WebAssign
131-FinalReview (Homework)
Current Score : 5 / 72
Sarah Saad
MTH131-SP2018, section 01, Spring 2018
Instructor: Mojtaba Sirjani
Due : Wednesday, May 2 2018 12:00 PM EDT
1. –/2 pointsHarMathAp11 0.3.061.
If $P is invested for n years at a rate i (as a decimal), compounded annually, the future value that accrues is
given by S = P(1 + i)n, and the interest earned is I = S − P. Find S and I for the given P, n and i. (Round your
answers to the nearest cent.)
$1200 for 4 years at 16%
S = $
I = $
2. –/1 pointsHarMathAp11 0.4.053.
Rationalize the denominator and then simplify.
5
11
3. –/1 pointsHarMathAp11 0.4.076.
Suppose it has been determined that the sales at a gallery decline after the end of an advertising campaign, with
daily sales given by
S = 9000(2−0.1x)
where S is in dollars and x is the number of days after the campaign ends. What are the daily sales 40 days after
the end of the campaign?
$
4. –/2 pointsHarMathAp11 0.5.070.
Suppose a company's revenue R (in dollars) from the sale of x units of its product is given by
R = 350x.
Suppose further that the total costs C (in dollars) of producing those x units is given by
C = 70x + 20,000.
(a) If profit is revenue minus cost, find an expression for the profit from the production and sale of x
units.
P=
(b) Find the profit received if 4500 units are sold.
P=$
5. –/2 pointsHarMathAp11 0.5.071.
A rental truck costs $50.45 for a day plus 54¢ per mile.
(a) If x is the number of miles driven, write an expression for the total cost C, in dollars, of renting the
truck for a day.
C=
(b) Find the total cost of the rental if it was driven 194 miles.
C=$
6. –/1 pointsHarMathAp11 0.6.006.
Factor by grouping.
2y − 10 − x2y + 5x2
7. –/4 pointsHarMathAp11 0.6.020.
Factor each expression as a product of binomials.
(a)
10x2 − 99x − 63
(b)
10x2 − 27x − 63
(c)
10x2 + 61x − 63
(d)
10x2 + 9x − 63
8. –/1 pointsHarMathAp11 0.6.030.
Factor completely.
x5 + 12x4 + 36x3
9. –/1 pointsHarMathAp11 0.7.001.
Simplify the fraction.
12x2y7
4x2z
10.–/1 pointsHarMathAp11 0.7.009.
Perform the indicated operation and simplify.
9x − 45
· 7x − 21
x−3
8x − 40
11.–/1 pointsHarMathAp11 0.7.023.
Perform the indicated operation and simplify.
a
a−2
−
a−2
a
12.–/1 pointsHarMathAp11 0.7.038.
Simplify the complex fraction.
7
+ 5
3y
y
1
1
+
4
5y
13.–/1 pointsHarMathAp11 0.7.047.MI.
Rationalize the denominator of the fraction and simplify.
5−
x
5+
x
14.–/1 pointsHarMathAp11 0.7.049.
Rationalize the numerator of the fraction and simplify.
5x + h −
5x
h
15.–/1 pointsHarMathAp11 1.1.029.
Solve S = P + Prt for t.
t=
16.–/2 pointsHarMathAp11 1.1.037.
Solve the inequality.
5(x − 1) − 6 > 8x + 1
Graph the solution.
17.–/1 pointsHarMathAp11 1.1.043.
A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The
value of the building, y, after x months of use is given by y = 654,000 − 1800x dollars. After how many months
will the value of the building be $412,800?
x=
months
18.–/1 pointsHarMathAp11 1.1.047.
Burnem, Inc. manufactures blank CDs and sells them to a distributor in packs of 500 CDs. Burnem's total cost
and total revenue (in dollars) for x packs of 500 CDs are given by the following equations.
Total cost = 4x + 4873 and Total revenue = 15x
How many packs of 500 CDs must Burnem sell to break even?
x=
packs
19.–/2 pointsHarMathAp11 1.1.059.
For a certain product, the revenue is given by R = 70x and the cost is given by C(x) = 50x + 1200. To obtain a
profit, the revenue must be greater than the cost. For what values of x will there be a profit?
x>
Graph the solution.
20.–/2 pointsHarMathAp11 1.2.023.
If f(x) = x − 8x2 and h ≠ 0, find the following and simplify.
(a)
f(x + h) =
(b)
f(x + h) − f(x)
=
h
21.2/4 points | Previous AnswersHarMathAp11 1.2.037.MI.
For f(x) = 6x and g(x) = x6, find the following.
(a)
(f + g)(x)
6x+x6
(b)
(f − g)(x)
6x−x6
(c)
(f · g)(x)
(d)
(f/g)(x)
, x≠0
22.–/2 pointsHarMathAp11 1.3.031.
Write the equation of the line that passes through the given point and has the given slope.
(−1, 5) with slope −
Graph the line.
3
4
23.–/1 pointsHarMathAp11 1.3.035.MI.
