A. 271 and 516
1. Find the greatest common divisor, d, of the two numbers from part A using the Euclidean algorithm. Show and explain all work.
2. Find all solutions for the congruence ax ? d
(mod b) where a and b are the integers from
part A and d is the greatest common divisor from part A1.
Show and explain all work.
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Construct the 2 × 2 matrix for the linear transformations R 2 → R 2 defined by the following compositions. In each case, write down the matrix of each transformation, then multiply the matrices in the correct order.
(a) A dilation by a factor of 4, then a reflection across the x-axis.
(b) A counterclockwise rotation through π/2 , then a dilation by a factor of 1/2 .
(c) A reflection about the line x = y, then a rotation though an angle of π.
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Please write a few sentences on the following two topics:
1. The system of coordinates is a "bridge" between algebra and geometry. Why? How? Etc....
2. Relations between straight lines and linear equations.
Please write neatly, and in detail. Thank you so much!
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A $1000 par value 4% bond with semiannual coupons matures at the end of 10 years. The bond is callable at $1050 at the ends of years 4 through 6, at $1025 at the ends of years 7 through 9, and at $1000 at the end of year 10. Find the maximum price that an investor can pay and still be certain of a yield rate of 5% convertible semiannually.
ANSWER: 922.05
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1. Discuss the different properties of Matrices for each matrix
2. What is the importance of interface in fiber reinforce composite?
In: Math
In: Math
The Oregon Atlantic company produces two types of paper:
newsprint and wrapping paper. Make 1 yard of newspaper
It takes 5 minutes to produce one yard of newspaper; and 8 minutes
to make one yard of wrapping paper. The company has 4,800 hours of
operation per week. Newspapers cost $ 0.20 per yard and wrapping
paper yields $ 0.25 per yard. Demand per week is 500 yards for
newspaper and 400 yards for wrapping paper. sales price need labour
hour is 1 hour.The company has established the following goals in
order of importance:
(1) Limit overtime to 480 hours or less.
(2) Create a profit of $ 300 per week.
(3) profit size.
(4) Do not make fun of production capacity.
a. Determining how many different types of paper should be
produced to satisfy various goals
Formulate it as a goal planning method model.
b. Use your computer to solve the problem.
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1) How much will you have accumulated over a period of 30 years if, in an IRA which has a 10% interest rate compounded quarterly, you annually invest:
a. $1 b. $4000 c. $10,000 d. Part (a) is called the effective yield of an account. How could Part (a) be used to determine Parts (b) and (c)? (Your answer should be in complete sentences free of grammar, spelling, and punctuation mistakes.)
2) How much will you have accumulated, if you annually invest $1,500 into an IRA at 8% interest compounded monthly for: a. 5 year b. 20 years c. 40 years d. How long will it take to earn your first million dollars? Your answer should be exact rounded within 2 decimal places. Please use logarithms to solve.
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Two balls are drawn in succession out of a box containing 3 red and 5 white balls. Find the probability that at least 1 ball was? red, given that the first ball was left parenthesis Upper A right parenthesis Replaced before the second draw. left parenthesis Upper B right parenthesis Not replaced before the second draw. ?(A) Find the probability that at least 1 ball was? red, given that the first ball was replaced before the second draw.
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A beverage company has introduced three new juice blends: carrot-canteloupe, kiwi-kale, and raspberry-rhubarb. They conducted a study where 210 volunteers tried all three blends and reported which ones they liked.
The number of volunteers who liked the carrot-canteloupe blend was 19.
The number of volunteers who liked the kiwi-kale blend was 18.
The number of volunteers who liked the raspberry-rhubarb blend was 21.
The number who liked both carrot-canteloupe and kiwi-kale was 14.
The number who liked both raspberry-rhubarb and kiwi-kale was 8.
The number who liked both carrot-canteloupe and raspberry-rhubarb was 10.
The number who liked all three blends was 6.
1. How many of the volunteers liked NONE of the three blends they tested?
2. How many liked just ONE of the blends?
3. How many liked kiwi-kale but not raspberry rhubarb?
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A committe of four is being formed randomly of from the students and staff of a school: 5 administrators, 37 students and 4 teachers. How many ways can a committee be formed?
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Suppose C is a m × n matrix and A is a n × m matrix. Assume CA = Im (Im is the m × m identity matrix). Consider the n × m system Ax = b.
1. Show that if this system is consistent then the solution is unique.
2. If C = [0 ?5 1
3 0 ?1]
and A = [2 ?3
1 ?2
6 10] ,,
find x (if it exists) when
(a) b =[1
0
3]
(b) b =[ 7
4
22] .
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An investment of $71,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $5490. The interest from the first investment was 6 times the interest from the second. Find the amounts of the three parts of the investment.
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1.
f(x)= 3x / x^2 + 1
- Vertical Asymtote
| As x → −, f(x) → |
As x → +, f(x) →
- Any hole in graph
- Horizontal asymtote
| As x → −, f(x) → |
As x → +, f(x) →
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