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random_syn_ori_query_syn6w_infer_part_3

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# Question A florist has 44 roses, 26 lilies, and 36 carnations. If he makes 1 bouquet of roses, 1 bouquet of lilies, and 1 bouquet of carnations, how many bouquets can he make? # Solution

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# Question Round $3.45$ to the nearest hundredth. # Solution

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# Question What is the value of $x$ in the equation $x^2 + 16x + 64 = 0$? # Solution

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# Question Find the value of $x$ in the equation: $\frac{x}{10}=\frac{3}{20}$ # Solution

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# Question Let $f(x) = x^3 - 3x + 2$ and $g(x) = 2x$. Find $f(g(x))$. # Solution

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# Question Twice the sum of three numbers is 30. Three times the difference of the first and second number is 18. The difference of the second and third numbers is 24. What is the sum of the second and third numbers? If we know the answer to the above question is 18, what is the value of unknown variable x? # Solution

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# Question If $x-y=15$ and $xy=4$, what is the value of $x^2+y^2$? # Solution

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# Question A bicycle costs $360. The sales tax on the bicycle is 8%. What is the total cost of the bicycle, including the tax? # Solution

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# Question The polynomial $f(x)$ is defined as $f(x) = 4x^3 - 20x^2 + 15x - 6$. If $f(x) = 0$, find the sum of all possible values of $x$. # Solution

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# Question In a certain state, licensed drivers have the option of purchasing a license for a 2-year period for either$45 or $135. The license for the 2-year period is$65, What is the total cost for the license under each option? # Solution

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# Question Evaluate $\log_3\frac{1}{9}$. # Solution

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# Question In the 1980s, the average height of a female in the United States was 5 feet 4 inches, and the average height of a male in the United States was 5 feet 8 inches. The average height of a female in 2010 was 5 feet 5 inches, and the average height of a male in 2010 was 5 feet 7 inches. How many inches did the average height of a female in the United States increase between 1980 and 2010? # Solution

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# Question The sum of two numbers is 150 and the difference between them is 20. What is the value of the bigger number? # Solution

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# Question The function f(x)=x^2+bx+c is a parabola that passes through the points (1,3) and (2,5). Find the values of b and c. # Solution

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# Question In a certain city, the average annual salary for 250 men is $45,000 and the average annual salary for 300 women is$40,000. What is the average annual salary for 550 people who live in the city? # Solution

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# Question Solve for $x>0$ in the following arithmetic sequence: $1^2, x^2, 3^2, \ldots$. # Solution

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# Question A box contains 1000 coins, of which 500 are gold coins and the rest are silver coins. If a coin is picked randomly, what is the probability that it is gold coin? # Solution

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# Question If 135 kids attended a school dance, which is 20% of the number of students in the school, how many students are in the school? # Solution

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# Question What is the remainder of $150\cdot 12 - 15\cdot 7 + 3$ when divided by $14$? # Solution

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# Question In a class of 45 students, 27 are girls. If 18 students are chosen at random, what is the probability that the class contains exactly 14 boys? # Solution

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# Question What is the sum of all the positive three-digit integers? # Solution

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# Question The surface area of a sphere is $4\pi r^2$. The surface area of a cube is $6s^2$. What is the ratio of the volume of the sphere to the volume of the cube? # Solution

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# Question How many days are there from 19/03/2014 to 21/03/2014? # 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 Which of the following is a factor of 20? # Solution

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# Question A car travels at a speed of 30 mph for 0.5 hours. What is the distance traveled? # Solution

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# Question If a gym charges $4.50 for each 30-minute class, what is the monthly fee for 20 classes? # Solution

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# Question What is the sum of the solutions to the following equation? $x^2 - 5x + 6 = 0$ # Solution

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# Question If the radius of a circle is 5, then the area of the circle is 25? # Solution

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# Question What is the value of $y$ if $2x + 3y = 5$ and $x - y = 4$? # Solution

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# Question If Joe is 36 inches tall and Sara is 24 inches taller than Joe, how tall is Sara? # Solution

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# Question Mirasol had $50 in her account. She spent $10 on coffee beans and $30 on a tumbler. How much is left in her account? # Solution

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# Question If there are 56 people in a room, what is the probability that 2 of them share a birthday? # Solution

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# Question If the weight of an object is 250 grams, how many kilograms does the object weigh? # Solution

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# Question A restaurant sells 200 3-inch hot dogs. They are sold in 2 packs of 10 hot dogs each. How many packs of hot dogs are sold in all? # Solution