Write the equation of the line described.
Through (3, 3) and (−1, −5)
24.–/1 pointsHarMathAp11 1.5.011.
Solve the system of equations by substitution. (Give an exact answer. Do not round.)
2x − y = 2
5x + 6y = 8
(x, y) =
25.–/6 pointsHarMathAp11 1.5.037.MI.
A concert promoter needs to make $58,100 from the sale of 1820 tickets. The promoter charges $30 for some
tickets and $35 for the others. Let x represent the number of $30 tickets and y represent the number of $35
tickets.
(a) Write an equation that states that the sum of the tickets sold is 1820.
(b) Write a formula for how much money is received from the sale of $30 tickets?
$
(c) Write a formula for how much money is received from the sale of $35 tickets?
$
(d) Write an equation that states that the total amount received from the sale is $58,100.
(e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the
$58,100.
x =
y =
26.–/3 pointsHarMathAp11 1.6.019.
A manufacturer sells belts for $13 per unit. The fixed costs are $1600 per month, and the variable cost per unit is
$9.
(a) Write the equations of the revenue R(x) and cost C(x) functions.
R(x) =
C(x) =
(b) Find the break-even point.
It takes
units to break even.
27.0/1 points | Previous AnswersHarMathAp11 1.6.044.MI.
Find the market equilibrium point for the following demand and supply functions.
Demand:
Supply:
p = −2q + 324
p = 8q + 2
(q, p) =
30210,183.2
28.0/1 points | Previous AnswersHarMathAp11 2.1.039.MI.
Multiply both sides of the equation by the LCD and solve the resulting quadratic equation. (Enter your answers as
a comma-separated list.)
x+
4
=5
x
x=
4
29.0/1 points | Previous AnswersHarMathAp11 2.1.045.MI.
If the profit from the sale of x units of a product is P = 115x − 300 − x2, what level(s) of production will yield a
profit of $1950? (Enter your answers as a comma-separated list.)
x=
1
units
30.1/4 points | Previous AnswersHarMathAp11 2.2.003.
Consider the following equation.
y = 8 + 8x − x2
(a) Find the vertex of the graph of the equation.
(x, y) =
(b) Determine if the vertex is a maximum or minimum point.
maximum
minimum
(c) Determine what value of x gives the optimal value of the function.
x=
(d) Determine the optimal (maximum or minimum) value of the function.
y=
31.–/2 pointsHarMathAp11 2.2.031.
The daily profit from the sale of a product is given by P = 12x − 0.1x2 − 200 dollars.
(a) What level of production maximizes profit?
units
(b) What is the maximum possible profit?
$
32.2/2 points | Previous AnswersHarMathAp11 2.4.013.
Decide whether each function whose graph is shown is the graph of a cubic (third-degree) or quartic (fourthdegree) function.
(a)
cubic
quartic
(b)
cubic
quartic
33.–/4 pointsHarMathAp11 2.4.033.
If k(x) =
2
x+4
1−x
if x < 0
if 0 ≤ x < 1 , find the following.
if x ≥ 1
(a)
k(−8)
(b)
k(0)
(c)
k(1)
(d)
k(−0.002)
34.–/1 pointsHarMathAp11 4.1.001.MI.
Graph the inequality.
y ≤ 4x − 3
35.–/1 pointsHarMathAp11 5.1.029.MI.
If $2000 is invested for x years at 8%, compounded quarterly, the future value that will result is represented by
the following equation.
S = 2000(1.02)4x
What amount will result in 6 years? (Round your answer to the nearest cent.)
$
36.–/1 pointsHarMathAp11 5.2.039.
Write the expression as the sum or difference of two logarithmic functions containing no exponents.
log3(x
3
x + 8)
37.–/1 pointsHarMathAp11 5.2.043.
Use the properties of logarithms to write the expression as a single logarithm.
log5(x + 6) +
1
log5(x)
3
38.–/2 pointsHarMathAp11 5.2.051.MI.
Use a change-of-base formula to evaluate each logarithm. (Round your answers to four decimal places.)
(a)
log6(17)
(b)
log3(0.54)
39.–/1 pointsHarMathAp11 5.2.063.
Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels
according to
L = 10 log(I/I0)
where I0 is the threshold of hearing for the average human ear.
Find the loudness when I is 10,000 times I0. This is the intensity level of the average voice.
L=
dB
40.–/1 pointsHarMathAp11 5.3.007.
Solve the equation. Give your answer correct to 3 decimal places.
10,000 = 1500e0.09x
x=
41.–/1 pointsHarMathAp11 5.3.015.
Solve the equation.
log4(9x + 19) = 3
x=
42.–/2 pointsHarMathAp11 5.3.043.
If $8500 is invested at 12.6% compounded continuously, the future value S at any time t (in years) is given by
the following formula. (Round your answers to two decimal places.)
S = 8500e0.126t
(a) What is the amount after 18 months?
S=$
(b) How long before the investment doubles?
t=
yr
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