The amount of money a worker makes varies directly with the hourly rate of pay. Worker A earns $168 for an 8-hour period. Worker B earns the same hourly rate as Worker A but works for only 6 hours. What does Worker B earn?
Responses
If Worker A earns $168 for an 8-hour period, their hourly rate of pay is $168/8 = $21/hour.
Worker B earns the same hourly rate as Worker A, which is $21/hour.
If Worker B works for only 6 hours, they will earn $21/hour * 6 hours = $126.
The baseball diamond is really a square. The distance between each of the bases is 90 feet.
How far does the catcher have to throw the ball to get from home plate to second base? Round your answer to the nearest foot.
To determine the distance from home plate to second base, we need to consider that the bases form the vertices of a square. The distance from home plate to second base is the same as the length of one side of the square.
Given that the distance between each base is 90 feet, the distance from home plate to second base is also 90 feet.
identify the rotation rule on a coordinate plane that verifies that triangle A(2,-1), B(4,1), C(3,3) and triangle A'(1,2), B'(-1,4), C'(-3,3) are congruent when rotated 90°.
Responses
To verify that the triangles A(2,-1), B(4,1), C(3,3) and A'(1,2), B'(-1,4), C'(-3,3) are congruent when rotated 90 degrees, we can use the rotation rule.
The rotation rule for a point (x, y) by 90 degrees counterclockwise is:
(x', y') = (-y, x), where (x', y') represents the coordinates of the rotated point.
Applying this rule to each point of triangle A(2,-1), B(4,1), C(3,3) gives us the following rotated points:
A' = (-(-1), 2) = (1, 2),
B' = (-1, 4),
C' = (-3, 3).
Comparing these rotated points with the coordinates of triangle A'(1,2), B'(-1,4), C'(-3,3), we can see that they are indeed congruent when rotated 90 degrees.
Point E(−5, 3) and point D(−4, −3) are located on the grid. Which measurement is closest to the distance between point E and point D in units?
To find the distance between two points (x1, y1) and (x2, y2) on a coordinate grid, you can use the distance formula.
The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point E are (-5, 3) and the coordinates of point D are (-4, -3). Plugging these values into the distance formula, we get:
d = √((-4 - (-5))^2 + (-3 - 3)^2)
= √(1^2 + (-6)^2)
= √(1 + 36)
= √37
Rounding the value to the nearest whole number, we find that the distance between point E and point D is closest to 6 units.
Point E(−5, 3) and point D(−4, −3) are located on the grid. Which measurement is closest to the distance between point E and point D in units?
Responses
A 6.1 units6.1 units
B 5.3 units5.3 units
C 6.5 units6.5 units
D 6.7 units
To find the distance between two points (x1, y1) and (x2, y2) on a coordinate grid, we can use the distance formula.
The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point E are (-5, 3) and the coordinates of point D are (-4, -3).
Plugging these values into the distance formula:
d = √((-4 - (-5))^2 + (-3 - 3)^2)
= √((1)^2 + (-6)^2)
= √(1 + 36)
= √37
The closest measurement to the distance between point E and point D is approximately 6.1 units. Thus, the correct answer is A.
Find the value of c.
Responses
A 5
B 6
C 10
D 25
Find the value of c.
Responses
A 55
B 66
C 1010
D 2525
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Apologies, but without more context or information provided, it is not possible to determine the value of c or the correct response.
Josh is buying a RV and is taking out a loan in the amount of $20,000. His choices for the loan are a 5-year loan at 6.00% annual simple interest and a 6-year loan at 7.00% annual simple interest. What is the difference in the amount of interest Josh would have to pay for these two loans?
To calculate the difference in the amount of interest Josh would have to pay for the two loans, we need to calculate the interest amount for each loan and then find the difference between the two.
