Equations
Solve for the roots of x2 - 5x + 6.
2 & 3
In an isosceles triangle, one of the base angles measures 37 degrees. What is the measure of the third angle?
106 degrees
What is the probability of rolling two sixes in a row on a fair six-sided die?
1/36
Given the formula of Vf = Vi + at, where Vf is the final velocity, Vi is the initial velocity, a is the acceleration (-10 m/s2), & t is the time passed, what is the final velocity of a ball shot at 14 m/s after 2 seconds?
-6 m/s
What is the x-coordinate of the vertex in 3x2 + 5x - 12?
-5/6
What is the volume of a sphere given that its radius is 6 cm?
288π cubic cm
A bag has 3 red balls and 5 blue balls. If I draw 1 red ball and 1 blue ball, what is the probability that the next ball drawn is red?
1/3
The population of a population is modeled as A = P(ert), where A is the final population after t years, r is the growth rate as a decimal, and P is the initial population. What is the population of a chicken population increasing continuously by 1% annually after 2 years initially at 20 chickens (round DOWN)?
150 chickens
Solve for x given |5x+4| = 34
x = 6, -38/5
In an isosceles trapezoid, its height is 8 cm, its lower base is 30 cm, and its upper base is 18 cm. What is the length of one of the angled sides?
10 cm
A card is drawn from a standard 52-card deck. What is the probability of drawing a queen or a spade?
4/13
Given that a microorganism population doubles everyday starting from today (March 15th) at exactly midnight when the population is 1, what day will the population cross 2024?
March 25th
What is the value of 2(sin2x) + 2(1 - sin2x)?
2
There is a circle O with a radius 5 inches. A line tangent to the circle is drawn, with the point tangent to the circle labeled as point A, a point B 12 inches away from point A which is on the tangent line. What is the length of OB?
13 inches
A committee of 2 students can be formed of a pool of 10 boys and 8 girls. How many committees of only boys are possible?
45
Given that the formula for the kinetic energy of an object is 0.5 * mv2, where m is the mass of the object and v is its velocity, by what percent does the object's velocity increase if its kinetic energy is tripled?
Roughly 73.2%
Solve the following system of equations:
3x - 9z = 33
7x − 4y − z = −15
4x + 6y + 5z = −6
x = -1, y = 3, z = -4
A dodecahedron has 12 faces and 20 vertices. How many edges does it have?
30
Given a random number at least 1000 and no greater than 9999, what is the probability that is has at least 1 nine in its digits (as a percent)?
35.2%
Convert 50 degrees Fahrenheit to Kelvin given the following equations:
F = 1.8 C + 32
K = C + 273
283 K