Amachine can stamp 40 envelopes in 8 minutes. how many of these machines, working simultaneously, are required or needed to stamp 120 envelopes per minute?

The number of machines, working simultaneously, that are required or needed to stamp 120 envelopes per minute is 3 machines.

Given the following data:

To find how many machines, working simultaneously, are required or needed to stamp 120 envelopes per minute:

In order to solve this mathematical problem, we would use direct proportion.

By direct proportion:

40 envelopes = 8 minutes

120 envelopes = X minutes

Cross-multiplying, we have:

X = 24 minutes

For the number of machines:

Machine = 3 machines

Read more: link

Divide 40 by 8 minutes to find the quantity per minute for one machine:

40 / 8 = 5 per minute.

One machine does 5 envelopes per minute.

Now divide 120 by 5 to find the number of machines needed:

120 / 5 = 24

24 machines would be needed.

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.