For the 5-year loan at 6.00% annual simple interest:
Interest = Principal * Rate * Time
= $20,000 * 0.06 * 5
= $6,000
For the 6-year loan at 7.00% annual simple interest:
Interest = Principal * Rate * Time
= $20,000 * 0.07 * 6
= $8,400
The difference in the amount of interest Josh would have to pay for these two loans is $8,400 - $6,000 = $2,400.
Charles needs a $10,000 loan in order to buy a car. Which loan option would allow him to pay the LEAST in interest?
To determine which loan option would allow Charles to pay the least in interest, we need to know the interest rates and terms of the available loan options. Without that information, it is not possible to determine which loan option would be the least costly in terms of interest.
Charles needs a $10,000 loan in order to buy a car. Which loan option would allow him to pay the LEAST in interest?
Responses
A A 2-year loan with a 4.75% interest rate compounded annually.A 2-year loan with a 4.75% interest rate compounded annually.
B A 3-year loan with a 4.00% interest rate compounded annually.A 3-year loan with a 4.00% interest rate compounded annually.
C A 4-year loan with a 3.75% interest rate compounded annually.A 4-year loan with a 3.75% interest rate compounded annually.
D A 5-year loan with a 3.00% interest rate compounded annually.
To determine which loan option would allow Charles to pay the least amount in interest, we need to calculate the total interest paid for each loan option.
For option A, a 2-year loan with a 4.75% interest rate compounded annually:
Interest = Principal * (1 + Rate)^Time - Principal
= $10,000 * (1 + 0.0475)^2 - $10,000
≈ $10,952.81 - $10,000
= $952.81
For option B, a 3-year loan with a 4.00% interest rate compounded annually:
Interest = Principal * (1 + Rate)^Time - Principal
= $10,000 * (1 + 0.04)^3 - $10,000
≈ $10,499.20 - $10,000
= $499.20
For option C, a 4-year loan with a 3.75% interest rate compounded annually:
Interest = Principal * (1 + Rate)^Time - Principal
= $10,000 * (1 + 0.0375)^4 - $10,000
≈ $10,634.38 - $10,000
= $634.38
For option D, a 5-year loan with a 3.00% interest rate compounded annually:
Interest = Principal * (1 + Rate)^Time - Principal
= $10,000 * (1 + 0.03)^5 - $10,000
≈ $10,152.93 - $10,000
= $152.93
Based on the calculations, option D, a 5-year loan with a 3.00% interest rate compounded annually, would allow Charles to pay the least amount in interest, with only approximately $152.93 in interest paid.
Pentagon CDEFG was reflected over the y-axis to create a new figure. 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) → (-y, x)( x, y ) → (- y , x )
D (x, y) → (y, -x)
The correct rule that describes the transformation of reflecting pentagon CDEFG over the y-axis is:
B. (x, y) → (x, -y)
The value of y varies directly with x. When y = 0.3, x = 1 . What is the value of y when x is 35?
5
Responses
A 52.552.5
B 1.51.5
C 1515
D 1010
To determine the value of y when x is 35, we can set up a proportion using the direct variation relationship between x and y.
Since y varies directly with x, we can write the equation as:
y = kx
Where k is the constant of variation.
We can find the value of k by using the given information that when y = 0.3, x = 1:
0.3 = k * 1
k = 0.3
Now we can substitute k into the equation to find y when x is 35:
y = 0.3 * 35
y = 10.5
Therefore, the value of y when x is 35 is 10.5. Therefore, the correct response is not provided in the options.
A tech company sells apps at a constant rate. After 8 days, the company has sold 400 apps. Sales continue at the same rate.
Which table shows the relationship between the number of days, x, and the number of apps sold, y?
Since the tech company sells apps at a constant rate, we can determine the relationship between the number of days, x, and the number of apps sold, y, by creating a table.
Based on the given information after 8 days the company has sold 400 apps. We can use this as an initial point.
One possible table that shows the relationship between the number of days, x, and the number of apps sold, y could be:
x (Number of Days) | y (Number of Apps Sold)
-----------------------------------------
8 | 400
9 | 450
10 | 500
11 | 550
12 | 600
This table represents a constant rate of sales, where for each additional day, 50 apps are sold.
