Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 1
Weighted averages: word problems
Olivia has taken an initial dose of a prescription medication.
\newline
The relationship between the elapsed time
t
t
t
, in hours, since she took the first dose, and the amount of medication
M
(
t
)
M(t)
M
(
t
)
, in milligrams (
m
g
\mathrm{mg}
mg
), remaining in her bloodstream is modeled by the following function.
\newline
M
(
t
)
=
50
⋅
e
−
0.75
t
M(t)=50 \cdot e^{-0.75 t}
M
(
t
)
=
50
⋅
e
−
0.75
t
\newline
How many milligrams of the medication will be remaining in Olivia's bloodstream after
6
6
6
hours? Round your answer, if necessary, to the nearest hundredth.
\newline
m
g
\mathrm{mg}
mg
Get tutor help
Yasemin deposited
$
1000
\$ 1000
$1000
into a savings account.
\newline
The relationship between the time,
t
t
t
, in years, since the account was first opened, and Yasemin's account balance,
B
(
t
)
B(t)
B
(
t
)
, in dollars, is modeled by the following function.
\newline
B
(
t
)
=
1000
⋅
e
0.03
t
B(t)=1000 \cdot e^{0.03 t}
B
(
t
)
=
1000
⋅
e
0.03
t
\newline
How many years will it take for Yasemin's account balance to reach
$
1500
\$ 1500
$1500
?
\newline
Round your answer, if necessary, to the nearest hundredth.
\newline
years
Get tutor help
Carlos has taken an initial dose of a prescription medication.
\newline
The relationship between the elapsed time
t
t
t
, in hours, since he took the first dose, and the amount of medication,
M
(
t
)
M(t)
M
(
t
)
, in milligrams (
m
g
\mathrm{mg}
mg
), in his bloodstream is modeled by the following function.
\newline
M
(
t
)
=
20
⋅
e
−
0.8
t
M(t)=20 \cdot e^{-0.8 t}
M
(
t
)
=
20
⋅
e
−
0.8
t
\newline
In how many hours will Carlos have
1
m
g
1 \mathrm{mg}
1
mg
of medication remaining in his bloodstream?
\newline
Round your answer, if necessary, to the nearest hundredth.
\newline
hours
Get tutor help
A large brine tank containing a solution of salt and water is being diluted with fresh water.
\newline
The relationship between the elapsed time,
t
t
t
, in hours, after the dilution begins, and the concentration of salt in the tank,
S
(
t
)
S(t)
S
(
t
)
, in grams per liter
(
g
/
l
)
(\mathrm{g} / \mathrm{l})
(
g
/
l
)
, is modeled by the following function.
\newline
S
(
t
)
=
600
⋅
e
−
0.3
t
S(t)=600 \cdot e^{-0.3 t}
S
(
t
)
=
600
⋅
e
−
0.3
t
\newline
How many hours will it take for the concentration of salt to decrease to
100
g
/
l
100 \mathrm{~g} / \mathrm{l}
100
g
/
l
?
\newline
Round your answer, if necessary, to the nearest hundredth.
\newline
hours
Get tutor help
Harper uploaded a funny video of her dog onto a website.
\newline
The relationship between the elapsed time,
d
d
d
, in days, since the video was first uploaded, and the total number of views,
V
(
d
)
V(d)
V
(
d
)
, that the video received is modeled by the following function.
\newline
V
(
d
)
=
4
1.25
d
V(d)=4^{1.25 d}
V
(
d
)
=
4
1.25
d
\newline
How many views will the video receive after
6
6
6
days?
\newline
Round your answer, if necessary, to the nearest hundredth.
\newline
views
Get tutor help
The bacteria in a Petri dish culture are self-duplicating at a rapid pace.
\newline
The relationship between the elapsed time
t
t
t
, in minutes, and the number of bacteria,
B
(
t
)
B(t)
B
(
t
)
, in the Petri dish is modeled by the following function.
