Combinations and Permutations
A fidget cube has a different design on each of its six faces. If each face is labelled A to F, how many ways are there to arrange six designs on the cube?
720
Find n if an = 52 belongs to the sequence 1, 2.5, 4, 5.5, 7…
35
(4x2+7x-8) - (2x2-9x4+2x+2)
9x4+2x2+5x-10
Who teaches multi-variable calculus at South High School
Robert Y. Imamura
Find the amount of interest paid on a loan of $2000 if it is repaid over three years at a simple interest rate of 4% annually
$240
A 3-course meal can be composed from 5 different appetizers, 3 main courses, and 7 desserts. If a diner is allergic to an ingredient in one of the appetizers and main courses, how many different meals can they create?
56 meals
Evaluate the series 39,366 + 13,122 + 4,374 + …
59,049
Express as a single polynomial
(3x^3+x^2)(2x-10x^2)
-30x^5-4x^4+2x^3
Find the coefficient of the x4 term of (x2 − 2) 7.
-672
Find the payout of an investment of $600 that earns 2.5% interest compounded monthly for 2 years.
$630.73
Which two people invented calculus
Issac Newton and Gottfried Wilhelm Leibniz
As which term does 1/27 appear in the sequence 81, 27, 9…?
8th
Who invented algebra
Expand (4x-2)4
Alfred North Whitehead and Bertrand Russell wrote what foundational math work
Principia Mathematica
In a local spelling bee competition, there are 6 students: Elan, Peelan, Elein, Elon, and Nale. The judges are going to select 3 students to stand in a line for a photo. How many different ways can the judges arrange these 3 students in the photo?
120
Evaluate the sum of the 1st to 20th terms of the series given by an = 6 + 14(k – 2).
2500
Express
sum_(n=0)^3 5(1/2)^n x^(2n
as a polynomial.
5/8x^6+5/4x^4+5/2x^2+5
Put (x2-3)12 into sigma notation
Express as a binomial
sum_(n=0)^12 [[12],[k]] (x^2)^(k)(-3)^(12-k)
After how many months will an annuity earning 2.4% annually be worth $500 if $25 is deposited monthly? Round your answer
20 months
Given a selection of n items, the number of ways to select one set of three items followed by one set of two items without replacement is
(n!)/(12(n-5)!
Evaluate
sum_(n=1)^7 2(1.5)^n
96.5
Express
3/4x^6+3/2x^3
in sigma notation
sum_(n=1)^2 3(1/2)^n x^n
Find the coefficient of the x5 term in the polynomial represented by
sum_(n=0)^10 [[10],[k]] (3x)^(10-k)(2)^(k)
1,959,552
A loan worth $15,000 is charged 3.7% annual interest over four years. How much will bimonthly payments of the loan be?
$168.22