1.
Describe the correlation in the given relationship.The distance a person runs and how physically tired that person is.
Correct Answer
A. Positive correlation
Explanation
The given relationship between the distance a person runs and how physically tired that person is shows a positive correlation. This means that as the distance a person runs increases, their level of physical tiredness also increases. In other words, the more a person runs, the more physically tired they become. This suggests that there is a direct relationship between the two variables, where an increase in one variable leads to an increase in the other variable.
2.
Describe the correlation in the given relationship.The number of cats in a barn and the number of mice in that barn.
Correct Answer
B. Negative correlation
Explanation
The given relationship between the number of cats in a barn and the number of mice in that barn suggests a negative correlation. This means that as the number of cats increases, the number of mice decreases, and vice versa. This can be attributed to the predatory nature of cats, as they are natural hunters of mice. Therefore, when the population of cats increases, they are likely to hunt and reduce the population of mice in the barn. Conversely, when the number of cats decreases, the population of mice may have a chance to increase.
3.
Describe the correlation in the given relationship.The number of miles driven and the number of gallons of gas left in the tank.
Correct Answer
B. Negative correlation
Explanation
The relationship between the number of miles driven and the number of gallons of gas left in the tank is a negative correlation. This means that as the number of miles driven increases, the number of gallons of gas left in the tank decreases. The two variables are inversely related to each other, indicating that more fuel is consumed as more miles are driven.
4.
Describe the correlation in the given relationship.The age of a person and the amount of broccoli that person eats.
Correct Answer
C. No correlation
Explanation
The given relationship between the age of a person and the amount of broccoli they eat suggests that there is no correlation between these two variables. This means that there is no consistent pattern or relationship between age and broccoli consumption. In other words, as a person's age increases or decreases, it does not necessarily have any impact on the amount of broccoli they consume.
5.
Describe the correlation in the given relationship.The number of first downs an offense makes in a football game and the number of punts in that game.
Correct Answer
B. Negative correlation
Explanation
The given relationship between the number of first downs an offense makes in a football game and the number of punts in that game is a negative correlation. This means that as the number of first downs increases, the number of punts decreases, and vice versa. In other words, when an offense is successful in making more first downs, they are less likely to punt the ball. Conversely, when an offense struggles to make first downs, they are more likely to punt the ball. Therefore, there is a negative relationship between the two variables.
6.
Which of the following graphs shows a positive correlation?
Correct Answer
A. GrapH A
Explanation
Graph A shows a positive correlation because as the x-values increase, the y-values also increase. This indicates that there is a direct relationship between the two variables, where an increase in one variable is accompanied by an increase in the other variable.
7.
Which of the following graphs shows a negative correlation?
Correct Answer
C. GrapH C
Explanation
Graph C shows a negative correlation because as the x-values increase, the corresponding y-values decrease. This indicates an inverse relationship between the two variables.
8.
Which of the following graphs might best show the length of a pencil as a function of the number of times it is sharpened?
Correct Answer
C. GrapH C
Explanation
Graph C might best show the length of a pencil as a function of the number of times it is sharpened because it shows a gradual decrease in length as the number of times sharpened increases. The other graphs either show no change in length or inconsistent patterns, which do not accurately represent the relationship between sharpening and length.
9.
Which of the following graphs might best show the grade average of a student as a function of the number of hours spent studying?
Correct Answer
A. GrapH A
Explanation
Graph A might best show the grade average of a student as a function of the number of hours spent studying because it shows a positive linear relationship between the two variables. As the number of hours spent studying increases, the grade average also increases. This suggests that the more time a student spends studying, the higher their grade average is likely to be.
10.
Which of the following graphs might best show the frequency of flossing teeth and number of trips to eye doctor?
Correct Answer
D. GrapH D
Explanation
Graph D might best show the frequency of flossing teeth and number of trips to the eye doctor because it appears to have two distinct axes, one representing the frequency of flossing teeth and the other representing the number of trips to the eye doctor. The other graphs (A, B, and C) do not clearly show these two variables on separate axes, making Graph D the most suitable option for representing the relationship between flossing teeth and trips to the eye doctor.
11.
Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference.−1, −3, −9, −27, ...
