University of Houston

Math

Permutations and Combinations Solutions

This test contains a total of 7 multiple choice questions, and each multiple choice question features 5 possible answers. (Someone guessing all "a's." for example, would have a string of multiple choice answers that reads "aaaaaaa.") How many total strings of multiple choice answers are possible for our test? (a) 7⁵ (b) 5! (c) (7/5) (d) 5⁷ (e) 1+2⁷ +3⁷ +4⁷ +5⁷

Math

Functions Solutions

Given that there exists a surjective function f : S -> T, which of the following substitutions for the sets S and T are possible? Select only one answer. (a) S = {1,2,3}. T= R. (b) S = {x ∈ R : x² - 4 = 0}, T = {5, π, -10} (C) S = {x ∈ R : (x² - 1)(x² - 4)=0}, T = {5,π,-10} (d) S = {1}, T = {x ∈ R : eˣ = 0}. (e) S = {n ∈ N : n ≤ 2022}, T={z ∈ Z : |z| ≤ 202}.

Math

Functions Solutions

Consider the function f : N→P(N) given by f(x) = {d ∈ N: d|x}. (a) Write out all of the elements of the set f(10) = {d ∈ N: d|x}. (b) Is f one-to-one? Prove your answer.

Math

Sets and Relations Solutions

Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives. a) Something is not in the correct place. b) All tools are in the correct place and are in excellent condition. c) Everything is in the correct place and in excellent condition. d) Nothing is in the correct place and is in excellent condition. e) One of your tools is not in the correct place, but it is in excellent condition.

Math

Functions Solutions

Graph an exponential that passes through the point (2,6) and has growth factor 3. Plot and label at least 3 other points (include an intercept).

Calculus

Application of derivatives Solutions

What is the effect in the time required to solve a problem when you double the size of the input from n to 2n, assuming that the number of milliseconds the algorithm uses to solve the problem with input size n is each of these function? [Express your answer in the simplest form possible, either as a ratio or a difference. Your answer may be a function of n or a constant.] a) log log n b) log n c) 100n d) n log n e) n² f) n³ g) 2ⁿ

Calculus

Differential equations Solutions

What is the effect in the time required to solve a problem when you double the size of the input from n to 2n, assuming that the number of milliseconds the algorithm uses to solve the problem with input size n is each of these function? [Express your answer in the simplest form possible, either as a ratio or a difference. Your answer may be a function of n or a constant.] a) log log n b) log n c) 100n d) n log n e) n² f) n³ g) 2ⁿ

Math

Differential equations Solutions

Consider the following differential equation and seek a power series solution centered at x₀ = 0. (x² + 4)y'' - xy' + 5y = 0 (7) Upon initially substituting in, all FOUR series have the same exponent on x EXCEPT for one. The one that has a different exponent has an exponent of (A) n (B) n-1 (C) n - 2 (D) n+1 (8) The recursion formula for the coefficients is (A) an+2 = (n(n-2)+5)an/(4(n + 2)(n + 1)) (B) an+2 = -(n(n - 2)+5)an/(4(n + 2)(n+1)) (C) an+2 = (n(n-2) +5)an/(4n(n-1)) (D) an+2 = (n(n - 2) + 5)an /(4n(n + 1))

Anatomy and Physiology

Introduction to Physiology Solutions

What is the reasoning behind bonobo sex, and why do they have sex with the same sex (female-female, male-male)? From my understanding, female bonobos can measure the change in oxytocin levels. This hormone plays a key role in social mobility, in competitive context; the need to ensure cooperation. That's why female bonobos prefer to engage in sexual interaction with other females, and males with males.

Physical Chemistry

General Solutions

What is the equivalence point? 1. The equivalence point is experimental point when an exact stoichiometric amount of each reactant has been added. 2. The equivalence point is experimental point when pH of the solution is 7. 3. The equivalence point is experimental point when pH of the solution is minimal. 4. The equivalence point is experimental point when the concentration of H+ is equal to the concentration of OH-.

Physical Chemistry

General Solutions

What are alkaloids? ○ Alkaloids are organic bases found in plants that are often poisonous. ○ Alkaloids are inorganic bases found in plants that are good for health. ○ Alkaloids are inorganic bases found in plants that are often poisonous. ○ Alkaloids are organic bases found in plants that are good for health.

Physical Chemistry

General Solutions

What is an acid-base neutralization reaction? (A) An acid-base neutralization reaction is when the hydroxide ion from the base reacts with water to form acid. (B) An acid-base neutralization reaction is when the hydroxide ion from the acid reacts with the hydrogen ion from the base to form water. (C) An acid-base neutralization reaction is when the hydroxide ion from the acid reacts with water to form base. (D) An acid-base neutralization reaction is when the hydrogen ion from the acid reacts with water to form base. (E) An acid-base neutralization reaction is when the hydrogen ion from the acid reacts with the hydroxide ion from the base to form water. (F) An acid-base neutralization reaction is when the hydrogen ion from the base reacts with water to form acid.