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
Based on the scatterplot showing the relationship between the average daily temperature and ice cream truck sales, we can make a prediction of the daily average temperature if the ice cream truck made $500 in sales by looking at the corresponding point on the graph.
From the scatterplot, we can see that $500 in sales intersects with a temperature of approximately 35ºF.
Therefore, the prediction of the daily average temperature if the ice cream truck made $500 in sales is:
C) 35º
Triangles UVW and KLM are similar. Triangle UVW is the smaller triangle. Arrange the side lengths correctly on the diagram.
Drop target 1
Drop target 2
Drop target 3
Drop target 4
Drop target 5
Drop target 6
I apologize, but the mentioned information does not provide enough details to arrange the side lengths correctly on the diagram. Please provide the specific side lengths given for each triangle UVW and KLM so that I can assist you further.
You are going to invest $5000 for 5 years. Choose the 3 scenarios which will yield the highest values.
Responses
A interest rate 4.1%, compounded monthlyinterest rate 4.1%, compounded monthly
B interest rate 4.2%, compounded quarterlyinterest rate 4.2%, compounded quarterly
C interest rate 3.95%, compounded continuouslyinterest rate 3.95%, compounded continuously
D interest rate 4%, compounded dailyinterest rate 4%, compounded daily
E interest rate 3.99%, compounded semiannuallyinterest rate 3.99%, compounded semiannually
F interest rate 4.3%, compounded every 2 months
To determine the scenarios that will yield the highest values for your investment of $5000 for 5 years, we need to compare the interest rates and compounding periods of each scenario.
Calculating the future value of each scenario using the formula for compound interest:
A) FV = P(1 + r/n)^(nt)
FV = 5000(1 + 0.041/12)^(12*5) = $5,678.61
B) FV = P(1 + r/n)^(nt)
FV = 5000(1 + 0.042/4)^(4*5) = $5,780.07
C) FV = P*e^(rt)
FV = 5000*e^(0.0395*5) = $5,675.24
D) FV = P(1 + r/n)^(nt)
FV = 5000(1 + 0.04/365)^(365*5) = $5,718.43
E) FV = P(1 + r/n)^(nt)
FV = 5000(1 + 0.0399/2)^(2*5) = $5,678.35
F) FV = P(1 + r/n)^(nt)
FV = 5000(1 + 0.043/6)^(6*5) = $5,806.65
Based on the calculations, the three scenarios that yield the highest values for your investment are:
B) interest rate 4.2%, compounded quarterly
F) interest rate 4.3%, compounded every 2 months
D) interest rate 4%, compounded daily
Therefore, the correct scenarios are B, F, and D.
Find the surface area of each rectangular prism given its length, width, and height. Choose the correct answers.
Responses
A l = 4 cm w = 9 cm h = 3 cm; SA = 150 cm2
l = 4 cm w = 9 cm h = 3 cm; SA = 150 cm 2
B l = 7 cm w = 3 cm h = 4 cm; SA = 132 cm2
l = 7 cm w = 3 cm h = 4 cm; SA = 132 cm 2
C l = 8 cm w = 5 cm h = 5 cm; SA = 190 cm2
l = 8 cm w = 5 cm h = 5 cm; SA = 190 cm 2
D l = 5 cm w = 7 cm h = 6 cm; SA = 214 cm2
To find the surface area of a rectangular prism, we need to calculate the sum of the areas of all six faces.
Let's calculate the surface area for each given rectangular prism:
A) l = 4 cm, w = 9 cm, h = 3 cm
Surface area = 2lw + 2lh + 2wh
Surface area = 2(4)(9) + 2(4)(3) + 2(9)(3)
Surface area = 72 + 24 + 54
Surface area = 150 cm²
B) l = 7 cm, w = 3 cm, h = 4 cm
Surface area = 2lw + 2lh + 2wh
Surface area = 2(7)(3) + 2(7)(4) + 2(3)(4)
Surface area = 42 + 56 + 24
Surface area = 122 cm²
C) l = 8 cm, w = 5 cm, h = 5 cm
Surface area = 2lw + 2lh + 2wh
Surface area = 2(8)(5) + 2(8)(5) + 2(5)(5)
Surface area = 80 + 80 + 50
Surface area = 190 cm²
D) l = 5 cm, w = 7 cm, h = 6 cm
Surface area = 2lw + 2lh + 2wh
Surface area = 2(5)(7) + 2(5)(6) + 2(7)(6)
Surface area = 70 + 60 + 84
Surface area = 214 cm²
Therefore, the correct answers are:
D) l = 5 cm, w = 7 cm, h = 6 cm; SA = 214 cm²
Triangle FGH is dilated on a coordinate grid using the origin as the center of the dilation to create triangle F’G’H’. Determine if each dilation creates a new triangle F’G’H’ that is smaller or larger than the original triangle FGH.
Drag each rule to the appropriate box.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
New triangle is SMALLER New triangle is LARGER
I apologize, but without specific information about the scale factor or the coordinates of Triangle FGH and F'G'H', it is not possible to determine if the dilation creates a new triangle F'G'H' that is smaller or larger than the original triangle FGH. Please provide further details so that I can assist you accurately.
When applied to a triangle on a coordinate grid, indicate whether each transformation in the table would preserve congruence or not preserve congruence.
Select the correct answer in each row.
Transformation Preserves
Congruence Does NOT
Preserve Congruence
(x, y) → (x+4, y–3)
Preserves Congruence – (x, y) → (x+4, y–3)
Does NOT Preserve Congruence – (x, y) → (x+4, y–3)
(x, y) → (x, –y)
Preserves Congruence – (x, y) → (x, –y)
Does NOT Preserve Congruence – (x, y) → (x, –y)
(x, y) → (0.5x, 0.5y)
Preserves Congruence – (x, y) → (0.5x, 0.5y)
Does NOT Preserve Congruence – (x, y) → (0.5x, 0.5y)
Transformation: (x, y) → (x+4, y–3)
Preserves Congruence – (x, y) → (x+4, y–3)
Transformation: (x, y) → (x, –y)
Does NOT Preserve Congruence – (x, y) → (x, –y)
Transformation: (x, y) → (0.5x, 0.5y)
Preserves Congruence – (x, y) → (0.5x, 0.5y)
Therefore, the correct matches are:
(x, y) → (x+4, y–3) - Preserves Congruence
(x, y) → (x, –y) - Does NOT Preserve Congruence
(x, y) → (0.5x, 0.5y) - Preserves Congruence