| 1- Choice A is correct
The correct answer is \(200\%\)
Write the equation and solve for B:
\(0.50\) A \(= 0.25\) B, divide both sides by \(0.25\), then:
\(0.65/0.25\) A \(=\) B, therefore:
B \(=2\) A, and B is \(2\) times of A or it’s \(200\%\) of A.
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| 2- Choice B is correct
The correct answer is \(16\)
average \(= \frac{sum \ of \ terms}{ number \ of \ terms}=\frac{17 \ + \ 13 \ + \ 7 \ + \ 21 \ + \ 22}{5} = 805 = 16\)
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| 3- Choice A is correct
The correct answer is \(2 : 1\)
The average speed of john is: \(180 \ ÷ \ 3=60 \) km\(/\)h
The average speed of Alice is: \(270 \ ÷ \ 9=30\) km\(/\)h
Write the ratio and simplify.
\(60 : 30 ⇒ 2 : 1\)
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| 4- Choice A is correct
The correct answer is \(1728\) cm\(^3\)
If the length of the box is \(36\), then the width of the box is one third of it, \(12\), and the height of the box is \(4\) (one third of the width).
The volume of the box is:
V \(=\) lwh \(= (36) \ (12) \ (4) = 1728\)
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| 5- Choice D is correct
The correct answer is \(5\)
Let \(x\) be the number.
Write the equation and solve for \(x\).
\((25 \ – \ x) \ ÷ \ x = 4\)
Multiply both sides by \(x\).
\((25 \ – \ x) = 4 \ x\), then add both sides.
\(25 = 5 \ x \), now divide both sides by 5.
\(x = 5\)
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| 6- Choice D is correct
The correct answer is \(2,401\)
\(7^4=7 \ × \ 7 \ × \ 7 \ × \ 7=2,401\)
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| 7- Choice A is correct
The correct answer is \(90\%\)
Use percent formula: part \(=\frac{ percent}{100} \ × \) whole
\(27=\frac{percent}{100} \ × \ 30 ⇒\)
\(27=\frac{ percent \ × \ 30}{100} ⇒\)
\(27=\frac{percent \ × \ 3}{10}\), multiply both sides by \(10\).
\(270=\) percent \(× \ 3\), divide both sides by \(3\).
\(90= \) percent
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| 8- Choice D is correct
The correct answer is \(13\) cm
Use Pythagorean Theorem: \(a^2 \ + \ b^2=c^2\)
\(5^2 \ + \ 12^2 = c^2 ⇒\)
\(25 \ + \ 144=c^2 ⇒\)
\(169=c^2⇒\)
\(c=13\) cm
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| 9- Choice A is correct
The correct answer is \(20^\circ\)
The sum of supplement angles is \(180\).
Let \(x\) be that angle.
Therefore, \(x \ + \ 8\ x = 180\)
\(9 \ x = 180\), divide both sides by \(9: \ x = 20^\circ\)
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| 10- Choice D is correct
The correct answer is \(420\)
Add the first \(5\) numbers.
\(35 \ + \ 40 \ + \ 45 \ + \ 25 \ + \ 50 = 195\)
To find the distance traveled in the next \(5\) hours, multiply the average by number of hours.
Distance \(=\) Average \(×\) Rate \(= 45 \ × \ 5 = 225\)
Add both numbers.
\(225 \ + \ 195 = 420\)
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| 11- Choice B is correct
The correct answer is \($80\)
\($12×8=$96\), Petrol use: \(8 \ × \ 2=16\) liters
Petrol cost: \(16 \ × \ $1=$16\)
Money earned: \($96 \ − \ $16=$80\)
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| 12- Choice D is correct
The correct answer is \(9\) hours and \(30\) minutes
Use distance formula: Distance \(=\) Rate \(×\) time \(⇒ 380 = 40 \ ×\) T, divide both sides by \(40\).
\(380 / 40 =\) T \(⇒\) T \(= 9.5\) hours.
Change hours to minutes for the decimal part.
\(0.5\) hours \(= 0.5 \ × \ 60 = 30\) minutes.
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| 13- Choice A is correct
The correct answer is \(50\%\)
Use the formula for Percent of Change \(\frac{New \ Value \ − \ Old \ Value}{old \ value} \ × \ 100\%\)
\(\frac{25−50}{50} \ × \ 100\%= \ – \ 50\%\) (Negative sign here means that the new price is less than old price).
