There were 3 apple, 1 mixed fruit, 2 grape, and 4 tropical fruit juice boxes in the cooler at the picnic. What is the probability that, when Jill reaches into the cooler to grab two juice boxes without replacing them, she grabs two that are grape? StartFraction 1 over 100 EndFraction StartFraction 1 over 50 EndFraction StartFraction 1 over 45 EndFraction StartFraction 1 over 25 EndFraction

There are 10 total juice boxes with 2 grape ones.

Picking the first grape would be 2/10 which can reduce to 1/5

Then there would be 9 juice boxes left with 1 grape.

Picking the second grape would be 1/9

Picking both would be 1/5 x 1/9 = 1/45

agree

step-by-step explanation:

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.