Answer:
B. Eve's table shows that those who enjoy dancing are likely girls.
C. Bob's table shows that boys are likely to not enjoy dancing.
E. The percentage of someone being a girl, given that the person enjoys dancing is lower than the percentage that someone enjoys dancing, given that the person is a girl.
Answer:
the last one 3(x+4) = 3x + 12
Step-by-step explanation:
When I see "at what rate", I know this question must come from
pre-Calculus, so I won't feel bad using a little Calculus to solve it.
-- The runner, first-base, and second-base form a right triangle.
The right angle is at first-base.
-- One leg of the triangle is the line from first- to second-base.
It's 90-ft long, and it doesn't change.
-- The other leg of the triangle is the line from the runner to first-base.
Its length is 90-24T. ('T' is the seconds since the runner left home plate.)
-- The hypotenuse of the right triangle is
square root of [ 90² + (90-24T)² ] =
square root of [ 8100 + 8100 - 4320T + 576 T² ] =
square root of [ 576 T² - 4320 T + 16,200 ]
We want to know how fast this distance is changing
when the runner is half-way to first base.
Before we figure out when that will be, we know that since
the question is asking about how fast this quantity is changing,
sooner or later we're going to need its derivative. Let's bite the
bullet and do that now, so we won't have to worry about it.
Derivative of [ 576 T² - 4320 T + 16,200 ] ^ 1/2 =
(1/2) [ 576 T² - 4320 T + 16,200 ] ^ -1/2 times (576T - 4320) .
There it is. Ugly but manageable.
How fast is this quantity changing when the runner is halfway to first-base ?
Well, we need to know when that is ... how many seconds after he leaves
the plate.
Total time it takes him to reach first-base = (90 ft)/(24 ft/sec) = 3.75 sec .
He's halfway there when T = (3.75 / 2) = 1.875 seconds. (Seems fast.)
Now all we have to do is plug in 1.875 wherever we see 'T' in the big derivative,
and we'll know the rate at which that hypotenuse is changing at that time.
Here goes. Take a deep breath:
(1/2) [ 576 T² - 4320 T + 16,200 ] ^ -1/2 times (576T - 4320) =
[ 576 T² - 4320 T + 16,200 ] ^ -1/2 times (1152T - 8640) =
[576(1.875)² - 4320(1.875) + 16,200]^-1/2 times [1152(1.875)-8640] =
[ 2,025 - 8,100 + 16,200 ] ^ -1/2 times [ 2,160 - 8640 ] =
- 6480 / √10,125 = - 64.4 ft/sec.
I have a strong hunch that this answer is absurd, but I'm not going to waste
any more time on it, (especially not for 5 points, if you'll forgive me).
I've outlined a method of analysis and an approach to the solution, and
I believe both of them are reasonable. I'm sure you can take it from there,
and I hope you have better luck with your arithmetic than I've had with mine.
Answer:
d. None of the above
Step-by-step explanation:
We assume the sequence of deposits is ...
month 0: $400
month 1: $200
month 2: $200
...
month 240: $200 . . . . accumulated interest is determined at this point
That is, no interest is earned on the last deposit.
_____
The value of the initial $400 deposit after 20 years at 2.15% interest compounded monthly is ...
$400×(1 +.0215/12)^(12×20) = $400×1.536666 ≈ $614.67
The value of the $200 annuity at the same interest rate is ...
$200((1 +.0215/12)^(12×20) -1)/(.0215/12) = $200×299.534612 ≈ $59,906.92
So, the total account value is ...
$614.67 +59,906.92 = $60521.59
The total amount deposited was ...
$400 +$200×240 = $48,400
The interest earned is the difference between the account value and the total of deposits:
$60,521.59 -48,400 = $12,121.59 . . . . interest earned
This value does not match any numerical answer choice, so we conclude the appropriate answer is ...
None of the above
Answer:
The diagonal of the base is 4√5 centimeters.
The area of a base is 40 square centimeters.
The area of a lateral side between the bases is about 126.5 square centimeters.
Step-by-step explanation:
