Math Solutions
Step-by-step solutions with Learning Insights, Quick Tips, and Common Mistakes.
1. Determine whether the relation R on the set {1, 2, 3, 4, 5} defined by (x, y) ∈ R if x + y ≤ 6 is reflexive, symmetric and/or transitive. 2. Give the equivalence class for the following: a. 3 modulo 5 b. 2 modulo 5 3. Give an algebraic proof for the binomial identity ( n k ) = ( n − 1 k − 1 ) + ( n − 1 k ). 4. A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes in three sizes for each sex. How many different types of this shirt are made? 5. A multiple-choice test contains 10 questions. There are four possible answers for each question. a. In how many ways can a student answer the questions on the test if the student answers every question? b. In how many ways can a student answer the questions on the test if the student can leave answers blank? 6. How many positive integers between 5 and 31 a. are divisible by 3? Which integers are these? b. are divisible by 4? Which integers are these? c. are divisible by 3 and by 4? Which integers are these? 7. In how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people, if a. the bride must be in the picture? b. both the bride and groom must be in the picture? c. exactly one of the bride and the groom is in the picture? d. the bride must be next to the groom? 8. How many bit strings contain exactly five 0s and 14 1s if every 0 must be immediately followed by two 1s? 9. How many bit strings of length 10 contain at least three 1s and at least three 0s? 10. What is the coefficient of x 101y 99 in the expansion of (2x − 3y) 200?
Oct 18, 2026
Write the equation of this line in slope-intercept form.
Oct 3, 2026
(9 points each part) Find the derivative of the function. PLEASE do not simplify. Label. a) f(x) = 1/(2x-4)^3 b) f(x) = ((2x+3)/(5x-2))^3 c) f(x) = (6x-7)^2 * (6x^2+2)^3 d) f(x) = sin(2x^3 + 2x) e) f(x) = (x^3 + 2x + 1)/(2x+1)^2 f) f(x) = (2x)cos^2(3x) g) f(x) = cos(tan(x)) h) If y = x^2 sin 2x, then dy/dx =
Sep 28, 2026
Write the equation of the line in fully simplified slope-intercept form.
Sep 28, 2026
Evaluate: g(f(-3))
Sep 16, 2026
Fill in the missing values in the 3x3 matrix: [ _, _, _ ] [ 6, 10, _ ] [ 8, _, 4 ]
Answer: Cannot be solved uniquely — no rule or pattern was specified
Jul 19, 2026