math 104
Katina4
math_104_homework.docxConsider the sets.
A = {distinct letters in the word pipe}
B = {13}
C = {p, i, e}
D = {3 + 1}
E = {four}
F = {4}
(a) What is the cardinality of each set?
|A| =
|B| =
|C| =
|D| =
|E| =
|F| =
Consider the following sets.
A = {17}
B = {10 + 7}
C = {10, 7}
D = {26}
E = {2, 6}
(a) What is the cardinality of each set?
|A| =
|B| =
|C| =
|D| =
|E| =
Perform the given set operation. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
{3, 4, 7} ∪ {4, 7, 9}
Perform the given set operation. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
{2, 4, 6} ∩ {4, 6, 10}
Perform the given set operation. Let
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(Enter your answers as a comma-separated list. Enter EMPTY or Ø for the empty set.)
{1, 5, 7} ∪ {2, 6, 9}
Perform the given set operation. Let
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(Enter your answers as a comma-separated list. Enter EMPTY or Ø for the empty set.)
{1, 2, 3, 4, 5} ∩ {3, 4, 5, 6, 7}
Perform the given set operation. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
{2, 7, 9}
Perform the given set operation. Let
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
{x | x is a multiple of 2} ∪ {x is a multiple of 7}
Let U = {2, 3, 4, 5, 6, 7, 8}, and A = {2, 3, 4, 5}. List all the members of the given set. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
A
From a survey of 100 college students, a marketing research company found that 55 students owned iPods, 45 owned cars, and 15 owned both cars and iPods.
(a) How many students owned either a car or an iPod (but not both)?
students
(b) How many students do not own either a car or an iPod?
Let U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}. List all the members of the given set. (Enter your answers as a comma-separated list.)
(A ∪ B) ∩ C
Let U = {8, 9, 10, 11, 12, 13, 14}, A = {8, 9, 10, 11}, B = {8, 9, 12, 13}, and C = {10, 12, 14}. List all the members of the given set. (Enter your answers as a comma-separated list.)
What is the sum of the first 25 consecutive odd numbers?
(a) What is the sum of the first 35 consecutive odd numbers?
(b) What is the sum of the first 900 consecutive odd numbers?
Here are the results of the voting by eight senators on voting by three bills in the U.S. Senate during the 107th Congress, second session (2002):
Senator Bill A Bill B Bill C
S. 2414 H.R. 2356 Amen. 3017
Clinton (D) yea yea yea
Kennedy (D) yea yea yea
Bayh (D) nay yea nay
Inouye (D) yea yea nay
Campbell (R) yea nay nay
Helms (R) yea nay nay
Thurmond (R) yea nay nay
Lott (R) yea nay nay
Assign each senator to the appropriate region of the figure below. A "yea" vote is recorded as supporting the bill and consequently places the senator inside the circle representing that particular bill.
Clinton
Kennedy
A poll was taken of 100 students at a commuter campus to find out how they got to campus. The results were as follows:
33 said they drove alone.
34 rode in a carpool.
30 rode public transportation.
8 used both carpools and public transportation.
10 used both a carpool and sometimes their own cars.
6 used buses as well as their own cars.
5 used all three methods.
How many used none of the above-mentioned means of transportation?
Simplify the expression.
(x + 3y − 6z) − (x − 4y + 5z)
Simplify the expression.
(x − 3)(2x − 4) − (x + 2)(x − 5)
If possible, completely factor the expression. (If the expression is not factorable, enter NF.)
x2 − 8x – 9
Completely factor the expression.
x2 + 8x + 12
Factor the expression by using areas.
x2 + x – 42
Determine the value of cell E1 if it contains the following formulas.
+3*A1 + 4*B1
+C1*(A1 + 4*B1)
+A1 + ⋯ + D1 or @sum(A1 . . D1)
Solve the equations.
(a)
2D + 4 = 8
D =
(b)
21E − 7 = 0
E =
Solve the equations.
(a)
3L
4
= 7
L =
(b)
2 =
2M
3
+ 6
M =
Solve the equation.
3(W + 4) − 4(W + 5) = 0
W =
Solve the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
x2 − 14x + 42 = 0
x =
Young's Rule for calculating a child's dosage for medication is
CHILD'S DOSE =
AGE OF CHILD
AGE OF CHILD + 12
× ADULT DOSE.
(a) If an adult's dose of a particular medication is 100 mg, what is the dose for a 6-year-old child? (Round your answer to one decimal place.)
(c) If a 12-year-old child's dose of a particular medication is 10 mg, what is the adult's dose?
Solve the inequality.
3(3F − 4) > 6F – 10
If you multiply a number by five and then subtract negative ten, the difference is negative twenty. What is the number?
The sum of three consecutive integers is 126. What are the integers? (Enter your answers as a comma-separated list.)
Two persons are to run a race, but one can run 10 meters per second, whereas the other can run 6 meters per second. If the slower runner has a 66-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?
A cement mixture calls for 80 pounds of cement for 2 gallons of water. What is the ratio of cement to water?
Write the ratio given as a simplified ratio.
