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Math
Math Statement
Problem 20701
Find the cost to produce the 16th unit given the total cost function
T
C
=
q
3
−
q
2
+
120
q
T C=q^{3}-q^{2}+120 q
TC
=
q
3
−
q
2
+
120
q
.
See Solution
Problem 20702
Find the price
P
P
P
that maximizes revenue
T
R
TR
TR
given the demand function
Q
=
90
−
1.5
P
Q=90-1.5P
Q
=
90
−
1.5
P
.
See Solution
Problem 20703
Choose the correct calculation for 27% of 3 million:
0.27
×
3
,
000
,
000
0.27 \times 3,000,000
0.27
×
3
,
000
,
000
or other options.
See Solution
Problem 20704
Find the marginal revenue when 3 units are sold, given the demand function
p
=
72
−
7.5
q
p=72-7.5q
p
=
72
−
7.5
q
.
See Solution
Problem 20705
Find the number of units
Q
Q
Q
(in thousands) to produce for maximum profit given
T
R
=
20
Q
−
4
Q
2
TR=20Q-4Q^2
TR
=
20
Q
−
4
Q
2
and
T
C
=
16
−
Q
2
TC=16-Q^2
TC
=
16
−
Q
2
.
See Solution
Problem 20706
Determine the x-intercepts and y-intercept of the function
f
(
x
)
=
−
x
2
+
2
x
+
8
f(x)=-x^{2}+2 x+8
f
(
x
)
=
−
x
2
+
2
x
+
8
.
See Solution
Problem 20707
Order these numbers from least to greatest:
2.74
,
1
9
,
4
2
,
−
2
3
,
32.5
%
,
−
6
2.74, \frac{1}{9}, 4^{2}, -2^{3}, 32.5\%, -6
2.74
,
9
1
,
4
2
,
−
2
3
,
32.5%
,
−
6
.
See Solution
Problem 20708
Solve for
t
t
t
:
−
5
t
≥
70
-5 t \geq 70
−
5
t
≥
70
.
See Solution
Problem 20709
Solve for
x
x
x
:
−
7
≥
13
−
5
x
-7 \geq 13 - 5x
−
7
≥
13
−
5
x
See Solution
Problem 20710
Solve for
d
d
d
:
5
+
d
>
5
−
d
5 + d > 5 - d
5
+
d
>
5
−
d
See Solution
Problem 20711
Solve for
x
x
x
:
4
(
x
+
1
)
≤
4
x
+
3
4(x+1) \leq 4x + 3
4
(
x
+
1
)
≤
4
x
+
3
See Solution
Problem 20712
Calcular:
7
+
(
6
×
5
2
+
3
)
7 + (6 \times 5^{2} + 3)
7
+
(
6
×
5
2
+
3
)
See Solution
Problem 20713
Calculate
98.58
k
m
+
10.0
k
m
98.58 \mathrm{~km}+10.0 \mathrm{~km}
98.58
km
+
10.0
km
with the correct significant digits. Options:
108.6
k
m
108.6 \mathrm{~km}
108.6
km
,
100
k
m
100 \mathrm{~km}
100
km
,
108.58
k
m
108.58 \mathrm{~km}
108.58
km
,
110
k
m
110 \mathrm{~km}
110
km
.
See Solution
Problem 20714
Find the product using FOIL:
(
x
+
5
)
(
x
2
−
3
x
)
(x+5)(x^{2}-3x)
(
x
+
5
)
(
x
2
−
3
x
)
. Choices: A.
x
3
+
5
x
2
−
15
x
x^{3}+5x^{2}-15x
x
3
+
5
x
2
−
15
x
, B.
x
3
+
2
x
2
−
15
x^{3}+2x^{2}-15
x
3
+
2
x
2
−
15
, C.
x
3
+
2
x
2
−
15
x
th
x^{3}+2x^{2}-15x^{\text{th}}
x
3
+
2
x
2
−
15
x
th
, D.
x
3
+
5
x
2
−
15
x^{3}+5x^{2}-15
x
3
+
5
x
2
−
15
.
See Solution
Problem 20715
Find
x
x
x
where
5
sin
x
+
3
cos
x
=
0
5 \sin x + 3 \cos x = 0
5
sin
x
+
3
cos
x
=
0
for
0
∘
≤
x
≤
36
0
∘
0^{\circ} \leq x \leq 360^{\circ}
0
∘
≤
x
≤
36
0
∘
. Simplify
cos
(
180
−
x
)
\cos(180 - x)
cos
(
180
−
x
)
.