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| 14- Choice A is correct
The correct answer is \(15\)
The ratio of boy to girls is \(3:8\). Therefore, there are \(3\) boys out of \(11\) students.
To find the answer, first divide the total number of students by \(11\), then multiply the result by \(3\).
\(55 \ ÷ \ 11=5 ⇒ 5 \ × \ 3=15\)
There are \(15\) boys and \(30 \ (55 \ – \ 15)\) girls.
So, \(15\) more boys should be enrolled to make the ratio \(1:1\)
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| 15- Choice B is correct
The correct answer is \(9.240\) kg
The weight of \(13.2\) meters of this rope is: \(13.3 \ × \ 700\) g \(=9,240\) g
\(1\) kg \(= 1,000\) g, therefore, \(9,240\) g \(÷ \ 1000=9.24\) kg
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| 16- Choice C is correct
The correct answer is \(64\) kg
average \(=\frac{sum \ of \ terms}{ number \ of \ terms}\)
The sum of the weight of all girls is: \(15 \ × \ 60=900\) kg
The sum of the weight of all boys is: \(30 \ × \ 66=1,980\) kg
The sum of the weight of all students is: \(900 \ + \ 1,980=2,880\) kg
average \(=\frac{2,880}{45}=64\)
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| 17- Choice D is correct
The correct answer is \(15\)
Some of prime numbers are: \(2, 3, 5, 7, 11, 13\)
Find the product of two consecutive prime numbers:
\(2 \ × \ 3 = 6\) (not in the options)
\(3 \ × \ 5 = 15\) (bingo!)
\(5 \ × \ 7 = 35\) (not in the options)
\(7 \ × \ 11 = 77\) (not in the options)
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| 18- Choice A is correct
The correct answer is \(10\%\)
Use this formula: Percent of Change \(\frac{New \ Value \ − \ Old Value}{pld \ value} \ × \ 100\%\)
\(\frac{18,000 \ − \ 20,000 }{20,000} \ × \ 100\%=10\%\) and
\(\frac{16,200 \ − \ 18,000}{18000} \ × \ 100\%=10\%\)
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| 19- Choice A is correct
The correct answer is \(50\%\)
The question is this: \(560.50\) is what percent of \(1,121\)?
Use percent formula:
part \(=\frac{percent}{100} \ ×\) whole
\(560.50= \frac{percent}{100} × \ 1,121 ⇒ 560.50=\frac{ percent \ × \ 1,121}{100 }⇒\)
\(56050 =\) percent \(× \ 1.121 ⇒\)
percent \(=\frac{56050}{1,121}=50\)
\(560.50\) is \(50\%\) of \(1,121\).
Therefore, the discount is: \(100\% \ – \ 50\%=50\%\)
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| 20- Choice D is correct
The correct answer is \($880\)
Let \( x\) be the original price.
If the price of the sofa is decreased by \(15\%\) to \($748\), then:
\(85\%\) of \(x=748 ⇒ 0.85 \ x =748 ⇒\)
\(x=748 \ ÷ \ 0.85=880\)
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| 21- Choice C is correct
The correct answer is \(15\)
If the score of Mia was \(90\), therefore the score of Ava is \(45\).
Since, the score of Emma was one third as that of Ava, therefore, the score of Emma is \(15\).
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| 22- Choice B is correct
The correct answer is \(30\)
Let \(x\) be the smallest number.
Then, these are the numbers:
\(x, x \ + \ 1, x \ + \ 2, x \ + \ 3, x \ +\ 4\)
average \(= \frac{sum \ of \ terms}{ number \ of \ terms} ⇒ 32=\frac{x \ + \ (x \ + \ 1) \ + \ (x \ + \ 2) \ + \ (x \ + \ 3) \ + \ (x \ + \ 4)}{5}⇒32=\frac{5 \ x \ +10}{5 }⇒ 160=5 \ x \ + \ 10 ⇒ 150=5 \ x ⇒ x=30\)
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| 23- Choice C is correct
The correct answer is \($420\)
Let \(x\) be the original price.
If the price of a laptop is decreased by \(10\%\) to \($378\), then:
\(90\%\) of \(x=378 ⇒ 0.90 \ x=378 ⇒ x=378 \ ÷ \ 0.90=420\)
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| 24- Choice A 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 \(9\).
