jeopardy of everything so far

combinatorics/counting

100

how many different ways are there to order the letters in the word 

MISSISSAUGA

831,600

200

A bag contains 15 marbles of which 10 are red and 5 are white. 4 marbles are selected from the bag.

How many samples have 2 red and 2 white marbles?

450

300

How many ways can a student schedule 3 mathematics courses -- algebra, geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)

24

400

what is the probability to draw 4 cards from a deck of 52 such that there are two of each suite?

0.1348

500

Bob rolls a pair of dice, what is the probability that the product is even?

3/4

completing the rectangle

100

factor:

xy + 66x - 88y = 23333

(x - 88)(y + 66) =  18253

200

What are all the possible side lengths of a rectangle (a,b)  whose area equals its perimeter?

(3, 6) 

(6, 3) 

(4, 4)

300

Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?

(C) 119

400

Find all the positive integer pairs (m,n) such that

mn + 3m - 8n = 59.

(15, 2) 

(13, 4) 

(9, 32)

500

Find 3x²y² if x and y are integers such that .

588

modcrt

100

if n is a positive integer, 

what is n(n+1)(n+2) (mod 6)

0

200

what is the units digit of

7¹⁰⁰

7¹⁰⁰ ≡ 1 (mod 10)

300

What is the remainder when 2²⁰²² is divided by 3?

r = 1

400

w is the smallest integer such that 

w ≡ 2(mod 3)

w ≡ 3(mod 4)

w ≡ 6(mod 7)

what is w?

w = 83

500

what are the last two digits of

2023²⁰²³

2023²⁰²³ ≡ 67 (mod 100)

imaginary numbers

100

what is 

(2+7i)(8+3i)

-5 + 62i

200

find

i²⁰²²

-1

300

Compute the value of

z = (i − 4) / (2i - 3)                                                                      

(14 / 13)  +  (15 / 13) i                                                             

400

determine all complex numbers z that satisfy the equation

z + 3 z' = 5 - 6i, where z' is the complex conjugate of z

z = 5/4 + 3i

500

The complex number 2 + 4i is one of the root to the quadratic equation x2 + bx + c = 0, where b and c are real numbers.

Find b and c

b= -4

c= 20

logarithms

100

if log(a/b) + log(b/a) = log(a+b)

then a + b =

a + b = 1

200

find the value of x if

log(6x) - log(4 - x) = log(3)

x = 4/3

300

If log(xy³) = 1 and log(x²y)=1, 

what is log(xy)?

log(xy) = 3/5

400

if log₂3 = a, what is 

log_√38 ?

6/a

500

if a > b >1, and log_ab + log_ba = 10/3

what is log_ab - log_ba

-8/3