1 Choice C is correct
The correct answer is \(39 \ π\) cm\(^2\) To find the area of the shaded region, find the difference of the area of two circles. (S\(_{1}\): the area of bigger circle. S\(_{2}\): the area of the smaller circle) Use the area of circle formula. S \(= π \ r^2\) S\(_{1} \ \) S\(_{2} = π \ ( 5 \ + \ 3\)cm)\(^2 \  \ π \ (5\) cm)\(^2 ⇒\) S\(_{1} \ \) S\(_{2} = π \ 64\) cm\(^2 \  \ π \ 25\) cm\(^2 ⇒\) S\(_{1} \ \) S\(_{2} = 39 \ π\) cm\(^2\)

2 Choice D is correct
The correct answer is \(\frac{5}{8}\) William ate \(\frac{1}{4}\) of \(8\) parts of his pizza that it means \(2\) parts out of \(8\) parts ( \(\frac{1}{4}\) of \(8\) parts \(= x ⇒ x = 2\)) and left \(6\) parts. Ella ate \(\frac{1}{2}\) of \(8\) parts of her pizza that it means \(4\) parts out of \(8\) parts ( \(\frac{1}{2}\) of \(8\) parts \(= x ⇒ x = 4\)) and left \(4\) parts. Therefore, they ate \((4 \ + \ 2)\) parts out of \((8 \ + \ 8)\) parts of their pizza and left \((6 \ + \ 4)\) parts out of \((8 \ + \ 8)\) parts of their pizza. It means: \(\frac{ 10}{16}\) After simplification we have: \(\frac{5}{8}\)

3 Choice D is correct
The correct answer is \(48 \ x^8 \ y^6\) Simplify. \(3 \ y^2 \ (2 \ x^2 \ y)^4=\) \(3 \ y^2 \ (16 \ x^8 \ y^4 ) =\) \(48 \ x^8 \ y^6\)

4 Choice D is correct
The correct answer is \(17\) cm Use Pythagorean Theorem: \(a^2 \ + \ b^2 = c^2\) \(8^2 \ + \ 15^2 = c^2 ⇒\) \(64 \ + \ 225 = c^2 ⇒\) \(c^2 =289 ⇒\) \(c=17\)

5 Choice B is correct
The correct answer is \(0.88\) D To find the discount, multiply the number by (\(100\% \ –\) rate of discount). Therefore, for the first discount we get: (D) \((100\% \ – \ 20\%) =\) (D) \((0.80) = 0.80\) D For increase of \(10\%: \ (0.80\) D) \((100\% \ + \ 10\%) = (0.85\) D) \( (1.10) = 0.88\) D \(= 88\%\) of D

6 Choice D is correct
The correct answer is \(– \ 126\) Use PEMDAS (order of operation): \(\left[ \ 6 \ × \ (– \ 24) \ + \ 12 \ \right] \ – \ (4) \ + \ \left[ \ 4 \ × \ 5 \ \right] \ ÷ \ 2 =\) \(\left[ \ – \ 144 \ + \ 12 \ \right] \ – \ 4 \ + \ \left[ \ 20 \ \right] \ ÷ \ 2 =\) \(\left[ \ – \ 144 \ + \ 12 \ \right] \ – \ 4 \ + \ 10 =\) \(\left[ \ – \ 132 \ \right] \ – \ 4 \ + \ 10 = \left[ \ – \ 132 \ \right] \ – \ 4 \ + \ 10 = – \ 126\)

7 Choice B is correct
The correct answer is \(16 \ π\) Use the formula of areas of circles. Area \(= π \ r^2 ⇒\) \(64 \ π = π \ r^2 ⇒\) \(64 = r^2 ⇒ r = 8\) Radius of the circle is \(8\). Now, use the circumference formula: Circumference \(= 2 \ π \ r = 2 \ π \ (8) = 16 \ π\)

8 Choice B is correct
The correct answer is \(30\%\) Use the formula for Percent of Change \(\frac{New \ ValueOld \ Value}{Old \ Value} \ × \ 100\%\) \(\frac{28 \  \ 40}{40} \ × \ 100\% = \ – \ 30\%\) (negative sign here means that the new price is less than old price).

9 Choice C is correct
The correct answer is \(140\%\) The question is this: \(1.75\) is what percent of \(1.25\)? Use percent formula: part \(= \frac{percent}{100} \ ×\) whole \(= \frac{percent}{100} \ × 1.25 ⇒\) \(1.75 = \frac{percent \ × \ 1.25}{100} ⇒\) \(175 =\) percent \(× \ 1.25 ⇒\) percent \(= \frac{175}{1.25} = 140\)

10 Choice A is correct
The correct answer is \(10\%\) Let \(x\) be the amount of students in the class. \(40\%\) of \(x =\) girls \(25\%\) of girls \(=\) tennis player Find \(25\%\) of \(40\%\). Then: \(25\%\) of \(40\%=0.25 \ × \ 0.40=0.10=10\%\)

11 Choice B is correct
The correct answer is \(28\) Write the numbers in order: \(2, \ 19, \ 28, \ 28, \ 35, \ 44, \ 67\) Since we have \(7\) numbers (\(7\) is odd), then the median is the number in the middle, which is \(28\).

