Answer:
total marbles;12
after drawing red total counts are 7 red and 4 white 11 in total
probabilities are 4/11
Answer:
Step-by-step explanation:
The triangle would end up back where it started. It is hard to explain without a graph. If you have graph paper, you might want to try drawing this out. Say that the original points are at A (1,2) B (2,0) and C(0,0). Now, when we reflect the points over the x axis, they will be the same distance below the x that the points original were about the x axis. Since A was 2 units above the axis, it will now be 2 units below at (1, -2). Points B and C will stay on the x axis and will remain in place at B(2.0) and C(0,0). Since these points are on the line, they were not above the x axis, so they will now not be below the x axis.
Now, we are going to reflect the triangle over the y axis. Since C (0,0) is already on the y axis, it will not move. It will remain there. Since B(2,1) is two units to the right of the y axis, when we flip it, it will now be 2 units to the left of the y axis B (-2,0). Point C will move one unit to the left of the y axis to become (-1,2).
The last thing left it to rotate this final triangle 180 degrees. Since a circle is 360 degrees and 180 is half of a circle, it does not matter if we rotate clockwise or counter-clockwise. If you could trace our new triangle and put a plus sign at the origin (0,0). You would put your pencil on the origin and rotate the two turns at the plus sign. This would put your triangle right back to the beginning. So the original value of B would be the same. In this case C ((2,0)
Answer:
167,886,383 basketballs
Step-by-step explanation:
We are asked to find how many basketballs would take to circle around the equator. We have given the earth's radius. So, we need the formula to obtain it's perimeter. Thus:
![Perimeter = Pi*diameter [m]\\Where Pi = 3.14](https://tex.z-dn.net/?f=Perimeter%20%3D%20Pi%2Adiameter%20%5Bm%5D%5C%5CWhere%20Pi%20%3D%203.14)
Earth's diameter is simply radius*2. It means:
![P= 3.14*6400*2 = 40,192 [km]](https://tex.z-dn.net/?f=P%3D%203.14%2A6400%2A2%20%3D%2040%2C192%20%5Bkm%5D)
On the other hand, we have a basketball crcumference; however, we need to obtain its diameter so that we can later calculate how many basketballs fit on earth's equator by simply dividing earth's circumference by a basketball's diameter.
Diameter of a basketball:
![D= Perimeter /Pi [m]](https://tex.z-dn.net/?f=D%3D%20Perimeter%20%2FPi%20%5Bm%5D)
We need to change units to fit in the international system.
29.6 in to cm = ![29.6*2.54 = 75.184 [cm]](https://tex.z-dn.net/?f=29.6%2A2.54%20%3D%2075.184%20%5Bcm%5D)
Then:
![Diameter=75.184/3.14 = 23.94 [cm]](https://tex.z-dn.net/?f=Diameter%3D75.184%2F3.14%20%3D%2023.94%20%5Bcm%5D)
We have to convert earth's perimeter in km to cm:
![Equator=40192[km]*100000=4,019,200,000 [cm]](https://tex.z-dn.net/?f=Equator%3D40192%5Bkm%5D%2A100000%3D4%2C019%2C200%2C000%20%5Bcm%5D)
Finally, dividing total earth's circumference by a basketball diameter:
![Totalbasketballs=4,019,200,000/23.94= 167,886,383 [basketballs]](https://tex.z-dn.net/?f=Totalbasketballs%3D4%2C019%2C200%2C000%2F23.94%3D%20167%2C886%2C383%20%5Bbasketballs%5D)
<span>B. The sample might not be representative of the population because it only includes students who are attending an after-school activity.</span>