in physical activity than participation on a sports team. (C) is incorrect because the control group did not decrease in physical activity over time. (D) is incorrect because although it may be true, this conclusion is not related to the data presented in the graph.

## 26.

Using process of elimination, you can see that (A) is incorrect because although there were fewer establishments in 2007 than in 2002, the value of shipments increased. (C) is incorrect because although there were fewer employees in 2007 than in 2002, the average pay increased. (D) is incorrect because although there were fewer establishments in 2007 than in 2002, there were more people employed.

## 27.

## 28.

## 29.

Using process of elimination, (A) is incorrect because the chart only presents some of the data collected, and does not incorporate other modes of transportation (subways, for example). You can confirm this by showing that no more than 7% of people combined walked or biked to work, so the other 93% of people must use other transportation.

(B) is incorrect because although the percentage of commuters who biked to work stayed about the same, the data does not show the number of commuters.

(C) is incorrect because by looking at the slope of each line segment, you can see that the percentage of commuters who walked to work actually decreased more slowly between 1990 and 2000 than between 1980 and 1990.

## 30.

*A*, then the triangle

*OAB*(where

*O*is the center of the circle) is isosceles, since two of its sides are radii of the circle (and so have length 10). This means that the angle

*BAO*is 50°, and so angle

*AOB*is 180° – 50° – 50° = 80°. Therefore, the angle

*AOC*is 180° – 80° = 100°. The circumference of the circle is 2π

*r*= 20π, so you know that . You can solve this to find that

*AC*= .

## 31.

*y*= 6, you can write 6 = 0.25

*x*+ 5, or 1 = 0.25

*x*. Multiplying both sides by 4 gives

*x*= 4.

## 32.

*x*= 70.

## 33.

## 34.

*f*(3) = 6(3) + 1 = 19, so the numerator of is 19. Then,

*f*(0) = 6(0) + 1 = 1. Plugging that in to

*g*(

*x*), you get g(1) = 2(1) – 1 = 1, so the denominator is 1. Finally, 19/1 = 19.

## 35.

## 36.

*m*= 162, and dividing by 9 gives

*m*= 18.