Basic Operations
Given the dataset [3, 4, 6, 7, 8, 10], calculate the mean, median, and mode.
Determine the x-intercept and y-intercept of the linear equation: y = 2x - 6
X-intercept: (3, 0); Y-intercept: (0, -6)
If f(x) = 3x - 2, what is f(4)?
f(4) = 10
Jenny invests $5,000 in a savings account that earns an annual interest rate of 4%. How much money will she have in the account after 5 years, assuming the interest is compounded annually?
Approximately $6,207.07
The velocity of a car is given by the function v(t) = 3t^2 - 6t + 2, where t is the time in seconds. Find the acceleration of the car at t = 4 seconds
18 m/s²
What is the quotient of 144 divided by 12?
12
Calculate the volume of a cylinder with a radius of 4 units and a height of 10 units. (Use π ≈ 3.14)
Approximately 502.4 cubic units
Solve for y in the equation: 2y^2 - 3y - 5 = 0.
y = -1 or y = 5/2
If a store offers a 10% discount on a $1,200 laptop, how much will you save?
$120
Solve the system of equations:
2x + y = 7
3x - 2y = 4
x = 2, y = 3
What is the sum of 45 and 37?
82
How many sides does a hexagon have?
6
f you have 1/4 of a pizza and you eat half of it, how much pizza is left?
Answer: 1/8
If a book costs $18 and you have $50, how much change will you receive?
$32
Solve for x in the equation: 2x + 5 = 17.
x = 6
Find the exact value of sin(45 degrees) without using a calculator.
Turtles
Calculate the area of a right triangle with a base of 6 units and a height of 8 units.
24 square units
If you roll a fair six-sided die twice, what is the probability that you will roll two 6s?
1/36 (There is 1 favorable outcome out of 36 possible outcomes when rolling two dice.)
A rectangular swimming pool measures 20 meters in length, 8 meters in width, and 2 meters in depth. If the pool is filled to its maximum capacity, how many cubic meters of water are in the pool?
320 cubic meters
In a deck of 52 playing cards, what is the probability of drawing a red card (heart or diamond) or a face card (king, queen, or jack)?
20/52 or 5/13 (rounded to two decimal places)
What is the difference between 68 and 29?
39
What is the name of a polygon with eleven sides?
Hendecagon
If you have 3/4 of a pie and you want to share it equally among 5 friends, how much does each friend get?
3/20 of the pie
If a bicycle travels at a speed of 12 miles per hour for 2.5 hours, how far does it go?
30 miles
Solve for y in the equation: 3y - 2 = 13.
y = 5
What is the product of 8 and 9?
72
What is the area of a rectangle with a length of 12 units and a width of 5 units?
60 square units
Express 3/5 as a decimal.
0.6
If a train travels at a speed of 60 miles per hour for 3 hours, how far does it travel?
180 miles
Solve for y in the equation: 2y - 7 = 11.
y = 9
What is the result of 5 multiplied by 6 squared?
180
Calculate the area of a triangle with a base of 10 units and a height of 6 units
30 square units
Add the fractions 2/5 and 3/8, and express the result in simplest form.
19/40
If a recipe calls for 2/3 cup of sugar, how much sugar is needed if you want to make 4 batches of the recipe?
8/3 cups (or 2 2/3 cups)
Solve for x in the equation: 4(x - 5) = 36.
x = 11
What is the result of 15 divided by 3?
5
Calculate the perimeter of a square with a side length of 8 units.
32 units
Convert 0.75 into a fraction in simplest form.
3/4
If a car travels at a constant speed of 50 miles per hour for 4 hours, how far does it go?
200 miles
Simplify the expression: 3(2x + 4) - 2(3x - 5).
12x + 12
What is the product of 7 and 15?
105
Who is often referred to as the "Father of Geometry" and is known for his work in Euclidean geometry?
Euclid
Simplify the expression: 2x^2 - 3x + 5x - 4.
2x^2 + 2x - 4
If a car depreciates in value by 15% each year, how much will it be worth after 4 years if it was originally valued at $20,000?
$11,016.25
Factor the quadratic expression: x^2 + 7x + 12.
(x + 3)(x + 4)
Find the derivative of the function f(x) = 2x^3 - 5x^2 + 3x - 7.
6x^2 - 10x + 3
Find the volume of a cube with a side length of 6 units.
216 cubic units
Solve for x in the equation: 2(x + 3) = 16.
x = 5
If a store offers a 20% discount on a $75 item, how much will you pay after the discount?
$60
Solve for x in the equation: 2(x + 3) = 16.
x = 5