Answer:
all work is pictured and shown
Volume of a cylinder = base x height
the base is the area of the circle at the bottom.
To find the area of a circle, you use:
A = πr²
where r is the radius of the circle.
radius is half of the diameter, so with a diameter of 12.3, (divide that by 2) the radius of the circle is 6.15 feet.
A = π(6.15)²
A ≈ 118.82
Since we know the height is 25 feet, we can solve for the area of the cylinder.
Area of the cylinder = 118.82 x 25 = 2,970.57 feet cubed
Answer:
an exponential equation has the form y=ar^x where y=final amount, a=initial amount, r=rate, and x=time, in this case
y=200(1.18)^x
Step-by-step explanation:
Answer: a) P = 0.5, b) P = 0.07
Step-by-step explanation:
Hi!
Lets call X₁ the time at which you arrive, and X₂ the time at which Bob arrives. Both are random variables with uniform density in the interval [0, 60] (in minutes). Their joint distribuition is uniform over the square in the image, with value P = 1/(60*60) = 1/3600.
a) For you to get more cake than Bob, you should arrive earlier. This event is A = { X₁ < X₂ }, the shaded triangle in the figure.The area of this event (set) is half the total area of the square, so P(A) = 0.5.
It makes sense, beacuse its equally probable for you or Bob to arrive earlier, as both have uniform density over the time interval.
b) In this case you arrive later than Bob, but less than 5 minutes later. So the event is B = { X₂ < X₁ < (X₂ + 5) } . This is the gray shaded area in b) part of the image. Its area is the difference two triangles (half square - blue triangle), then the probability is:

9t = 27.99
5t = ?
Cross-multiply : 9t? = 139.95t
?=15.55