The length of the line segment AB where

and


We have:

subtitute

Answer: b. 14.1
Answer:
x= 2√37
Step-by-step explanation:
First thing you want to do is find the length of the missing side where the the right angle is at. You can find that with the pythagorean theorem of the other triangle, since you are already given 2 sides.
Pythagorean Theorem

a=2
b=?
c=2√2
Plug in and solve for b.
2^2+b^2=(2√2)^2
4+b^2=8
b^2=4
b=2
Now use the pythagorean theorem again to find your x side.
a=2
b=12
c=?
2^2+12^2=c^2
4+144=c^2
148=c^2
c=√148
c=2√37
SOLUTION
This is a binomial probability. For i, we will apply the Binomial probability formula
i. Exactly 2 are defective
Using the formula, we have

Note that I made the probability of being defective as the probability of success = p
and probability of none defective as probability of failure = q
Exactly 2 are defective becomes the binomial probability

Hence the answer is 0.1157
(ii) None is defective becomes

hence the answer is 0.4823
(iii) All are defective

(iv) At least one is defective
This is 1 - probability that none is defective

Hence the answer is 0.5177
<h3>2
Answers: Choice B and Choice D</h3>
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Work Shown:
c = price of coat before discount
0.33c = discount = amount you save
c - 0.33c = original price minus discount = final price
c - 0.33c = 1c - 0.33c = (1-0.33)c = 0.67c = final price
In short, c - 0.33c = 0.67c
They are two ways of expressing the same thing.
You can think of it like saying 100% - 33% = 67%
If you save 33%, then you still have to pay the remaining 67% of the original cost.
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Example:
Let's say the coat is $100 before the discount
c = 100
0.33*c = 0.33*100 = 33 dollars is how much you save
c - 0.33c = 100 - 33 = 67 dollars is the final price
0.67c = 0.67*100 = 67 matches with the previous figure above
Let z = sin(x). This means z^2 = (sin(x))^2 = sin^2(x). This allows us to go from the equation you're given to this equation: 7z^2 - 14z + 2 = -5
That turns into 7z^2 - 14z + 7 = 0 after adding 5 to both sides. Use the quadratic formula to solve for z. The only solution is z = 1 (see attached image). Since we made z = sin(x), this means sin(x) = 1. All solutions to this equation will be in the form x = (pi/2) + 2pi*n, which is the radian form of the solution set. If you need the degree form, then it would be x = 90 + 360*n
The 2pi*n (or 360*n) part ensures we get every angle coterminal to pi/2 radians (90 degrees), which captures the entire solution set.
Note: The variable n can be any integer.