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random_syn_ori_query_syn6w_infer_part_3

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# Question If $f(x) = \frac{2}{3}x^3-2x^2-2x$, find $f(2)$. # Solution

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# Question A rectangular box of height 18 cm has a square base with an edge length of 10 cm. What is the volume of the box? # Solution

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# Question Compute $123-13$. # Solution

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# Question A taxi driver charges a base fee of $2.50, and an additional $0.75 per mile. If John’s taxi ride was 5 miles, how much did he pay? # Solution

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# Question In a recent election for mayor, the candidate with the most votes received 0.54 of the votes. If 7,777 voters cast their ballots, how many votes did the winning candidate receive? # Solution

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# Question What is the value of $1000 \cdot \frac{2}{3} \cdot \frac{1}{2} \cdot \frac{3}{5} \cdot \frac{5}{4} \cdot \frac{4}{3} \cdot \frac{3}{2} \cdot \frac{2}{1}?$ # Solution

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# Question A farmer has 1000 acres of land and 1000 head of cattle. He sells 100 acres of land and 100 head of cattle. He then sells 10 acres of land and 10 head of cattle. How many acres of land and how many head of cattle does he have left? # Solution

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# Question The sum of 4 consecutive even integers is 116. What is the value of the smallest integer? # Solution

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# Question A test contains 4 questions, each with 3 possible answers, with only one answer correct. What is the probability of getting exactly two questions correct if you make a random guess on each question? # Solution

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# Question A standardized test has a mean of 80 with a standard deviation of 5. If the student scores 95, then he is at what percentile? # Solution

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# Question If a box of a certain size can be made in 20 hours, how many can be made in 4 hours? # Solution

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# Question Which of the following expressions is equal to the expression $\frac{1}{x}$? # Solution

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# Question What is the value of the following expression: $\frac{1}{2} - \frac{1}{4} + \frac{1}{6} - \frac{1}{8} + \frac{1}{10}$? # Solution

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# Question What is the value of x? # Solution

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# Question Avery has 20 marbles. He gave x marbles to his friend, and he has 13 left. How many marbles did Avery give his friend? If we know the answer to the above question is 7, what is the value of unknown variable x? # Solution

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# Question A store sold 200 cellphones in a week. The store's average weekly sales for the first 5 weeks of the year were X cellphones per week. If the store's average weekly sales for the first 6 weeks of the year was 10 more than its average weekly sales for the first 5 weeks of the year, what was the store's average weekly sales, in cellphones, for the first 5 weeks of the year? # Solution

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# Question A bag contains 10 marbles numbered 1 through 10. A marble is drawn at random from the bag, and then a second marble is drawn without replacing the first marble. What is the probability that both marbles are even-numbered? Express your answer as a common fraction. # Solution

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# Question The sum of three consecutive integers is 39. What is the largest integer? # Solution

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# Question The price of a pound of apples has been reduced from $3.50$ to $2.50$ a pound. By what percent has the price of a pound of apples been reduced? # Solution

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# Question If a rectangle is 15 meters long and 6 meters wide, what is the area of the rectangle? # Solution

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# Question If $x$ is the number of digits of $2^{2002}$ and $y$ is the number of digits of $3^{3003}$, then what is the value of $x-y$? # Solution

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# Question If 21*21*21*21*21*21 = 21,609,125,625, what is 21*21*21*21? # Solution

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# Question If a car goes from a speed of 20 mph to 25 mph, how many miles will it travel? # Solution

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# Question If the sum of the first n odd numbers is 159, what is the value of n? # Solution

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# Question For how many positive integers N is it true that $N$ is divisible by 2 and 3, and the sum of all of the odd positive divisors of $N$ is 64? # Solution

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# Question If a student scored 95% on a math exam which had 40 problems, how many problems did the student answer correctly? # Solution

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# Question The number of inches in the perimeter of a square is equal to the number of square inches in its area. Find the length, in inches, of a side of the square. # Solution

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# Question Tom, Sam, and Billy are friends. Sam is 3 years older than Tom, and Billy is 3 years older than Sam. If the average age of the three friends is 11 years, what is the age of Tom? # Solution

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# Question A rectangular field is 50 meters long and 30 meters wide. How many meters will 1200 meters of fencing enclose? # Solution

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# Question Let $x$ and $y$ be two positive real numbers such that $x^2 + y^2 = 25.$ What is the maximum value of $xy?$ # Solution

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# Question Convert the point $\left( 4, \frac{\pi}{2}, \sqrt{3} \right)$ in cylindrical coordinates to rectangular coordinates. # Solution

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# Question A shoe store buys a pair of shoes from a factory for $30. They sell the shoes for $40. What is the markup? # Solution

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# Question How many days will it take for the toothpaste to run out? # Solution

