40. Games To win a prize at a carnival game, you must toss a quarter, so that it lands entirely within a circle as shown at the right. Assume that the center of a tossed quarter is equally likely to land at any point within the 8-in. square.
a. What is the probability that the quarter lands entirely in the circle in
one toss?
b. Reasoning On average, how many coins must you toss to win a
prize? Explain.

a) 0.0139

b) 73

Step-by-step explanation:

a) The circle has a radius of 1 inch.  For the quarter to land entirely within the circle, the center of the quarter must lie within a circle with radius 17/32 inches.

The probability is the ratio of the area of this circle to the area of the square.

P = πr² / s²

P = π (17/32)² / (8)²

P ≈ 0.0139

b) Expected value = probability × frequency

1 = 0.0139 × n

n = 72.2

Rounding up to the nearest integer, you would expect to toss on average 73 quarters before getting one in the circle.

i believe that the slope of the line is -5

step-by-step explanation:

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough