Number Theory
2021x101
204121
If area of a square is 2, what is the length of its diagonal.
2
What is the probability of picking a prime number among a set of positive integers from 1 to 10 as a fraction?
2/5
(x+6)-(5x-32) = -6. Find x
11
Square root of 1089
33
Value of 1+3+5+7....+99
2500
11
There are 10 students in a class. They take Spanish or French or both languages. There are 8 students that take Spanish and 5 that take French and none that take no language. What is the probability that a student picked in the class will be taking both Spanish and French?
3/10
Find the roots of the quadratic equation x2+4x-2021=0
47,-43
Convert 1100010102 to base 8
612
Find the sum of 20% of 16 and 16% of 20 as a fraction.
32/5
What is the equation of a line in slope intercept form that is perpendicular to the line joining (1,1) and (5,5) and passes through its midpoint?
y=-x+6
What is the number of ways in which the word LINCOLN can be arranged?
1260
3x2+15x+14 =0. What is the sum of roots for an equation whose roots are reciprocal of the roots of the above equation.
-15/14
62x222
13764
4^(x+y) = 1024 and 5^y = 125, find x.
2
If x+2, x and x+4 are sides of a right triangle, what is the area of the triangle.
24
Two dice are rolled. What is the probability that their product is a composite number?
5/6
Square root of 124+(70*sqrt(3)) is of form a+sqrt(b). What is a+b?
82
63x13x11
9009
Eight-digit number A234543B is divisible by 99. Compute 10A + B.
78
A circle of radius 2 is cut into four congruent arcs. The four arcs are joined to form the star figure shown. What is the ratio of the area of the star figure to the area of the original circle?
(4-pi)/pi
A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?
3/10
Sum of 1/n(n+1) values for n going from 1 to 100
100/101
0.0363636...repeat 36 forever. What is the fraction equivalent in simplified form
2/55