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# Question If the sum of three numbers is 10 and the product of two of them is 15, what is the value of the largest number? # Solution

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# Question A football team scored 27 points in the first half of a game. In the second half they scored 2 points for every 4 points scored in the first half. How many points did they score in all? # Solution

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# Question A taxi driver is paid 2.5 times the number of miles he rides. If he rides 15 miles, he earns 175 dollars. What is his rate per mile? # Solution

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# Question A group of 5 people went to the movie theater. They spent $135 altogether, including$15 for a soda. If each ticket was $10, what is the value of unknown variable x? # Solution

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# Question In a park, there are 21 benches, and each bench is seating 4 people. The park manager wants to seat 100 people in the park. How many more benches does the manager need to buy? # Solution

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# Question If 500000000 is divided by 5000, what is the remainder? # Solution

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# Question For the three numbers in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, what is the average of the largest and the smallest number? # Solution

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# Question If a factory produced 12,000 dolls and their associated accessories last month, with each doll requiring 2 shoes, 3 bags, 1 set of cosmetics, and 5 hats, and each doll took 45 seconds to make while each accessory took 10 seconds to make, what was the total machine operation time, in seconds, required to manufacture all the dolls and accessories? # Solution

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# Question If 20% of a number is 40, what is 20% of 3 times the number? # Solution

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# Question The sum of two consecutive numbers is 75. What is the smaller number? # Solution

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# Question If $f(x) = x^2 + 3x - 4$, what is the value of $f(-2)$? # Solution

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# Question The price of a new car has decreased by $1,200 from 1999 to 2001. If the price of the car is $p in 2001, how much was the car priced in 1999? # Solution

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# Question Find the area of the triangle whose vertices are \[(0,0), \ (1,2), \ (3,1).\] # Solution

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# Question If 120% of a number is 1.5, what is 300% of the number? # Solution

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# Question How many perfect squares are divisors of the number $2014^{4}$? # Solution

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# Question Adlai has 2 dogs and 1 chicken. How many animal legs are there in all? # Solution

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# Question There are 480 students at a school, 25% of the students are in the band. How many students are not in the band? # Solution

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# Question The length of a rectangle is 3 cm more than its width. If the length were decreased by 3 cm and the width increased by 3 cm, the area of the rectangle would decrease by 18 cm^2. What is the perimeter of the rectangle? # Solution

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# Question The number of words in a book is $11001_2$. What is the number of pages in the book? # Solution

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# Question What is the greatest common divisor of 12 and 16? # Solution

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# Question If a cyclist can travel 50 miles in 2 hours, how many miles can he travel in 3 hours? # Solution

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# Question A mother is buying a sweater for her son. The sweater cost $10. The mother has $x$ dollars. The mother buys the sweater. How much money does the mother have left? # Solution

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# Question Express as a fraction in lowest terms: $0.\overline{3} + 0.\overline{15}$ # Solution

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# Question Let $\mathbf{a}$ and $\mathbf{b}$ be vectors such that $\|\mathbf{a}\| = 2,$ $\|\mathbf{b}\| = 3,$ and $\|\mathbf{a} \times \mathbf{b}\| = 5.$ Find $\|\mathbf{a} + \mathbf{b}\|.$ # Solution

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# Question Which of the following is a solution to the system of equations? # Solution

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# Question A car drives for 2 hours at 50 mph (miles per hour) and then drives for 3 hours at 25 mph. Find the average speed of the car for the entire journey. # Solution

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# Question If $35$ is subtracted from a number, the result is $41$. What is the number? # Solution

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# Question We have two boxes with numbered balls. The first box contains 15 balls, numbered from 1 to 15. The second box contains 25 balls, numbered from 1 to 25. We randomly select 1 ball from each box. What's the probability that the sum of the numbers on the balls is 28? # Solution

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# Question In a survey of 1000 people, 20% of the participants said they had visited Paris, 30% said they had visited London, and 10% said they had visited both Paris and London. How many people have visited Paris or London? # Solution

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# Question If $x$ is multiplied by 2, increased by 3, and then divided by 5, the result is 11. What is the value of $x$? # Solution

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# Question What is the value of $x$ in the following equation: $\frac{1}{2} + \frac{3}{x} = \frac{3}{4}$ # Solution

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# Question If x is a positive integer less than 10, and 2x + 1 is a perfect square, what is the value of x? # Solution

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# Question If a student scores 92 on an examination with a maximum score of 100, what percent did the student earn? # Solution

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# Question If the roots of the quadratic equation $x^2 - (a+1)x + (b+1) = 0$ are real and positive, what is the minimum value of $a+b$ ? # Solution