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# Question If 3x + 4y = 22 and 3x – 4y = 2, what is the value of x? # Solution

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# Question There are 120 people in a room. If 25% of the people in the room own a car, how many people in the room do not own a car? # Solution

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# Question Real numbers $x$ and $y$ have an arithmetic mean of 18 and a geometric mean of $\sqrt{92}$. Find $x^2+y^2$. # Solution

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# Question What is the smallest prime number that is a factor of $600$? # Solution

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# Question In a certain country, 60% of all automobiles have airbags, 20% have anti-lock brakes (ABS), and 30% have both. What is the probability that a randomly selected car has both an airbag and ABS? # Solution

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# Question A basketball player made 30 free throws and missed 50. What is the percentage of free throws she made? # Solution

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# Question If the area of a square is 25 square inches, what is the length of a side? # Solution

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# Question A line $L$ in the plane is perpendicular to a line $M$ in the plane if and only if the slope of $L$ is the negative reciprocal of the slope of $M$. # Solution

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# Question At a party, there are 3 times as many boys as girls. There are 2 more girls than boys. How many people are at the party? # Solution

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# Question 20% of the 300 shirts made by factory are defective. If 25% of the defective shirts are sold, what percent of the total shirts sold are defective? # Solution

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# Question Determine all real values of $x$ and $y$ such that $x^2 - 4xy + 5y^2 = 16$ and $3x + 2y = 4. # Solution

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# Question In a certain class, 40% of the students play sports, 25% of the students are part of the music club, and 15% of the students are in both clubs. What percentage of the students play sports or are in the music club? # Solution

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# Question There are 40 students in a class. Each student has to read 20 pages for a test. The library has 250 pages of reading material. How many days will it take to finish the test? # Solution

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# Question A manufacturing plant produces 540,000 items a week. The items are packaged in 500-item boxes. How many boxes are produced a week? # Solution

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# Question The following is a list of ages of 15 children in a class: 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15. What is the median age of the class? # Solution

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# Question The length of a rectangle is 50% more than its width. If the area of the rectangle is 300 square meters, what is the length of the rectangle? # Solution

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# Question In a certain class, 10 students have red shirts, 15 students have blue shirts, and 12 students have green shirts. If 1 student is randomly selected, what is the probability that the student selected will have a shirt that is not green? # Solution

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# Question A shopkeeper sells his items at a price that is 50 percent more than the cost price. He sells 10 items and makes a profit of $120. What is the cost of each item? # Solution

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# Question The sum of the squares of three consecutive positive integers is 1106. What is the smallest of these numbers? # Solution

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# Question Simplify the expression $\frac{x^2 - 4x + 4}{x^2 - 6x + 5}$ as much as possible. # Solution

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# Question If a man walks at 14 km/h, he misses the train by 7 minutes. If he walks at 16 km/h, he reaches the station 5 minutes before the arrival of the train. What is the distance covered by the man to reach the station? # Solution

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# Question The number of students in a class is 10. When the students stand in rows of 4, there is 1 student left over. When the students stand in rows of 5, there is 1 student left over. When the students stand in rows of 6, there is no students left over. What is the number of students in each row? If we know the answer to the above question is 3, what is the value of unknown variable x? # Solution

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# Question The angles in a triangle are in the ratio 3:4:5. What is the measure of the largest angle, in degrees? # Solution

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# Question A theater has 200 seats and charges $10 per ticket. The theater has found that every$1 increase in ticket price leads to 10 fewer ticket sales. What ticket price should the theater charge to maximize revenue? # Solution

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# Question A toy factory produced x toys. The total cost of producing x toys is $12x^2 + 30x + 3000$. What is the total cost of producing 400 toys? # Solution

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# Question If 2/3 of the total number of students in a class are girls, and there are 18 girls in the class, how many students are in the class? # Solution

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# Question A certain manufacturer found that if she sells the bicycles at a price of $150, then she will sell 3000 bicycles and if she decreases the price by $25, then she will sell 4000 bicycles. Assuming that the elasticity of demand is constant, what will be the number of bicycles sold when she charges $125 per bicycle? # Solution

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# Question If there were a total of 50 raspberries, blackberries, and blueberries picked, with half of them being raspberries and a third of them being blackberries, how many of them were blueberries? # Solution

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# Question If the sum of the three numbers is 100, and the second number is 15 more than the first number, and the third number is 20 more than the first number, what is the third number? # Solution

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# Question If $3^x=27$, what is $x^3$? # Solution

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# Question If the probability of A to occur is 10% and the probability of B to occur is 20%, and both events are independent to each other, then what is the probability that both events occur? # Solution

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# Question A right triangle has sides of lengths $a$ and $b$, where $a < b$. The hypotenuse has length $c$. Find $c^2$ in terms of $a$ and $b$. # Solution