See Solution
Problem 20716
Simplify
7
(
B
+
3
)
+
2
B
7(B+3)+2B
7
(
B
+
3
)
+
2
B
and choose the correct answer:
9
B
+
10
9B+10
9
B
+
10
,
9
B
+
3
9B+3
9
B
+
3
, or
9
B
+
21
9B+21
9
B
+
21
.
See Solution
Problem 20717
Simplify the expression:
10
(
2
x
+
3
)
−
20
10(2x + 3) - 20
10
(
2
x
+
3
)
−
20
and find the result.
See Solution
Problem 20718
Simplify
8
(
x
+
6
)
−
10
8(x+6)-10
8
(
x
+
6
)
−
10
and choose the correct answer:
8
x
+
28
8x+28
8
x
+
28
,
8
x
−
4
8x-4
8
x
−
4
, or
8
x
+
38
8x+38
8
x
+
38
.
See Solution
Problem 20719
Convert
2
4
∘
F
24^{\circ} \mathrm{F}
2
4
∘
F
to Celsius using the formula
∘
C
=
(
∘
F
−
32
)
/
1.8
{ }^{\circ} \mathrm{C}=\left({ }^{\circ} \mathrm{F}-32\right) / 1.8
∘
C
=
(
∘
F
−
32
)
/1.8
.
See Solution
Problem 20720
Find the probability that the sample mean exceeds 80 for
μ
=
75
\mu=75
μ
=
75
and
σ
=
12
\sigma=12
σ
=
12
. Options: 2.5, 0.0062, 0.9938, 0.065.
See Solution
Problem 20721
Find the probability that the sample mean exceeds 80 given
m
u
=
75
m u=75
m
u
=
75
and
σ
=
12
\sigma=12
σ
=
12
.
See Solution
Problem 20722
Find points that satisfy the inequalities
y
≥
−
3
x
−
4
y \geq -3x - 4
y
≥
−
3
x
−
4
and
y
>
1
2
x
−
6
y > \frac{1}{2}x - 6
y
>
2
1
x
−
6
.
See Solution
Problem 20723
What symbol represents the sample proportion statistic? Options: pi,
x
x
x
, e, sigma, delta, alpha, or
p
^
\hat{p}
p
^
.
See Solution
Problem 20724
Identify the relationship: If
a
⇒
b
a \Rightarrow b
a
⇒
b
and
b
⇒
a
b \Rightarrow a
b
⇒
a
, this is the A. converse, B. contrapositive, C. contradiction, or D. inverse?
See Solution
Problem 20725
If
x
⇒
y
x \Rightarrow y
x
⇒
y
and
y
⇒
z
y \Rightarrow z
y
⇒
z
, which must be true: A.
x
⇒
z
x \Rightarrow z
x
⇒
z
, B.
z
⇒
x
z \Rightarrow x
z
⇒
x
, C.
¬
x
⇒
¬
z
\neg x \Rightarrow \neg z
¬
x
⇒
¬
z
, D.
¬
x
⇒
z
\neg x \Rightarrow z
¬
x
⇒
z
?
See Solution
Problem 20726
Identify the correct term for: If
p
⇒
q
p \Rightarrow q
p
⇒
q
and
q
⇒
r
q \Rightarrow r
q
⇒
r
, then
p
⇒
r
p \Rightarrow r
p
⇒
r
. A. Inverse B. Converse C. Syllogism D. Contrapositive
See Solution
Problem 20727
Solve the inequality:
∣
2
y
−
7
∣
>
9
|2y - 7| > 9
∣2
y
−
7∣
>
9
. Find
y
<
[
?
]
y < [?]
y
<
[
?]
or
y
>
[
?
]
y > [?]
y
>
[
?]
.
See Solution
Problem 20728
Solve the inequality:
∣
3
x
−
4
∣
<
2
|3x - 4| < 2
∣3
x
−
4∣
<
2
.
See Solution
Problem 20729
Calculate the sum:
7
+
(
−
9
)
=
7 + (-9) =
7
+
(
−
9
)
=
See Solution
Problem 20730
Calculate the sum:
−
11
+
(
−
1
)
=
-11 + (-1) =
−
11
+
(
−
1
)
=
See Solution
Problem 20731
Select the numeric expression: negative eight cubed,
(
−
8
)
3
(-8)^{3}
(
−
8
)
3
, or the third root of negative eight?