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| 25- Choice A is correct
The correct answer is \(7\%\)
The percent of girls playing tennis is:
\(35\% \ × \ 20\% = 0.35 \ × \ 0.20 = 0.07 = 7\%\)
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| 26- Choice C is correct
The correct answer is \(6\)
Let \(x\) be the number.
Write the equation and solve for \(x\).
\(\frac{1}{3} \ × \ 12= \frac{2}{3} \ x\).
\(x ⇒ \frac{1 \ × \ 12}{3}= \frac{2 \ x}{3}\) , use cross multiplication to solve for \(x\).
\(3 \ × \ 12=2 \ x \ × \ 3 ⇒36=6 \ x ⇒ x=6\)
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| 27- Choice A is correct
The correct answer is \(28\)
The area of the floor is: \(8\) cm \(× \ 35\) cm \(= 280\) cm\(^2\)
The number of tiles needed \(= 288 \ ÷ \ 10 = 28\)
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| 28- Choice C is correct
The correct answer is \(x=- \ 24, \ y=18\)
\( \begin{cases}x \ + \ 2 \ y = 12\\3 \ x \ + \ 5 \ y= 18\end{cases} →\) Multiply the top equation by \(- \ 3\) then,
\( \begin{cases}- \ 3 \ x \ - \ 6 \ y = - \ 36\\3 \ x \ + \ 5 \ y= 18\end{cases} →\) Add two equations
\(- \ y = - \ 18→y=18\) plug in the value of \(y\) into the first equation
\(x \ + \ 2 \ y = 12 → x \ + \ 2 \ (18) = 12→ x \ + \ 36 = 12\)
Subtract \(36\) from both sides of the equation. Then: \(x \ + \ 36=12→x=- \ 24\)
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| 29- Choice D is correct
The correct answer is \(600\) ml
\(5\%\) of the volume of the solution is alcohol.
Let \(x\) be the volume of the solution.
Then: \(5\%\) of \(x=30\) ml \(⇒ 0.05 \ x =30 ⇒ x=30÷0.05=600\)
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| 30- Choice C is correct
The correct answer is \(5\) cm
Formula for the Surface area of a cylinder is:
\(SA=2 \ \pi \ r^2 \ + \ 2 \ \pi \ r \ h →150 \ π=2 \ \pi \ r^2 \ + \ 2 \ \pi \ r \ (10)→r^2 \ + \ 10 \ π \ − \ 75=0 \ (r \ + \ 15) \ (π \ − \ 5)=0→π=5\) or \(π= \ − \ 15\) (unacceptable)
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| 31- Choice D is correct
The correct answer is \(I \ > \ 4000 \ x \ + \ 21000\)
Let \(x\) be the number of years.
Therefore, \($2,000\) per year equals \(2000 \ x\).
starting from \($24,000\) annual salary means you should add that amount to \(2000 \ x\).
Income more than that is:
\(I \ > \ 4000 \ x \ + \ 21000\)
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| 32- Choice D is correct
The correct answer is \(840\)
Use simple interest formula: \(I=prt\)
(\(I=\) interest, \(p=\) principal, \(r=\) rate,\(t=\) time)
\(I=(7,000) \ (0.04) \ (3)=840\)
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| 33- Choice A is correct
The correct answer is \(50\) miles
Use the information provided in the question to draw the shape.
\(40\) miles
Use Pythagorean Theorem: \(a^2 \ + \ b^2 = c^2\)
\(40^2+ 30^2=c^2 ⇒ 1600 \ + \ 900= c^2 ⇒ 2500=c^2 ⇒ c=50\)
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| 34- Choice A 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.
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| 35- Choice A is correct
The correct answer is \(12 \ \pi\)
Area of the circle is less than \(49 \ π\).
Use the formula of areas of circles.
Area \(= \pi \ r^2 ⇒ 49 \ \pi \ > \ \pi \ r^2⇒\)
\(49 > r^2⇒ r \ < \ 7\)
Radius of the circle is less than \(7\).
Let’s put \(7\) for the radius.
Now, use the circumference formula:
Circumference \(=2 \ \pi \ r =2 \ \pi \ (7)=14 \ \pi\)
Since the radius of the circle is less than \(7\).
Then, the circumference of the circle must be less than \(14 \ \pi\).
Only choice A is less than \(14 \ \pi\).
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| 36- Choice A is correct
The correct answer is \(\frac{2}{7}, \frac{3}{8}, \frac{5}{11}, \frac{3}{4}\)
Let’s compare each fraction:
\(\frac{2}{7} \ < \ \frac{3}{8} \ < \ \frac{5}{11} \ < \ \frac{3}{4}\)
Only choice A provides the right order.
