(b) To have no winner within the first 6 tosses means that there must be 3 tails and 3 heads tossed. So we count how many ways can that happen. The number of ways to choose 3 heads (or tails, doesn't matter) from 6 tosses is
so 20 ways winthin the 6 tosses. but the question was "how many ways among the 128 of 7 tosses" so we need to add the 7th toss by multiplying by another 2 possibilities for the outcome of the 7th toss, giving us the answer: among the 128 there are 40 games that are tied and need the 7th toss.
(c) The probability is the number of tied games (after 6 tosses) divided by the total number of possible configurations among 6 tosses:
Answer:
1/2
Step-by-step explanation:
Answer:
∠1 = 23°
Step-by-step explanation:
∠WXZ = ∠WXY + ∠YXZ
Note that ∠2 = 4∠1 ( angle 2 is 4 times angle 1 )
Hence
4∠1 + ∠1 = 115
5∠1 = 115 ( divide both sides by 5 )
∠1 = 23°
(-1.5,1) is the midpoint of the line segment
Answer:
Step-by-step explanation:
<u>Given polynomial is:</u>
![\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Crule%5B225%5D%7B225%7D%7B2%7D)
First factor is (x-1)
Let x - 1 = 0 => x = 1
Putting this in the above polynomial
Given that it's remainder is 3
Subtracting 7 to both sides
<h2>a + b = -4 -------------------------- (1)</h2>
Second Factor is 2x + 1
Let 2x + 1 = 0 => x = - 1 / 2
Putting in the above polynomial
The remainder is 6
<h2>-a + 2b = 28 --------------------------------(2)</h2>
Adding both equations
a + b - a + 2b = -4 + 28
3b = 24
Dividing both sides by 3
b = 8
Putting b = 8 in Equation (1)
a + 8 = -4
a = - 4 - 8
a = -12