See Solution
Problem 20732
Calculate the sum of -8 and 7:
−
8
+
7
=
-8 + 7 =
−
8
+
7
=
See Solution
Problem 20733
Calculate:
−
8
+
(
−
5
)
=
-8 + (-5) =
−
8
+
(
−
5
)
=
See Solution
Problem 20734
Select the correct expression for one-fifth cubed:
(
1
5
)
3
\left(\frac{1}{5}\right)^{3}
(
5
1
)
3
1
5
3
\sqrt[3]{\frac{1}{5}}
3
5
1
(
1
3
)
5
\left(\frac{1}{3}\right)^{5}
(
3
1
)
5
See Solution
Problem 20735
Select the correct expression for twelve squared: 12(2),
12
12
\sqrt[12]{12}
12
12
,
12
\sqrt{12}
12
, or
1
2
2
12^{2}
1
2
2
?
See Solution
Problem 20736
Calculate:
−
5
+
0
=
-5 + 0 =
−
5
+
0
=
See Solution
Problem 20737
Add the fractions:
−
2
13
+
2
5
=
□
-\frac{2}{13}+\frac{2}{5}=\square
−
13
2
+
5
2
=
□
(Provide your answer as a simplified fraction or integer.)
See Solution
Problem 20738
Add the fractions:
−
2
13
+
2
5
-\frac{2}{13}+\frac{2}{5}
−
13
2
+
5
2
. Simplify your answer to an integer or a fraction.
See Solution
Problem 20739
Calculate the sum:
−
4
18
+
3
5
-\frac{4}{18}+\frac{3}{5}
−
18
4
+
5
3
. Simplify your answer to an integer or a fraction.
See Solution
Problem 20740
Express -64 as a base and exponent: 3, -4. Consider
(
−
4
)
3
(-4)^{3}
(
−
4
)
3
,
4
3
4^{3}
4
3
,
3
−
4
3^{-4}
3
−
4
, and
−
4
3
\sqrt[3]{-4}
3
−
4
.
See Solution
Problem 20741
Find the inverse of the function
f
(
x
)
=
−
5
x
−
4
f(x)=-5 x-4
f
(
x
)
=
−
5
x
−
4
.
See Solution
Problem 20742
Express 9 and 2 as a base and exponent to equal 81. Options:
9
2
9^{2}
9
2
,
9
2
4
2
\frac{9^{2}}{4^{2}}
4
2
9
2
,
2
9
2^{9}
2
9
,
2
(
9
)
2
2(9)^{2}
2
(
9
)
2
.
See Solution
Problem 20743
Find the opposite of -29. What is the result? The opposite of -29 is
29
29
29
.
See Solution
Problem 20744
Solve for
x
x
x
:
x
3
≤
−
6
\frac{x}{3} \leq -6
3
x
≤
−
6
.
See Solution
Problem 20745
Express 20 and 2 as a base and exponent to equal 400. Options:
2
0
2
20^{2}
2
0
2
,
2
20
2^{20}
2
20
,
40
0
2
\sqrt{400^{2}}
40
0
2
,
2
0
2
\sqrt{20^{2}}
2
0
2
.
See Solution
Problem 20746
Solve for
x
x
x
:
−
7
≥
13
−
5
x
-7 \geq 13 - 5x
−
7
≥
13
−
5
x
See Solution
Problem 20747
Solve the equation
3
x
2
−
5
x
−
2
=
0
3 x^{2}-5 x-2=0
3
x
2
−
5
x
−
2
=
0
.
See Solution
Problem 20748
Find the opposite of the number
−
1
6
-\frac{1}{6}
−
6
1
. What is it?
See Solution
Problem 20749
Find the additive inverse of -28.8. It is
28.8
28.8
28.8
.
See Solution
Problem 20750
Express the number -125 as a base and exponent using
3
3
3
and
−
5
-5
−
5
. Answer:
(
−
5
)
3
(-5)^{3}
(
−
5
)
3
.
See Solution
Problem 20751
Solve the inequality and graph the solution:
(
m
−
2
)
(
m
+
8
)
<
0
(m-2)(m+8)<0
(
m
−
2
)
(
m
+
8
)
<
0
See Solution
Problem 20752
Find the real solutions of the equation
x
2
−
14
=
0
x^{2}-14=0
x
2
−
14
=
0
.
See Solution
Problem 20753
Calculate the sum:
−
6
+
(
−
15
)
=
-6 + (-15) =
−
6
+
(
−
15
)
=
See Solution
Problem 20754
Express the number as a base and exponent to equal the answer:
−
1
7
,
2
Answer:
1
49
-\frac{1}{7}, 2 \text{ Answer: } \frac{1}{49}
−
7
1
,
2
Answer:
49
1
.
