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Math Problems
Algebra 1
Interpret regression lines
Read the following description of a data set.
\newline
Alec is a math teacher at a large school. He wonders if his test problems are too wordy. Alec is curious whether the wordiness is affecting student performance.For the last several tests, Alec computes the average number of words in each question,
x
x
x
, as well as the average percentage scores on the tests,
y
y
y
.The least squares regression line of this data set is:
y
=
−
3.128
x
+
86.387
y = -3.128x + 86.387
y
=
−
3.128
x
+
86.387
\newline
Complete the following sentence:
\newline
If the average question length increased by one word, the least squares regression line predicts that the average percentage score would decrease by
_
_
_
\_\_\_
___
.
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Read the following description of a data set.
\newline
For a science project, Deb wants to see if a larger body of water has more heat energy than a smaller body of water at the same temperature. She prepared a number of buckets filled with various amounts of water at a fixed temperature and dropped an ice cube of the same size into each one.Deb then recorded the volume of water in each bucket (in milliliters),
x
x
x
, and the amount of time it took for each ice cube to melt (in minutes),
y
y
y
.The least squares regression line of this data set is:
y
=
−
0.034
x
+
41.845
y = -0.034x + 41.845
y
=
−
0.034
x
+
41.845
\newline
Complete the following sentence:
\newline
The least squares regression line predicts that if the volume of water increases by one milliliter, the time it takes for the ice cube to melt will drop by
_
_
\_\_
__
minutes.
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Read the following description of a data set.
\newline
Lorenzo's baseball card collection includes sets from many different seasons. His older sets seem to be missing more cards than the newer sets, so he investigated to see whether this was actually the case.For each set, he recorded the number of years since its release,
x
x
x
, and the number of missing cards,
y
y
y
.The least squares regression line of this data set is:
y
=
4.087
x
+
42.187
y = 4.087x + 42.187
y
=
4.087
x
+
42.187
\newline
Complete the following sentence:
\newline
If a set were one year older, the least squares regression line predicts that there would be
_
_
\_\_
__
extra cards missing from it.
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Read the following description of a data set.
\newline
Cassie manages the student health services department at Belleville University. She suspects that the students' poor breakfast habits are contributing to the school's academic decline. Cassie surveyed several students asking how many times they ate breakfast in the past month. She also checked each student's GPA.The data shows the number of times each student ate breakfast in the past month,
x
x
x
, and his or her GPA,
y
y
y
.The least squares regression line of this data set is:
y
=
0.011
x
+
2.117
y = 0.011x + 2.117
y
=
0.011
x
+
2.117
\newline
Complete the following sentence:
\newline
If a student ate breakfast one more time in the past month, the least squares regression line predicts that their GPA would increase by ___.
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Read the following description of a data set.
\newline
A gym franchise was considering a television marketing campaign to increase its membership. The franchise's market researchers wanted to get a better sense of the television and exercise habits of the gym's target demographic. To begin, the market researchers surveyed some of the current members about how many hours they had spent watching television and exercising last month.Using the survey responses, the researchers compared the number of hours of television watched,
x
x
x
, to the number of hours of exercise,
y
y
y
, for each member.The least squares regression line of this data set is:
y
=
−
0.461
x
+
18.468
y = -0.461x + 18.468
y
=
−
0.461
x
+
18.468
\newline
Complete the following sentence:
\newline
If a gym member had watched one additional hour of television last month, the least squares regression line predicts that they would have spent ___ hours less exercising that month.
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Read the following description of a data set.
\newline
A French car company wants to cut costs by using cheaper low-carbon steel in its car frames. To determine how varying the carbon content will affect strength, company engineers manufactured several car frames.For each car frame, the engineers noted the percentage of carbon,
x
x
x
, as well as the weight it could support (in kilograms),
y
y
y
.The least squares regression line of this data set is:
y
=
152.693
x
+
838.499
y = 152.693x + 838.499
y
=
152.693
x
+
838.499
\newline
Complete the following sentence:
\newline
If a car frame has one additional percentage point of carbon, the least squares regression line predicts it can support ___ more kilograms.
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Read the following description of a data set.