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| 37- 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 \(10\%: (0.85\) D) \((100\% \ + \ 10\%) = (0.85\) D) \((1.10) = 0.88\) D \(= 88\%\) of D
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| 38- Choice D is correct
The correct answer is \(70\)
To find the number of possible outfit combinations, multiply number of options for each factor: \(7 \ × \ 2 \ × \ 5=70\)
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| 39- Choice B is correct
The correct answer is \((5, 7)\)
The equation of a line is in the form of \(y=m \ x \ + \ b\), where \(m\) is the slope of the line and \(b\) is the \(y−\)intercept of the line.
Two points \((5, 3)\) and \((6, 4)\) are on line A.
Therefore, the slope of the line A is:
slope of line \(A=\frac{y_{2} \ − \ y_{1}}{x_{2} \ − \ x_{1}}= \frac{4 \ − \ 3}{6 \ − \ 5}=\frac{1}{1}=1\)
The slope of line A is \(1\).
Thus, the formula of the line A is:
\(y=x \ + \ π\), choose a point and plug in the values of \(x\) and \(y\) in the equation to solve for .
Let’s choose point \((5, 3)\).
Then: \(y=x \ + \ b→5=3 \ + \ b→b=5 \ − \ 3= 2\)
The equation of line A is: \(y=x \ + \ 2\)
Now, let’s review the choices provided:
A. \((− \ 1, 2) \ \ y=x \ + \ 2→2=− \ 1 \ + \ 2=1\) This is not true.
B. \((5, 7) \ \ y=x \ + \ 2→7=5 \ + \ 2=7\) This is true!
C. \((3, 4) \ \ y=x \ + \ 2→4=3 \ + \ 2=5\) This is not true.
D. \((− \ 1, − \ 2) \ \ y=x \ + \ 2→− \ 2=− \ 1 \ + \ 2=1\) This is not true.
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| 40- Choice C is correct
The correct answer is \(46\) cm
The area of the trapezoid is: Area \(=\frac{1}{2} \ h \ (b1 \ + \ b2)=\frac{1}{2} \ (x)(13+8)=126→10.5 \ x=126→x=12\)
\(y=\sqrt{5^2 \ + \ 12^2}=\sqrt{25 \ + \ 144}=\sqrt{169}=13\)
The perimeter of the trapezoid is: \(12 \ + \ 13 \ + \ 8 \ + \ 13=46\)
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| 40- Choice C is correct
The correct answer is \(46\) cm
The area of the trapezoid is: Area \(=\frac{1}{2} \ h \ (b1 \ + \ b2)=\frac{1}{2} \ (x)(13+8)=126→10.5 \ x=126→x=12\)
\(y=\sqrt{5^2 \ + \ 12^2}=\sqrt{25 \ + \ 144}=\sqrt{169}=13\)
The perimeter of the trapezoid is: \(12 \ + \ 13 \ + \ 8 \ + \ 13=46\)
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| 41- Choice I is correct
The correct answer is \(26.75\)
\(2 \ x \ - \ 6=10.5→2 \ x=10.5+6=16.5→x=\frac{16.5}{2}=8.25\)
Then; \(3 \ x \ + \ 2=3 (8.25) \ + \ 2=24.75 \ + \ 2=26.75\)
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| 42- Choice C is correct
The correct answer is \(- \ 2\)
Use PEMDAS (order of operation):
\(- \ 16 \ + \ 6 \ × \ (– \ 5) \ – \ [ \ 6 \ + \ 22 \ × \ (- \ 4) \ ] \ ÷ \ 2 \ + \ 5=\)
\(− \ 16 \ − \ 30 \ − \ [ \ 6 \ − \ 88 \ ] \ ÷ \ 2 \ + \ 5=\)
\(− \ 43 \ − \ [ \ − \ 82 \ ] \ ÷ \ 2 \ + \ 5=\)
\(− \ 48 \ +\ 82 \ ÷ \ 2 \ + \ 5=\)
\(− \ 48 \ + \ 41 \ + \ 5= \ - \ 2\)
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| 43- Choice C is correct
The correct answer is \(21\)
The input value is \(3\).
