Find how many 7s are in 1762 . the remainder is the number of garbage bags you will take. the quotient is the classroom number. how can carlos use partial products to find the information he needs?

There are 251 7s in 1762

Step-by-step explanation:

* Lets explain how to solve the problem

- To find how many 7s in 1762 lets distribute the number by parts

# First we will take the two left digits (17)  

∵ 7 × 2 = 14 the nearest number to 17

- Subtract 14 from 17

∵ 17 - 14 = 3 (the remainder)

- Now we will take 3 with the digit 6 ⇒ 36

∵ 7 × 5 = 35 the nearest number to 36

- Subtract 35 from 36

∵ 36 - 35 = 1 (the reminder)

- Take 1 with the digit 2 ⇒ 12

∵ 7 × 1 = 7 the nearest number to 12

- Subtract 7 from 12

∵ 12 - 7 = 5 (The last reminder)

- From all above the quotient is 251 and the remainder is 5

* There are 251 7s in 1762

∵ The quotient is 251 and the remainder is 5

∵ The quotient is the classroom numbers

∴ There are 251 classrooms

∵ The remainder is the number of garbage bags

∴ There are 5 garbage bags

∴ The reminder is 5

* To check the answer lets use the partial product

# 251 × 7

- 7 × 200 = 1400

- 7 × 50 = 350

- 7 × 1 = 7

# Add the answers

∴ 1400 + 350 + 7 = 1757

∵ 1762 - 1757 = 5

∴ 251 × 7 + 5 = 1762

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.