A ball is dropped from a height of 10 feet and returns to a height that is one-half of the height from which it fell. The ball c
ontinues to bounce half the height of the previous bounce each time. How far will the ball have traveled when it hits the ground for the fourth time?
1 answer:
Ok, so this is a sum of aruthmetic sequence and also use some logic
it goes 10 feet down, then 5 up, 5 down, etc (see attachment)
so the total distance is the sum of all the numbers in the sequence doubled, minus the first term (since it didn't bounce 10 feet up, it started from top)
the sum of an aruthmetic is
Sn=
where a1=first term, r=common ratio and n=which time
first term=10
common ratio is 0.5
n=4
so
2[
]-10=answer27.5
the answer is 27.5 feet
it goes 10 feet down, then 5 up, 5 down, etc (see attachment)
so the total distance is the sum of all the numbers in the sequence doubled, minus the first term (since it didn't bounce 10 feet up, it started from top)
the sum of an aruthmetic is
Sn=
where a1=first term, r=common ratio and n=which time
first term=10
common ratio is 0.5
n=4
so
2[
the answer is 27.5 feet
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The probability that, at the tip of the fourth round, each of the players has four coins is 5/192.
Given that game consists of 4 rounds and every round, four balls are placed in an urn one green, one red, and two white.
It amounts to filling in an exceedingly 4×4 matrix. Columns C₁-C₄ are random draws each round; row of every player.
Also, let be the quantity of nonzero elements in
Let .
Parity demands that and
must equal 2 or 4.
Case 1: =4 and
=4. There are
=3 ways to put 2-1's in
, so there are 3 ways.
Case 2: =2 and
=4. There are 3 ways to position the -1 in
, 2 ways to put the remaining -1 in
(just don't put it under the -1 on top of it!), and a pair of ways for one among the opposite two players to draw the green ball. (We know it's green because Bernardo drew the red one.) we are able to just double to hide the case of
for a complete of 24 ways.
Case 3: . There are 3 ways to put the -1 in
. Now, there are two cases on what happens next.
- The 1 in
goes directly under the -1 in
. There's obviously 1 way for that to happen. Then, there are 2 ways to permute the 2 pairs of 1,-1 in
and
. (Either the 1 comes first in
- The 1 in
Hence, there are 3(2+2×2)=18 ways for this case. There's a grand total of 45 ways for this to happen, together with 12³ total cases. The probability we're soliciting for is thus 45/(12³)=5/192
Hence, at the top of the fourth round, each of the players has four coins probability is 5/192.
Learn more about probability and combination is brainly.com/question/3435109
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