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# Basic Algebra

### Concept Checks for Binomial Coefficients

1. Determine the binomial coefficient for the fifth term in the expansion of (x+y)^9 Write the binomial expansion for each expression: 1. (a-b)^7 Write the indicated term of each binomial expansion: 1. Twelfth term of (2x+y^2)^16

### Slopes, Lines and Graphs

An airplane climbs from sea level to a cruising altitude of 31,500 feet at a rate of 6300 ft/min. After cruising for 20 minutes, the airplane begins its descent at a rate of 3500 ft/min. If we were to sketch a graph of the airplane's flight pattern, which measurement would the x-axis represent? Which measurement would the y-axis

### Properties of Logarithms and Simplification of Expressions

Use the properties of logarithms to rewrite each expression. Simplify the result if possible. 1. log2 ((2*square root 3)/5) Given log10 (2) = 0.3010 and log10 (3) = 0.4771, find each logarithm without using a calculator. 2. log10 (20/27)

### Variation Problems

Solve each variation problem: 1. If m varies jointly as z and p, and m=10 when z=2 and p=7.5, find m when z=5 and p=7. 2. Current in a circuit: The current in a simple electrical circuit varies inversely as the resistance. If the current is 50 amps when the resistance is 10 ohms, find the current if the resistance is 5

### College Algebra: Polynomial Functions

For each polynomial function, find all zeros and their multiplicities: 1. f(x)=(x+1)^2(x-1)^3(x^2-10) Find a polynomial function of degree 3 with real coefficients that satisfies the given conditions: 1. Zeros of 2, -3, and 5; f(3)=6 2. Zero of 4 having multiplicity 2 and zero of 2 having multiplicity 1; f(1)= -18

### Problems in Galois Theory Involving a Cubic PolynomialK

Let f be a cubic monic polynomial and char K not 3. a. Show how to make a change of variables x' = x - lamda in f (x) = 0 to reduce to a monic equation where the coefficient of x^2 is zero b. Suppose K = R. Let D be the discriminant of f. Prove that f has one real root if D < 0 and three real roots if D > or equal to 0. c. Le

### Forward Rate for the Japenese Yen

Use the information below to answer the following questions. (Do not include the dollar signs (\$). Round your answers to 4 decimal places, (e.g., 32.1616)) CURRENCY PER U.S. \$ Japan Yen 115.76 6-months forward 112.91 Canadian Dollar

### Double angular formula

Find the exact value of a) sin a/2, b) cos a/2, C) tan a/2 tan a= 4/3, a lies in quadrant 3 sin a/2 = cos a/2 = tan a/2 = (type an exact answer, using radicals as needed. simplify answer)

### Applications of rational expressions

Look at the example application of rational expressions on page 315 of your textbook. Then, using the Internet, locate a Web site that has an additional example that interests you. (Use the search words "rational expressions applications.") Following the example of problems 51-54 on page 315, formulate two to three values for yo

### Expected value of certainty in investments

What is expected value under certainty of the following investments, and the expected value of perfect info In a good market in a bad market Houses +10 -5 Dogs +7 -4 Cats +5 -2 Chances of bad market 60%

### Half angle formulas

Use the given information to find the exact value of a) sin alpha/2 = b) cos alpha/2 = c) tan alpha/2 = when sec alpha = -17/8, alpha lies in quadrant 2 (Type an exact answer, using radicals as needed. simplify answer)

### Solving and graphing Quadratic equations

Some homework practice I would like your assistance to prepare for exam. 1. Y^2-6y+9=8 ( exact solutions to three decimal places) Y=_______ 2. Solve 7x+x(x-4) = 0 the solution is x = _________ Find the x intercepts of f(x) = 7x+x(x-4) the x intercepts are _____ 3. F(x) = -1/2x^2 The vertex is _______

### Factor the following expression completely.

Please explain how to solve the given problems. Factor the following expression completely. 1. 81m^3-63m^4+8m^5 Solve each quadratic equation by whatever method you choose. Round the answer to the nearest tenth, if necessary. If there is no answer, mention that clearly. 2. 56-y^2 = 0 3. 5x^2+13x-1=0 4. x^2+3x=-6

### Mathematics and Language

1. Is math independent of human influence? Why or why not? 2. Why is it important for math to have its own language? What other disciplines have their own language?

### Prove the arithmetic-geometric mean inequality.

Prove the arithmetic-geometric mean inequality by using an elementary method (no use of calculus, derivative or limit), that is, (X1...Xn)^1/n <= (X1+...+Xn)/n for non-negative real numbers X1, X2, ..., Xn.

