You expect to receive $34,000 at graduation in two years. you plan on investing it at 10 percent until you have $169,000.
how long will you wait from now?

You have to wait for 19 years

Step-by-step explanation:

expected money to be receive =  $34,000

rate of interest = 10 %

Amount to be received = $169,000

time = ?

taking log both side

t × ln (1.1) = ln (4.97)

t = 16.82

t = 17 (approx.)

so, he have to wait for 17 + 2 = 19 years .

 The correct combinations are:

(A). 4 sizes and 3 toppings.

(D). 2 sizes and 6 toppings.

(F). 3 sizes and 4 toppings.

Step-by-step explanation:  Given that a A pizzeria makes pizzas in different sizes and with different toppings. The pizzeria wants its customers to have 12 options when they create a pizza.

We are to select the combination of size and toppings will give customers 12 options.

Combination (A): 4 sizes and 3 toppings.

Here, the number of options that customer will get = 4 × 3 = 12.

So, this combination is correct.

Combination (B): 2 sizes and 10 toppings.

Here, the number of options that customer will get = 2 × 10 = 20 ≠ 12.

So, this combination is NOT correct.

Combination (C): 3 sizes and 9 toppings.

Here, the number of options that customer will get = 3 × 9 = 27 ≠ 12.

So, this combination is NOT correct.

Combination (D): 2 sizes and 6 toppings.

Here, the number of options that customer will get = 2 × 6 = 12.

So, this combination is correct.

Combination (E): 4 sizes and 8 toppings.

Here, the number of options that customer will get = 4 × 8 = 32 ≠ 12.

So, this combination is NOT correct.

Combination (F): 3 sizes and 4 toppings.

Here, the number of options that customer will get = 3 × 4 = 12.

So, this combination is correct.

Thus, the correct combinations are A, D and F.