\newline
B
(
t
)
=
100
⋅
2
t
10
B(t)=100 \cdot 2^{\frac{t}{10}}
B
(
t
)
=
100
⋅
2
10
t
\newline
How many minutes will it take for the culture to achieve
10
10
10
,
000
000
000
bacteria?
\newline
Round your answer, if necessary, to the nearest hundredth.
\newline
minutes
Get tutor help
Vince went on a
3
3
3
day hiking trip.
\newline
Each day, he walked
3
4
\frac{3}{4}
4
3
the distance that he walked the day before.
H
e
\mathrm{He}
He
walked
83
83
83
.
25
25
25
kilometers total in the trip.
\newline
How far did Vince walk on the
1
st
1^{\text {st }}
1
st
day of the trip?
\newline
Round your final answer to the nearest kilometer.
\newline
k
m
\mathrm{km}
km
Get tutor help
A monkey is swinging from a tree. On the first swing, she passes through an arc of
20
m
20 \mathrm{~m}
20
m
. With each swing, she passes through an arc
4
5
\frac{4}{5}
5
4
the length of the previous swing.
\newline
What is the total distance the monkey has traveled when she completes her
1
0
th
10^{\text {th }}
1
0
th
swing? Round your final answer to the nearest meter.
\newline
m
Get tutor help
A monkey is swinging from a tree. On the first swing, she passes through an arc of
10
m
10 \mathrm{~m}
10
m
. With each swing, she passes through an arc
9
10
\frac{9}{10}
10
9
the length of the previous swing.
\newline
What is the total distance the monkey has traveled when she completes her
2
5
th
25^{\text {th }}
2
5
th
swing? Round your final answer to the nearest meter.
\newline
m
Get tutor help
Rosie went on a hiking trip. The first day she walked
18
18
18
kilometers. Each day since, she walked
90
%
90 \%
90%
of what she walked the day before.
\newline
What is the total distance Rosie has traveled by the end of the
1
0
th
10^{\text {th }}
1
0
th
day?
\newline
Round your final answer to the nearest kilometer.
\newline
k
m
\mathrm{km}
km
Get tutor help
A monkey is swinging from a tree. On each swing, she travels along an arc that is
75
%
75 \%
75%
as long as the previous swing's arc. The total length of the arcs from her first
4
4
4
swings is
175
m
175 \mathrm{~m}
175
m
.
\newline
How long was the monkey's
1
st
1^{\text {st }}
1
st
swing?
\newline
Round your final answer to the nearest meter.
\newline
m
Get tutor help
New York City has a population density of
27
27
27
,
000
000
000
residents per
1
1
1
square mile. The area of New York City is
301
301
301
square miles, and there is approximately
1
1
1
subway car for every
1
1
1
,
300
300
300
New York City residents. Rounded to the nearest one hundred subway cars, approximately how many total subway cars are in New York City?
Get tutor help
There are about
946
946
946
milliliters in a quart. There are
2
2
2
pints in a quart.
\newline
About how many milliliters are in a pint?
\newline
milliliters
Get tutor help
A veterinarian prescribes fleaprevention medicine for cats based on the weight of the cat. The dosage is
0
0
0
.
03
03
03
milliliters of medicine per pound the cat weighs. How many milliliters of medicine would the veterinarian prescribe for a
15
15
15
-pound cat?
Get tutor help
A restaurant runs the following food challenge: If a customer can finish a
72
72
72
-ounce steak in
60
60
60
minutes or less, then the restaurant will pay for the steak. What is the weight of the steak to the nearest tenth of a pound?
\newline
(
1
1
1
pound
=
16
=16
=
16
ounces)
Get tutor help
A soup manufacturer sells its soup in right cylindrical cans. The cans have a diameter of
6
6
6
centimeters
(
c
m
)
(\mathrm{cm})
(
cm
)
and a height of
10
c
m
10 \mathrm{~cm}
10
cm
. If the manufacturer fills each can to
90
%
90 \%
90%
capacity with soup, what is the volume of soup in each can rounded to the nearest cubic centimeter?
