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Solving linear equations
1.Solve for k:
k + 22 = 29
k =
Correct answer: 7 Difficulty level: 1
2.Solve for n:
-8 + n = 23
n =
Correct answer: 31 Difficulty level: 1
3.Solve for x:
x – 9 = 1
x =
Correct answer: 10 Difficulty level: 1
4.Solve for n:
18 = n - 18
n =
Correct answer: 36 Difficulty level: 1
5.Solve for k:
k + 10 = 27
k =
Correct answer: 17 Difficulty level: 1
Interpreting linear functions
1.A researcher wants to conduct a survey to gauge United States (U.S.) voters’ opinions about the U.S. Congress. Which of the following should NOT be a component of this survey?
A.The researcher collects data from the survey takers.
B.The researcher analyzed data from the survey takers.
C.The researcher distributes the survey to 10,1000 randomly selected U.S. citizens aged 18 and older.
D.The researcher distributes the survey to 10,000 residents of a Washington D.C. neighborhood.
Correct answer: D Difficulty level: 2 Tag: Data collection and conclusions
2.A scientist wants to collect data about the effects of gravity on the growth of soybean plants. To test her hypothesis that soybeans grow better in a zero-gravity setting, she randomly assigns the plants into one of two groups. The first group is grown in typical soybean growing conditions in a greenhouse on earth, and the second group is grown in a zero-gravity, yet otherwise identical greenhouse in a space station. Which of the following is the best description of the research design for this study?
A.Controlled experiment
B.Observational study
C.Sample survey
D.None of the above
Correct answer: A Difficulty level: 2 Tag: Data collection and conclusions
3.A researcher representing a city government wants to measure public opinion about recycling by asking 1,000 randomly selected residents a series of questions on the subject. Which of the following is the best description of the research design for this study?
A.Observational study
B.Sample survey
C.Controlled experiment
D.None of the above
Correct answer: B Difficulty level: 2 Tag: Data collection and conclusions
4.In order to determine whether children who have just watched cartoons will perform better on cognitive tasks than children who have not just watched cartoons, researchers randomly divided 60 preschoolers into three groups. For nine minutes, one group watched a rapid-paced cartoon, one group watched a slower-paced educational program, and one group colored. They then administered standardized tests to determine the immediate impact of the children’s previous nine minutes of activity. Which of the following is the best description of this type of research design?
A.An observational study, a study in which investigators observe subjects and measure variables of interest without assigning treatments to the subjects.
B.A controlled experiment, a study in which an investigator separates subjects into a control group that does not receive a treatment and an experimental group that receives a treatment, and then observes the effect of the treatment on the experimental group.
C.A sample survey, a study that obtains data from a subset of a population, usually through a questionnaire or interview, in order to estimate population attributes.
D.None of the above
Correct answer: B Difficulty level: 2 Tag: Data collection and conclusions
5.Abby is buying a widescreen TV that she will hang on the wall between two windows. The windows are 36 inches apart, and wide screen TVs are approximately twice as wide as they are tall. Of the following, which is the longest that the diagonal of a widescreen TV can measure and still fit between the windows?
A.32 inches
B.42 inches
C.55 inches
D.60 inches
Correct answer: A Difficulty level: 2 Tag: Right triangle word problems
Systems of linear equations word problems
1.1.The owner of a landscaping company is developing a proposal to maintain the grounds of a building. It is estimated that 75 gardening hours and 25 foreman hours will be required. The total budget for these hours is $1600. The hourly wage for a foreman is 30% more than a gardener plus an additional $1.65 per hour. Which of the following systems of equations can be used to determine the hourly wages of a gardener, g, and a foreman, f, so the total wages are $1600?
A.25g+75f=1600
f=1.3g+1.65
B.25f+75g=1600
f=1.3g+1.65
C.25g+75f=1600
g=1.3f+1.65
D.25f+75g=1600
g=1.3f+1.65
Correct answer: B Difficulty level: 2
2.3.Ricardo had two types of homework assignments for his college math class. The amount of mmm mini assignments he had was one fewer than twice the amount of l long assignments he had. If he had a total of 46 mini and long assignments, which of the following systems of equations can be used to find out how any mini and long assignments he had?
A.m=2l−1
m+l=46
B.m=2l−1
m=l+46
C.l=2m−1
m+l=46
D.l=2m−1
m=l+46
Correct answer: A Difficulty level: 2
3.5.A piece of glass with an initial temperature of 99∘C is cooled at a rate of 3.5∘C per minute. Concurrently, a piece of copper with an initial temperature of 0∘C is heated at 2.5∘C per minute. Which of the following systems of equations can be used to solve for the temperature, T, in degrees Celsius, and the time, m, in minutes, when the glass and copper reach the same temperatures?
A.T=99+3.5m
T=2.5m
B.T=99−3.5m
T=2.5m
C.T=99+2.5m
T=3.5m
D.T=99−2.5m
T=3.5m
4.6.A vegetable stand sells p pumpkins for $5.00 each and s squashes for $3.00 each. On Monday, the stand sold 6 more squashes than pumpkins and made a total of $98.00. Which system of equations can be used to determine the number of pumpkins and squashes sold?
A.3p+5s=98
s=p+6
B.3p+5s=98
p=s+6
C.5p+3s=98
s=p+6
D.5p+3s=98
p=s+6
5.7.Mikayla is the communications director for a politician and has recommended that a total of 41 talks are given by the politician before election day. She also recommends a total of 9 more formal speeches, s, than informal talks, t. Which of the following systems of equations can be used to find out how many formal speeches versus informal talks she had?
A.t=s+9
s+t=41
B.t=s+9
s=t−41
C.s=t+9
s+t=41
D.s=t+9
s=t−41
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