An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $60,000. If the economy grows at a moderate pace, the investment will result in a profit of $10,000. However, if the economy goes into recession, the investment will result in a loss of $60,000. You contact an economist who believes there is a 30% probability the economy will remain strong, a 60% probability the economy will grow at a moderate pace, and a 10% probability the economy will slip into recession. What is the expected profit from this investment?

expected profit = 18,000 dollars

Step-by-step explanation:

expected value formulae = x * p(x)

x= data value, p(x) = probability of data value

When the economy is strong

profit to be made = 60,000 dollars

probability that economy will be strong = 30/100 = 0.3

expected value = profit * probability at which profit is made

expected value = 0.3 * 60000

expected value = 18,000 dollars

When economy grows at moderate pace

profit to be made = 10,000

probability that economy will be moderate = 60/100 = 0.6

expected value = 0.6 * 10000

expected value = 6,000 dollars

When economy is in recession

loss to be made = -60,000

probability that economy will be in recession = 10/100=0.1

expected value = 0.1 * -60000 = -6000 dollars

negative sign denotes loss.

total investment = 18,000 + 6000 - 6000

total investment = 18,000 dollars

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.