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

2 Choice A is correct
The correct answer is \(x \ < \ 3\) \(2 \ x \ + \ 4 \ > \ 11 \ x \  \ 12.5 \  \ 3.5 \ x→\) Combine like terms: \(2 \ x \ + \ 4 \ > \ 7.5 \ x \  \ 12.5→\) Subtract \(2 \ x\) from both sides: \(4 \ > \ 5.5 \ x \  \ 12.5\) Add \(12.5\) both sides of the inequality. \(16.5 \ > \ 5.5 \ x\), Divide both sides by \(5.5\). \(\frac{16.5}{5.5} \ > \ x→\) \(x \ < \ 3\)

3 Choice C is correct
The correct answer is \(97.6\) Area of a square: S \(= a^2 ⇒ 595.36 = a^2 ⇒ a = 24.4\) Perimeter of a square: P \(= 4 \ a ⇒\) P \(= 4 \ × \ 24.4 ⇒\) P \(= 97.6\)

4 Choice A is correct
The correct answer is \(2.25\) ft. Write the proportion and solve for the missing number. \(\frac{32}{12} = \frac{6}{x}→ \) \(32 \ x=6 \ × \ 12=72\) \(32 \ x=72→\) \(x=\frac{72}{32}=2.25\)

5 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 \(x=360⇒\) \(0.90\ x=360 ⇒\) \(x=360 \ ÷ \ 0.90=400\)

6 Choice C is correct
The correct answer is \(130\) The perimeter of the trapezoid is \(54\) cm. Therefore, the missing side (high) is \(= 54 \ – \ 18 \ – \ 12 \ – \ 14 = 10\) Area of a trapezoid: A \(= \frac{1}{2} \ h \ (b1 \ + \ b2) = \frac{1}{2} \ (10) \ (12 \ + \ 14) = 130\)

7 Choice C is correct
A graph represents y as a function of \(x\) if \(x_{1}=x_{2}→y_{1}=y_{2}\) In choice C, for each \(x\), we have two different values for \(y\).

8 Choice A is correct
The correct answer is \( \ 8 \ < \ x \ < \  \ 5\) \(13 \ < \  \ 3 \ x \  \ 2 \ < \ 22→\) Add \(2\) to all sides. \(13 \ + \ 2 \ < \  \ 3 \ x \  \ 2 \ + \ 2 \ < \ 22 \ + \ 2→\) \(15 \ < \  \ 3 \ x \ < \ 24→\) Divide all sides by \( \ 3\). (Remember that when you divide all sides of an inequality by a negative number, the inequality sing will be swapped. \(<\) becomes \(>\)) \(\frac{15}{ \ 3} \ > \ \frac{ \ 3 \ x}{ \ 3} \ > \ \frac{24}{ \ 3}\) \( \ 8 \ < \ x \ < \  \ 5\)

9 Choice B is correct
The correct answer is \(\frac{1}{6}\) Number of biology book: \(35\) Total number of books; \(35 \ + \ 95 \ + \ 80=210\) The ratio of the number of biology books to the total number of books is: \(\frac{35}{210}=\frac{1}{6}\)

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

11 Choice B is correct
The correct answer is \(16 \ π\) Use the formula for area 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 \(= 2 \ π \ r = 2 \ π \ (8) = 16 \ π\)

12 Choice D is correct
The correct answer is \((200) \ (0.85) \ (0.85)\) To find the discount, multiply the number by (\(100\% \ –\) rate of discount). Therefore, for the first discount we get: \((200) \ (100\% \ – \ 15\%) = (200) \ (0.85)\) For the next \(15\%\) discount: \((200) \ (0.85) \ (0.85)\)

13 Choice C is correct
The correct answer is Mathematics Compare each mark: In Algebra Joe scored \(20\) out of \(25\) in Algebra. It means Joe scored \(80\%\) of the total mark. \(\frac{20}{25} = \frac{x}{100} ⇒x= 80\%\) Joe scored \(30\) out of \(40\) in science. It means Joe scored \(75\%\) of the 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.