\newline
Every summer, the Stamford Fair has a grasshopper catching contest. Grasshoppers are released into a fenced area, and participants are given five minutes to catch as many as they can. To even the playing field, the organizers developed a handicap system based on the results of this year's competition. The system takes into account the different experience levels of the contest participants.To create the system, the organizers recorded the number of times each contestant had previously participated,
x
x
x
, and the number of grasshoppers each contestant had caught this year,
y
y
y
.The least squares regression line of this data set is:
y
=
4.633
x
−
9.024
y = 4.633x - 9.024
y
=
4.633
x
−
9.024
\newline
Complete the following sentence:
\newline
The least squares regression line predicts that a participant would have caught ___ more grasshoppers for each additional year of participation.
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Read the following description of a data set.
\newline
A pharmaceutical company is testing a new headache medication. Researchers at the company conducted an observational study using volunteer participants. All participants were given a supply of tablets of the new medication.The participants then recorded how many headaches they had had for a week,
x
x
x
, and how many tablets they had taken,
y
y
y
.The least squares regression line of this data set is:
y
=
0.151
x
+
2.818
y = 0.151x + 2.818
y
=
0.151
x
+
2.818
\newline
Complete the following sentence:
\newline
For each additional headache someone had had, the least squares regression line predicts that he or she would have taken
_
_
\_\_
__
additional tablets.
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Read the following description of a data set.
\newline
Omar is preparing for the national spelling bee and is following a strict study plan. To create the plan, he timed how long it had taken him to memorize several words.Omar recorded the number of letters in each word,
x
x
x
, and how many minutes,
y
y
y
, it had taken him to memorize it.The least squares regression line of this data set is:
y
=
0.082
x
+
4.603
y = 0.082x + 4.603
y
=
0.082
x
+
4.603
\newline
Complete the following sentence:
\newline
The least squares regression line predicts that Omar would take ___ additional minutes to memorize a word with an additional letter.
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Read the following description of a data set.
\newline
Fans of the science fiction television show Space Cruiser Zeta are hosting a convention. To figure out how much space the event will require, an employee at the convention center looked at the space requirements for previous conventions.For each convention, the employee recorded the number of attendees,
x
x
x
, and the floor space required (in square meters),
y
y
y
.The least squares regression line of this data set is:
y
=
2.069
x
+
12
,
552.043
y = 2.069x + 12,552.043
y
=
2.069
x
+
12
,
552.043
\newline
Complete the following sentence:
\newline
The least squares regression line predicts that a convention would use
_
_
\_\_
__
additional square meters of floor space for each additional attendee.
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How People Travel to Work by Region (estimated in millions)
\newline
\begin{tabular}{lccc}
\newline
US Geographic Region & Drove or Carpooled & Public Transportation & Total \\
\newline
\hline Northeast &
20
20
20
&
4
4
4
&
24
24
24
\\
\newline
Midwest &
28
28
28
&
1
1
1
&
29
29
29
\\
\newline
South &
47
47
47
&
1
1
1
&
48
48
48
\\
\newline
West &
28
28
28
&
1
1
1
&
29
29
29
\\
\newline
Total &
123
123
123
&
7
7
7
&
130
130
130
\newline
\end{tabular}
\newline
The table shows data from the U.S. Census Bureau regarding the methods people use to travel to work categorized by geographic region. All the data is estimated in millions of people. Based on the information in the table, what is the relative frequency of people in the Northeast region who take public transportation?
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The following figure is made of
1
1
1
triangle and
2
2
2
rectangles. A
5
5
5
sided figure made of a large rectangle with a small rectangle and small right triangle attached to the right side. A dashed line parallel to the height of the rectangle runs from the top, right vertex of the large rectangle to the bottom, right vertex of the large rectangle. This dashed line is the height of the right triangle and the height of the small rectangle that is attached to the right side of the large rectangle. The large rectangle, labeled
A
A
A
, has a base of
6
6
6
units and a height of
9
9
9
units. The right triangle is labeled
B
B
B
. The small rectangle, labeled
C
C
C
, has a height of
7
7
7
units. The base of the figure is
9
9
9
units. Find the area of each part of the figure and the whole figure.
