Twice last? month, Judy Carter rented a car in? Fresno, California, and traveled around the Southwest on business. The car rental agency rents its cars for a daily? fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4? days, she drove 360 ?miles, and the rental cost her ?$226.00 On her second business trip she drove 190 miles in 3? days, and paid ?$149.50 for the rental. Find the daily fee and the mileage charge.

Assume that you have a balance of $5300 on your Discover credit card and that you make no more charges. Assume that Discover charges 21% APR and that each month you make only the minimum payment of 2% of the balance.

Find how many months it will take to bring the remaining balance down to $2500. (Round your answer to the nearest whole number.)

Answer is NOT 301

1. Consider the three vectors, u and v are 10 degrees above and below the x-axis respectively, and ||u|| = 1, ||v|| = 2, and ||w|| = 3. Arrange the dot products taken among these vectors from least to greatest

2. Let A be a 4 x 6 matrix. Find the elimination matrix E that corresponds with the row operation "switch rows 1 and 3, and scale row 4 by a factor of 6.

3. Find the formula for the entry in the ith row and j column of the product AB in terms of the entries of A and B. Assume A is m x n and B is n x p.

explain why a matrice can have many row echelon forms

23. Show that for any numbern, n andn+1 are coprime.

28. Show that if (a,b)=1 and c divides a, then (c,b)=1.

In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 7%probability that a nonsmoker will begin smoking a pack or less per day, and a 3% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 6% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)

A) in 1 month

non-smokers --------------------------- people

1 pack/day or less---------------------people

more than 1 pack/day ----------------people

B) in 2 month

non-smokers --------------------------- people

1 pack/day or less---------------------people

more than 1 pack/day ----------------people

C) in 1 year

non-smokers --------------------------- people

1 pack/day or less---------------------people

more than 1 pack/day ----------------people

Communication is considered an important component of mathematics education in order for deep learning to occur.


1. Choose a specific algebra concept (SeeM2.Fractions and Mixed Numbers or M4.Intro to Algebra in MFL) that you think you understand well, and explain it in your own words.

2. Then, present a math problem for your classmates to solve, making use of this concept (the one you selected). Remember to make your initial post prior to the close of Wednesday of each week.

1. If (1, -1) is an eigenvector of A with associated eigenvalue -2, and (1, 1) is an eigenvector of A with associated eigenvalue 4, then what the entries of A ,a11 , a12, a21 and a22 ?

2. If A has a repeated eigenvalue, the A definitely isn't diagonalizable. (True or False)

use the two-phase method and big.M method to solve the LPP: min z=x1-2x2 st: x1+x2>=2 -x1+x2>=1 x2<=3 x1,x2>=0 (two method!)

Determine the student's Level of Van Hiele Model of Geometric Thought based on the response given. For example: Is the student at Level 1 (Basic Level): Visualization, Level 2: Analysis, Level 3: Informal Deduction, Level 4: Formal Deduction, or Level 5: Rigor? Explain your decision.

Miss Gonmez gave her students a paper polygon and asked them to identify the given shape and explain how they decided which polygon it was.

James responded that the shape was a rectangle. He decided this because he folded the polygon in half length-wise and found that it had opposite sides the same length.

He compared the corners of the polygon by placing them on top of each other and found they were all the same. He concluded they must all be right angles.

A land surveyor places two stakes 500 ft apart. He locates the midpoint between the two stakes and creates a perpendicular to the line that connects these two stakes. He needs to place a third stake 100 ft away along this perpendicular line. To apply the Perpendicular Bisector Theorem, the land surveyor would need to identify

  the location of the third stake as equidistant from the original two stakes

the location of the third stake as closer to one of the original two stakes

a line parallel to the line connecting the two stakes

a line congruent to the line connecting the two stakes

Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $3.00. Also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day. Because of a backlog of orders for model A grates, Kane's manager had decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit?

How many 5-card hands have at least one pair?

Chloe is buying souvenirs on vacation. She wants to spend 70 dollars at most, but only has 60 cubic inches of space available in her luggage. If bracelets cost 7 dollars and take up 3 inches of space and t-shirts are 5 dollars but take 15 inches of space, write and graph a system of four inequalities that model Chloe's possible purchases.Let x=the number of bracelets and y=the number of t-shirts. Use a scale of 2 on both axes.

So my inequalities are as follows: x >= 0
y >= 0
7x+5y<=70
3x+15y<=60

Can you please check if my inequalities are correct and show me how to graph them? Thanks!

a) For the following polynomial; a. Use the Rational Zero Test to list all possible rational roots b. Use Descartes Rule of Signs to provide the possible numbers of positive and negative real roots c. Factor the polynomial completely. ? 3 + 4? 2 + 9? + 36

b) For the following polynomial; d. Use the Rational Zero Test to list all possible rational roots e. Use Descartes Rule of Signs to provide the possible numbers of positive and negative real roots f. Factor the polynomial completely. ? 4 + 3? 3 − 7? 2 − 27? − 18