Help with these two math questions please
2 answers:
Answer:
1) D.
2) D. $122 million.
Step-by-step explanation:
1. We have been given two similar figures and we are asked to find the measure of angle B.
Since we know that corresponding angles of similar figures are equal.
We can see from our given figures that the measure of angle corresponding to angle B is 130 degrees, therefore, the measure of angle B is 130 degrees and option D is the correct choice.
2. We have been given a scatter plot that shows a regression line of advertising dollars spent and sales.
To find the predicted sales, when company spent $350,000 on advertising, we need to find the y-value corresponding to x= 350 as x-axis represents the advertising cost in thousand dollars.
We can see from our attached file that at x=350 the corresponding y value is 122.
Since y-axis represents the sales in millions, so the predicted sales of company will be $122 million and option D is the correct choice.
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We call:
T = Tom's paiting rate
G = George's paiting rate
M = Mario's paiting rate
As the first statement says that they can work together, then:
T + G + M = Painting rate working together, that is the surface area they paint per hour.
Since the problem says that they last four hours painting a
room, then we need to multiply the amount of hours times the painting rate that is equal the surface area of the room, so:
4(T + G + M) = 600
Applying a similar reasoning, the George and Mario's painting rate is:
0 + G + M
Note that 0 implies that Tom didn't work in this case.
As they last eight hours painting the room, then:
8(0 + G + M) = 600
The same reasoning is applied to Tom and George working together. In this case 0 implies that Mario didn't work, so:
6(T + G + 0) = 600
We have a system of linear equations in three variables T, G, M:
<span>4(T+G+M)=600
8(0+G+M)=600
6(T+G+0)=600
</span>
Solving:
(1) T + G + M = 150
(2) G + M = 75
(3) T + G = 100
Substitute (3) in (1):
100 + M = 150 ∴ M = 50
Replace M in (2):
G + 50 = 75 ∴ G = 25
Substitute G in (3)
T + 25 = 100 ∴ T = 75
Then, the painting rates are:
Tom = 75
George = 25
Mario = 50
<span>Solving for Time to determine how long it would take Tom to paint the room alone:
</span>
<span>Painted Area = Painting Rate×Time, so:
</span>
T = Tom's paiting rate
G = George's paiting rate
M = Mario's paiting rate
As the first statement says that they can work together, then:
T + G + M = Painting rate working together, that is the surface area they paint per hour.
Since the problem says that they last four hours painting a
4(T + G + M) = 600
Applying a similar reasoning, the George and Mario's painting rate is:
0 + G + M
Note that 0 implies that Tom didn't work in this case.
As they last eight hours painting the room, then:
8(0 + G + M) = 600
The same reasoning is applied to Tom and George working together. In this case 0 implies that Mario didn't work, so:
6(T + G + 0) = 600
We have a system of linear equations in three variables T, G, M:
<span>4(T+G+M)=600
8(0+G+M)=600
6(T+G+0)=600
</span>
Solving:
(1) T + G + M = 150
(2) G + M = 75
(3) T + G = 100
Substitute (3) in (1):
100 + M = 150 ∴ M = 50
Replace M in (2):
G + 50 = 75 ∴ G = 25
Substitute G in (3)
T + 25 = 100 ∴ T = 75
Then, the painting rates are:
Tom = 75
George = 25
Mario = 50
<span>Solving for Time to determine how long it would take Tom to paint the room alone:
</span>
<span>Painted Area = Painting Rate×Time, so:
</span>
Answer:
The volume of the rectangular prism is <u>19.25 inches³</u>.
Step-by-step explanation:
Given:
It takes 154 cubes with side lengths of 1/2 inch to fill a rectangular prism.
Now, to find the rectangular prism's volume.
We first find the volume of a cube to fill in the rectangular prism.
The side length of the cube =
Now, to get the volume of cube we put formula:
<em>Thus, the volume of a cube is </em><em />
<em>Number of cubes = 154.</em>
<u><em>According to question, it takes 154 cubes to fill the rectangular prism.</em></u>
<u><em>So, to get the volume of prism we need to find the volume of 154 cubes.</em></u>
Now, to get the volume of 154 such cubes we multiply the volume of a cube by number of cubes:
Therefore, the volume of the rectangular prism is 19.25 inches³.