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The following figure is made of
1
1
1
triangle and
2
2
2
rectangles. A
5
5
5
-sided figure made of a large rectangle with a small rectangle and small right triangle attached to the right side. A dashed line parallel to the height of the rectangle runs from the top, right vertex of the large rectangle to the bottom, right vertex of the large rectangle. This dashed line is the height of the right triangle and the height of the small rectangle that is attached to the right side of the large rectangle. The large rectangle, labeled
A
A
A
, has a base of
6
6
6
units and a height of
9
9
9
units. The right triangle is labeled
B
B
B
. The small rectangle, labeled
C
C
C
, has a height of
7
7
7
units. The base of the figure is
9
9
9
units. Find the area of each part of the figure and the whole figure.
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29
29
29
. Multiple choice - Bushels of corn exported from the U.S., in millions, from
2008
2008
2008
to
2012
2012
2012
, can be modeled by a quadratic function. In
2008
2008
2008
, the U.S. exported approximately
1849
1849
1849
million bushels of com. In
2009
2009
2009
, the U.S. exported approximately
1979
1979
1979
million bushels of corn, which was a maximum for that time period. According to the above information, which of the following best approximates the U.S. corn exports in
2012
2012
2012
?
\newline
A.
809
809
809
million bushels
\newline
B.
1170
1170
1170
million bushels
\newline
C.
1589
1589
1589
million bushels
\newline
D.
2369
2369
2369
million bushels
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Bushels of corn exported from the U.S., in millions, from
2008
2008
2008
to
2012
2012
2012
, can be modeled by a quadratic function. In
2008
2008
2008
, the U.S. exported approximately
1849
1849
1849
million bushels of corn. In
2009
2009
2009
, the U.S. exported approximately
1979
1979
1979
million bushels of corn, which was a maximum for that time period. According to the above information, which of the following best approximates the U.S. corn exports in
2012
2012
2012
?
\newline
A.
809
809
809
million bushels
\newline
B.
1170
1170
1170
million bushels
\newline
C.
1589
1589
1589
million bushels
\newline
D.
2369
2369
2369
million bushels
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A list of positive integers has the following properties:
\newline
- The sum of the items in the list is
30
30
30
.
\newline
- The unique mode of the list is
9
9
9
.
\newline
- The median of the list is a positive integer that does not appear in the list itself.
\newline
Find the sum of the squares of all the items in the list.
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Chopter
8
8
8
Homework (
3
3
3
\newline
Saned
\newline
Hels
\newline
Save is txit
\newline
submit.
\newline
4
4
4
\newline
Part
1
1
1
old
\newline
Required informetion
\newline
(The following information applies to the quesions displayed below, ]
\newline
The following events apply to Gulf Seafocd for the Year
1
1
1
fiscal year:
\newline
The compary stared when in acquired
$
75000
\$75000
$75000
cash by issuing common snock.
\newline
Purchased a new cooknop that cost
$
15700
\$15700
$15700
cash.
\newline
Earned
$
22000
\$22000
$22000
in cash revenue.
\newline
Paid
$
11900
\$11900
$11900
cash for salaries expenae.
\newline
Adjuated the reconds
10
10
10
reflect the use of the cooktop. Purchased on January
1
1
1
, Year
1
1
1
, the cooktiop has an expected useful like of four years and an estimated salvage value of
$
3000
\$3000
$3000
. Use straight-line depreciation. The adjustment was made as of December
31
31
31
. Mear
1
1
1
.
\newline
Check my wark
\newline
aes
\newline
points
\newline
sipend
\newline
( made as of December
31
31
31
. Vear
1
1
1
.
\newline
Required:
\newline
a. Record the above transactions in a horizontal statemencs model.
\newline
Nole: In the Sutement of Cash Flows column, vel the initibls (OA), an imresting activity (IA), a finsncing bctivity (FA) and net chonge in eash (NC). Enter any decresses to bceoum balances and ebsh outlows with a minus sign. Not all cells require input.
\newline
Event
\newline
Multion
\newline
nevila
\newline
Asaing ior viet incut.
\newline
Aepert abug
\newline
fire
\newline
Pqterencet
\newline
Event
\newline
Could you please provide more detals on where to find the "SnapSolve Ar" leature on the page? I ans unable to lecale it basied on the currest browidet content. If there is a specific bution or link I should click on, please lat me know its description or ary text antociated with it.