See Solution
Problem 20755
Calculate the sum:
−
4
+
(
−
91
)
-4 + (-91)
−
4
+
(
−
91
)
.
See Solution
Problem 20756
Solve for
n
n
n
:
3
(
n
+
5
)
≥
3
n
+
8
3(n+5) \geq 3n + 8
3
(
n
+
5
)
≥
3
n
+
8
See Solution
Problem 20757
Solve the equation by factoring:
z
2
+
6
z
−
7
=
0
z^{2}+6z-7=0
z
2
+
6
z
−
7
=
0
.
See Solution
Problem 20758
Calculate:
7
+
5
7 + 5
7
+
5
See Solution
Problem 20759
Calculate:
84.5
+
(
−
96.3
)
=
84.5 + (-96.3) =
84.5
+
(
−
96.3
)
=
(Enter an integer or decimal.)
See Solution
Problem 20760
Solve for real solutions using the quadratic formula:
4
y
2
−
y
+
4
=
0
4 y^{2}-y+4=0
4
y
2
−
y
+
4
=
0
.
See Solution
Problem 20761
Calculate the sum:
−
129.3
+
(
−
20.3
)
=
-129.3 + (-20.3) =
−
129.3
+
(
−
20.3
)
=
(Type an integer or a decimal.)
See Solution
Problem 20762
Evaluate the expression for x=2:
2
x
2
+
3
(
x
+
x
)
+
4
=
[
?
]
2 x^{2}+3(x+x)+4=[?]
2
x
2
+
3
(
x
+
x
)
+
4
=
[
?]
See Solution
Problem 20763
Solve for real solutions of the equation using the quadratic formula:
3
x
(
x
+
2
)
=
4
3 x(x+2)=4
3
x
(
x
+
2
)
=
4
.
See Solution
Problem 20764
Evaluate
2
a
2
−
4
b
−
4
a
(
b
−
a
)
2 a^{2}-4 b-4 a(b-a)
2
a
2
−
4
b
−
4
a
(
b
−
a
)
for
a
=
4
a=4
a
=
4
and
b
=
7
b=7
b
=
7
. What is the result?
See Solution
Problem 20765
What is
1
/
2
÷
1
/
8
1 / 2 \div 1 / 8
1/2
÷
1/8
?
See Solution
Problem 20766
Simplify the expression:
(
6
−
4
)
⋅
49
÷
7
(6-4) \cdot 49 \div 7
(
6
−
4
)
⋅
49
÷
7
.
See Solution
Problem 20767
Solve the inequality:
3
x
2
+
10
x
>
8
3 x^{2}+10 x>8
3
x
2
+
10
x
>
8
.
See Solution
Problem 20768
Simplify the expression:
22
x
y
3
x
\frac{22 x y}{3 x}
3
x
22
x
y
.
See Solution
Problem 20769
Calculate:
−
2
+
(
−
9
)
=
-2 + (-9) =
−
2
+
(
−
9
)
=
See Solution
Problem 20770
Calculate:
−
7
+
(
−
4
)
=
-7 + (-4) =
−
7
+
(
−
4
)
=
See Solution
Problem 20771
Add 83.3 and -91.2. What is the result?
83.3
+
(
−
91.2
)
=
83.3 + (-91.2) =
83.3
+
(
−
91.2
)
=
(Type an integer or a decimal.)
See Solution
Problem 20772
Factor the quadratic function
f
(
x
)
=
5
x
2
−
21
x
+
4
f(x)=5 x^{2}-21 x+4
f
(
x
)
=
5
x
2
−
21
x
+
4
.
See Solution
Problem 20773
Calculate the sum:
−
11
+
(
−
6
)
=
-11 + (-6) =
−
11
+
(
−
6
)
=
See Solution
Problem 20774
Calculate the sum:
9
+
(
−
7
)
=
9 + (-7) =
9
+
(
−
7
)
=
See Solution
Problem 20775
Calculate the sum of -92 and -88:
−
92
+
(
−
88
)
-92 + (-88)
−
92
+
(
−
88
)
.
See Solution
Problem 20776
Solve the inequality
3
x
2
+
10
x
>
8
3 x^{2}+10 x>8
3
x
2
+
10
x
>
8
and graph the solution.
See Solution
Problem 20777
Calculate the sum:
−
4
13
+
3
5
=
□
-\frac{4}{13}+\frac{3}{5}=\square
−
13
4
+
5
3
=
□
(Provide your answer as an integer or fraction.)