12 Choice C is correct
The correct answer is \(60000\) Three times of \(24,000\) is \(72,000\). One sixth of them cancelled their tickets. One sixth of \(72,000\) equals \(12,000 (1/6 \ × \ 72000 = 12000)\). \(60,000 (72000 \ – \ 12000 = 60000)\) fans are attending this week

13 Choice A is correct
The correct answer is \(7\) Write the ratio and solve for \(x\). \(\frac{45}{40} =\frac{2 \ x \ + \ 4}{16} ⇒\) \(40 \ (2 \ x \ + \ 4)=45 \ × \ 16 ⇒ x=7\)

14 Choice B is correct
The correct answer is \(8 \ (4 \ − \ x)=96\) Only option B is correct. Other options don’t work in the equation. \(8 \ (4 \  \ ( \ 8))=96\)

15 Choice A is correct
The correct answer is \(8\) Let \(x\) be the number of balls. Then: \(\frac{1}{3} \ x \ + \ \frac{1}{6} \ x \ + \ \frac{1}{4} \ x \ + \ 12 = x\) \((\frac{1}{3} \ + \ \frac{1}{6} \ + \ \frac{1}{4}) \ x \ + \ 12 = x\) \((\frac{9}{12}) \ x + 12 = x\) \(x = 48\) In the bag of small balls \(\frac{1}{6}\) are white, then: \(\frac{48}{6} = 8\) There are \(8\) white balls in the bag.

16 Choice B is correct
The correct answer is \(50\) Use the information provided in the question to draw the shape. Use Pythagorean Theorem: \(a^2 \ + \ b^2 = c^2\) \(40^2 \ + \ 30^2 = c^2 ⇒\) \(1600 \ + \ 900 = c^2 ⇒\) \(2500 = c^2 ⇒\) \(c = 50\)

17 Choice B is correct
The correct answer is \(15\%\) The question is this: \(530.40\) is what percent of \(624\)? Use percent formula: part \(= \frac{percent}{100} \ ×\) whole \(530.40 =\frac{ percent}{100} \ × 624 ⇒\) \(530.40 = \frac{percent \ × \ 624}{100} ⇒\) \(53040 =\) percent \(× \ 624 ⇒\) percent \(= \frac{53040}{624 }= 85\) \(530.40\) is \(85\%\) of \(624\). Therefore, the discount is: \(100\% \ – \ 85\% = 15\%\)

18 Choice B is correct
The correct answer is \(15\) If the score of Mia was \(60\), then the score of Ava is \(30\). Since, the score of Emma was half as that of Ava, therefore, the score of Emma is \(15\).

19 Choice D is correct
The correct answer is \(\frac{17}{18}\) If \(17\) balls are removed from the bag at random, there will be one ball in the bag. The probability of choosing a brown ball is \(1\) out of \(18\). Therefore, the probability of not choosing a brown ball is \(17\) out of \(18\) and the probability of having not a brown ball after removing \(17\) balls is the same.

20 Choice C is correct
The correct answer is \(7.32\) The weight of \(12.2\) meters of this rope is: \(12.2 \ × \ 600\) g \(= 7320\) g \(1\) kg \(= 1000\) g, therefore, \(7320\) g \(÷ \ 1000 = 7.32\) kg

21 Choice C is correct
The correct answer is \(600\) ml \(4\%\) of the volume of the solution is alcohol. Let \(x\) be the volume of the solution. Then: \(4\%\) of \(x = 24\) ml \(⇒\) \(0.04 \ x = 24 ⇒\) \(x = 24 \ ÷ \ 0.04 = 600\)

22 Choice C is correct
The correct answer is \(400\) Let \(x\) be the original price. If the price of a laptop is decreased by \(10\%\) to \($360\), then: \(90\%\) of \(x=360 ⇒\) \(0.90 \ x=360 ⇒\) \(x=360 \ ÷ \ 0.90=400\)

23 Choice B is correct
The correct answer is \(9\) Write the numbers in order: \(4, \ 5, \ 8, \ 9, \ 13, \ 15, \ 18\) Since we have \(7\) numbers (\(7\) is odd), then the median is the number in the middle, which is \(9\).

