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Let’s check out your problem:
Suppose the
diameter of a circle
is
16
16
16
units. What is its circumference?
\newline
Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
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Home
Math Problems
Algebra 1
Weighted averages: word problems
Full solution
Q.
Suppose the diameter of a circle is
16
16
16
units. What is its circumference?
\newline
Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
Question Prompt:
The question_prompt: What is the
circumference of a circle
with a diameter of
16
16
16
units?
Formula for Circumference:
To find the circumference of a circle, use the formula
C
=
π
d
C = \pi d
C
=
π
d
, where
C
C
C
is the circumference and
d
d
d
is the diameter.
Substitute Diameter:
Given that the diameter
d
d
d
is
16
16
16
units, we can substitute this value into the formula.
C
=
π
×
16
C = \pi \times 16
C
=
π
×
16
Calculate Circumference:
We are instructed to use
3.14
3.14
3.14
for
π
\pi
π
. Therefore, we calculate the circumference as follows:
\newline
C
=
3.14
×
16
C = 3.14 \times 16
C
=
3.14
×
16
Perform Multiplication:
Perform the multiplication to find the circumference.
C
=
50.24
C = 50.24
C
=
50.24
units
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Rosie went on a hiking trip. The first day she walked
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18
18
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90
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90 \%
90%
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\newline
What is the total distance Rosie has traveled by the end of the
1
0
th
10^{\text {th }}
1
0
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\newline
Round your final answer to the nearest kilometer.
\newline
k
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\newline
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25^{\text {th }}
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\newline
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Question
S
E
=
σ
n
S E=\frac{\sigma}{\sqrt{n}}
SE
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σ
\newline
The given equation relates the standard error,
S
E
S E
SE
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σ
\sigma
σ
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n
n
n
. Which of the following equations correctly gives the size of the sample in terms of the standard error and the population standard deviation?
\newline
Choose
1
1
1
answer:
\newline
(A)
n
=
(
σ
S
E
)
2
n=\left(\frac{\sigma}{S E}\right)^{2}
n
=
(
SE
σ
)
2
\newline
(B)
n
=
σ
2
S
E
n=\frac{\sigma^{2}}{S E}
n
=
SE
σ
2
\newline
(C)
n
=
(
σ
S
E
)
n=\sqrt{\left(\frac{\sigma}{S E}\right)}
n
=
(
SE
σ
)
\newline
(D)
n
=
σ
S
E
n=\frac{\sqrt{\sigma}}{S E}
n
=
SE
σ
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Question
Avery is designing a large rectangular sign. They want the sign to have an area of
2
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2
2 \mathrm{~m}^{2}
2
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2
and a width of
4
5
m
\frac{4}{5} \mathrm{~m}
5
4
m
.
\newline
How tall should the sign be?
\newline
m
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Question
The bacteria in a Petri dish culture are self-duplicating at a rapid pace.
\newline
The relationship between the elapsed time
t
t
t
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B
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t
)
B(t)
B
(
t
)
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\newline
B
(
t
)
=
10
⋅
2
t
12
B(t)=10 \cdot 2^{\frac{t}{12}}
B
(
t
)
=
10
⋅
2
12
t
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How many bacteria will make up the culture after
120
120
120
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\newline
Round your answer, if necessary, to the nearest hundredth.
\newline
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Question
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
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S
(
t
)
S(t)
S
(
t
)
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(
g
/
l
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(\mathrm{g} / \mathrm{l})
(
g
/
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)
, is modeled by the following function.
\newline
S
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t
)
=
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⋅
e
−
0.25
t
S(t)=500 \cdot e^{-0.25 t}
S
(
t
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=
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−
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\newline
What will the concentration of salt be after
10
10
10
hours?
\newline
Round your answer, if necessary, to the nearest hundredth.
\newline
g/
1
1
1
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Question
After the closing of the mill, the town of Sawyerville experienced a decline in its population.
\newline
The relationship between the elapsed time,
t
t
t
, in years, since the closing of the mill, and the town's population,
P
(
t
)
P(t)
P
(
t
)
, is modeled by the following function.
\newline
P
(
t
)
=
12
,
000
⋅
2
−
t
15
P(t)=12,000 \cdot 2^{-\frac{t}{15}}
P
(
t
)
=
12
,
000
⋅
2
−
15
t
\newline
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9000
9000
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\newline
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Carlos has taken an initial dose of a prescription medication.
\newline
The relationship between the elapsed time
t
t
t
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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
−
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t
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M
(
t
)
=
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⋅
e
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t
\newline
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1 \mathrm{mg}
1
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\newline
Round your answer, if necessary, to the nearest hundredth.
\newline
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Question
To take a taxi, it costs
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$3.00
plus an additional
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2.00
\$ 2.00
$2.00
per mile traveled. You spent exactly
$
20
\$ 20
$20
on a taxi, which includes the
$
1
\$ 1
$1
tip you left.
\newline
How many miles did you travel?
\newline
miles
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Question
Polygon
Y
Y
Y
is a scaled copy of Polygon
X
X
X
using a scale factor of
1
3
\frac{1}{3}
3
1
.
\newline
Polygon
Y
′
Y^{\prime}
Y
′
's area is what fraction of Polygon
X
X
X
's area?
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