The expected value is $0.11.
The probability that the player will make the next free throw is 233/402. The probability that the next 3 are made will be (233/402)^3. To find the expected value of this, we multiply by the winnings we would have in this case, 166. So far we have:
((233/402)^3)(166)
The probability that the next 3 are not made is 1-((233/402)^3). Multiply this by the loss, -40, to get its expected value. This gets us to:
((233/402)^3)(166)-(1-((233/402)^3)).
This comes out to $0.11.
Answer:
$2502.60
Step-by-step explanation:
The formula for the amount of an annuity due is ...
A = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)
where P is the monthly payment (100), r is the annual interest rate (.04), n is the number of compoundings per year (12), and t is the number of years (2). Given these numbers, the formula evaluates to ...
A = $100(1.00333333)(1.00333333^24 -1)/0.00333333
= $100(301)(0.08314296)
= $2502.60
_____
This value is confirmed by a financial calculator. The given answer choices all appear to be incorrect. The closest one corresponds to an annual interest rate (APR) of 4.286%, not 4%.
We are asked in the problem to simplify the expression one divided by cotangent of theta to the second power. + sec θ cos θ. the first term is expressed as tan2 θ. sec theta is the inverse of cos θ in which the second term is equal to 1. tan2 θ + 1 is equal to sec2 θ
512.700 is the correct answer
True - specifically, that parallelogram could be a parallelogram, rhombus, rectangle or a square.
