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## Question Explanations For

##
* Test (Math Test - Calculator)*

## 1.

*f*(0) by plugging in 0 for

*x*to get

*f*(0) = 0 + 1 = 1. Similarly,

*g*(0) = 0 – 4 = –4, so

*f*(0) ×

*g*(0) = 1 × (–4) = –4

*x*.

## 2.

If you got (B), you found the number of novels Virginia Woolf wrote and stopped there.

## 3.

*x*represents the number of citizens of Omaha who read 3 or more books per month, and solve to find

*x*= 105,000.

## 4.

The printer conveniently prints at a rate of 300 pages per hour, so it will take one hour to print 300 pages.

## 5.

^{12}⁄

_{20}= 60% , so (C) is true. However, the median of this data set is 3; there are 1 + 7 + 8 + 4 = 20 students surveyed in total, so the middle value is the average of the 10th and 11th student, both of whom spent 3 hours a day on the internet. Therefore, (D) is false, so it is the correct answer.

## 6.

## 7.

*x*increases, so does

*y*). It crosses the

*y*-axis below the

*x*-axis, so it has a negative

*y*-intercept. The line in option (C) has a slope of 2 and a

*y*-intercept of –1, and it is the only answer option that has a positive slope and a negative

*y*-intercept.

## 8.

## 9.

^{–3}⁄

_{2}. Since a rat in the control group produces 41 mL of urine per day, the

*y*-intercept of this linear relationship is 41, so it can be modeled by the equation

*y*= (

^{–3}⁄

_{2})

*x*+ 41, where

*x*is the amount of tannin given to a rat and

*y*is the amount of urine produced. Plugging in

*x*= 11 gives you

*y*= 24.5 milliliters of urine in a day.

## 10.

*x*equal the dose of tannin, then the amount of sodium can be modeled by the expression 0.1

*x*+ 1.6 and the amount of potassium can be modeled by the expression 0.2

*x*+ 0.3. These will be equal when 0.1

*x*+ 1.6 = 0.2

*x*+ 0.3, which you can solve to get

*x*= 13.

## 11.

(C) and (D) are incorrect because the question tells you nothing about the number of students at each university.

## 12.

*x*represents the store's original stock, you know that 36 = 0.4

*x*, because 36 pieces was 40% of the stock. Dividing both sides by 0.4 gives you

*x*= 90. Since the question is asking for the remaining stock, you can subtract 36 from 90 to get 90 – 36 = 54 pieces still in the store.

If you got (D), you found the number of pieces total in the store before any were bought.

## 13.

*y*-intercept of the line will be positive. Option (C) is the only choice that satisfies these conditions.

## 14.

^{90}⁄

_{2}= 45 grams of fat, which would be a total of 135 grams. However, she needs to eat more than 135 grams of these combined per day, so this is not possible.

## 15.

## 16.

*x*

^{2}– 81, so

*a*= 0 and

*b*= –81. Therefore,

*ab*= 0 × –81 = 0.

## 17.

*⁄*

^{xy}_{xy}and cancel out so that the denominators of each of the terms are the same:

## 18.

## 19.

*f*(2) = 3, you know that (2, 3) is a point on the line. The line also passes through the point (–6, –13), so you can find the slope of the line by dividing the difference in

*y*-values by the difference in

*x*-values: . You can then solve for the

*y*-intercept,

*b*, by plugging either point into the equation

*y*= 2

*x*+

*b*to get 3 = 2(2) +

*b*, so

*b*= –1.

## 20.

*x*and 4

*x*, meaning their hypotenuses must each have length 5

*x*, using the Pythagorean Theorem. The semicircle at the top has diameter 6

*x*, so it has a circumference of

^{6πx}⁄

_{2}= 3π

*x*. In total, the perimeter of the shape is 5

*x*+ 5

*x*+ 3π

*x*= 10

*x*+ 3π

*x*.

## 21.

*x*:

## 22.

^{2}⁄

_{(2+1)}=

^{2}⁄

_{3}. Since the chance that the female will reproduce asexually is 75%, the overall chance that a male will be born is

^{2}⁄

_{3}× 0.75 = 0.5

## 23.

*s*= 0.2(4,500 +

*s*) and solve to get

*s*= 1,125. Next, since you know the total number of 16-ounce cans sold, you can set 1,525 +

*m*+ 1,125 = 3,000 and find that

*m*= 350.

## 24.

*x*+ 2)

^{2}= 4, you know that

*x*+ 2 = 2 or

*x*+ 2 = –2. Solving these equations gives you

*x*= 0 or

*x*= –4, and of these, only –4 is an answer option.

## 25.

*b*, by using the given TD:INT ratio for him: 1.53 =

^{508}⁄

_{b}, so

*b*=

^{508}⁄

_{1.53}= 332. You can use the same process to find the number of interceptions thrown by Peyton Manning,

*p*: 2.13 =

^{539}⁄

_{p}, so

*p*=

^{539}⁄

_{2.13}= 253, which is a difference of 332 - 253 = 79.

## 26.

*y*-coordinate of this dot to find that Joe Montana passed just over 40,000 yards in his career. The only answer choice that is close to this is 40,500, so (C) is correct.

## 27.

## 28.

## 29.

^{3}⁄

_{√3}= √3.

## 30.

*a*is positive. Since the

*y*-intercept of the parabola is positive, you know that

*c*is positive. Therefore,

*ac*must be positive since it is the product of two positive numbers.

(A) is incorrect since *b* must be negative, because at some positive *x*-value the function is negative, but *ax*^{2} and *c* are both still positive, so *bx* must be negative, meaning *b* is negative.

(B) is incorrect because *b* – *a* is a negative number minus a positive number, which will always be negative.

(C) is incorrect because *c* is positive, so -*c* is negative.

## 31.

## 32.

^{2016}⁄

_{3}= 672 molecules of nitrogen trifluoride.

## 33.

*A*+

*B*+

*C*+

*D*= 15. You can then add the bottom two equations together to find that

*A*+

*B*+

*C*+

*D*= 5

*x*, so you know 5

*x*= 15, meaning

*x*= 3.

## 34.

Now that both sides have the same denominator of , you can set the numerators equal to each other to get . Since the question gives you the value of *A*, you can start by plugging in 2.5 where *A* appears. It may help to then multiply each term by 2 to eliminate the decimal in the coefficient 2.5:

From here, distribute the 5 and move the resulting terms to the left side of the equation:

You should now notice that also shares the factor , so you can factor the left side of the equation and divide both sides by :

You now know that . Therefore,

## 35.

The total distance she ran in an hour is *M* + *N*, which will be 1(6) + 0.5(1 – 0.5)(2) = 6.5 miles.

Alternately, you can recognize that her speed in mph is equal to the distance, miles, divided by time, hours. So, the distance can be found by multiplying the speed by the time. You can see that she ran 3 miles in the first half hour, because .5 hours × 6 mph = 3 miles. In the second half hour, she starts at 6mph and ends at 8mph, making her average speed 7mph. So, .5 hours × 7 mph = 3.5 miles. Finally, 3 miles + 3.5 miles = 6.5 miles.

## 36.

^{60°}⁄

_{360°}=

^{1}⁄

_{6}of the circle’s area, meaning that the circle has an area of 24π × 6 = 144π . Since

*A*= π

*r*

^{2}, the radius of the circle is √144 = 12.

## 37.

^{300}⁄

_{6}= 50 problems presented in one trial.

## 38.

^{60}⁄

_{50}= 1.20 times as many questions correctly as Participant 2, which is a percentage growth of 20%.