Given:
4log1/2^w (2log1/2^u-3log1/2^v)
Req'd:
Single logarithm = ?
Sol'n:
First remove the parenthesis,
4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)
Simplify each term,
Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;
Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;
Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:
log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)
log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)
We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):
Thus,
Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)
then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)
Therefore,
log of 1/2 (w^4 u^2 / v^3)
and for the final step and answer, reorder or rearrange w^4 and u^2:
log of 1/2 (u^2 w^4 / v^3)
The profitability index of an investment with cash flows in years 0 thru 4 of -340, 120, 130, 153, and 166, respectively, and a discount rate of 16 percent is: 15%.
<h3>
Profitability index</h3>
First step is to find the Net present value (NPV) of the given cash flow using discount rate PVF 16% and PV of cash flow which in turn will give us net present value of 49.7.
Second step is to calculate the profitability index
Profitability index = 49.7/340
Profitability index = .15×100
Profitability index=15%
Therefore the profitability index of an investment with cash flows in years 0 thru 4 of -340, 120, 130, 153, and 166, respectively, and a discount rate of 16 percent is: 15%.
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Answer:
Confidence interval: (0.04649,0.04913)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 100,000
Number of people who donated, x = 4781
95% Confidence interval:
Putting the values, we get:
is the required 95% confidence interval for the true proportion of their entire mailing list who may donate.
Answer:
42 strawberries are in each basket. 4 strawberries are left over.
Step-by-step explanation:
To find out how many she put into each basket, you need to divide 256/6. Your answer should 42.6666667. Round down to 42.
To find out how many are left over, multiply 42 x 6. You need to do this to figure out how many strawberries total she used trying to put them evenly into the baskets. Your answer should be 252. Then, you subtract 256 - 252. You do this to find out how many are left over. Your answer is 4.
Answer:
IQR: 20
Range: 52
Step-by-step explanation:
IQR = 88 - 68 = 20
Range = 100 - 48 = 52
