jaekg

43 Questions
12 Answers

0

1

0

+190

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

jaekg 20.10.2024

0

1

0

+190

Algebra

Let $x$ and $y$ be complex numbers. If $x + y = 2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

jaekg 20.10.2024

0

1

0

+190

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{39} + \sqrt{40}} + \frac{1}{\sqrt{40} +\sqrt{45}}

jaekg 20.10.2024

0

1

0

+190

Algebra

Find all values of c such that 3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18. If you find more than one value of c, then list your values in increasing order, separated by commas.

jaekg 20.10.2024

0

1

3

+190

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?

jaekg 17.10.2024

0

1

0

+190

Counting

At a meeting, $4$ scientists, $3$ mathematicians, and $2$ journalists are to be seated around a circular table. How many different arrangements are possible if every mathematician must sit next to a journalist? (Two seatings are considered mehr ..

jaekg 17.10.2024

0

1

2

+190

Counting

A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people, not including Mark?

jaekg 16.10.2024

0

1

3

+190

Counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $6,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

jaekg 16.10.2024

0

2

0

+190

Counting

In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving at least four pieces each?

jaekg 16.10.2024

0

1

0

+190

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

jaekg 16.10.2024

0

1

1

+190

Number Theory

When expanded as a decimal, the fraction $\frac{1}{7}$ has a repetend (the repeating part of the decimal) of $142857$. The last three digits of the repetend are $857$.
When expanded as a decimal, the fraction $\frac{1}{13}$ mehr ..

jaekg 15.10.2024

0

1

0

+190

Number Theory

When $N$ is divided by $10$, the remainder is $a$. When $N$ is divided by $2$, the remainder is $b$. What is $N$ modulo $10$, in terms of $a$ and $b$?

jaekg 15.10.2024

0

1

1

+190

Algebra

Let x and y be integers. If x and y satisfy 37x + 82y = -172 and x + y = -1, then find x.

jaekg 15.10.2024