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random_syn_ori_query_syn6w_infer_part_1

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# Question What is the sum of the first 15 positive integers? # Solution

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# Question What is the area of a square with a diagonal of 10? # Solution

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# Question The length of a rectangle is 3 times its width. If the length is 4 more than the width, what is the area of the rectangle? # Solution

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# Question In a certain class of 10 students, 3 students are in the chess club, 4 are in the drama club, and 2 are in both clubs. How many students are in neither club? # Solution

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# Question If Mike has 210 coins in his collection, and one-fifth of them are nickels, and there are twice as many dimes as nickels, how many quarters does he have? # Solution

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# Question If $f(x) = \frac{2x}{3} + 1$ and $g(x) = 2x^2 + 3$, what is the value of $g(f(x))$? # Solution

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# Question A box is 12 inches long, 8 inches wide, and 6 inches high. What is the volume of the box? # Solution

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# Question If 125 mL of water are added to 1 L of a 20% solution of alcohol, the resulting mixture will be 15% alcohol. How much of the 1 L should be alcohol? # Solution

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# Question Find the mean of the numbers 10, 12, 15, 17, 19, and 20. # Solution

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# Question In a school, 3/4 of the students are girls. If there are 1500 students in all, how many boys are there? # Solution

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# Question The total cost of 10 pounds of apples and 5 pounds of bananas is $2.20. The total cost of 3 pounds of apples and 1 pound of bananas is $1.20. What is the cost per pound of apples and bananas? # Solution

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# Question A certain species of bird has an average wing chord of 6.5 inches. What is the average wing chord, in inches, of this species of bird if the length of each bird's wings is 37 inches? # Solution

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# Question The number of cats in the cat shelter is 15 more than twice the number of dogs in the shelter. If there are 40 more dogs than cats in the shelter, how many cats are there? # Solution

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# Question The sum of the digits of a two digit number is 10. If the digits are reversed, the new number is 18 less than the original number. What is the original number? # Solution

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# Question If 123456789 is multiplied by 8 and the first 9 digits are added together, what is the units digit of the answer? # Solution

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# Question The volume of a right circular cylinder is 120 in3. If the height of the cylinder is equal to the radius of its base, what is the radius of the cylinder? # Solution

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# Question If the price of 1 liter of gas is 2 dollars, how much will 10 liters of gas cost? # Solution

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# Question What is the average of $5.\overline{2}$ and $2.\overline{6}$? # Solution

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# Question A person has 20 coins consisting of dimes and quarters. The total amount of money is $3.75. If there are 5 more dimes than quarters, how many dimes does the person have? # Solution

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# Question Which of the following is equivalent to x + 2x? # Solution

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# Question A bag contains 10 red marbles, 8 white marbles, and 5 blue marbles. If you draw 3 marbles out at random, what is the probability that all three are white? # Solution

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# Question In a university project involving a total of 70 scientists, half of them are from Europe and one-fifth are from Canada. The remaining scientists are from the USA. How many scientists in this project are from the USA? # Solution

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# Question John has 3 bags of oranges. The first bag contains 30 oranges, the second bag contains 40 oranges and the third bag contains 50 oranges. If he has to divide them into some baskets with same number of oranges in each basket, how many baskets can he make at most? # Solution

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# Question If you have a bag of 15 marbles, 4 of which are red, and you add 5 more red marbles to the bag, then what percent of the marbles in the bag are red? # Solution

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# Question In a math class, 3/4 of the students are girls. The rest are boys. If there are 15 boys in the class, how many students are there in total? # Solution

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# Question What is the value of $\binom{7}{2}$ when computed? # Solution

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# Question In a certain class, 10 students had a total of 200 dollars. If each student had an equal number of dollars, what is the number of students in the class? If the answer to the above question is 5, what is the value of unknown variable x? # Solution

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# Question What is the value of $(-1)^{47} + 2^{(3^3+4^2-6^2)}$? # Solution

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# Question Find the value of $\sqrt{4^2+2^2}$. # Solution

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# Question In a class of 300 students, 50 are juniors and 120 are seniors. If 30 students are chosen at random, what is the probability that there will be 20 juniors and 10 seniors in the sample? # Solution

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# Question In 5 years, Raven will be x times as old as Phoebe. If Phoebe is currently 10 years old, Raven is 55 years old. What is the value of unknown variable x? # Solution

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# Question A school has 1200 students. If there are 200 students in the cafeteria, how many students are in the school? # Solution

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# Question If 50% of the students in a school are boys, what percent of the girls are taller than 5 feet? # Solution

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# Question 123456789 - 87654321 = # Solution

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# Question If 50% of a class of 30 students are present on a particular day, what is the probability that at least 4 students of the class are present? # Solution

