Stephen, a forward on his school basketball team, has played in 5 games since starting high school. The number of points he scored at those games are listed below.
2, 4, 8, 9, 4
What is the mean absolute deviation of the number of points scored?
Responses
A 2.482.48
B 5.45.4
C 6.286.28
D 3.9
To find the mean absolute deviation, we need to find the mean of the data set first.
Mean = (2 + 4 + 8 + 9 + 4) / 5 = 27 / 5 = 5.4
Next, we subtract the mean from each point and take the absolute value:
|2 - 5.4| = 3.4
|4 - 5.4| = 1.4
|8 - 5.4| = 2.6
|9 - 5.4| = 3.6
|4 - 5.4| = 1.4
Then, we find the sum of these absolute values:
3.4 + 1.4 + 2.6 + 3.6 + 1.4 = 12.4
Finally, we divide the sum by the number of data points:
12.4 / 5 = 2.48
Therefore, the mean absolute deviation of the number of points scored is 2.48.
The answer is A) 2.48.
Hexagon PQRSTU is shown on the grid. A student reflected hexagon PQRSTU across the x-axis to create hexagon P՚Q՚R՚S՚T՚U՚.
Which rule describes this transformation?
Responses
A (x, y) → (-x, y)( x, y ) → (- x, y )
B (x, y) → (x, -y)( x, y ) → ( x, -y )
C (x, y) → (-x, -y)( x, y ) → (- x, -y )
D (x, y) → (-y, x)
The reflection across the x-axis changes the sign of the y-coordinate while keeping the x-coordinate the same.
Therefore, the correct transformation rule would be:
B) (x, y) → (x, -y)
Marvin’s weekly pay varies directly to the number of hours he worked. He earns $125 for 10 hours of work.
How much does Marvin earn if he works 7 hours?
Responses
A $87.50$87.50
B $1.79$1.79
C $12.50$12.50
D $66.75
Marvin's weekly pay varies directly with the number of hours he works, which means there is a constant rate of pay per hour.
We can set up a proportion to solve for Marvin's earnings:
125/10 = x/7
Cross-multiplying, we get:
10x = 875
Dividing both sides by 10, we find:
x = 87.50
Therefore, Marvin earns $87.50 if he works 7 hours.
The answer is A) $87.50.
Downloading songs from Source A costs $2.00 a song plus a monthly fee of $5.50. Downloading songs from Source B costs $3.00 a song with no monthly fee. The monthly cost to download songs depends on the number of songs, s, downloaded. Which inequality represents the situation when the monthly cost from Source A is greater than the monthly cost from Source B?
Responses
A 2s + 5.50 < 3s 2 s + 5.50 < 3 s
B 3s > 2s + 5.50 3 s > 2 s + 5.50
C 2s + 5.50 > 3s2 s + 5.50 > 3 s
D 7.5s > 3s
To represent the situation when the monthly cost from Source A is greater than the monthly cost from Source B, we need to compare the costs of the two sources.
For Source A, the monthly cost is given by the formula: 2s + 5.50, where s is the number of songs downloaded.
For Source B, there is no monthly fee, so the monthly cost is simply equal to the cost per song times the number of songs: 3s.
To represent the situation when the monthly cost from Source A is greater than the monthly cost from Source B, we write the inequality:
2s + 5.50 > 3s
Therefore, the correct inequality is:
A) 2s + 5.50 < 3s
Katherine has a new job and earns a salary of $55,000. Max has a new job and earns a salary of $64,000. Katherine will receive a salary increase of $2,500 per year, and Max will receive a salary increase of $1,500 per year.
Which equation can be used to find x, the number of years it will take Katherine to earn the same salary as Max?
Responses
A 55,000x + 2,500= 64,000x + 1,50055,000 x + 2,500= 64,000 x + 1,500
B 55,000 + 64,000x = 2,500 + 1,500x55,000 + 64,000 x = 2,500 + 1,500 x
C 55,000x + 2,500x = 64,000 + 1,500x55,000 x + 2,500 x = 64,000 + 1,500 x
D 55,000 + 2,500x = 64,000 + 1,500x
To find the number of years it will take Katherine to earn the same salary as Max, we need to set up an equation based on their salaries and salary increases per year.
Katherine's salary after x years will be: 55,000 + 2,500x
Max's salary after x years will be: 64,000 + 1,500x
We want to find the value of x when their salaries are equal. Therefore, the correct equation is:
55,000 + 2,500x = 64,000 + 1,500x
Therefore, the correct equation is:
D) 55,000 + 2,500x = 64,000 + 1,500x
Rebecca made a scatterplot to show the relationship between the average daily temperature and her ice cream truck sales over several days.
Ice Cream Sales
Ice Cream Sales (dollars)
Temperature (ºF)
Based on this scatterplot, what is a prediction of the daily average temperature if the ice cream truck made $500 in sales?
Responses
A 80º80º
B 10º10º
C 35º35º
D 25º