Correct Answer
A. Not an arithmetic sequence
Explanation
The given sequence does not appear to be an arithmetic sequence because the common difference between consecutive terms is not constant. The first difference between the terms is -2, then -6, and then -18, indicating that the common difference is not consistent. Therefore, the correct answer is "Not an arithmetic sequence."
12.
Choose the scatter plot that best represents the relationship between the number of movie tickets sold and the amount of concession sales.
Correct Answer
A. GrapH A
Explanation
Graph A is the best representation of the relationship between the number of movie tickets sold and the amount of concession sales because it shows a positive correlation between the two variables. As the number of movie tickets sold increases, the amount of concession sales also increases. This indicates that there is a direct relationship between these two variables, suggesting that more movie tickets sold lead to higher concession sales. The scatter plot in Graph A shows a clear pattern of points that are clustered in an upward direction, supporting this positive correlation.
13.
Choose the scatter plot that best represents the relationship between the number of movie tickets sold and the number of available seats.
Correct Answer
C. GrapH C
Explanation
Graph C best represents the relationship between the number of movie tickets sold and the number of available seats. In Graph C, as the number of available seats increases, the number of movie tickets sold also increases. This positive correlation suggests that as more seats become available, more tickets are sold. The scatter plot in Graph C shows a clear upward trend, indicating a strong positive relationship between the two variables.
14.
Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference.3, −2, −7, −12, …
Correct Answer
C. Arithmetic sequence; common difference is −5
Explanation
The given sequence is an arithmetic sequence because there is a common difference between each term. The common difference can be found by subtracting each term from the previous term. In this case, when we subtract -2 from 3, we get -5. Similarly, when we subtract -7 from -2, we also get -5. Therefore, the common difference is -5.
15.
Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference.2, 4, 8, 16…
Correct Answer
A. Not an arithmetic sequence
Explanation
The given sequence does not appear to be an arithmetic sequence because the differences between consecutive terms are not constant. The difference between the first two terms is 2, the difference between the second and third terms is 4, and the difference between the third and fourth terms is 8. Since the differences are not the same, the sequence is not arithmetic.
16.
Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference.165, 150, 135, 120, …
Correct Answer
C. Arithmetic sequence; common difference is −15
Explanation
The given sequence is an arithmetic sequence because there is a common difference between each term. The common difference can be determined by subtracting each term from the previous term. In this case, we can see that each term is decreasing by 15. Therefore, the common difference is -15.
17.
Find the 60^{th} term of the arithmetic sequence.−20, −8, 4, 16, …
Correct Answer
688
Explanation
The arithmetic sequence is increasing by 12 each time. To find the 60th term, we can use the formula: term = first term + (n-1) * common difference. Plugging in the values, we get term = -20 + (60-1) * 12 = -20 + 59 * 12 = 688. Therefore, the 60th term of the arithmetic sequence is 688.
18.
Find the 35^{th} term of the arithmetic sequence.32, 35, 38, 41, …
Correct Answer
134
Explanation
The arithmetic sequence is increasing by 3 each time. To find the 35th term, we can start with the first term of 32 and add 3 for each subsequent term. By adding 3 thirty-four times, we get 102. Adding 3 one more time gives us the 35th term, which is 105. Therefore, the correct answer is 105.
19.
Find the 41^{st} term of the arithmetic sequence given a_{1} = 120 and d = −7.
Correct Answer
-160
Explanation
To find the 41st term of an arithmetic sequence, we can use the formula: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. In this case, a1 = 120, d = -7, and n = 41. Plugging these values into the formula, we get a41 = 120 + (41-1)(-7) = 120 + 40(-7) = 120 - 280 = -160. Therefore, the 41st term of the arithmetic sequence is -160.
20.
Find the 21^{st} term of the arithmetic sequence given a_{1} = 24 and d = −3.
Correct Answer
-36
Explanation
The arithmetic sequence given has a first term of 24 and a common difference of -3. To find the 21st term, we can use the formula: an = a1 + (n-1)d. Plugging in the values, we get a21 = 24 + (21-1)(-3) = 24 + 20(-3) = 24 - 60 = -36. Therefore, the 21st term of the arithmetic sequence is -36.
21.
Find the 19^{th} term of the arithmetic sequence given a_{1} = −200 and d = −7.
