# Math, Calculus Questions

math homework problems ranging from algebra to calculus..need to see formulas written out with answers..thanksWhat is three raised to the power of four? (34)What is seven raised to the power of negative one fourth? (7-1/4)What is the common log of 10,000?What is the natural log of 10,000?What is the anti-log (base 10) of 4?What is the anti-log (base “e”) of 9.210340?Consider the equation for a straight line Y = mx + b, where m is the slope and b is the intercept. If the slope is 3, x is 15, and the intercept is 5; what is Y?Consider the equation Y = m(x + b). If m is 3, x is 15, and b is 5; what is Y?Consider the equation for a straight line Y = mx + b, where m is the slope and b is the intercept. If the slope is negative 3, x is 15, and the intercept is 5; what is Y?Consider the equation for calculating indirect rates – Rate (R) = Expense Pool (P) ÷ Allocation Base (B), R=P/B, you learned in a prior pricing course. A contractor is proposing an engineering overhead rate of 175% using an allocation base of $145M in direct engineering labor cost (dollars). We want to find out the amount of engineering overhead expense pool that the contractor is contemplating.Our formula R=P÷B is set up to solve for Rate (R), but we want to solve for the Pool (P)!ANSWER CHOICESSubtract both sides of the equality by B.Add B to both sides of the equality.Divide both sides of the equality by B.Multiply both sides of the equality by BConsider the equation for calculating indirect rates – Rate (R) = Expense Pool (P) ÷ Allocation Base (B), R=P/B, you learned in a prior pricing course. A contractor is proposing an engineering overhead rate of 175% using an allocation base of $145M in direct engineering labor cost (dollars). We want to find out the amount of engineering overhead expense pool that the contractor is contemplating. What is the amount of engineering overhead in millions of dollars ($M) the contractor should be contemplating?Consider the Learning Curve, Unit Formulation, formula: YX = A(X)B, where YX is the cost of Unit “X”, A represents the cost of the first production unit, X is the unit’s number (serial) since the start of production, and B is an exponent corresponding to the Learning Curve percentage. You have been asked to estimate the cost of the 26th unit (Y26) on an 80% Learning Curve where B = -0.321928. You have been told that data does not exist regarding the cost of the first unit (A), but it is known that the 25th unit (Y25) cost $7,500 to produce on this same 80% curve.The basic formula, YX = A(X)B, set up to solve for the 26th unit, becomes Y26 = A(26)-0.321928. You immediately find you first REALLY need the value for A. But the general equation is set up to solve for YX, not A; and the A on the right side of the equality is being multiplied by (X)B. Do you recall how to rearrange any formula to solve for another variable? In this case, to undo the multiplication on the right side of the equality, would you (add, subtract, multiply, or divide) both sides by XB to find an equation that solves for A? Once you have rearranged this formula to solve for A, also recall you have been given the cost of another unit (the cost of the 25th unit, Y25=$7,500). Using this information you should next be able to solve for A, and then solve for the cost of the 26th unit.With these additional instructions, what is your estimate, rounded to whole dollars, for the cost of the 26th unit on an 80% curve, where B=-0.321928, and the cost of the 25th unit is $7,500?Given a series of values, the “central tendency” of the data can be described by the:[removed]Mean, variance, and standard deviation.[removed]Mean, median, and mode.[removed]Median, absolute deviation, and the MAD.[removed]Variance, standard deviation, and coefficient of variation.Consider this series of historically observed prices properly normalized for quantity and economics, ranked from smallest to largest: $100; $100; $104; $110; $120; and $132. In the following order, what are the values for the mean, median, and mode?[removed]$100; $107; $111.[removed]$107; $100; $100.[removed]$111; $107; $100.[removed]$100; $100; $107.There are various measures used to describe the variability or dispersion in a data series. What is the range of the following prices: $100; $100; $104; $110; $120; and $132?What is the variance for the following prices: $100; $100; $104; $110; $120; and $132?What is the standard deviation for the following prices: $100; $100; $104; $110; $120; and $132? (Round your answer to two decimal places.)What is the coefficient of variation (CV) for the following prices: $100; $100; $104; $110; $120; and $132? (Enter your answer as a percentage, without the percentage symbol, and rounded to two decimal places.)Consider yourself to be an estimator working for a contractor. You are informed that your fixed cost is $1.2M, variable cost is $0.125M/unit, and projected sales/production is 120 units. Assuming sales of all 120 units, what is the minimum price per unit you can charge without suffering a loss (i.e. that price where you would break even to cover your total cost and not make any profit)? (Round and express in whole dollars, not millions, using the $ sign.)[removed]Consider yourself to be a buyer. The contractor is reluctant to bear the expense of producing (or making up) detailed data. They have, however, submitted their total cost to produce 120 units last year was $20M, and the year before their total cost to produce 100 units was $17.5M. What is the contractor’s fixed cost? (Express in dollars million, using the $ sign and a capital “M”, rounding to three decimal places – e.g. $6.275M.)