Math Answers

Prove that a real number 𝑥 is irrational if and only if 5𝑥 is irrational

Find out if the following functions are one-to-one and/or onto. a. 𝑓: 𝑍 → 𝑅, 𝑓(𝑥) = 𝑥 3 + 1 b. 𝑓: 𝑅 + → 𝑅 +, 𝑓(𝑥) = |𝑥| + 5

Letv1 = (0,3,6,0),v2 = (0,2,4,6), and v3 = (1,−1,−2,1). Express (4,−1,−2,−11) as a

linear combination of v1,v2, and v3

Find the general solutions of the following differential equations using D-operator methods:

2.1 (D² - 2D + 5)y = x+5

2.2 (D+4)² x = sinh4t

Just before a referendum on a school​ budget, a local newspaper polls 405 voters to predict whether the budget will pass. Suppose the budget has the support of 55​% of the voters. What is the probability that the​ newspaper's sample will lead it to predict​ defeat?

Let  . P(x): x²/2 = x

Find the following then identify their truth values.

1. P (1)
2. P (2)
3. ꓯn, P(n)
4. ⱻn, P(n)

The expression that is equivalent to (a3b2)3 is

In a beauty contest, the ages of the contestants are normally distributed with a mean of

24 years and a standard deviation of 1.5. What percent of the contestants have age

between 22.5 and 27 years old?

In a beauty contest, the ages of the contestants are normally distributed with a mean of

24 years and a standard deviation of 1.5. What percent of the contestants have age

between 22.5 and 27 years old?

4. For each of these pairs of sets, determine whether the first is a subset of the second, the second is a subset of the first, or neither is a subset of the other. a) the set of people who speak English, the set of people who speak English with an Australian accent b) the set of fruits, the set of citrus fruits c) the set of students studying discrete mathematics, the set of students studying data structures