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# Question 10 students take a math test. On the test, 5 students get an A, 4 students get a B, and 1 student gets a C. If 3 of the students are randomly chosen to receive a certificate, what is the probability that all 3 of them get A's? # Solution

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# Question Simplify $\frac{2x^2 - 3x - 5}{x^2 - 4}$ # Solution

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# Question Let $P$ be the point $(1, 2)$ and let $Q$ be the point $(12, 5).$ The line $y = mx + c$ is chosen such that it passes through the point $Q$ and is perpendicular to the line passing through $P$ and the origin. Find the value of $c.$ # Solution

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# Question Determine the value(s) of $a$ such that the equation $x^2 - 5x + a = 0$ has two distinct real roots. # Solution

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# Question What is the measure of angle $x$ in degrees? # Solution

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# Question The volume of a cylinder is $250\pi$ cubic units and the height of the cylinder is $10$ units. What is the radius of the cylinder? # Solution

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# Question If the sum of the first 30 positive odd integers is equal to the sum of the first 40 positive odd integers, then what is the sum of the first 49 positive odd integers? # Solution

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# Question A train covers 600 miles in 6 hours, traveling at a constant rate. If the train were to increase its speed by 50 miles per hour, how long would it take to cover the 600 miles? # Solution

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# Question Let $f(x)=x^2+1$ and $g(x)=\sqrt{x+2}$. What is $g(f(f(3)))$? # Solution

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# Question The 3rd and 5th terms of an arithmetic sequence are 17 and 39, respectively. What is the 7th term of the same sequence? # Solution

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# Question The sequence $a_1,$ $a_2,$ $a_3,$ $\dots$ satisfies $a_1 = 19,$ $a_9 = X and for all $n \ge 3,$ $a_n$ is the arithmetic mean of the first $n - 1$ terms. Find $a_2.$ If we know the answer to the above question is 179, what is the value of unknown variable X? # Solution

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# Question What is the value of $44$ divided by $11$? # Solution

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# Question A certain television is advertised to have a viewing angle of 40 degrees. If the same television is set up in a room where the ceiling is 20 feet high, what is the distance from the television to the ceiling? # Solution

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# Question How many cans are there in a full 3-pack of soda? # Solution

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# Question In a movie, 1000 people were seated in 10 rows of 100 people. If the first row was 100% full, how many people would be left if one row was removed? # Solution

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# Question If $x+y=27$ and $x-y=5$, what is the value of $x^2-y^2$? # Solution

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# Question Find the sum of the squares of the roots of the equation $2x^2 + 3x - 5 = 0$. # Solution

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# Question A student has to take 2 courses out of 6. How many ways are there to pick 2 courses? # Solution

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# Question What is the smallest positive integer that is not a factor of any integer greater than 1? [asy] size(75); draw((0,0)--(0,12)); dot((0,12)); draw((0,12)--(8,12)--(8,11)--(0,11)); draw((8,11)--(8,9)--(0,9)); draw((8,9)--(8,6)--(0,6)); [/asy] # Solution

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# Question What is the value of $x$ in the following equation? # Solution

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# Question Write a linear function to model the total cost of renting a bike, where the cost is $4 plus $1.50 per hour. # Solution

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# Question Given that $f(x) = x^2 + 3x + 2$ and $g(x) = 4x - 2$, what is the value of $f(2) + g(2) - 3f(3) - 2g(1)$? # Solution

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# Question How many days are there in a 2012 calendar year? # Solution

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# Question The total value of a used car is $4,000. If the car is worth 60% of what it was a year ago, what was the car worth a year ago? # Solution

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# Question Determine the value of the expression below. # Solution

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# Question The ratio of men to women working at a factory is 2 to 5. If there are 110 men working there, how many women are there? # Solution

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# Question A man travels 24 km due north, then 16 km due south. How far is he from the starting point? # Solution

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# Question A carpenter is making a table top that measures 45 cm by 75 cm. He has 230 cm of wood and must use all of it. What is the maximum area of the table top that the carpenter can make? # Solution

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# Question Find the distance between the points $(-5,12)$ and $(10,-18)$. # Solution

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# Question If $f(x) = x^2 - 2x$, what is the value of $f(f(f(f(-1))))$? # Solution

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# Question If $x + y = 5$ and $x^2 + y^2 = 10$, find the value of $xy$. # Solution

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# Question In a convex pentagon, the interior angles have measures of $x + 1$, $2x$, $3x$, $4x$, and $5x - 1$ degrees. What is the measure of the smallest angle? # Solution

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# Question If you are able to ride a scooter at 60 mph for 30 minutes, how far will you travel? # Solution

