Please see attached.
1. A factory working at 83% of capacity produces 231 widgets per day. How many widgets would it produce if it worked at full capacity?
2. Solve for X: x - 2.4 = 1.5
3. Simplify: (Recall: x-3 = 1/x3)
91/2 a2/3 b-1/5
4. PROTRAC, Inc. produces two lines of heavy equipment. One of these product line (E-9), termed earthmoving equipment, is essentially for construction applications. The other line (F-9) is for forestry use. The two lines are produced in the same departments (A and B) with the same machines. For next month's production, Dept. A has 150 hours available and Dept. B has 120 hours available. The table below summarizes this information:
HOURS NEEDED PER UNIT
DEPT. A DEPT.B
Per E-9 10 12
Per F-9 15 8
Total Available 150 120
5. Under which scenario is the final price of the stock higher? Explaiin
A. The price goes up by 5% and then down by 5%
B. The price goes down by 5% and then up by 5%
7. Find the point where the two lines meet.
y = -2x + 4
x - 2y = 4
8. For the function f(x) = x - 2
x - 4
A. Find f(8)
B. Are there any values for which f(x) is not defined? Explain.
9. A company has the following total cost and total revenue functions when producing and selling Q units of a product.
TC = 15Q + 100 TR = Q2
Find the breakeven values. Also, sketch below the cost and revenue functions showing the breakeven values. Put Q on the horizontal Axis and TC and TR on the vertical axis.
10. Hoe much money will you have in an account two years from now, if today you deposit $100 into that account and the interest rate is 10% per year compounded semi-annually?
11. What amount would be needed now in order to generate $1000 five years from now id the interest is 3.7% per year compounded annually?
12. Solve for X: logx 16 = 4
Evaluate to 3 decimal places LN 7 =
13. An economist want to use the percentage change in productivity in the U.S. (X) to predict the percent change in the Standard & Poor's index (Y). He ran a regression using data for a period of 50 years and the following model was produced:
Y = -5.0 +7X
A. Use the model to predict the percentage change in the S&P if the percentage change in productivity is @% (X=2)
B. Identify the Y-intercept of this line. Interpret that number in terms of the model.
C. Identify the slope. Interpret that number in terms of the model.
There are a variety of topics covered in this solution including: percentage, solving for a variable, simplifying exponents and fractions, graphing equations of lines, points of intersection, points at which a function is undefined, logarithms and natural logs.