\newline
Hew did I dop? Give a rating :
\newline
Wribe a command.
\newline
Prer
\newline
Next
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WAMAP
\newline
\text{wamap.org/assess2/?cid=35882&aid=2016687} // skip
\newline
//
1
1
1
\newline
wamap.org
\newline
Home | My Classes | User Settings| Log Out
\newline
Course
\newline
Messages
\newline
Forums
\newline
Calendar
\newline
Gradebook
\newline
Home > MATHE
146
146
146
WINTER
2024
2024
2024
-
24474
24474
24474
> Assessment
\newline
Homework
12
12
12
.
3
3
3
:The Regression line and Prediction
\newline
Score:
50.2
/
97
50.2/97
50.2/97
15
/
19
15/19
15/19
answered
\newline
×
\times
×
Question
1
1
1
\newline
Score on last try:
0
0
0
of
6
6
6
pts. See Details for more.
\newline
Next question
\newline
\(\newlineabla\)
\newline
Get a similar question
\newline
You can retry this question below
\newline
\newline
x
x
x
\newline
1
1
1
\newline
2
2
2
\newline
50.2
/
97
50.2/97
50.2/97
0
0
0
\newline
50.2
/
97
50.2/97
50.2/97
1
1
1
\newline
50.2
/
97
50.2/97
50.2/97
2
2
2
\newline
6
6
6
\newline
\newline
50.2
/
97
50.2/97
50.2/97
4
4
4
\newline
50.2
/
97
50.2/97
50.2/97
5
5
5
\newline
50.2
/
97
50.2/97
50.2/97
6
6
6
\newline
50.2
/
97
50.2/97
50.2/97
7
7
7
\newline
50.2
/
97
50.2/97
50.2/97
8
8
8
\newline
50.2
/
97
50.2/97
50.2/97
9
9
9
\newline
15
/
19
15/19
15/19
0
0
0
\newline
\newline
Use linear regression to find the equation for the linear function that best fits this data. Round numbers to two decimal places.
\newline
15
/
19
15/19
15/19
1
1
1
\newline
Hint
\newline
Question Help: Video
\newline
Submit Question
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Complet the T chart of values for the Quadratic:
\newline
When you have checked your quiz and know that your T-Chart is correct, graph this Quadratic and upload it (along with the others) on the Graph Upload Assignment f points
\newline
x
=
y
2
+
4
x=y^{2}+4
x
=
y
2
+
4
\newline
\newline
x
x
x
\newline
y
y
y
\newline
\newline
−
1
-1
−
1
\newline
\newline
−
1
-1
−
1
\newline
\newline
−
2
-2
−
2
\newline
\newline
−
2
-2
−
2
\newline
\newline
−
3
-3
−
3
\newline
\newline
Complet the T chart of values for the Quadratic:
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Perpetual inventory using LIFO
\newline
Beginning inventory, purchases, and sales data for DVD players are as follows:
\newline
Nov,
1
1
1
Inventory
\newline
140
140
140
units at
\newline
$
29
\$29
$29
\newline
10
10
10
Sale
110
110
110
units
\newline
15
15
15
Purchase
\newline
150
150
150
units at
\newline
$
30
\$30
$30
\newline
20
20
20
Sale
\newline
120
120
120
units
\newline
24
24
24
Sale
35
35
35
units
\newline
30
30
30
Purchase
\newline
140
140
140
units at
\newline
$
34
\$34
$34
\newline
The business maintains a perpetual inventory system, costing by the last-in, first-out method.
\newline
Determine the cost of goods sold for each sale and the inventory balance after each sale, presenting the data in the form illustrated in Exhibit
4
4
4
. Un LIFO, if units are in inventory at two different costs, enter the units with the HIGHER unit cost first in the cost of Goods Sold Unit cost column and LOWER unit cost first in the Inventory Unit cost column.
\newline
LIFO Method
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A small accounting firm has
4
4
4
accountants who each earn a different salary between
52
52
52
,
000
000
000
dollars and
58
58
58
,
000
000
000
dollars. For extra help during tax season, they hire a
5
th
5^{\text {th }}
5
th
accountant who earns
10
10
10
,
000
000
000
dollars. [Show data].