Sarah joined three squares at their vertices to create the figure shown in the diagram. She then covered each of the three squares with square centimeter tiles.
Based on the information, which statement is true?
Responses
A The number of tiles needed to cover both Region P and Region R is greater than the number of tiles needed to cover Region S.The number of tiles needed to cover both Region P and Region R is greater than the number of tiles needed to cover Region S.
B The number of tiles needed to cover Region R is the same as the number of tiles needed to cover both Region P and Region S.The number of tiles needed to cover Region R is the same as the number of tiles needed to cover both Region P and Region S .
C The number of tiles needed to cover Region S is greater than the number of tiles needed to cover both Region P and Region R.The number of tiles needed to cover Region S is greater than the number of tiles needed to cover both Region P and Region R .
D The number of tiles needed to cover Region S is the same as the number of tiles needed to cover both Region P and Region R.The number of tiles needed to cover Region S is the same as the number of tiles needed to cover both Region P and Region R .
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Without the diagram or a clear description of Regions P, R, and S, it is impossible to determine which statement is true.
Which transformations do not preserve congruence? (Choose 2)
Responses
A (x, y) → (x+2, y–1)( x , y ) → ( x +2, y– 1)
B
(x, y) → ( 1 x, 1 y)
8 8( x , y ) → ( 1 x , 1 y ) 8 8
C (x, y) → (–x, –y)( x , y ) → (– x , – y )
D (x, y) → (x, –y)( x , y ) → ( x , – y )
E (x, y) → (2.5x, 2.5y)( x , y ) → (2.5 x , 2.5 y )
F (x, y) → (y, –x)
Transformations that preserve congruence are translations, rotations, and reflections. Translations involve shifting points without changing their shape or size, rotations involve rotating points around a fixed point, and reflections involve flipping points over a line.
The two transformations that do not preserve congruence are:
B. (x, y) → (1x, 1y)
This transformation scales the coordinates by a factor of 8, which changes the shape and size of the figure.
F. (x, y) → (y, -x)
This transformation involves swapping the x and y coordinates and changing the sign of one of them, which also changes the shape and size of the figure.
Thus, options B and F do not preserve congruence.
Match each data set with its mean absolute deviation.
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.
1.456
1.728
3.333
2.741
Apologies, but there is no information given about the data sets to match each one with its mean absolute deviation. Can you provide the data sets or additional information to help with the matching?
Darla has a recipe for pot roast. There is a proportional relationship between the weight (in pounds) of the pot roast, x, and the total cooking time (in hours), y. Her recipe says that a 6-pound pot roast should take 3 hours to cook.
The equation for the relationship between x and y is Response area = Response area Response area
If Darla's pot roast weighs Response area pounds, it will take Response area hours to cook
Select All that go in the boxes
Y
0.5
x
2
4
The equation for the relationship between x and y can be determined using the given information.
We know that there is a proportional relationship between the weight (in pounds) of the pot roast, x, and the total cooking time (in hours), y. When the pot roast weighs 6 pounds, it takes 3 hours to cook.
To find the equation for the relationship, we can set up a proportion:
x/6 = y/3
To solve for y, we can cross-multiply:
3x = 6y
Now we can rearrange the equation to solve for y:
y = 3x/6
Simplifying the equation:
y = 0.5x
Therefore, the equation for the relationship between x and y is y = 0.5x.
To determine how many hours it would take for a pot roast weighing a certain number of pounds, we can substitute that weight into the equation and solve for y. In this case, the weight is Response area pounds, so the number to put in the first box is Response area. The corresponding time in the second box can be found by substituting the weight into the equation:
y = 0.5 * (Response area pounds)
y = Response area hours
So, the values to put in the boxes are:
x = Response area pounds in the first box
y = Response area hours in the second box
Selecting All options that go in the boxes:
x = Response area in the first box
y = Response area in the second box