All Questions ⁺⁰230622 Questions

0

240

1

Probability

A positive integer divisor of 11 is chosen at random. What is the probability that this divisor is prime? Express your answer as a common fraction.

Guest Jul 12, 2022

0

207

1

+166

Counting

Consider the sequence such that and for every positive integer , , where is the largest prime factor of . The first few terms of the sequence are . What is the largest value of such that is a four-digit number?

RainbowSquirrel53 Jul 12, 2022

0

131

0

help plz

Bertrand has 12 cards: on the front of each card is a digit, and on the back of each card is either a triangle, square, pentagon or circle. Bertrand looks through the pile of cards and says to his friend Georg, "For each card in the pile, if the number read more ..

Guest Jul 12, 2022

0

200

1

Algebra

If 3a + b + c = -3, a+3b+c = 9, a+b+3c = 1, then find abc.

Guest Jul 12, 2022

0

218

3

Help

Let and be the solutions of the equation . What is the value of ?

Guest Jul 12, 2022

0

213

1

Digits

If n = 10^{2020} + 10^{2019} + 10^{2018} + 10^{2017} + ... + 10^2 + 10^1, what is the sum of digits of the integer n?

Guest Jul 12, 2022

-2

215

1

geometry

In the figure, triangle ABC is inscribed in a semicircle with diameter AC of length 20 inches, and AB = 10 inches. When the area of the shaded region, in square inches, is expressed in the form a*pi - b what is the value of a + b? read more ..

Guest Jul 12, 2022

0

122

0

triples

Find the number of triples (a, b, c) of positive integers, such that 1 <= a, b, c <= 100 and
a^2 + b^2 + c^2 = ab + ac + bc + 4.

Guest Jul 12, 2022

-2

128

0

how

did you do that

Guest Jul 12, 2022

0

169

2

Polynomials

Let p(x) be a monic polynomial of degree 6 such that p(1) = 1, p(2) = 2, p(3) = 3, p(4) = 4, p(5) = 25, and p(6) = 6. Find p(7).

Guest Jul 12, 2022

0

121

0

system

If w, x, y, and z are real numbers satisfying:
w + x + y = -2
w + x + z = 4
w + y + z = 9 read more ..

Guest Jul 12, 2022

0

200

1

Algebra

If x and y are positive integers for which 3x + 2y + xy = 117, then what is x + y?

Guest Jul 12, 2022

0

220

2

Algebra

Find 1/(a - 1) + 1/(b - 1) where a and b are the roots of the quadratic equation 2x^2-7x+2 = x^2-11x+1.

Guest Jul 12, 2022

0

121

0

Arithmetic sequence

Let a1, a2, a3, ... be an arithmetic sequence. If a2/a4 = 3, what is a5/a3?

Guest Jul 12, 2022

0

206

1

Complex sum

What is the value of the sum where z ranges over all 7 solutions (real and nonreal) of the equation z^7 = -1?

Guest Jul 12, 2022

0

124

0

geometry

In triangle ABC, points D and F are on AB and E is on AC such that DE || BC and EF || CD. If AF = 9 and DF = 2, then what is BD?

Guest Jul 12, 2022

0

143

0

trig problem

Calculate

As usual, the output of an inverse trig function should be in radians.

Guest Jul 12, 2022

0

165

0

Probability

In a regular icosagon (20-sided polygon), all the diagonals are drawn. If a diagonal is selected at random, what is the probability of selecting a diagonal that is either the shortest possible length, the second-shortest possible length, or the third-shortest read more ..

Guest Jul 12, 2022

0

203

1

Number Theory

x,y, and z are positive integers such that gcd(x, y, z) = 14 and lcm(x, y, z) = 630 and y = 3x. What is the smallest possible value of x + y + z?

Guest Jul 12, 2022

+11

278

3

+1162

One of my friend's questions from high school. LOL

If

then for how many values of x is ?

nerdiest Jul 12, 2022

0

135

0

Counting

A haiku is a poem with three lines: the first line contains 5 syllables, the second line 7 syllables, and the last line 5 syllables. If each word in each list shown is used at most once, how many different haiku can be made with these read more ..

Guest Jul 12, 2022

0

176

1

Percent

If 2/3 of 75% of 0.8x is equal to 100, what is 4/3 of 60% of 0.75x? Express your answer as a decimal to the nearest tenth.

Guest Jul 12, 2022

0

205

1

Prisms

Both of the right triangular prisms shown have bases that are right triangles with hypotenuse length 10 cm. One prism has height x and a base leg of length 6 cm. The other prism has height x - 2 cm and a base leg of length 5*sqrt(2) cm. read more ..

Guest Jul 12, 2022

0

226

2

Rates

While driving, Carl notices that his odometer reads 25,952 miles, which happens to be a palindrome. He thought this was pretty rare, but 2.5 hours later, his odometer reads as 36,563 miles, anoher palindrome. What was Carl's average speed during read more ..

Guest Jul 12, 2022

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