Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 1
Multi-step problems with unit conversions
The formula for the density of a bacteria population is
N
A
\frac{N}{A}
A
N
where there's an average of
N
N
N
bacteria in an area size
A
A
A
. Guang and Orion are doing an experiment in school for which they need to measure the density of a bacteria population after a certain solution has been introduced. Guang reports a density of
4500
4500
4500
bacteria per square centimeter and Orion reports a density of
50
50
50
bacteria per square millimeter. Which one reports a higher density? Choose
1
1
1
answer:
\newline
(A) Guang reports a higher density than Orion.
\newline
(B) Orion reports a higher density than Guang.
\newline
(C) Guang and Orion report equal densities.
Get tutor help
The formula for calculating wage is
p
t
\frac{p}{t}
t
p
where
t
t
t
is the time duration for which an amount
p
p
p
of money is paid.
\newline
Astrid is looking for a job at a call center. Call center A offers her (
15
15
15
per hour and call center B offers her )
0
0
0
.
25
25
25
per minute.
\newline
Which place offers a higher wage?
\newline
Choose
1
1
1
answer:
\newline
(A) Call center A offers a higher wage than call center B.
\newline
(B) Call center B offers a higher wage than call center A.
\newline
(C) Call centers A and B offer equal wages.
Get tutor help
The formula for the length of the hypotenuse in a right triangle is
a
2
+
b
2
\sqrt{a^{2}+b^{2}}
a
2
+
b
2
where
a
a
a
and
b
b
b
are the lengths of the triangle's sides (this formula is derived from the Pythagorean theorem).
\newline
From the side, a certain ramp has a right-triangular shape. Its height is
30
30
30
centimeters and its horizontal length is
3
3
3
meters.
\newline
What calculation will give us the estimated length of the ramp in meters?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
3
0
2
10
0
2
)
+
3
2
\sqrt{\left(\frac{30^{2}}{100^{2}}\right)+3^{2}}
(
10
0
2
3
0
2
)
+
3
2
\newline
(B)
3
0
2
+
3
2
⋅
10
0
2
\sqrt{30^{2}+3^{2}\cdot 100^{2}}
3
0
2
+
3
2
⋅
10
0
2
\newline
(C)
3
0
2
⋅
10
0
2
+
3
2
\sqrt{30^{2}\cdot 100^{2}+3^{2}}
3
0
2
⋅
10
0
2
+
3
2
\newline
(D)
3
0
2
+
(
3
2
10
0
2
)
\sqrt{30^{2}+\left(\frac{3^{2}}{100^{2}}\right)}
3
0
2
+
(
10
0
2
3
2
)
Get tutor help
In physics, work is defined as
\newline
F
⋅
D
F \cdot D
F
⋅
D
where
\newline
F
F
F
is the force applied over a distance of
\newline
D
D
D
.
\newline
A box is dragged across
20
20
20
meters with a force of
60
60
60
Newtons, which are
\newline
(
kg
⋅
m
s
2
)
\left(\frac{\text{kg} \cdot \text{m}}{\text{s}^{2}}\right)
(
s
2
kg
⋅
m
)
.
\newline
What calculation will give us the work done, in Joules (which are
\newline
(
kg
⋅
m
2
s
2
)
\left(\frac{\text{kg} \cdot \text{m}^{2}}{\text{s}^{2}}\right)
(
s
2
kg
⋅
m
2
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
20
⋅
60
20 \cdot 60
20
⋅
60
\newline
(B)
20
⋅
1000
⋅
60
20 \cdot 1000 \cdot 60
20
⋅
1000
⋅
60
\newline
(C)
20
1000
⋅
60
\frac{20}{1000} \cdot 60
1000
20
⋅
60
\newline
(D)
F
F
F
0
0
0
Get tutor help
According to Newton's Second Law of Motion, the sum of the forces that act on an object with a mass
m
m
m
that moves with an acceleration
a
a
a
is equal to
m
⋅
a
m \cdot a
m
⋅
a
. An object whose mass is
80
80
80
grams has an acceleration of
20
20
20
meters per seconds squared. What calculation will give us the sum of the forces that act on the object, in Newtons (which are
kg
⋅
m
s
2
\frac{\text{kg} \cdot \text{m}}{\text{s}^2}
s
2
kg
⋅
m
)?