\newline
How will hiring the
5
th
5^{\text {th }}
5
th
accountant affect the mean and median?
\newline
Choose
1
1
1
answer:
\newline
(A) Both the mean and median will decrease, but the median will decrease by more than the mean.
\newline
(B) Both the mean and median will decrease, but the mean will decrease by more than the median.
\newline
(C) The mean will decrease, and the median will increase.
\newline
(D) The mean will increase, and the median will decrease.
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Chucky grabbed
11
11
11
items in the grocery store. Each item had a different price, and the mean was about
$
4.44
\$ 4.44
$4.44
. On his way to the register, he added a
1
2
th
12^{\text {th }}
1
2
th
item: a jug of olive oil for
$
39.99
\$ 39.99
$39.99
. [show data].
\newline
How will adding the jug of olive oil affect the mean and median?
\newline
Choose
1
1
1
answer:
\newline
(A) Both the mean and median will increase, but the median will increase by more than the mean.
\newline
(B) Both the mean and median will increase, but the mean will increase by more than the median.
\newline
(C) The mean will increase, and the median will decrease.
\newline
(D) The median will increase, and the mean will decrease.
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Diego is a wildlife researcher. They were analyzing the mean and median lengths of
9
9
9
whales their team had observed. The whales all had different lengths between
23
m
23 \mathrm{~m}
23
m
and
27
m
27 \mathrm{~m}
27
m
.
\newline
Diego found out that they were misreading the shortest length. It was actually
20
m
20 \mathrm{~m}
20
m
, not
23
m
23 \mathrm{~m}
23
m
.
\newline
How will this length decreasing affect the mean and median?
\newline
Choose
1
1
1
answer:
\newline
(A) Both the mean and median will decrease.
\newline
(B) The mean will decrease, and the median will increase.
\newline
(C) The mean will decrease, and the median will stay the same.
\newline
(D) The mean will stay the same, and the median will decrease.
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The following data points represent the number of chicken nuggets on each family member's plate.
\newline
1
,
3
,
0
,
6
,
?
1,3,0,6, ?
1
,
3
,
0
,
6
,
?
\newline
If the mean of the data set is
3
3
3
chicken nuggets, find the missing number of chicken nuggets.
\newline
nuggets
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A zookeeper weighs her animals once a month and compares their weights to the previous month.
\newline
The lemur lost
3
k
g
3 \mathrm{~kg}
3
kg
between January and February.
\newline
The rhino gained
12
k
g
12 \mathrm{~kg}
12
kg
between January and February.
\newline
The otter lost
2
k
g
2 \mathrm{~kg}
2
kg
between January and February.
\newline
The penguin gained
4
k
g
4 \mathrm{~kg}
4
kg
between January and February.
\newline
Which animal had the least amount of change in weight?
\newline
Choose
1
1
1
answer:
\newline
(A) Lemur
\newline
(B) Rhino
\newline
(C) Otter
\newline
(D) Penguin
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Based on her research, Aria estimates that
75
%
75 \%
75%
of the students at her college work while they're in school. The margin of error of her estimation is
5
%
5 \%
5%
. Based on her estimate and margin of error, Aria would most likely agree with which of the following statements?
\newline
Choose
1
1
1
answer:
\newline
(A) Between
70
%
70 \%
70%
and
80
%
80 \%
80%
of the students at Aria's college work while they're in school.
\newline
B Between
70
%
70 \%
70%
and
75
%
75 \%
75%
of the students at Aria's college work while they're in school.
\newline
(C) Between
72.5
%
72.5 \%
72.5%
and
77.5
%
77.5 \%
77.5%
of the students at Aria's college work while they're in school.
\newline
(D) Between
74.5
%
74.5 \%
74.5%
and
75.5
%
75.5 \%
75.5%
of the students at Aria's college work while they're in school.
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Vicente surveyed a random sample of New Mexico residents ages
18
18
18
to
24
24
24
about how much they typically tip at a restaurant. The results of the survey are most representative of which of the following populations?
