Convert the system
3x1 +13x2 - 14x3 = -14
x1 + 4x2 -5x3 = -4
-7x1 - 25x2 +39x3 = 20
to an augmented matrix. Then reduce the system to echelon form and determine if the system is consistent. If the system in consistent, then find all solutions.
Augmented matrix:
Echelon form:
Is the system consistent?
Solution (x1,x2,x3) =
In: Math
In: Math
A consonsultant wishes to invest up to a total of $25000 in two types of securities, one that yields 10% per year and another than yields 8% per year. They believe that the amount invested in the first security should be at most one third of the amount invested in the second security. What investment program should the consultant pursue in order to maximize income? (Use constraint inqualities with objective function)
In: Math
In: Math
Let f(x) = 5x+3 and g(x) =2x-5. Find (f+g)(x),(f-g)(x),(fg)(x), and (f/g) (x). Give the domain of each.
(f+g) (x) =
(f-g)(x) =
(fg)(x) =
(f/g)(x) =
The domain of f+g is_
The domain of f-g is_
The domain of fg is _
The domain of f/g is _
Please at the end provide showed work.
In: Math
Calculate a t-test for the following scenario. An engineer is designing a stationary parts bin at a work table and considers using an established... Calculate a t-test for the following scenario. An engineer is designing a stationary parts bin at a work table and considers using an established functional grip reach of 29.55 inches taken from the overall population mean, which was published in a textbook. However, the individuals who work in the facility represent a demographic that the engineer has noticed to be a bit small in stature. She decides to take a small sample to test her theory and randomly selects seven individuals and measures their reach. She comes up with the following data: 27.87, 29.49, 28.34, 28.20, 29.00, 29.56, 27.95 (inches). Calculate a mean and sample standard deviation, and use these values to perform a t-test on this data. Report all of these values. Also, discuss the concept of the p value and whether the data was significantly different from the population mean. Discuss whether the engineer was correct in assuming the reach of the worker population may be less than the population mean.
In: Math
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.
In: Math
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
In: Math
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.
In: Math
explain why a matrice can have many row echelon forms
In: Math
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.
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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
In: Math
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.
In: Math
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)
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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!)
In: Math