Bases
Write 2137 in base 10.
10810
On a standard die, what is the probability of rolling a prime number? Express your answer as a fraction in simplified form.
1/2
Where does the line y-2=3x cross the y-axis?
2
What is the sum of the solutions to x2+3x=10?
-3
Write 9910 in base 4.
12034
Give two standard dice, what is the probability of rolling a sum of 6? Express your answer as a fraction in simplified form.
5/36
Given the line x+y=4, what is the sum of the x-intercept and the y-intercept?
8
How many solutions does the equation x2+2x+5=0 have?
zero
What is 10112+11012? Express your answer in base 2.
110002
Jimmy has a cloth marble bag containing 3 blue marbles, 4 red marbles, and 1 white marble. What is the probability that he pulls out two marbles and they match in color? Express your answer as a fraction in simplified form.
9/28
What are the coordinates where the lines 2x+y=4 and y=-x+1 intersect?
(3,-2)
-1
What is 1179-329? Express your answer in base 9.
759
Given 3 standard dice, what is the probability of rolling a three-of-a-kind in one roll? Express your answer as a fraction in simplified form.
1/36
What is the slope of the line 3x-4y=2(4-2y)?
Undefined
Solve for x: (x-6)(x-1)=5x-30
6
For which base does 971x-235x=738x?
12
John has a cloth marble bag containing 5 blue marbles, 2 red marbles, and x white marble. If the probability that he pulls out two marbles that match in color is 7/22, then how many white marbles does John have?
Given the line x-y=6 and the point (3,3), what is the equation of the line that both is perpendicular to the given line and goes through the given point? Give answer in slope-intercept form.
y=-x+6
Evaluate the expression (x2-1)/(x2-2x+1) when x=101. Give your answer as a decimal.
1.02