Angle x° and angle 154° are supplementary angles, meaning that they equal 180° when added.
At your gym, the bar you lift weighs 45 pounds. You add weights to the bar that are 10 pounds each. If you add 8 weights to the
2 answers:
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Answer:
D
Step-by-step explanation:
So we have the expression:
And we want to evaluate it when x=25, y=10, w=11, and z=18.
So, substitute these values for the variables:
First, subtract within the parentheses:
Square 15:
Now, multiply the terms on the right. 10 times 11 is 110:
Multiply:
Finally, add:
So, our answer is D.
And we're done!
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.
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