You drive from your home to a vacation resort 420 miles away. You return on the same highway. The average velocity on the return trip is 15 miles per hour slower than the average velocity on the outgoing trip. Express the total time required to complete the round​ trip, T, as a function of the average velocity on the outgoing​ trip, x.

NOT A MULTIPLE CHOICE QUESTION, I NEED AN ANSWER FOR ALL!!!I. The Bread Machine (25 points)
In real life, you must often make choices about whether to buy something pre-made or make it yourself. There are many things to consider: quality of homemade vs. bought, expense, convenience, enjoyment of making something, etc. In this response, you will be looking at the choice of buying a bread machine or relying exclusively on store bought bread.

A. The bread machine you are interested in costs $100 with tax.
The ingredients to make one loaf of bread cost $0.80.
What is the rate of cost of one loaf of bread?

B. What is your start up cost? (cost of machine)

C. Write a linear equation, y = mx + b for the total cost.

D. Graph the equation on the graph provided. You may use either Point Plotting or Slope-Intercept. Be sure to locate at least 3 points. You may want to do this in pencil in case you decide to use more points later in the problem.

Let (Ω,F,P) be a probability space. Recall the R.V. X is called simple, if there exist A₁, …., Aₙ ∈ F and b₁, …, bₙ ∈ R such that X = ᵢ₌ₗ∑ⁿ bᵢ 1{A ᵢ }. Note that A; need not be disjoint. ...) ... a) Show that if R.V. X,Y are simple, then so is the linear combination aX + bY. b) Is it true that if X₁, X₂ are all simple then so are X₁ + X₂, and X₁ ∧ X₂ = min X1, X₂? c) Is the representation of X (i.e. the sets A₁,.., Aₙ and the scalars b₁, ..., bₙ) unique? d) What if Aᵢ are known to be disjoint? How many values can X take then? e) Show that R.V. X is simple if and only it takes finitely many values. f) Show that E[X] is well defined for X simple R.V.. In other words, if X has two representations: X = ᵢ₌ₗ∑ⁿ bᵢ 1{Aᵢ } and X = ᵢ₌ₗ∑ᵐ Cᵢ 1{Bᵢ), such that B₁, ..., Bₘ ∈ F and C₁, ..., Cₘ ∈ R, then we must have ᵢ₌ₗ∑ⁿ Bᵢ P(Aᵢ) = ᵢ₌ₗ∑ᵐ cᵢP(Bᵢ).

The work of a student to solve a set of equations is shown:Equation A: y = 4 − 2z
Equation B: 4y = 2 − 4z


Step 1: −4(y) = −4(4 − 2z) [Equation A is multiplied by −4.]
4y = 2 − 4z [Equation B]
Step 2: −4y = 4 − 2z [Equation A in Step 1 is simplified.]
4y = 2 − 4z [Equation B]
Step 3: 0 = 6 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 6
Step 5: z = 1


In which step did the student first make an error?
Step 1
Step 3
Step 4
Step 2

George usually takes 1.5 hours to mow his neighbor’s grass and trim the bushes. Today he has only 0.75 of the usual amount of time to complete the job. Which operation describes how to find the amount of time George has to complete the job?

Share 56 pound in the ratio 1:3:4

7 - 3(5x - 10) - 67
​