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1. Find the sum: 2+4 +6+...+2n. (Hint: you can use induction)
2. Arc the following statements logically equivalent?
(a) ~(p٨q) and (~pV~q)
(b) ~(pVq) and (~p٨~q)
(e) (A U B)c and Ac ∩ Bc (remember: Ac denotes the complement of the set A)
Solve the equation by graphing.
Graph y^2=x^2 and explain why the graph is not a function. Determine the period and amplitude of the function y=sin 6x then graph it.
The revenue of Theta Corporation is given as R=15x, where x is the number of units produced (in thousands). If the cost is how many units will have to be produced before the company breaks even?
Transportation problem
Write a quadratic equation in the variable x having the given number as solutions. Type the equation in standard form, ax^2+bx+c=0 Solution:5, only
compare and contrast permutations and distinguishable permutations. provide a formula for each. state the fundamental
Find the dimension of the solution space of the following homogenous system of linear equations
Let's say you are a hospital dietician. A patient must have at least 165 milligrams and no more than 330 milligrams of cholesterol per day from a diet of eggs and meat.
Find the exact value to the expressions cos(alpha+beta) and sin(alpha+beta) and tan(alpha+beta) under the following conditions.. cos(alpha)=21/29, alpha lies in quadrant 4, and sin(beta)= -4/11, beta lies in quadrant 3.
Create a proof by mathematical induction that demonstrates that the sum of the first n even numbers is equal to n(n + 1)
two sessions of swimming lessons were held at a pool. in the first session 40 students attended. of these 40 students
consider the first 10 even natural numbers 2468101214161820as a sequence with nth term alittle n- a. explain why the
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