14 Choice C is correct
The correct answer is \(12\) m\(^3\) Use the volume of the triangular prism formula. \(V = \frac{1}{2} \) (length) (base) (high) \(V = \frac{1}{2} \ ×\ 4 \ × \ 3 \ × \ 2 ⇒ V = 12\) m\(^3\)

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

16 Choice D is correct
The correct answer is \((7, \  \ 9)\) When a point is reflected over \(x\) axes, the \((y)\) coordinate of that point changes to \(( \ y)\) while its \(x\) coordinate remains the same. C \((7, \ 9) →\) C’ \((7, \  \ 9)\)

17 Choice B is correct
The correct answer is \(0.97\) Ratio of women to men in city A: \(\frac{570}{600}=0.95 \) Ratio of women to men in city B: \(\frac{291}{300}=0.97 \) Ratio of women to men in city C: \(\frac{665}{700}=0.95 \) Ratio of women to men in city D: \(\frac{528}{550}=0.96\)

18 Choice D is correct
The correct answer is \(1.05\) Percentage of men in city A \(= \frac{600}{1170} \ × \ 100=51.28\% \) Percentage of women in city C \(= \frac{665}{1365} \ × \ 100=48.72\%\) Percentage of men in city A to percentage of women in city C \(= \frac{ 51.28}{48.72}=1.05 \)

19 Choice B is correct
The correct answer is \(12\) let \(x\) be the number of gallons of water the container holds when it is full. Then; \(\frac{7}{24} \ x=3.5→\) \(x=\frac{24 \ × \ 3.5}{7}=12\)

20 Choice C is correct
The correct answer is \(4\) \((3^a )^b=81→3^{a \ b}=81\) \(81=3^4→3^{a \ b}=3^4\) \(→a \ b=4\)

21 Choice A is correct
The correct answer is \(− \ 8 \ < \ x \ < \ − \ 5\) \(13 \ < \  \ 3 \ x \  \ 2 \ < \ 22→\) Add \(2\) to all sides. \(13 \ + \ 2 \ < \  \ 3 \ x \  \ 2 \ + \ 2 \ < \ 22 \ + \ 2\) \(→15 \ < \  \ 3 \ x \ < \ 24→\) Divide all sides by \( \ 3\). (Remember that when you divide all sides of an inequality by a negative number, the inequality sing will be swapped. \(<\) becomes \(>\)) \(\frac{15}{ \ 3} \ > \ \frac{ \ 3 \ x}{ \ 3} \ > \ \frac{24}{ \ 3}\) \( \ 8 \ < \ x \ < \  \ 5\)

22 Choice C is correct
The correct answer is \(\frac{5}{2}\) The value of y in the xintercept of a line is zero. Then: \(y=0→2 \ x \  \ 2 \ (0)=5 → 2 \ x=5→x=\frac{5}{2}\) then, \(x\)intercept of the line is \(\frac{5}{2}\)

23 Choice B is correct
The correct answer is \(x \ ≤ \ – \ 3\) Simplify: \(10 \ – \ \frac{2}{3} \ x \ ≥ \ 12 ⇒\) \(– \ \frac{2}{3} \ x \ ≥ \ 2 ⇒\) \(– \ x \ ≥ \ 3 ⇒\) \(x \ ≤ \ – \ 3\)

24 Choice A is correct
The correct answer is \(84\) \(120 \ × \ \frac{70}{100 }= 84\)

25 Choice B is correct
The correct answer is \(y = x \ + \ 1\) Solve for each equation: \((− \ 1, 2)\) A. \(y = 1 \ – \ x ⇒ 2 = 1 \ – \ (– \ 1) ⇒ 2 = 2\) B. \(y = x \ + \ 1 ⇒ 2 = \ – \ 1 \ + \ 1 ⇒ 2 ≠ 0\) C. \(x = \ – \ 1 ⇒ \ – \ 1 = \ – \ 1\) D. \(y = x \ + \ 3 ⇒ 2 = \ – \ 1 \ + \ 3 ⇒ 2 = 2\)

26 Choice C is correct
The correct answer is \((3, 18)\) \(y = 5 \ x \ – \ 3\) A. \((1, 2)\) \(⇒ 2 = 5 \ – \ 3 ⇒ 2 = 2\) B. \((–\ 2, – \ 13)\) \(⇒ \ – \ 13 = \ – \ 10 \ – \ 3 ⇒ \ – \ 13 = \ – \ 13\) C. \((3, 18)\) \(⇒ 18 = 15 \ – \ 3 ⇒ 18 ≠ 12\) D. \((2, 7)\) \(⇒ 7 = 10 \ – \ 3 ⇒7 = 7\)

27 Choice B is correct
The correct answer is \(35\) \(a \ + \ b \ + \ c = 45\) \(\frac{a \ + \ b \ + \ c \ + \ d}{4 }= 20 ⇒\) \(a \ + \ b \ + \ c \ + \ d = 80 ⇒\) \(45 \ + \ d = 80\) \(d = 80 \ – \ 45 = 35\)

