Answer:
Yes, because they have the same scale factor and look the same when graphed. It's just rotated and bigger.
Note that √(4 - t²) is defined only as long as 4 - t² ≥ 0, or -2 ≤ t ≤ 2. Then the real integral exists only if -2 ≤ x ≤ 2. (Otherwise we deal with complex numbers.)
If x = 2, then the integral corresponds to the area of a quarter-circle with radius 2. This means that the integral has a maximum value of 1/4 • π • 2² = π.
On the opposite end, if x = -2, then the integral has the same value, but the integral from 0 to -2 is equal to the negative integral from -2 to 0. So the minimum value is -π.
For all x in between, we observe that the integrand is continuous over the rest of its domain, so F(x) is continuous.
Then the range of F(x) is the interval [-π, π].
Answer:
He should expect to select 75 yellow cards.
Step-by-step explanation:
Since there is replacement, for each trial, we have:
1 yellow card
1 red card
1 blue card
1 green card.
If Greg does this 300 times, how many yellow cards should he expect to select?
Each trial, there are 4 cards, one of which is yellow. So 1/4 = 0.25 probability of selecting a yellow card.
Over 300 trials
0.25*300 = 75
He should expect to select 75 yellow cards.
The formula to find the surface area of a sphere is A=4(3.14)r². So if you plug in the data you would get,
A=4(3.14)4²
A=(12.56) (16)
A=200.96
You mught want to check over it so you will be able to solve it for yourself the next time you have this question.
