(A) Your sister has loaned you $ 1 , 000 with the understanding that you will repay the principal plus 4 % simple interest when you can. How much would you owe her if you repaid the loan after 1 year? After 2 years? After 5 years? After 10 years? (B) How is the interest after 10 years related to the interest after 1 year? After 2 years? After 5 years? (C) Explain why your answers are consistent with the fact that for simple interest, the graph of future value as a function of time is a straight line (Fig. 1 ).
(A) Your sister has loaned you $ 1 , 000 with the understanding that you will repay the principal plus 4 % simple interest when you can. How much would you owe her if you repaid the loan after 1 year? After 2 years? After 5 years? After 10 years? (B) How is the interest after 10 years related to the interest after 1 year? After 2 years? After 5 years? (C) Explain why your answers are consistent with the fact that for simple interest, the graph of future value as a function of time is a straight line (Fig. 1 ).
(A) Your sister has loaned you
$
1
,
000
with the understanding that you will repay the principal plus
4
%
simple interest when you can. How much would you owe her if you repaid the loan after
1
year? After
2
years? After
5
years? After
10
years?
(B) How is the interest after
10
years related to the interest after 1 year? After
2
years? After
5
years?
(C) Explain why your answers are consistent with the fact that for simple interest, the graph of future value as a function of time is a straight line (Fig.
1
).
Q9. If A and B are two events, prove that P(ANB) ≥ 1 − P(Ā) – P(B). [Note: This
is a simplified version of the Bonferroni inequality.]
Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 222 grams of protein and at least 162 grams of fat. If chicken costs 11¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost? (If an answer does not exist, enter DNE.)
Q6. Consider a situation where cars entering an intersection could turn right, turn left,
or go straight. An experiment consists of observing two vehicles moving through
the intersection.
(a) How many sample points are there in the sample space? List them.
(b) Assuming that all sample points are equally likely, what is the probability that
at least one car turns left?
(c) Again assuming equally likely sample points, what is the probability that at
most one vehicle turns right?
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