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    Basic Algebra

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    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.

    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.

    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.

    Substituting series expansions into each other

    Consider the formal power series f(x) = x + x^2/2 + x^3/6 + x^4/24 and g(x) = x - x*/2 + x^3/3 - x^4/4. Compute by hand the first five coefficients (i.e., up to the coefficient of x^4) of (a) h(x) = x^f(x) (d) k(x) = log(1 + g(x)) (c) m(x) = (h o k)(x)

    The solution of basic algebra problems

    Use Equation Editor to write mathematical expressions and equations. 1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C = 6,000/(200 - 2x) a. What is the cost to remove 75% of the pollutant? b. What is the cost to remove 90% of the pollutant? c. What is the cost to remove 99% of t

    Find the generating function for the strings

    Find the generating function with respect to length for the set of {0,1}- strings having the property that each block of 1's contains an even number of 1's and each block of 0's contains an of number of 0's.

    Finding the finite formula for the infinite sum

    1) When is sin(x)=0? Why is it plausible that sin(x)=x(1-x/pi)(1+x/pi)(1-x/2*pi)(1+x/2*pi) ... ? 2) Explain how Euler concludes from 1) that pi^2/6=1+1/4+1/9+1/16 ... . 3) Compare the formula in 2) to Archimedes' calculation for pi. Which of these methods is more efficient and why? 4) Why does the argument from 3) not w

    Unique Linear Polynomial that Contains Two Points

    a. Consider the simplest case of a linear polynomial f(x) = mx + b. Suppose f(?) = 0 and f(0) = ?. Does this information allow you to find m and b? Explain. b. Now we look at a quadratic function f(x)=ax^2 +bx+c. Suppose ?1 does not equal ?2 and f(?1) = f(?2) = 0. How much does this information allow you to conclude a

    simplifying the square and finding values

    2. simplify the square of 96b(cubed)/144a(4th power) 3. Find the value(s) of b that would make the following true: 5b(squared)-125=0. 4. Solve using the quadratic formula: 2x(squared)+2x=3. 5. State the number of zeroes for each equation: x(squared)=4x x(squared)+9=6x x(squared)+25=0 6. a mode

    The Exact Value of the Expressions

    Find the exact value to the expressions cos(alpha+beta) and sin(alpha+beta) and tan(alpha+beta) under the following conditions.. cos(alpha)=21/29, alpha lies in quadrant 4, and sin(beta)= -4/11, beta lies in quadrant 3.

    Present Value: Jim Nance has been offered a future payment

    Present Value: Jim Nance has been offered a future payment of $500 three years from today. a. If his opportunity cost is 7% compounded annually, what value should he place his opportunity today? b .What is the most he should pay to purchase this payment today? c.what is the most he should pay to purchase this payment tod

    Factor the following trinomial completely.

    5. Factor c^2 + 6c + 9. 6. Factor w^2 - 8w + 16. 7. Factor the following trinomial completely. x^2 - 0.2x + 0.01 8. Factor the trinomial completely. 2x^2 + 8x +8 9. Factor 16c^2 - 40ct + 25t^2. 10. Factor the trinomial completely. - 48h^3 + 72h^2y - 27hy^2

    Algebra

    3. In 2002, Home Depotââ?¬â?¢s sales amounted to $58,200,000,000. In 2006, its sales were $90,800,000,000. a. Write Home Depotââ?¬â?¢s 2002 sales and 2006 sales in scientific notation. You can find the percent of growth in Home Depotââ?¬â?¢s sales from 2002 to 2006 by following these steps: ââ?¬¢ Find

    What is the effective annual rate?

    The Baxter, Inc. borrowed $100,000 for six months from the bank. The rate is prime plus 2 percent. The prime rate was 8.5 percent at the beginning of the loan and changed to 9 percent after two months. This was the only change. How much interest must The Jackson Corporation pay? What is the effective annual rate?

    total overtime wages

    Consider the following aggregate production planning problem: January February Dema Demand 100 units 120 units Produ Production plan

    Profit equation as a function of output using demand equation

    Mickey Mouse has a trap company with fixed costs of $89,000 and operating costs of $50 per trap and a market demand curve of: price=950-.10(output). Since Mick can't set his price find the revenue equation for his mousetrap business. a) Construct the profit equation as a function of output using the demand equation. What doe