The ball have traveled 33 m when it hits the ground for the fourth time.
The correct option is D .
Given, that a ball falls from 12feet.
Analyzing the fall of ball every time.
Fall 1:
Ball dropped from height = 12 m .
Ball returns to half the distance from which it is dropped .
Rebound distance covered by ball = 6 m .
Fall 2:
Ball dropped from height = 6 m .
Ball returns to half the distance from which it is dropped .
Rebound distance covered by ball = 3 m .
Fall 3:
Ball dropped from height = 3 m .
Ball returns to half the distance from which it is dropped .
Rebound distance covered by ball = 1.5 m .
Fall 4:
Ball dropped from height = 1.5 m .
Ball returns to half the distance from which it is dropped .
Rebound distance covered by ball = 0.75 m .
Total distance covered when ball hits the ground for fourth time:
12 + 6 + 6 + 3 + 3 + 1.5 + 1.5
= 33 meters.
The correct option is D .
Know more about distance, here:
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I picked reduction
Answer:To determine if the dashed triangle is a dilation image of the solid triangle with the center at the origin, and whether it is an enlargement or a reduction, we need to compare the corresponding side lengths of the triangles.
Given that the dashed triangle has vertices A'(-8, -12), B'(8, 12), and D'(-4, 16), let's calculate the side lengths of the solid triangle and the dashed triangle.
1. Solid triangle side lengths:
- Side AB: Distance between A(4, 6) and B(-4, -6)
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-4 - 4)^2 + (-6 - 6)^2)
= sqrt((-8)^2 + (-12)^2)
= sqrt(64 + 144)
= sqrt(208)
2. Dashed triangle side lengths:
- Side A'B': Distance between A'(-8, -12) and B'(8, 12)
A'B' = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((8 - (-8))^2 + (12 - (-12))^2)
= sqrt((16)^2 + (24)^2)
= sqrt(256 + 576)
= sqrt(832)
Comparing the side lengths, we have sqrt(832) for the dashed triangle and sqrt(208) for the solid triangle.
Since sqrt(832) is greater than sqrt(208), this means the dashed triangle is larger than the solid triangle.
Therefore, the dashed triangle is an enlargement.
The correct answer is "enlargement."
Please let me know if there's anything else I can help you with.
Step-by-step explanation:
Answer:
D 1,5 is the answer
Step-by-step explanation:
Answer:
The best way to solve a problem like this is to set up two equations. First assign a variable to each thing you are trying to find. In this case, it's two different kinds of cars. Let's call the cars that weigh 3,000 pounds x, and the ones that weigh 5,000 y. The two equations you should write are:
x+y=18 (because the problem tells you there were 18 cars in total)
3000x+5000y=60000 (because that is the total weight in the problem)
Next, you need to solve for one of the variables. I will solve for x first by subtracting y from both sides of the first equation.
x=18-y
Then you have to plug that into the other equation to get:
3000(18-y)+5000y=60000
Simplify and solve for y:
54000-3000y+5000y=60000
54000+2000y=60000
2000y=6000
y=3
Now that you know what y equals, you can put it into the equation we solved for x:
x=18-3
x=15
So there are 15 cars that weigh 3000 pounds and 3 that weigh 5000.
Step-by-step explanation:
Answer:
≈ 13.98%
Step-by-step explanation:
As the total population is 5769 in the initial period, you must find the percentage that repesents 4963 that is the expected population.
4963/5769=0.8602
Then you multiply it by 100 to transform it into percentage
0.8602*100=86.02%
Then it's just necesary to subtract that from 100% and that numbers is the percentage of decrease
100% - 86.02% = 13.98%
Also you can say that is approximately 14%
Answer: confidence interval = 27.5 +/- 1.68
= ( 25.82, 29.18)
Step-by-step explanation:
Given;
Number of samples n = 64
Standard deviation r = 6mi/gallon
Mean x = 27.5mi/gallon
Confidence interval of 97.5%
Z' = t(0.0125) = 2.24
Confidence interval = x +/- Z'(r/√n)
= 27.5 +/- 2.24(6/√64)
= 27.5 +/- 1.68
= ( 25.82, 29.18)