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# Question A boat is traveling in still water at a speed of 20 km/hr. If the boat is traveling in a river from point A to point B and the current is moving in the direction of the river, the actual distance between the two points will be: # Solution

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# Question In a box there are 12 red balls, 15 blue balls, and 18 green balls. If we pick out 6 balls, what is the probability that we get 3 red balls, 1 blue ball, and 2 green balls? # Solution

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# Question A man has a wife who was 25 years old when he was 15 years old. How old is the man when the woman is 50 years old? # Solution

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# Question Find the degree of the polynomial $7(x^4 + x^3 + 2x) - 3(x^2 + 2x) + 8(x^2 + 1)$ after it is simplified. # Solution

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# Question Let $a$, $b$, and $c$ be three real numbers such that $a+b+c=0$. Find the value of $\frac{a^3+b^3+c^3}{3}$. # Solution

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# Question If 50% of a number is 100, what is 15% of the number? # Solution

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# Question Solve the equation $2(x^2-3x+1)+5(x^2-5x+3)=0$. # Solution

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# Question How many meters are there in 25 kilometers? # Solution

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# Question The length of a rectangle is 3 cm more than twice its width. If the area of the rectangle is 72 cm$^2$, what is the length of the rectangle? # Solution

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# Question What is the value of $c$ that satisfies the equation $\frac{c-23}{2} = \frac{2c +5}{7}$? # Solution

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# Question A man buys 5 books for 10 dollars. He buys another 5 books for 15 dollars. What is the average price per book? # Solution

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# Question A school has 250 students. If 20 students are absent on Monday and 15 on Tuesday, how many students are present on Wednesday? # Solution

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# Question In a certain warehouse, there are $1335$ boxes, each containing $39$ books. #Melvin's boss orders him to unpack all the books and repack them so that there are $40$ books in each box. After packing as many such boxes as possible, Melvin has how many books left over? # Solution

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# Question A business person can travel 480 miles per day. How many days will it take him to drive 1,000 miles? # Solution

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# Question A bakery sells 144 cakes. The number of cookies they sell is 10 times the number of cakes they sell. If they sell 12 times as many cookies as pies, how many pies do they sell? # Solution

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# Question If the vector $\begin{pmatrix} 1 \\ 2 \end{pmatrix}$ is rotated $90^\circ$ clockwise, what is the new vector? # Solution

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# Question The arithmetic progressions X, 5, 8, 11, \ldots\}$ and $\{3, 10, 17, 24, \ldots \}$ have some common values. What is the largest value less than 500 that they have in common? If we know the answer to the above question is 479, what is the value of unknown variable X? # Solution

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# Question What is the probability that a randomly chosen American has never visited a foreign country? # Solution

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# Question A car travels $32$ miles on a gallon of gas when it is driven at $40$ miles per hour. At what speed will the car travel $25$ miles on a gallon of gas? # Solution

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# Question If a box contains 20 balls of different colors, and 10% of the balls are red, 20% of the balls are blue, and 30% of the balls are green, what is the total number of balls in the box? # Solution

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# Question Let $\mathbf{A}$ be a $4 \times 4$ matrix. If $\det (\mathbf{A}) = -1,$ then what is $\det (\mathbf{A^T})?$ # Solution

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# Question If you multiply the sum of two numbers by the difference of the same two numbers, you get 60. If you multiply the difference of the same two numbers by the sum of the same two numbers, you get 160. What is the difference of the two numbers? # Solution

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# Question The value of a house decreases by 1% every year. If the value of the house is 100,000 dollars today, what will be its value in 10 years? # Solution

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# Question A student scored a 82 on his first test and a 78 on his second test. What must he score on his third test to have an average of 80? # Solution

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# Question Write the expression $\frac{4}{5}$ as a decimal. # Solution

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# Question A teacher gave a test to a class of 40 students and the average score was 72. When the scores of 3 students, who got the same score, were removed from the list, the average score of the class was 70. What was the average score of the 3 students who were removed from the list? # Solution

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# Question What is the area of a circle with diameter 32cm? # Solution

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# Question A fruit company sells apples, pears, and oranges. If the cost of 1 pear is twice the cost of 1 orange and the cost of 1 apple is three times the cost of 1 orange, then what is the ratio of the cost of 1 orange to cost of 1 pear to cost of 1 apple? # Solution

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# Question A car dealer offers to sell you a car for $22,000 or for payments of $250 a month for five years. What is the equivalent interest rate per annum? # Solution

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# Question Solve the following system of equations. # Solution

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# Question Determine the value of the expression below. # Solution

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# Question The sum of two numbers is $18$. Their difference is 12$. The greater of the two numbers is X$. What is the value of unknown variable X? # Solution

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