24 Choice A is correct
The correct answer is \($300\) Let \(L\) be the price of laptop and \(C\) be the price of computer. \(3 \ (L) =5 \ (C)\) and \(L = $200 \ + \ C\) Therefore, \(3 \ ($200 \ + \ C) =5 \ C ⇒\) \($600 \ + \ 3C = 5C ⇒\) \(C=$300\)

25 Choice C is correct
The correct answer is \(97.6\) Use the area of square formula. S \(= a^2 ⇒ 595.36 = a^2 ⇒ a = 24.4\) One side of the square is \(24.4\) feet. Use the perimeter of square formula. P \(= 4 \ a ⇒\) P \(= 4(24.4) ⇒\) P \(= 97.6\)

26 Choice C is correct
The correct answer is \(6\) hours The distance between Jason and Joe is \(9\) miles. Jason running at \(5.5\) miles per hour and Joe is running at the speed of \(7\) miles per hour. Therefore, every hour the distance is \(1.5\) miles less. \(9 \ ÷ \ 1.5 = 6\)

27 Choice D is correct
The correct answer is \(80\%\) The failing rate is \(11\) out of \(55 = \frac{11}{55}\) Change the fraction to percent: \(\frac{11}{55} \ × \ 100\%=20\%\) \(20\) percent of students failed. Therefore, \(80\) percent of students passed the exam.

28 Choice C is correct
The correct answer is \(60\) Jason needs an \(75\%\) average to pass for five exams. Therefore, the sum of \(5\) exams must be at least \(5 \ × \ 75 = 375\) The sum of \(4\) exams is: \(68 \ + \ 72 \ + \ 85 \ + \ 90 = 315\). The minimum score Jason can earn on his fifth and final test to pass is: \(375 \ – \ 315 = 60\)

29 Choice B is correct
The correct answer is \(840\) Use simple interest formula: \(I = prt\) (\(I =\) interest, \(p =\) principal, \(r =\) rate, \(t =\) time) \(I=(12000) \ (0.035) \ (2)=840\)

30 Choice D is correct
The correct answer is \(44\) Let \(x\) be the integer. Then: \(2 \ x \ – \ 5 = 83\) Add \(5\) both sides: \(2 \ x = 88\) Divide both sides by \(2: \ x = 44\)

31 Choice B is correct
The correct answer is \(( \ 1, \ 3)\) Input the points instead of \(x\) and \(y\) in the formula. Only option B works in the equation. \(4 \ x \ + \ 6 \ y=14\) \(4 \ (– \ 1) \ + \ 6 \ (3) =14\)

32 Choice C is correct
The correct answer is \(90\) To find the number of possible outfit combinations, multiply number of options for each factor: \(6 \ × \ 3 \ ×\ 5 = 90\)

33 Choice B is correct
The correct answer is \(30\) The sum of supplement angles is \(180\). Let \(x\) be that angle. Therefore, \(x \ + \ 5 \ x = 180\) \(6 \ x = 180\), divide both sides by \(6: \ x = 30\)

34 Choice C is correct
The correct answer is \(5 : 9\) The average speed of John is: \(150 \ ÷ \ 6 = 25\) km The average speed of Alice is: \(180 \ ÷ \ 4 = 45\) km Write the ratio and simplify. \(25: 45 ⇒ 5: 9\)

35 Choice C is correct
The correct answer is \(210\) Let \(x\) be the number of soft drinks for \(252\) guests. It’s needed to have a proportional ratio to find \(x\). \(\frac{10 \ soft \ drinks}{12 \ guests} = \frac{x}{252 \ guests}\) \(x = \frac{252 \ × \ 10}{12 }⇒x=210\)

36 Choice B is correct
The correct answer is \($23.8\) Let \(x\) be the number of cans. Write a proportion and solve for \(x\). \(\frac{5 \ cans}{$3.40) }= \frac{35 \ cans}{x}\) \(x =\frac{3.40\ × \ 35}{5} ⇒x=$23.8\)

37 Choice B is correct
The correct answer is \(5\) \(x\%\) of \(24\) is \(1.2\), then: \(x\% 24 =1.2 ⇒\) \(0.24 \ x=1.2 ⇒\) \(x=1.2 \ ÷ \ 0.24=5\)

38 Choice C is correct
The correct answer is Mathematics Compare each score: In Algebra Joe scored \(20\) out of \(25\) in Algebra that it means \(80\%\) of total mark. \(\frac{20}{25} = \frac{x}{100} ⇒x= 80\) Joe scored \(30\) out of \(40\) in science that it means \(75\%\) of total mark. \(\frac{30}{40} = \frac{x}{100} ⇒x= 75\) Joe scored \(68\) out of \(80\) in mathematic that it means \(85\%\) of total mark. \(\frac{68}{80} = \frac{x}{100} ⇒x= 85\) Therefore, his score in mathematic is higher than his other scores.

39 Choice C is correct
The correct answer is \(480\) m\(^3\) Use the volume of square pyramid formula. \(V= \frac{1}{3} \ a^2 \ h ⇒\) \(V= \frac{1}{3} \ (12\) m)\(^2 \ × \ 10\) m \(⇒ V= 480\) m\(^3\)

39 Choice C is correct
The correct answer is \(480\) m\(^3\) Use the volume of square pyramid formula. \(V= \frac{1}{3} \ a^2 \ h ⇒\) \(V= \frac{1}{3} \ (12\) m)\(^2 \ × \ 10\) m \(⇒ V= 480\) m\(^3\)