28 Choice A is correct
The correct answer is \($2660\) \(45 \ × \ $124=$5580\) Payable amount is: \($8240 \  \ $5580=$2660\)

29 Choice C is correct
The correct answer is \(y = \frac{6}{7} \ x \ + \ \frac{12}{7}\) \( \ 7 \ y= \  \ 6 \ x \  \ 12⇒\) \(y=\frac{ \ 6}{ \ 7} \ x \  \ \frac{12}{ \ 7}⇒\) \(y=\frac{6}{7} \ x \ + \ \frac{12}{7}\)

30 Choice C is correct
The correct answer is \((1, 4)\) \(\begin{cases}5 \ x \ + \ y=9 \\10 \ x \  \ 7 \ y = \  \ 18\end{cases} ⇒ \) Multiply \((– \ 2)\) to the first equation \(\begin{cases} \ 10 \ x \  \ 2 \ y= \  \ 18 \\10 \ x \  \ 7 \ y = \  \ 18\end{cases} ⇒ \) Add two equations together \(⇒ \ – \ 9 \ y = \ – \ 36 ⇒ y = 4\), then: \(x = 1\)

31 Choice C is correct
The correct answer is \(2 \ x \ – \ y = 4\) If two lines are parallel with each other, then the slope of the two lines is the same. Then in line \(y=2 \ x\), the slope is equal to \(2\) And in the line \(2 \ x \  \ y=4⇒y=2 \ x \  \ 4\), the slope equal to \(2\)

32 Choice D is correct
The correct answer is \(11\) \(\frac{a \ + \ b}{2} = 8 ⇒ a \ + \ b = 16\) \(\frac{a \ + \ b \ + \ c}{3} = 9 ⇒ a \ + \ b \ + \ c = 27\) \(16 \ + \ c = 27 ⇒ c = 27 \ – \ 16 = 11\)

33 Choice C is correct
The correct answer is \(4 \ x \ – \ 2 \ y = 2 \ x\) \(4 \ x \ – \ 2 \ y = 2 \ x\) has a graph that is a straight line. All other options are not equations of straight lines.

34 Choice C is correct
The correct answer is \(5\) Use distance formula: C \(= \sqrt{(x_{A} \  \ x_{B})^2 \ + \ (y \  \ y_{B})^2 }\) C \(= \sqrt{(1 \  \ ( \ 2))^2 \ + \ (3 \  \ 7)^2 }\) C \(= \sqrt{(3)^2 \ + \ ( \ 4)^2 }\) C \(= \sqrt{9 \ + \ 16}\) C \(= \sqrt{25} = 5\)

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

36 Choice C is correct
The correct answer is \(30\) Let \(x\) be the number. Write the equation and solve for \(x\). \(\frac{2}{3} \ × \ 18= \frac{2}{5 }, x ⇒ \frac{2 \ × \ 18}{3}= \frac{2 \ x}{5}\), use cross multiplication to solve for \(x\). \(5 \ × \ 36=2 \ x \ × \ 3 ⇒180=6 \ x ⇒ x=30\)

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

38 Choice B is correct
The correct answer is \(36\) Let \(x\) be the smallest number. Then, these are the numbers: \(x, x \ + \ 1, x \ + \ 2, x \ + \ 3, x \ + \ 4\) average \(= \frac{sum \ of \ terms}{number \ of \ terms} ⇒\) \(38 = \frac{x \ + \ (x \ + \ 1) \ + \ (x \ + \ 2) \ + \ (x \ + \ 3) \ + \ (x \ + \ 4)}{5}⇒\) \(38=\frac{5 \ x \ + \ 10 }{5} ⇒ 190 = 5 \ x \ + \ 10 ⇒\) \(180 = 5 \ x ⇒ x=36\)

39 Choice B is correct
The correct answer is \(61.28\) average \(= \frac{sum \ of \ terms}{number \ of \ terms}\) The sum of the weight of all girls is: \(18 \ × \ 60 = 1080\) kg The sum of the weight of all boys is: \(32 \ × \ 62 = 1984\) kg The sum of the weight of all students is: \(1080 \ + \ 1984 = 3064\) kg average \(= \frac{3064}{50} = 61.28\)

40 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 \(x=360⇒ 0.90 \ x=360 ⇒ x=360 \ ÷ \ 0.90=400\)