\newline
Choose
1
1
1
answer:
\newline
(A) New Mexico residents
\newline
(B) Albuquerque, New Mexico residents
\newline
(C) New Mexico residents ages
18
18
18
to
24
24
24
\newline
(D) Albuquerque, New Mexico residents ages
18
18
18
to
24
24
24
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A writer for a high school newspaper is conducting a survey to estimate the number of students that will vote for a particular candidate in an upcoming student government election. All students at the high school are eligible to vote in the election, and the writer decides to select a sample of students to take the survey. Which of the following sampling methods is most likely to produce valid results?
\newline
Choose
1
1
1
answer:
\newline
(A) Survey every fifth student to enter the school library.
\newline
(B) Survey every fifth student to arrive at school one morning.
\newline
(C) Survey every fifth senior to arrive at school one morning.
\newline
(D) Survey every fifth student to enter the school stadium for a football game
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In which of the following scenarios can the decline of Littleroot Town's population be described as linear?
\newline
Choose
1
1
1
answer:
\newline
(A) Each year,
2.5
%
2.5 \%
2.5%
of the current population leaves Littleroot Town.
\newline
(B) Each year, an increasing number of people leave Littleroot Town.
\newline
(C) Each year, a decreasing number of people leave Littleroot Town.
\newline
(D) Each year, a constant number of people leave Littleroot Town.
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Phytoremediation is the use of plant growth to purify pollutants from soil, water, or air. Suppose that a crop of brake ferns can remove
15
15
15
milligrams
(
m
g
)
(\mathrm{mg})
(
mg
)
per square meter of a particular pollutant from the soil in
20
20
20
weeks. After
20
20
20
weeks, the ferns are harvested and a new crop is planted. If
c
c
c
represents the number of crops of brake ferns needed to phytoremediate soil contaminated with
170
m
g
170 \mathrm{mg}
170
mg
per square meter of the pollutant down to healthy levels of
5
m
g
5 \mathrm{mg}
5
mg
per square meter, which equation best models the situation?
\newline
Choose
1
1
1
answer:
\newline
(A)
170
−
20
c
=
5
170-20 c=5
170
−
20
c
=
5
\newline
(B)
170
+
20
c
=
5
170+20 c=5
170
+
20
c
=
5
\newline
(C)
170
−
15
c
=
5
170-15 c=5
170
−
15
c
=
5
\newline
(D)
170
+
15
c
=
5
170+15 c=5
170
+
15
c
=
5
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A large truck, traveling
30
30
30
miles per hour, carries a letter from the central post office to the local post office. The letter is then loaded onto a local vehicle, which travels at an average speed of
10
10
10
miles per hour, until the letter reaches its destination. The large truck carried the letter for
a
a
a
minutes and the local vehicle carried the letter for
b
b
b
minutes. If the total distance that the letter travelled from the central post office to its destination was
24
24
24
miles, which of the following equations correctly relates
a
a
a
and
b
b
b
?
\newline
Choose
1
1
1
answer:
\newline
(A)
30
60
a
+
10
60
b
=
24
\frac{30}{60} a+\frac{10}{60} b=24
60
30
a
+
60
10
b
=
24
\newline
(B)
60
30
a
+
60
10
b
=
24
\frac{60}{30} a+\frac{60}{10} b=24
30
60
a
+
10
60
b
=
24
\newline
(C)
30
a
+
10
b
=
24
30 a+10 b=24
30
a
+
10
b
=
24
\newline
(D)
60
⋅
30
a
+
60
⋅
10
b
=
24
60 \cdot 30 a+60 \cdot 10 b=24
60
⋅
30
a
+
60
⋅
10
b
=
24
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Read the following description of a data set. Rod Diamond is a singer who appeals to an older demographic. For a comedy segment on a late night show, he asked random people on the street how old they were and how many of his songs they could name, if any. Rod noted the age of each person he spoke with,
x
x
x
, and the number of songs each could name,
y
y
y
. The least squares regression line of this data set is:
y
=
0.886
x
−
23.764
y = 0.886x - 23.764
y
=
0.886
x
−
23.764
Complete the following sentence: The least squares regression line predicts that if a person is one year older, they will be able to name
_
_
_
_
\_\_\_\_
____
more songs.
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