Answer:
![P[at\ least\ 1] = 0.9961](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%200.9961)
Step-by-step explanation:
Given


Required
Probability that s/he gets at least one correctly
First, we calculate the probability of answering a question correctly
Since, there are just 2 choices (true or false), the probability is:

Similarly, the probability of answering a question, wrongly is:

The following relationship exists, in probability:
![P[at\ least\ 1] = 1 - P[none]](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%201%20-%20P%5Bnone%5D)
So, to calculate the required probability.
First, we calculate the probability that he answers none of the 8 questions correctly.
![P[none] = p(wrong)^8](https://tex.z-dn.net/?f=P%5Bnone%5D%20%3D%20p%28wrong%29%5E8)
![P[none] = (\frac{1}{2})^8](https://tex.z-dn.net/?f=P%5Bnone%5D%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E8)
Substitute
in ![P[at\ least\ 1] = 1 - P[none]](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%201%20-%20P%5Bnone%5D)
![P[at\ least\ 1] = 1 - (\frac{1}{2})^8](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%201%20-%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E8)
![P[at\ least\ 1] = 1 - \frac{1}{256}](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%201%20-%20%5Cfrac%7B1%7D%7B256%7D)
Take LCM
![P[at\ least\ 1] = \frac{256 - 1}{256}](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%20%5Cfrac%7B256%20-%201%7D%7B256%7D)
![P[at\ least\ 1] = \frac{255}{256}](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%20%5Cfrac%7B255%7D%7B256%7D)
![P[at\ least\ 1] = 0.9961](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%200.9961)
<em></em>
<em>Hence, the probability that s/he gets at least one correctly is 0.9961</em>
1 is D
2 is
7x + 7 = 112
7x = 105
x = 15 (B)
Answer:
no solution
Step-by-step explanation:
8(3x-6)=6(4x+8)- remove the parentheses
24x-48=24x+48 - then you cancel the equal terms
-48=48
that is false showing that there is no solution
we know that
<u>Alternate interior angles</u> are two interior angles which lie on different parallel lines and on opposite sides of a transversal. Alternate interior angles are congruent
see the attached figure with letters to better understand the problem
in this problem
the parallel lines are the lines a and b
the transversal line is the line c
so
the alternate interior angles are the Angle
and Angle 
m∠3=m∠6
therefore
<u>the answer is the option</u>
Angle
and Angle 