\newline
Choose
1
1
1
answer:
\newline
(A)
80
⋅
20
80 \cdot 20
80
⋅
20
\newline
(B)
80
⋅
1000
⋅
20
80 \cdot 1000 \cdot 20
80
⋅
1000
⋅
20
\newline
(C)
80
1000
⋅
20
\frac{80}{1000} \cdot 20
1000
80
⋅
20
\newline
(D)
80
6
0
2
⋅
20
\frac{80}{60^2} \cdot 20
6
0
2
80
⋅
20
Get tutor help
The formula for the distance traveled over time
t
t
t
and at an average speed
v
v
v
is
v
⋅
t
v \cdot t
v
⋅
t
. Amit ran for
40
40
40
minutes at a speed of about
5
5
5
kilometers per hour. What calculation will give us the estimated distance Amit ran in kilometers? Choose
1
1
1
answer:
\newline
(A)
5
⋅
40
⋅
60
5 \cdot 40 \cdot 60
5
⋅
40
⋅
60
\newline
(B)
5
⋅
1000
⋅
40
5 \cdot 1000 \cdot 40
5
⋅
1000
⋅
40
\newline
(C)
5
⋅
40
60
5 \cdot \frac{40}{60}
5
⋅
60
40
\newline
(D)
5
1000
⋅
40
\frac{5}{1000} \cdot 40
1000
5
⋅
40
Get tutor help
The formula for the size of a file that was downloaded over time
t
t
t
and at an average rate
r
r
r
is
r
⋅
t
r \cdot t
r
⋅
t
. Siena downloaded a file at a rate of
800
kilobytes per second
800 \text{ kilobytes per second}
800
kilobytes per second
for about
110
seconds
110 \text{ seconds}
110
seconds
. What calculation will give us the estimated size of the file Siena downloaded, in megabytes? Choose
1
1
1
answer:
\newline
(A)
800
⋅
110
⋅
60
800 \cdot 110 \cdot 60
800
⋅
110
⋅
60
\newline
(B)
800
⋅
110
60
800 \cdot \frac{110}{60}
800
⋅
60
110
\newline
(C)
800
⋅
1000
⋅
110
800 \cdot 1000 \cdot 110
800
⋅
1000
⋅
110
\newline
(D)
800
1000
⋅
110
\frac{800}{1000} \cdot 110
1000
800
⋅
110
Get tutor help
The formula for the time it takes to travel a distance of
d
d
d
at an average speed
v
v
v
is
d
v
\frac{d}{v}
v
d
. Tessa ran a
100
100
100
-meter dash at a speed of about
7.5
7.5
7.5
meters per second. What calculation will give us the estimated duration of Tessa's dash in seconds? Choose
1
1
1
answer:
\newline
(A)
7.5
100
\frac{7.5}{100}
100
7.5
\newline
(B)
100
7.5
\frac{100}{7.5}
7.5
100
\newline
(C)
7.5
100
×
60
\frac{7.5}{100 \times 60}
100
×
60
7.5
\newline
(D)
100
×
60
7.5
\frac{100 \times 60}{7.5}
7.5
100
×
60
Get tutor help
Maureen can't wait to make chocolate chip zucchini bread with zucchini from her garden. Her recipe calls for
8
8
8
ounces of chocolate chips per loaf. If she has enough zucchini to make
4
4
4
loaves of zucchini bread, how many pounds of chocolate chips does she need?
\newline
Hint: There are
16
16
16
ounces in
1
1
1
pound.
\newline
Write your answer as a whole number, decimal, or simplified fraction. Do not round.
\newline
____ pounds
Get tutor help
Previous
1
2