Correct Answer
-326
Explanation
To find the 19th term of an arithmetic sequence, we can use the formula:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
In this case, a1 = -200, d = -7, and we need to find the 19th term. Plugging these values into the formula, we get:
a19 = -200 + (19-1)(-7)
a19 = -200 + 18(-7)
a19 = -200 - 126
a19 = -326
Therefore, the 19th term of the arithmetic sequence is -326.
22.
Find the 44^{th} term of the arithmetic sequence.120, 110, 100, 90, …
Correct Answer
-310
Explanation
The given arithmetic sequence starts with 120 and each term decreases by 10. To find the 44th term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. Plugging in the values, we get a44 = 120 + (44-1)(-10) = 120 + 43(-10) = 120 - 430 = -310. Therefore, the 44th term of the sequence is -310.
23.
Find the 40^{th} term of the arithmetic sequence.−40, −38, −36, −34, …
Correct Answer
38
Explanation
The given arithmetic sequence starts at -40 and increases by 2 each time. To find the 40th term, we can use the formula for the nth term of an arithmetic sequence: nth term = first term + (n-1) * common difference. In this case, the first term is -40 and the common difference is 2. Plugging in n = 40, we get: 40th term = -40 + (40-1) * 2 = -40 + 39 * 2 = -40 + 78 = 38. Therefore, the 40th term of the arithmetic sequence is 38.
24.
Find the 67^{th} term of the arithmetic sequence.−32, −24, −16, −8, …
Correct Answer
496
Explanation
The given arithmetic sequence starts with -32 and has a common difference of 8. To find the 67th term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. Plugging in the values, we get a67 = -32 + (67-1)8 = -32 + 66*8 = -32 + 528 = 496. Therefore, the 67th term of the arithmetic sequence is 496.
25.
Mark’s new job has a starting salary of $39,000 and annual increase of $1200. How much will he earn during his 15^{th} year?
Correct Answer
A. $55,800
Explanation
Mark's starting salary is $39,000 and he receives an annual increase of $1200. To find out how much he will earn during his 15th year, we need to calculate the total increase in his salary over the 15 years and add it to his starting salary.
The total increase in his salary over 15 years can be calculated by multiplying the annual increase of $1200 by the number of years, which is 15. So, the total increase in his salary is $1200 * 15 = $18,000.
Adding the total increase to his starting salary, we get $39,000 + $18,000 = $57,000.
Therefore, the correct answer is $57,000.
26.
A tube containing 5 ounces of toothpaste is being used at a rate of 0.2 ounces per day. How much toothpaste will be in the tube after two weeks?
Correct Answer
2.4, 2.4 ounces, 2.4 oz., 2.4 oz
Explanation
The toothpaste is being used at a rate of 0.2 ounces per day. In two weeks, there are 14 days. So, the total amount of toothpaste used in two weeks is 14 * 0.2 = 2.8 ounces. Since the tube initially contains 5 ounces of toothpaste, subtracting the amount used from the initial amount gives us 5 - 2.8 = 2.2 ounces. Therefore, the amount of toothpaste remaining in the tube after two weeks is 2.2 ounces.
27.
A photographer charges a sitting fee of $70 for oneperson. Each additional person in the picture is $25. Whatis the total sitting fee charge if a group of 14 people wishto be photographed?
Correct Answer
395, $395.00, 395.00, 395 dollars
Explanation
The photographer charges a sitting fee of $70 for one person. For each additional person, the fee is $25. Since there are 14 people in the group, we need to calculate the additional fee for the 13 additional people. 13 x $25 = $325. Adding this to the initial sitting fee of $70 gives us a total sitting fee of $395.
28.
Mr. Jones purchases a tollway tag for traveling on toll roads and highways. He adds $80 to his account to start (day 1) and has $2.50 deducted for tolls each day he travels. How much money is in his account at the beginning of day 20?
Correct Answer
$32.50, 32.50, 32.5, $32.5, 32.50 dollars
Explanation
Mr. Jones starts with $80 in his account. Each day he travels, $2.50 is deducted from his account. Since he travels for 19 days (day 1 to day 19), a total of $47.50 (19 x $2.50) will be deducted from his account. Therefore, the amount of money in his account at the beginning of day 20 will be $80 - $47.50 = $32.50.