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# Question A 10 m long and x m wide rectangular floor is to be covered with a square carpet with 4 m sides. 64 square meters of the floor are uncovered. What is the value of unknown variable x? # Solution

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# Question A car rental agency charges a daily fee plus a charge per mile driven. If a car is rented for 4 days, 180 miles are driven, and the total cost is$279, what is the daily fee? # Solution

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# Question If $A = 12$ and $B = 3$, what is the value of $A + B - 3 \times 4 \div 2$? # Solution

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# Question A cyclist rode a certain distance at 10 miles per hour and then rode twice that distance at 15 miles per hour. If the cyclist's total time for the trip was 2 hours, how many miles was the distance between the two cities? # Solution

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# Question If $ab = 4$ and $a - b = 3$, what is the value of $a^2 + b^2$? # Solution

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# Question The arithmetic mean of the nine numbers in the sequence $13, x, 2x+3, 4x+3, 5x+3, 6x+3, 8x+3$, and $9x+3$ is $6x-2$. What is the median of the nine numbers? # Solution

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# Question In the table above, the points $(x, y)$ lie on a straight line. If the point $(10, 3)$ lies on the same line, what is the value of $x + y?$ # Solution

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# Question Solve for $x$: $x + 5 = 8$. # Solution

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# Question Find the remainder when $3 \times 13 \times 23 \times 33 \times \ldots \times 183 \times 193$ is divided by $5$. # Solution

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# Question A car travels at a constant speed. It travels 10 miles in 5 minutes. How many miles does it travel in 10 minutes? # Solution

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# Question How many triangles can you see in the given picture? # Solution

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# Question A train is traveling at 100 miles per hour. The train is traveling 140 miles. How many minutes will it take the train to travel the 140 miles? # Solution

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# Question If there are initially 2,000 kids in camp and half of them are going to soccer camp, with 1/4 of those kids attending in the morning, how many kids are going to soccer camp in the afternoon? # Solution

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# Question If the number of miles driven is directly proportional to the number of gallons used, and 15 gallons is used for 180 miles, how many miles will be driven for 16 gallons? # Solution

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# Question How many different three-digit numbers can be formed by using the digits 2, 3, 5, and 6? # Solution

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# Question What is the value of the expression below? $2018^{2019}-2019^{2018}$ # Solution

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# Question What is the range of the function $$v(x) = \sqrt x - 2~?$$ Express your answer in interval notation. # Solution

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# Question If 6, 10, 18, and 30 are all multiples of $x$, what is the least possible value of $x$? # Solution

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# Question What is the product of 8 and 20? # Solution

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# Question A farmer has 100 animals. He has 20 chickens, 30 pigs and 50 cows. How many cows does he have? # Solution

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# Question There are 26 students in a class. Each student either likes math or likes science, but not both. If 14 students like math and 13 students like science, how many students like both math and science? # Solution

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# Question Find the sum of all the natural numbers from 1 to 1000. # Solution

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# Question The area of a rectangle is $48 \text{cm}^2$. If the length is $2 \text{cm}$ longer than the width, what are the dimensions of the rectangle? # Solution

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# Question A farmer has 1360 feet of fencing to use to make three identical pens, each with an area of 1345 square feet. What is the length of one side of each pen? # Solution

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# Question A 30-foot ladder is leaning against a building. If the base of the ladder is 9 feet from the building, how many feet is the top of the ladder from the ground? # Solution

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# Question If a=5 and b=7, then find the value of a+b+ab+a2+b2. # Solution

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# Question 23 people are going to the movies. There are 4 cars that can accommodate 5 people each. How many cars will be needed to transport all 23 people? # Solution

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# Question If the number of girls in a class is 5 more than twice the number of boys, how many boys are there in the class if there are 55 girls? # Solution

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# Question If the product of the roots of the quadratic equation $x^2 + 3x + k = 0$ is 3, what is the value of k? # Solution

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# Question Find the value of $X$ in the following equation: $$X \cdot 3 \cdot 4 \cdot 5 = 4 \cdot X \cdot 5 \cdot 3$$ # Solution

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# Question In a class of 30 students, there are 2/3 boys and 1/6 girls. What is the number of girls in the class? # Solution

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# Question A certain school has three student body councils: Academic, Cultural, and Service. If there are 100 total students body councils members of all three groups, and there are 7 more Academic Council members than Service Council members, how many members are on the Cultural Council? # Solution

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# Question If the graph of $y = f(x)$ is continuous, what is the sum of all possible values of $n$ in the function \[f(x) = \begin{cases} x^2 + 2 &\text{if } x < n, \\ 2x + 5 &\text{if } x \geq n. \end{cases} \] # Solution

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# Question The sum of two numbers is 11. If the smaller number is 6 more than the larger number, what are the two numbers? # Solution

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# Question What is the average of all positive three-digit multiples of 3? # Solution