Answer:
866.64
Step-by-step explanation:
40/2 = 20
A = πr²
3.14*20² = 1256
52/2 = 26
3.14*26² = 2122.64
2122.64 - 1256 = 866.64
Answer:
<em>b. 0.6024</em>
Step-by-step explanation:
<u>Conditional Probability</u>
Suppose two events A and B are not independent, i.e. they can occur simultaneously. It means there is a space where the intersection of A and B is not empty:

If we already know event B has occurred, we can compute the probability that event A has also occurred with the conditional probability formula

Now analyze the situation presented in the question. Let's call F to the fair coin with 50%-50% probability to get heads-tails, and U to the unfair coin with 32%-68% to get heads-tails respectively.
Since the probability to pick either coin is one half each, we have

If we had picked the fair coin, the probability of getting heads is 0.5 also, so

If we had picked the unfair coin, the probability of getting heads is 0.32, so

Being A the event of choosing the fair coin, and B the event of getting heads, then



The closest answer is
b. 0.6024
Original Statement: If x = 3, then x^2 = 9 (true)
Converse: If x^2 = 9, then x = 3 (false; this is half the story and x = -3 must be included)
Since the converse isn't completely true, we can't combine the two statements to get a biconditional.
keeping in mind that perpendicular lines have <u>negative reciprocal</u> slopes, let's find the slope of 3x + 4y = 9, by simply putting it in slope-intercept form.
![\bf 3x+4y=9\implies 4y=-3x+9\implies y=-\cfrac{3x+9}{4}\implies y=\stackrel{slope}{-\cfrac{3}{4}}x+\cfrac{9}{4} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{4}{3}}\qquad \stackrel{negative~reciprocal}{+\cfrac{4}{3}}\implies \cfrac{4}{3}}](https://tex.z-dn.net/?f=%20%5Cbf%203x%2B4y%3D9%5Cimplies%204y%3D-3x%2B9%5Cimplies%20y%3D-%5Ccfrac%7B3x%2B9%7D%7B4%7D%5Cimplies%20y%3D%5Cstackrel%7Bslope%7D%7B-%5Ccfrac%7B3%7D%7B4%7D%7Dx%2B%5Ccfrac%7B9%7D%7B4%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bperpendicular%20lines%20have%20%5Cunderline%7Bnegative%20reciprocal%7D%20slopes%7D%7D%20%7B%5Cstackrel%7Bslope%7D%7B-%5Ccfrac%7B3%7D%7B4%7D%7D%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cstackrel%7Breciprocal%7D%7B-%5Ccfrac%7B4%7D%7B3%7D%7D%5Cqquad%20%5Cstackrel%7Bnegative~reciprocal%7D%7B%2B%5Ccfrac%7B4%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7B4%7D%7B3%7D%7D%20)
so we're really looking for the equation of a line whose slope is 4/3 and runs through 8, -4.
