Carolyn received a check last week . She invested part at 15% and 1000 more than this amount at 16%. If she will earn $780 in interest in a year, how much was invested at each rate?

$2,000 was invested at 15% rate.

$3,000 was invested at 16% rate.

Step-by-step explanation:

Carolyn received a check last week.

She invested part at 15%  and;

$1000 more than this amount at 16%

She will earn simple interest of $780 in one year.

Simple interest formula is;

I = PRT

Where I is the interest, P is the amount invested, R is the rate and T is the time.

Interest earned here = $x × × 1 = $0.15x

Interest earned here = ($x + $1000) × × 1 = $0.16x + $160

$0.15x + $0.16x + $160 = $780

$0.31x = $780 - $160 = $620

$x = $620 ÷ 0.31 = $2000

So the amount invested at 15% rate was $2000 and;

The amount invested at 16% rate was $2000 + $1000 = $3000

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560