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# Question What is the sum of all integers from 1 to 100? # Solution

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# Question If a given number is multiplied by 2.5, then added to 12, and finally divided by 2, the result is 13. What is the number? # Solution

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# Question Suppose that x and y are positive real numbers that satisfy the equation $x^{2} + y^{2} = xy.$ What is the value of $x^{2} + y^{2}?$ # Solution

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# Question A small town has 150 citizens. 85 citizens are over 65 years old. If 50% of the town’s citizens are over 65, what is the town’s total population? # Solution

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# Question What is the value of cosine of 225 degrees? # Solution

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# Question If $\frac{x}{3} = \frac{y}{4}$ and $x$ and $y$ are both positive integers, what is the least possible value of $x + y$? # Solution

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# Question The sum of the digits of the number $N$ is 11. The sum of the digits of the number $2N$ is 17. What is the value of $N$? # Solution

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# Question Evaluate $\sqrt[3]{108+\!\sqrt[3]{108 + \!\sqrt[3]{108 + \!\sqrt[3]{108 + \!\sqrt[3]{108 + \cdots}}}}}$. # Solution

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# Question The sum of 5 consecutive even integers is 30. What is the largest of the 5 integers? # Solution

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# Question A train is traveling at a constant speed. If the train is 15 kilometers away from its destination and is traveling at a speed of 45 kilometers per hour, how long will it take the train to reach its destination? # Solution

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# Question If the sum of the ages of a father and his son is 50 years, and the product of their ages is 225 years, then how old is the father? # Solution

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# Question Find the value of $x$ in the equation $4^{2x}=8^{x+1}.$ # Solution

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# Question If Maria's mother is 46 years old and her daughter is 2 years old, how many years ago was Maria's mother twice as old as her daughter? # Solution

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# Question A school has x students. Half of the students are girls, the other half are boys. 20% of the girls have dogs at home and 10% of the boys have dogs at home. 15 students own dogs. What is the value of unknown variable x? # Solution

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# Question What is the smallest prime number greater than 3? # Solution

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# Question Find the number of three-digit positive integers whose digits are in strictly decreasing order. # Solution

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# Question The sum of two numbers is 5, and their difference is 1. What are the numbers? # Solution

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# Question A man's salary is increased by 20% every year. If his salary was 100000 in 2000 and 120000 in 2001, what was his salary in 2002? # Solution

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# Question At a banquet, there were 25 tables of people. There were 14 people at each table. There were 4 fewer men than women. How many men were at the banquet? # Solution

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# Question What is the number of students in the classroom? # Solution

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# Question The sum of three numbers is 50. The first number is one more than the second and the third number is twice the second number. What is the value of the first number? # Solution

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# Question In a certain state, 51% of the population is male and 49% is female. Of the males, 51% has a college diploma or higher and 19% has some college education but no diploma. Of the females, 26% has a college diploma or higher and 8% has some college education but no diploma. If a person is selected at random from the state, what is the probability that the person has a college diploma or higher? # Solution

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# Question Alex, Betty and Carmen shared 30 pieces of cake. Alex took 1/6 of the cake, Betty took 1/2 of the remaining cake and Carmen took the rest. What fraction of the cake did Carmen take? # Solution

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# Question A car is traveling 25 miles per hour. If it travels 180 miles in 4 hours, how long will it take to travel 450 miles? If we know the answer to the above question is 15, what is the value of unknown variable x? # Solution

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# Question Danny had 100 marbles. He lost 5 of them. He then gave 14 of the remaining marbles to his friend. How many did he give to his friend? # Solution

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# Question Let $x$ be a positive number such that $x + \frac{1}{x} = 1$. Find the value of $\frac{x^4 + 1/x^4}{x^2 + 1/x^2}$. # Solution

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# Question A house is 32 feet long and 24 feet wide. How many square feet of carpet are needed to cover the floor of the house? # Solution

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# Question In a room there are 100 people. 50% of the people are female, and 50% of the people are male. 40% of the males are smokers. 60% of the females are smokers. If a person is randomly chosen, what is the probability that the person is a smoker? # Solution

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# Question If $x = \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}$, then $x = \frac{a}{b}$, where $a$ and $b$ are coprime positive integers. Find $a+b$. # Solution

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# Question What is the volume of a cube with side length of 4 feet? # Solution

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# Question If I took 1000 grams of rice and 700 grams of milk and I mixed them together and heated them until they were all melted, how much of the mixture was rice? # Solution