Then: \(x=3, \ π(x)=x^2 \ + \ 4 \ x→\)
\(f(3)=9 \ + \ 4 \ (3)=9 \ + 12=21\)
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| 44- Choice C is correct
The correct answer is \(220\)
The perimeter of the trapezoid is \(58\).
Therefore, the missing side (height) is \(= 58 \ – \ 16 \ – \ 12 \ – \ 10= 20\)
Area of a trapezoid: A \(= \frac{1}{2} \ h \ (b1 \ + \ b2) = \frac{1}{2} \ (20) \ (10 \ + \ 12) = 220\)
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| 45- Choice C is correct
The correct answer is \(13\)
Since \(π=5\), substitute \(5\) for \(N\) in the equation \(\frac{x \ + \ 2}{3}=N\), which gives \(\frac{x \ + \ 2}{3}=5\).
Multiplying both sides of \(\frac{x \ + \ 2}{3}=5\) by \(3\) gives \(x \ + \ 2=15\) and then adding \(- \ 2\) to both sides of
\(x \ + \ 2=15\) then, \(x=13\).
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| 46- Choice F is correct
The correct answer is \(\frac{3}{2}\)
Let \(x\) be the length of an edge of cube, then the volume of a cube is: \(π=x^3\)
The surface area of cube is: \(ππ΄=6 \ x^2\)
The volume of cube A is \(\frac{1}{4}\) of its surface area. Then:
\(x^3=\frac{6 \ x^2}{4}→x^3=\frac{3}{2} \ x^2\), divide both side of the equation by \(x^2\).
Then: \(\frac{x^3}{x^2}=\frac{3 \ x^2}{2 \ x^2}→x=\frac{3}{2}\)
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| 47- Choice C is correct
The correct answer is \(8\)
First draw an isosceles triangle.
Remember that two sides of the triangle are equal.
Let put \(a\) for the legs. Then:
\(π=4⇒ \) area of the triangle is \(=\frac{1}{2}(4 \ × \ 4)=\frac{16}{2}=8\)
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| 48- Choice C is correct
The correct answer is \(7\)
average \(=\frac{sum \ of \ terms}{ number \ of \ terms} ⇒\)
\(15=\frac{13 \ + \ 16 \ + \ 24 \ + \ x}{4}⇒\)
\(60=53 \ + \ x⇒x=7\)
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| 49- Choice C is correct
The correct answer is \(90^\circ\)
The relationship among all sides of special right triangle
\(30^\circ \ − \ 60^\circ \ − \ 90^\circ\) is provided in this triangle:
In this triangle, the opposite side of \(30^\circ\) angle is half of the hypotenuse.
Draw the shape of this question.
The latter is the hypotenuse.
Therefore, the latter is \(90\) feet.
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| 50- Choice C is correct
The correct answer is \(150\)
The question is this: \(1.95\) is what percent of \(1.30\)?
Use percent formula:
part \(= \frac{percent}{100 } \ ×\) whole
\(1.95 = \frac{percent}{100} \ × \ 1.30 ⇒ 1.95 =\frac{ percent \ × \ 1.30}{100} ⇒195 =\) percent \(× \ 1.30 ⇒\) percent \(= \frac{195}{1.30} = 150\)
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| 51- Choice E is correct
The correct answer is \(\frac{1}{5}\) or \(0.2\)
Write the ratio of \(3 \ π \) to \(4 \ b\).
\(\frac{3 \ a}{6 \ b}=\frac{1}{10}\)
Use cross multiplication and then simplify.
\(3 \ a × 10= 6 \ b × 1 → 30 \ a = 6 \ b → a = \frac{6 \ b}{30} = \frac{ b}{5}\)
Now, find the ratio of \(a\) to \(b\).
\(\frac{a}{b} = \frac{\frac{ b}{5}}{b} →\frac{ b}{5} ÷ b =\frac{ b}{5} × \frac{1}{b} = \frac{b }{5 \ b} = \frac{1}{5} =0.2\)
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| 52- Choice E is correct
The correct answer is \(33.75\) m
The rate of construction company \(=\frac{50 \ cm}{1 \ min}=50 \) cm\(/\)min
Height of the wall after \(45\) minutes \(=\frac{ 50 \ cm}{1 \ min}× \ 45\) min \(=2,250\) cm
Let \(x\) be the height of wall, then \(\frac{2}{3} \ x=2,250\) cm \(→x=\frac{3 \ × \ 2,250}{2}→x=3,375\) cm \(= 33.75\) m
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