Practice Quiz 9_ Attempt review
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School
Thompson Rivers University *
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Course
1901
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
8
Uploaded by CaptainArt11246
Started on
Saturday, 8 July 2023, 1:56 PM
State
Finished
Completed on
Saturday, 8 July 2023, 2:13 PM
Time taken
16 mins 54 secs
Question 1
Correct
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Numerical question: Sherri pays $60 per month for her cellphone plan, and an additional $15 activation fee. One function that arises
from this situation in one where the inputs are the number of months, m
, and the outputs are the corresponding total costs, c
.
A formula for the function is c =
60
m +
15
. When m = 4 months, then c = $
255
. When c = $135, then m =
2
months. (Write a whole number for each number; do not include the $ symbol or any words or calculations.)
Answer:
A formula for the function is c = 60m + 15. When m = 4 months, then c = $255. When c = $135, then m = 2 months.
Question 2
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Question 3
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Sherri pays $60 per month for her cellphone plan, and an additional $15 activation fee. One function that arises from this situation is
one where the inputs are the number of months, m
, and the outputs are the corresponding total costs, c
. How should you plot a line
graph of this function?
Select one:
a.
Put m
on the horizontal axis and c
on the vertical axis, draw a line starting at m
= 0 and c
= 15 with slope 60.
b.
Put m
on the horizontal axis and c
on the vertical axis, draw a line starting at m
= 0 and c
= 60 with slope 15.
c.
Put c
on the horizontal axis and m
on the vertical axis, draw a line starting at c
= 15 and m
= 0 with slope 60.
d.
Put c on the horizontal axis and m on the vertical axis, draw a line starting at c = 60 and m = 0 with slope 15.
Your answer is correct.
The correct answer is: Put m
on the horizontal axis and c
on the vertical axis, draw a line starting at m
= 0 and c
= 15 with slope 60.
The Widget Company sells boxes of widgets, all the same size and costing the same amount, by mail order. The company charges a
fixed amount for shipping, no matter how many boxes of widgets are ordered, but no sales tax. The total cost (including shipping) for
6 boxes of widgets is $30, and the total cost (including shipping) for 10 boxes of widgets is $46. Therefore, the cost of shipping is $
6
and the price of one box of widgets is $
4
. A formula for the total cost (including shipping) for w
boxes of widgets is
4
w
+
6
. (Write a whole number for each answer; do not include the $ symbol or words or calculations.)
Since the shipping cost is fixed, the difference in total cost for 6 boxes and 10 boxes is purely for the price of the widgets. Thus 10 –
6 = 4 boxes cost $46 – $30 = $16, which we use to get the price of one box: $16 / 4 = $4. Then comparing the unit price to the cost of
shipping 6 boxes gives us the shipping cost: $30 – $4 × 6 = $30 – $24 = $6.
Question 4
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Question 5
Correct
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If today is a Monday, one year from today will be a
if there is not a February 29 during the coming year or
if there is a February 29 during the coming year.
Tuesday
Wednesday
Your answer is correct.
A year is 365 days or 52 weeks and 1 day if there is not a February 29. A year is 366 days or 52 weeks and 2 days if there is a
February 29 in the year.
The correct answer is:
If today is a Monday, one year from today will be a [Tuesday] if there is not a February 29 during the coming year or [Wednesday] if
there is a February 29 during the coming year.
Suppose you owe $100 on a credit card that charges you 1% interest on the amount you owe at the end of every month. Assume that
you do not pay off your debt and that you do not add any more debt other than the interest you are charged. How much do you owe
at the end of m months and how much do you owe after 2 years?
Select one:
a.
You owe 1.01 × 100 × m at the end of m months and $2424 after 2 years.
b.
You owe (1 + 0.01
m
) × 100 at the end of m months and $124 after 2 years.
c.
You owe 1.01
× 100 at the end of m months and $126.97 after 2 years.
d.
You owe 0.01 × 100 × m + 100 at the end of m months and $124 after 2 years.
e.
None of alternatives a-d are correct.
m
Your answer is correct.
