<h2>
Question:</h2>
At Priscilla's school, the final grade for her Calculus course is weighted as follows: Tests: 50% Quizzes: 30% Homework: 20% Priscilla has an average of 87% on her tests, 100% on her quizzes, and 20% on her homework. What is Priscilla's weighted average?
<h2>
Work:</h2>
Weighted Average gives weights to each percent of the average as follows:
Weighted Average = Average * weighting percent
Weighted Average = Test Average * Test Weighting + Quiz Average. * Quiz Weighting + Homework Average * Homework Weighting
Weighted Average = 87% * 50% + 100% * 30% + 20% * 20%
Weighted Average = 43.5% + 30% + 4%
Weighted Average = 77.5%
<h2>
Answer:</h2>
77.5%
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Answered by: ms115
The preferred gig is the first one since its today's worth is greater than the today's value of the second gig
What is the today's worth of $5000 each year?
The worth of the second gig, which pays $5000 every year for the next 6 years in today's dollar is the present value of all the six annual cash flows discounted using the present value formula of an ordinary annuity as shown below:
PV=PMT*(1-(1+r)^-N/r
PV=present value of annual payments for 6 years=unknown
PMT=annual payment=$5000
r=required return=discount rate=8%
N=number of annual cash flows=6
PV=$5000*(1-(1+8%)^-6/8%
PV=$5000*(1-(1.08)^-6/0.08
PV=$5000*(1-0.630169626883105)/0.08
PV=$5000*0.369830373116895
/0.08
PV=$23,114.40
The fact that the present value of the second option which pays $5000 annually is lesser than the amount receivable immediately, which is $25,000, hence, the first gig is preferred
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This is a permutation question because we care about the order.
We can demonstrate this by letting each person be a person in the pie eating contest.
A B C D E F G H I J K
_ _ _
Now, there are 11 ways for the first prize to be won, since there are no restrictions upheld. Let's say A wins the first prize.
B C D E F G H I J K
A _ _
Now, assuming prizes aren't shared, there are only ten people left to win the second prize.
Using this logic, then we can say that nine can win the third prize.
Thus, our answer is 11 · 10 · 9 = 990 ways.
However, this method works for this question.
What happens when the number of places we want gets significantly larger?
That's when we introduce the permutation formula.
We know that 11·10·9·8·7·6·5·4·3·2·1 = 11!, but we don't want 8! of them.
This is the formula for permutation.
Answer:
2,057.18
Step-by-step explanation: