Answer:
68 %
Step-by-step explanation:
Since we have our mean x = 250 and standard deviation σ = 20, we need to find how many standard deviations away the values 230 and 270 are.
Note x - σ = 250 - 20 = 230 and x + σ = 250 + 20 = 270
The values are one standard deviation away.
So, the values between 230 and 270 lie in the range x - σ to x + σ.
Since the batting averages are approximately normally distributed and for a normal distribution, 68 % of the values lie in the range x - σ to x + σ.
So, 68 % of Braves players fall between 230 and 270.
Obtuse because it only takes one obtuse angle to make an obtuse triangle
(a) First find the intersections of

and

:

So the area of

is given by

If you're not familiar with the error function

, then you will not be able to find an exact answer. Fortunately, I see this is a question on a calculator based exam, so you can use whatever built-in function you have on your calculator to evaluate the integral. You should get something around 0.5141.
(b) Find the intersections of the line

with

.

So the area of

is given by


which is approximately 1.546.
(c) The easiest method for finding the volume of the solid of revolution is via the disk method. Each cross-section of the solid is a circle with radius perpendicular to the x-axis, determined by the vertical distance from the curve

and the line

, or

. The area of any such circle is

times the square of its radius. Since the curve intersects the axis of revolution at

and

, the volume would be given by
Answer:
a ≤ b + 5
a + b ≥ 40
2.5
a + 1.5
b ≤ 105
Step-by-step explanation: