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## Question Explanations For

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*MATH (CALCULATOR) (MATH (CALCULATOR))*

## 1.

The Correct Answer is (B) —
We can solve this problem by plugging in the value given for y in order to solve for x. x = 2(x - 2) + 4. Simplify x = 2x - 4 + 4. Simplify further x = 0. The correct answer is (B).

## 2.

The Correct Answer is (B) —
The equation for a line can be represented by f(x) = mx + b where b is the y-intercept (where x equals zero and the line crosses the y-axis). From the table we know when x = 0, f(x) = 3. The y-intercept is 3 so we can eliminate answers (C) and (D). Plug in the next coordinates for answer (A) 4 does not equal 2 + 3, so knock out (A). The correct answer is (B). Double-check that the coordinates make the expression true.

## 3.

The Correct Answer is (B) —
We can set up an algebraic ratio of pigs/acres to solve the problem. Cross multiply 8 pigs/1.5 acres = x pigs/6 acres. 48 = 1.5x. x = 48/1.5 = 32, the answer is (B).

## 4.

The Correct Answer is (B) —
We can cross multiply to get 4(x - 1) = 3(2x - 6). Simplify 4x - 4 = 6x -18. Subtract 4x from both sides of the equations and add 18 to both sides of the equation. 14 = 2x, x = 7. The correct answer is (B).

## 5.

The Correct Answer is (D) —
The population(p) = current population x 2 every 5 years. So, the initial population is 300, in 5 years the population will be 600, in 5 more years the population will be 1200, in 5 more years the population will be 2400. The correct answer is (D).

## 6.

The Correct Answer is (C) —
We know there are 180 degrees in a triangle. Therefore angle ACB = 180 degrees - 30 degrees - 40 degrees = 110 degrees. Angles on one side of a straight line will always add up to 180 degrees. We know angle BCE = 180 degrees - 110 degrees = 70 degrees. Because we know that line BC is parallel to line DE, we know that the value of angle BCE = the value of angle x. Answer (C) is correct.

## 7.

The Correct Answer is (A) —
We can write out 2 equations to represent the word problem: 10b + 7m = $50.95 and m = b - 0.25. Solve for b in terms of m in the second equation: b = m + $0.25. Plug this value of b back into the first equation in order to solve for price of a chocolate milkshake. Simplify 10(m + $0.25) + 7m = $50.95 = 10m + $2.50 + 7m = $50.95 = 17m + $2.50 = $50.95. Subtract $2.50 from both side of the equation. 17m = $48.45, divide each side of the equation by 17, m = $2.85, the correct answer is (A).

## 8.

The Correct Answer is (B) —
We know the 3 angles of a triangle add up to 180 degrees. A right triangle has an angle of 90 degrees so the remaining acute angles must add up to 90 degrees. The problem gives us the ratio of 12/3 so we can set up the equation 12/3 = (90 –x)/x to solve for the value of the smaller acute angle. Cross multiply and we get 12x = 270 – 3x = 15x = 270. Divide each side of the equation by 15 and we get x = 18 degrees which is the smaller acute angle. The larger acute angle = 90 – x = 90 – 18 = 72 degrees. The question is asking for the difference in the two angles measures. Subtract 18 from 72 and we get 54 degrees. The answer is (B).

## 9.

The Correct Answer is (D) —
The fastest way to solve this problem is by plugging in the answer choices to the inequality. Plugging in -3, -2, or -1 to the inequality makes it false. Plugging 0 into the inequality we get 0 times 0 – 1 < 0 times 0 times 0. 0 multiplied by any number is 0. This inequality is true -1 < 0. The correct answer is therefore (D).

## 10.

The Correct Answer is (C) —
We can solve for y by plugging in 12 as the value for x in the second equation. 3(12) = 4y^2. Multiply 3 and 12 and we get 36 = 4y^2. Divide both sides of the equation by 4 and we get 9 = y^2. Take the square root of each side of the equation and we get 3 = y. The question is asking for the value of x^2y. Plug in x =12 and y =3 and we get 12 times 12 times 3 = 432. The correct answer is (C).

