Answer:
Angle PAB is a right angle.
Step-by-step explanation:
Angle PAB is a right angle. In circles, tangent lines are always perpendicular to radii.
Try to relax. Your desperation has surely progressed to the point where
you're unable to think clearly, and to agonize over it any further would only
cause you more pain and frustration.
I've never seen this kind of problem before. But I arrived here in a calm state,
having just finished my dinner and spent a few minutes rubbing my dogs, and
I believe I've been able to crack the case.
Consider this: (2)^a negative power = (1/2)^the same power but positive.
So:
Whatever power (2) must be raised to, in order to reach some number 'N',
the same number 'N' can be reached by raising (1/2) to the same power
but negative.
What I just said in that paragraph was: log₂ of(N) = <em>- </em>log(base 1/2) of (N) .
I think that's the big breakthrough here.
The rest is just turning the crank.
Now let's look at the problem:
log₂(x-1) + log(base 1/2) (x-2) = log₂(x)
Subtract log₂(x) from each side:
log₂(x-1) - log₂(x) + log(base 1/2) (x-2) = 0
Subtract log(base 1/2) (x-2) from each side:
log₂(x-1) - log₂(x) = - log(base 1/2) (x-2) Notice the negative on the right.
The left side is the same as log₂[ (x-1)/x ]
==> The right side is the same as +log₂(x-2)
Now you have: log₂[ (x-1)/x ] = +log₂(x-2)
And that ugly [ log to the base of 1/2 ] is gone.
Take the antilog of each side:
(x-1)/x = x-2
Multiply each side by 'x' : x - 1 = x² - 2x
Subtract (x-1) from each side:
x² - 2x - (x-1) = 0
x² - 3x + 1 = 0
Using the quadratic equation, the solutions to that are
x = 2.618
and
x = 0.382 .
I think you have to say that <em>x=2.618</em> is the solution to the original
log problem, and 0.382 has to be discarded, because there's an
(x-2) in the original problem, and (0.382 - 2) is negative, and
there's no such thing as the log of a negative number.
There,now. Doesn't that feel better.
Answer:
D. 100
Step-by-step explanation:
1. Find the z-score: 165-176/11.4 = -1.2
2. Find the percentage of the z-score. Here it's 16.85%
3. Because we are searching for the amount of members that weigh MORE than 165 pounds and not LESS, we need to find the greater percentage by subtracting 16.85% from 100% which is 83.15%. This is the percentage of people that weigh more than 165 pounds.
4. Multiply the percentage by the number of members: 83.15%*120 = 99.78
5. Round it to a whole number because someone can't be 0.78 of a person. You get 100 members.
Also, I took the test :)
It looks like it counts up by 2 when adding. so add 4, then add 6, then add 8, then add 10, etc. to find the output you simply add 2 more than the last time you added, to find the input, you subtract 2 more than last time. hope this makes sense haha.
You need to find "dollars per hour". So you need to know the total dollars and the total hours.
You already know the total dollars ... it's 54.
What are the total hours ? 2-1/2 plus 4-1/4 . Can you add those ?
Once you add up the total hours, divide ($54) divided by (total hours).
The quotient is the number of dollars she earns for each hour she works.
