A store gives a customer 20% off if $10 or more amount of product is purchased. Otherwise the customer pays the usual price at checkout. The amount of product a customer purchases is modeled by a continuous random variable X with density

The expected payment by the customer at the checkout is $9.

Step-by-step explanation:

The amount of the product is given as

Now the expected payment is given as

Here 0.8 x is used in the second integral because of the discount of 20% i.e. the expected price is 80% of the value such that

The expected payment by the customer at the checkout is $9.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.