## 11.

The Correct Answer is (B) —
The likelihood of choosing any one of the three numbers on the first selection is 3/5. When choosing the second number, 2 out of 4 of the remaining numbers are the correct ones, so the likelihood of selecting 1 of the 2 is 2/4. The likelihood of selecting the last number from the remaining 3 numbers is then 1/3. We can calculate the likelihood of all 3 of these events occurring to be (3/5)(2/4)(1/3)= 6/60 = 1/10. This means that (B) is correct.

## 12.

The Correct Answer is (B) —
The ratio of d:c can be rewritten as d/c = 3/1. The second sentence tells us that d + c = s. We are looking for d in terms of s, so we are looking to get rid of the variable c. We can isolate c in the first equation and substitute its value into the second equation. Substituting c=d/3, we get d + d/3 = s. Adding the terms on the left side, we get (4d/3)= s, and dividing both sides by 4/3, we get d= (3/4)s. (B) is the correct answer.

## 13.

The Correct Answer is (B) —
According to the table, 75.75% of juniors drink 2 or more cups of coffee per day. From here, the simplest thing to do is to estimate the fraction fraction of Seniors who drink 2 or more cups of coffee, in order to determine that it is a higher percentage (94.1%, to be precise).
All the other answer choices are true, which makes (B) the only answer choice not supported by the table.

## 14.

The Correct Answer is (C) —
When we model this like a linear function, we see that the y-intercept is 1500. We can then eliminate (A) and (B), which do not have this y-intercept. The number of passengers increase by 100 with each month, so we know m is multiplied by 100 in the function, which gives us (C) as the correct answer.

## 15.

The Correct Answer is (C) —
We can solve this question by setting up a system of equations with the information given in the question. A ratio of (j + n):k = 1:3 can be written as the fraction (j+n)/k=1/3. The ratio of n:(j +k) can also be written as a fraction, but this time we can set the proportion of (j + n) to 100, giving us n/(j+n)=x/100, where x is n expressed as a percentage of j + n. Plugging in our given values for j and k into equation 1, we get (925+n)/5550=1/3. We can then multiply both sides by 5550 and subtract both sides by 925 to solve for n. This gives us n = 925. Plugging in the values of n and j into equation 2, we get 925/(925+925)=x/100. Multiplying both sides by 100 to solve for x, we get x = 50, which means n is 50% of (j + n). (C) is thus the correct answer.

## 16.

The Correct Answer is (A) —
We can first find the average number of languages offered across the 20 schools, which is ((1×0)+(3×1)+(5×2)+(8×3)+(2×4)+(1×5))/20 = 2.5. This means that any school offering 2 languages or less offer fewer than the average. We can see from the graph that 1 school offers 0 languages, 3 offer 1, and 5 offer 2. This makes it a total of 1 + 3 + 5 = 9 schools that offer fewer languages than the average. (A) is the correct choice.

## 17.

The Correct Answer is () —
We can first expand the brackets to get –30 – 15n = –16n + 112. Isolating all the terms containing n to one side, we get –15n + 16n = 112 + 30. Simplifying this, we get n = 142.

## 18.

The Correct Answer is () —
We know that the angles within the rectangle are all right angles, so the larger triangles created by the diagonal lines are right-angle triangles. If 2 of the sides are 3 and 4, this makes the triangle with the diagonal line as its hypotenuse a 3:4:5 triangle. We can extrapolate from this that the length of the diagonal line is 5. There are 2 solid lines with a length of 3 and 2 solid lines with a length of 5. Therefore, the total length of the solid lines is 2 × 3 + 2 × 5 = 16.

## 19.

The Correct Answer is (117) —
First, plug the initial values for

*P*and*V*into the equation*PV*=*k*to find that*k*= 78 kPa × 30 cm^{3}= 2,340. Using the same equation, plug in the new volume (20 cubic centimeters) and the*k*value to solve for*P*:*P*× 20 = 2,340

*P*= 117 kPa

## 20.

The Correct Answer is (80) —
First, calculate the

*k*value for the gas in each syringe by using the formula*PV*=*k*. For syringe A,*k*= 50 × 15.6 = 780. For syringe B,*k*= 40 × 15.6 = 624.Now, plug the new volume (30 cubic centimeters) for each syringe into their respective equations to solve for pressure:

Therefore, the new pressure in B as a percent of A is^{20.8}⁄_{26}× 100% = 80%.