If you drive 225 miles on
12
1
2
gallons of gas, what is the simplified ratio of miles to gallons?
Solve the proportion for the item represented by a letter.
|
4 |
|
1 |
=
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A |
|
6 |
If 4 melons sell for $0.48, how much would 6 melons cost?
If a 121-mile trip took
5 ½ gallons of gas, how many miles can be driven with a full tank of 13 gallons?
The pitch of a roof is the ratio of the rise to the half-span. If a roof has a rise of 8 feet and a span of 12 feet, what is the pitch?
If the sales tax is 7% and the purchase price is $261, what is the amount of tax?
Write the equations in logarithmic form.
(a)
216 = 63
16= (1/4) 2 power
a = bc
Use the definition of logarithm to simplify each expression.
(a)
log10 10
(b)
log10 10,000
(c)
log10 10−3
Solve each exponential equation. Give the exact value for x.
(a)
5x =
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1 |
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25 |
(b)
7x = 10
(c)
6x = 4.5
(d)
4x = 5
Evaluate the given expressions (to two decimal places).
(a)
log 16.7
(b)
log2 512
(c)
log7 1
(d)
log 0.046
Write each expression in terms of common logarithms, and then give a calculator approximation (correct to four decimal places).
(a)
log7 10
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exact value |
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approximation |
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(b)
log3 311
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Find a simplified value for x by inspection. Do not use a calculator.
(a)
log6 36 = x
(b)
log2 32 = x
(c)
log3 243 = x
(d)
log4 256 = x
Contract the expressions. That is, use the properties of logarithms to write each expression as a single logarithm with a coefficient of 1.
ln 3 − 2 ln 7 + ln 14
ln 3 − 2 ln(7 + 5)
ln 3 − 2(ln 4 + ln 8)
An advertising agency conducted a survey and found that the number of units sold, N, is related to the amount a spent on advertising (in dollars) by the following formula:
N = 1,500 + 400 ln a (a ≥ 1)
How many units are sold after spending $1,000? (Round your answer to the nearest whole number.)
Solve the equations by finding the exact solution.
3 = x – 3
3 ln e = ln
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||
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x |
− 3 ln e
Solve the equation by finding the exact solution.
The "learning curve" describes the rate at which a person learns certain tasks. If a person sets a goal of typing N words per minute (wpm), the length of time t (in days) to achieve this goal is given by
t = −62.5 ln
|
|
1 −
|
N |
|
|
|
80 |
Find the number of decibels for the power of the sound given. Round to the nearest decibel.
A rocket engine,
2.41 10−5
watts/cm2
A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of
4.8 cross product 102
µm. Find this earthquake's magnitude. (Round your answer to one decimal place.)
An artifact was found and tested for its carbon-14 content. If 70% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years.)
The atmospheric pressure P in pounds per square inch (psi) is given by
P = 14.7 e−0.21 a
where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 12.23 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)
Find the future value, using the future value formula and a calculator. (Round your answer to the nearest cent.)
$822 at 5.5% compounded quarterly for 3 years
Find the present value, using the present value formula and a calculator. (Round your answer to the nearest cent.)
Achieve $225,500 at 8.25% compounded continuously for 8 years, 125 days.
If $38,500 is invested at 6.1% for 30 years, find the future value if the interest is compounded the following ways. (Round your answers to the nearest cent.)
b) semiannually
(c) quarterly
(d) monthly
(e) daily
Suppose that an insurance agent offers you a policy that will provide you with a yearly income of $70,000 in 30 years. What is the comparable salary today, assuming an inflation rate of 5% compounded annually? (Round your answer to the nearest cent.)
Convert the credit card rate to the APR.
Oregon,
1
|
1 |
|
4 |
%
per month
Calculate the monthly finance charge for the credit card transaction. Assume that it takes 10 days for a payment to be received and recorded, and that the month is 30 days long. (Round your answers to the nearest cent.)
$200 balance, 18%, $50 payment
(d) average daily balance method
Assume the car can be purchased for 0% down for 60 months (in lieu of rebate).
A car with a sticker price of $42,150 with factory and dealer rebates of $5,100
a) Find the monthly payment if financed for 60 months at 0% APR. (Round your answer to the nearest cent.)
b) Find the monthly payment if financed at 2.5% add-on interest for 60 months. (Round your answer to the nearest cent.)
c) Use the APR approximation formula to find the APR for part (b). (Round your answer to one decimal place.)
d) State whether the 0% APR or the 2.5% add-on rate should be preferred.
For the car loan described, give the following information.
A newspaper advertisement offers a $4,500 used car for nothing down and 36 easy monthly payments of $154.62.
(a) amount to be paid
(b) amount of interest
(c) interest rate (Round your answer to two decimal places.)
(d) APR (rounded to the nearest tenth percent)
Use a calculator to evaluate an ordinary annuity formula
A = m
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1 +
− 1 |
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for m, r, and t (respectively). Assume monthly payments. (Round your answer to the nearest cent.)
$150; 5%; 40 yr
Find the amount of periodic payment necessary for the deposit to a sinking fund. (Round your answer to the nearest cent.) $