Get tutor help
An intermediate chemical is formed during a chemical reaction. Assuming the mass is positive, the mass of the intermediate chemical,
m
m
m
, in grams
t
t
t
milliseconds after mixing the initial chemicals is given by:
\newline
m
=
−
18.79
(
t
−
3.68
)
(
t
−
7.58
m=-18.79(t-3.68)(t-7.58
m
=
−
18.79
(
t
−
3.68
)
(
t
−
7.58
\newline
According to the model, how long did the intermediate chemical have positive mass? Round your answer to the nearest tenth of a millisecond.
Get tutor help
Lúcia posted a video of her cat playing on the piano. She found that the following expression modeled the total number of people who had viewed her video
t
t
t
days after she posted it.
\newline
18
⋅
1
6
0.0125
t
18 \cdot 16^{0.0125 t}
18
⋅
1
6
0.0125
t
\newline
After how many days did the total number of people viewing the video double from the original number of people?
\newline
(Round your answer to the nearest day.)
Get tutor help
0.30
P
+
0.25
G
=
57
0.30 P+0.25 G=57
0.30
P
+
0.25
G
=
57
\newline
A homeowner uses
G
G
G
hours of natural gas heat and
P
P
P
hours of heat from a pellet stove to heat her house one month, with a total of
57
57
57
therms of output. How many therms per hour does the pellet stove output?
Get tutor help
A local grocer wants to mix candied pecans, priced at
$
14.00
/
\$ 14.00 /
$14.00/
pound (lb), and candied cashews, priced at
$
10.00
/
l
b
\$ 10.00 / \mathrm{lb}
$10.00/
lb
. How many pounds of candied cashews must he mix with
8
l
b
s
8 \mathrm{lbs}
8
lbs
of candied pecans to make a mixture that costs
$
12.50
/
l
b
\$ 12.50 / \mathrm{lb}
$12.50/
lb
? (Round the answer to the nearest tenth of a pound.)
Get tutor help
As an object's depth below the surface of a body of salt water increases, so does the pressure acting on the object due to atmospheric and water conditions. The rate at which pressure increases is approximately
11
11
11
pounds per square inch (psi) for every increase in depth of
25
25
25
feet
(
f
t
)
(\mathrm{ft})
(
ft
)
. The pressure at the surface of the water is
15
p
s
i
15 \mathrm{psi}
15
psi
. Rounded to the nearest foot, at what depth will the pressure acting on the object be
50
50
50
psi?
Get tutor help
A circle in the
x
y
x y
x
y
-plane has its center at the point
(
0.4
,
−
0.3
)
(0.4,-0.3)
(
0.4
,
−
0.3
)
. If the point
(
6
,
5
)
(6,5)
(
6
,
5
)
lies on the circle, what is the diameter of the circle? Round the answer to the nearest tenth.
\newline
Choose
1
1
1
answer:
\newline
(A)
7
7
7
.
7
7
7
units
\newline
(B)
15.4
15.4
15.4
units
\newline
(C)
59
59
59
.
5
5
5
units
\newline
(D)
119
119
119
units
Get tutor help
Wyatt, a chemist at a chemical supply company, has carefully measured out
100
100
100
gallons of a solution containing
14
%
14\%
14%
acetone. He also has access to unlimited quantities of a
9
%
9\%
9%
acetone solution. How many gallons of the
9
%
9\%
9%
acetone solution must Wyatt add to the
14
%
14\%
14%
acetone solution to create a solution that contains
10
%
10\%
10%
acetone?
\newline
Write your answer as a whole number or as a decimal rounded to the nearest tenth.
\newline
\newline
____ gallons
\newline
Get tutor help
Previous
1
2