See Solution
Problem 20778
Calculate the sum:
−
8
+
(
−
6
)
=
-8 + (-6) =
−
8
+
(
−
6
)
=
See Solution
Problem 20779
Add:
4
+
7
=
4 + 7 =
4
+
7
=
See Solution
Problem 20780
Add
23
+
(
−
23
)
23 + (-23)
23
+
(
−
23
)
and write the answer in a number line:
23
+
(
−
23
)
=
23 + (-23) =
23
+
(
−
23
)
=
See Solution
Problem 20781
Solve the inequality
3
x
2
+
10
x
>
8
3 x^{2}+10 x>8
3
x
2
+
10
x
>
8
and graph the solution.
See Solution
Problem 20782
Solve the inequality:
x
+
3
x
+
6
≥
0
\frac{x+3}{x+6} \geq 0
x
+
6
x
+
3
≥
0
.
See Solution
Problem 20783
Find the opposite of the number
−
4
7
-\frac{4}{7}
−
7
4
. What is it?
See Solution
Problem 20784
Find the opposite of -15. What is it?
See Solution
Problem 20785
Evaluate:
8
−
(
+
5
)
=
8 - (+5) =
8
−
(
+
5
)
=
See Solution
Problem 20786
Subtract 1 from 4. What is
4
−
1
4 - 1
4
−
1
?
See Solution
Problem 20787
Find the slope and
y
y
y
-intercept of the line given by
y
=
9
+
4
x
y=9+4x
y
=
9
+
4
x
.
See Solution
Problem 20788
Simplify the expression:
5
c
−
2
c
5c - 2c
5
c
−
2
c
.
See Solution
Problem 20789
Calculate the result of the subtraction:
−
4
−
(
−
1
)
=
-4 - (-1) =
−
4
−
(
−
1
)
=
See Solution
Problem 20790
Simplify the expression:
2
r
+
2
r
−
r
2r + 2r - r
2
r
+
2
r
−
r
.
See Solution
Problem 20791
Find the zeroes of
f
(
x
)
=
4
(
x
+
1
)
(
x
+
5
)
4
(
4
x
+
5
)
4
(
x
+
2
)
5
f(x)=4(x+1)(x+5)^{4}(4 x+5)^{4}(x+2)^{5}
f
(
x
)
=
4
(
x
+
1
)
(
x
+
5
)
4
(
4
x
+
5
)
4
(
x
+
2
)
5
. State the degree and end behavior.
See Solution
Problem 20792
Find the values of
x
x
x
for which the profit
P
=
3
x
2
−
32
x
+
20
P=3x^{2}-32x+20
P
=
3
x
2
−
32
x
+
20
is positive.
See Solution
Problem 20793
Evaluate:
−
3
−
19
=
-3 - 19 =
−
3
−
19
=
See Solution
Problem 20794
Find the
y
y
y
-intercept,
x
x
x
-intercepts, and limits of
P
(
x
)
=
x
(
x
+
4
)
(
x
−
3
)
P(x)=x(x+4)(x-3)
P
(
x
)
=
x
(
x
+
4
)
(
x
−
3
)
as
x
→
±
∞
x \to \pm\infty
x
→
±
∞
.
See Solution
Problem 20795
Calculate
(
−
8
+
c
)
2
(-8+c)^{2}
(
−
8
+
c
)
2
for
c
=
−
3
c=-3
c
=
−
3
.
See Solution
Problem 20796
Evaluate -6 - (-15). What is the result?
See Solution
Problem 20797
Subtract 4 from 20. What is the result? Calculate:
20
−
4
=
20 - 4 =
20
−
4
=
See Solution
Problem 20798
Calculate 22.2 - 50.5. What is the result?
See Solution
Problem 20799
Find the end behavior of the polynomial function
f
(
x
)
=
4
x
5
+
5
x
4
−
4
x
−
3
f(x) = 4x^5 + 5x^4 - 4x - 3
f
(
x
)
=
4
x
5
+
5
x
4
−
4
x
−
3
.
See Solution
Problem 20800
Solve for
m
m
m
:
−
7
+
1
6
m
=
5
-7+\frac{1}{6} m=5
−
7
+
6
1
m
=
5
. Choose A
m
=
−
12
m=-12
m
=
−
12
, B
m
=
2
m=2
m
=
2
, C
m
=
37
m=37
m
=
37
, D
m
=
72
m=72
m
=
72
.
See Solution
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