Answer:
0.0433
Step-by-step explanation:
Since we have a fixed number of trials (N = 25) and the probability of getting heads is always p = 0.05, we are going to treat this as a binomial distribution.
Using a binomial probability calculator, we find that the probability of obtaining heads from 8 to 17 times is 0.9567 given that the con is fair. The probability of obtaining any other value given that the coin is fair is going to be:
1 - 0.9567 = 0.0433
Since we are going to conclude that the coin is baised if either x<8 or x>17, the probability of judging the coin to be baised when it is actually fair is 4.33%
Answer:
a = 3 7/18 or 3.388889
Step-by-step explanation:
First, you want to get the a by itself, so you would subtract 4 from the left side of the equals sign.
6a + 4 = 61 / 3 + 4
-4 -4
6a = 61 / 3
By doing that, they cancel each other out, so you are left with
6a = 61 / 3
Then you want to get a by itself, so you divide 6 from both sides.
6a / 6 = 61 / 3 / 6
Remember that 6 can also be written as 6/1
Remember that dividing a fraction is multiplying the reciprocal.
6a / 6 = 61 / 3 / 6 / 1
When dividing fractions remember to Skip the first fraction, Flip the second fraction, and Multiply the two fractions together.
61 / 3 x 1 / 6
skip multiply flip
Multiply across the top, and across the bottom.
61(1) and 3(6)
Then you get
61 / 18
So a = 61 / 18
If you want to convert that to a mixed number, it would be 3 7 / 18
If you want that in a decimal, it would be 3.388889
U = ( -8 , -8)
v = (-1 , 2 )
<span>the magnitude of vector projection of u onto v =
</span><span>dot product of u and v over the magnitude of v = (u . v )/ ll v ll
</span>
<span>ll v ll = √(-1² + 2²) = √5
</span>
u . v = ( -8 , -8) . ( -1 , 2) = -8*-1+2*-8 = -8
∴ <span>(u . v )/ ll v ll = -8/√5</span>
∴ the vector projection of u onto v = [(u . v )/ ll v ll] * [<span>v/ ll v ll]
</span>
<span> = [-8/√5] * (-1,2)/√5 = ( 8/5 , -16/5 )
</span>
The other orthogonal component = u - ( 8/5 , -16/5 )
= (-8 , -8 ) - <span> ( 8/5 , -16/5 ) = (-48/5 , -24/5 )
</span>
So, u <span>as a sum of two orthogonal vectors will be
</span>
u = ( 8/5 , -16/5 ) + <span>(-48/5 , -24/5 )</span>