### Equation of the Plane that Passes Through a Point

Find an equation of the plane that passes through the point (6,0,-2) and contains the line x = 4 - 2t, y = 3 + 5t, z = 7 + 4t.

### Homework problem

Solve each system of inequalities by graphing. Name the coordinates of the vertices of the polygonal convex set using a matrix. Y is greater than or equal to -.5x = 1 Y is less than or equal to -3x + 5 Y is less than or equal to 2x + 2 *Please show how you find the vertices, I am unsure how to do so by hand and do not h

### Algebra problem

Problem: John and his son are hauling Christmas trees to market. The market is 420 miles from the tree farm. John's truck averages 32 MPH and leaves at 8 am. Owen's truck averages 46 MPH and leaves at 9 am. At what time will the two trucks be in the same location?

### Break-even analysis: A look at profit and loss

I recently opened a specialty pizza business. I can sell my specialty pizzas for \$15. The cost for making the pizzas includes a fixed cost of \$55. And a labor cost of \$4.00 per pizza. 1. Create an equation to determine revenue. 2. Create an equation to determine total cost. 3. How many pizzas must be sold to break even (i.e.,

### M&M Restaurant Bowls

3 guys walked out a restaurant and saw a bowl of M&Ms. Guy 'A' took a third and returned 4. Guy 'B' took a quarter of what's left and returned 3. Guy 'C' took half of the rest and returned 2. How many M&Ms was in the bowl if 17 is left?

### Octahedral group

a) Determine the class equation of the octahedral group. b) This group contains two proper normal subgroups. Find them, show that they are normal, and show that there are no others.

### Monetary question

1. Nick is one-forth his grandfatherâ??s age. Five years ago, he was one-fifth his grandfatherâ??s age. How old are Nick and his Grandfather now? 2. Eloise bought new clothes for school. In the first store, she spent half the money she had, plus \$10. In the second store, she spent half of what was left, plus \$5. In th

### Real - World Math Algebra: solving equations and problems

In general, the area of a rectangular shape is found by multiplying the length of the area by the width of the area. This can be represented by the formula area = length x width or A = L x W. If you were to measure the length and width in feet, then the result of this equation will be in square feet (ft^2). The resulting number

### Nearest tenth the median of these attendance numbers

The table below gives the total spectator attendance for various U.S. sports in 1997. Sport Attendance (millions) Pro Baseball 64.9 College Basketball (Menâ??s) 27.7 College Basketball (Womenâ??s) 6.7 Pro Basketball (Menâ??s) 21.7 College Football 36.9 Pro Football 14.

### Calculating the Needed Score

To get a C in history, Nandan must average 74 on four tests. Scores on the first three tests were 69, 75, and 60. What is the lowest score that Nandan can get on the last test and still receive a C?

### Midrange of the Prices

The price in dollars of a gallon of gasoline at the end of each month is recorded for one year. The results are: 1.19 1.28 1.55 1.76 1.85 1.85 1.83 1.76 1.66 1.52 1.48 1.47 Find the mid-range of these prices.

### A liquid tank system is explored and using a number of input sensor conditions boolena expressions for and overfill alarm OV and an Empty alarm EP are derived for the conditions/scenarios given The boolean expression for an Overflow fill alarm OV which is active 1. if the input flow rate sensor is high while the output sensor is low, the pressure is low and the level is high 2. If both flow rates are high while the output flow rates are low and the pressure is low Is derived. Also the EP = Empty alarm boolean expression is derived for conditions where EP is high when 1. Both input rates are low, the level is low and the output flow rate is high 2. If either input flow rate is low, the output flow rte high and the pressure in the tank is high

A liquid tank system is explored and using a number of input sensor conditions boolena expressions for and overfill alarm OV and an Empty alarm EP are derived for the conditions/scenarios given The boolean expression for an Overflow fill alarm OV which is active 1. if the input flow rate sensor is high while the output se

### Monthly car payments on a loan.

So you're buying a car.You know that interest today is low. But you found a place where you can earn 1% interest per month. You invest \$1000 on the 1st of each month. By the end of the month, that \$1000 is now \$1010. You keep doing this for 4 months, then take that money to use on a down payment for a car that is \$22,323 (incl t

### Legs on a Bus

This is a 5th grade math problem. This is not a trick question. This is a real, straight-forward math problem, so don't say that "a bus has no legs", even though that would be a good "lateral thinking" type of answer. You don't count any undescribed driver, nor any boys who might also be on the bus. The problem is neither more n

### Minimal Polynomial of T

Let V be an inner-product space and suppose T element of L(V) is normal. a) Prove that null T^k = null T for all positive integer k. b) Prove that the minimal polynomial of T has no repeated roots.