The correct answer is: You owe 1.01
× 100 at the end of m months and $126.97 after 2 years.
m
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Question 6
Correct
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A skydiver falls out of a plane. At first, the skydiver falls faster and faster, but then the skydiver reaches a point where he falls with a
constant speed. After falling at a constant speed for a while, the skydiver’s parachute opens and the skydiver falls at a slower speed
until he lands safely on the ground. We could define different functions that fit with this story, for example one that describes height
as a function of time (
t
) and another that describes speed as a function of time (
t
). Graphs of the functions in which the labels on the
vertical axis are missing are as follows:
Which graph represents which function?
Height function:
Speed function:
Second graph
First graph
Your answer is correct.
The skydiver falls to the ground without ever going back up, so the height function graph must start at t
= 0 at its highest point and
eventually reach height = 0 when the skydiver is on the ground. The skydiver begins at rest with a speed of 0 at t
= 0, then the speed
increases, reaches a plateau, then decreases when the parachute opens, then remains steady while the parachute remains open
until the skydiver reaches the ground and speed = 0 again.
The correct answer is:
A skydiver falls out of a plane. At first, the skydiver falls faster and faster, but then the skydiver reaches a point where he falls with a
constant speed. After falling at a constant speed for a while, the skydiver’s parachute opens and the skydiver falls at a slower speed
until he lands safely on the ground. We could define different functions that fit with this story, for example one that describes height
as a function of time (
t
) and another that describes speed as a function of time (
t
). Graphs of the functions in which the labels on the
vertical axis are missing are as follows:
Which graph represents which function?
Height function: [Second graph]
Speed function: [First graph]
Question 7
Incorrect
Mark 0.00 out of 1.00
Consider the following table for function .
x
2
4
6
8
10
f
(
x
)
4
7
10
13
16
What kind of function is and what is its formula?
Select one:
a.
f
(
x
)
is a linear function with formula f
(
x
) = 3
x
+ 1
b.
\(f\left( x \right)\) is a linear function with formula \(f\left( x \right) = \;\frac{3}{2}x + 1\).
c.
\(f\left( x \right)\) is a linear function with formula \(f\left( x \right) = \;\frac{3}{2}x + 4\).
d.
\(f\left( x \right)\) is a non-linear function.
Your answer is incorrect.
When \(x\) increases by 2, \(f\left( x \right)\) increases by 3, so the slope is 3/2. When \(x\; = \;0\), \(f\left( x \right)\) would be 4 – 3 = 1
The correct answer is: \(f\left( x \right)\) is a linear function with formula \(f\left( x \right) = \;\frac{3}{2}x + 1\).
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Question 8
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Question 9
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Consider the following table for function \(f\left( x \right)\).
x
0
1
2
3
4
f
(
x
)
–6
–2
1
3
4
What kind of function is \(f\left( x \right)\) and what is its formula?
Select one:
a.
\(f\left( x \right)\) is a linear function with formula \(f\left( x \right) = \;4x - 6\).
b.
\(f\left( x \right)\) is a linear function with formula \(f\left( x \right) = \;3x - 6\)
c.
\(f\left( x \right)\) is a linear function with formula \(f\left( x \right) = \;2x - 6\)
d.
\(f\left( x \right)\) is a non-linear function.
Your answer is correct.
The differences between successive inputs are not constant. So the function cannot be linear
The correct answer is: \(f\left( x \right)\) is a non-linear function.
Consider the linear function y
= m
x
+ b with inputs x and outputs y. Suppose when x
= 0 then y
= 9 and when x
= 1 then y
= 10. The
values of m and b are therefore m =
1
and b =
9
. (Write an integer for each number; do not include any words or calculations.)
When x
increases by 1, y
increases by 1, so the slope is 1. When x
= 0, y
is 9.
Question 10
Correct
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Consider the linear function y
= m
x
+ b with inputs x
and outputs y
. Suppose when x
= 1 then y
= –10 and when x
= 3 then y
= –20.
The values of m and b are therefore m =
-5
and b =
-5
. (Write an integer for each number; do not include any words or calculations.)
When x
increases by 2, y
decreases by –10, so the slope is –10/2 = –5. When x
= 0, y
must be –10 – (–5) = –10 + 5 = –5