Question

Need help on these 3 questions

Answer 1

a) The change in the system per minute is 0.35 or
`(7)/(20)` milliliters per minute.

b) -2
`(1)/(6)` ÷ 7
`(4)/(5)` =
`-(65)/(234)`. The first step in finding the quotient is D) Convert the mixed numbers to fractions. The fractions are
`-(13)/(6)` and
`(39)/(5)`.

c) The water level decreased by 0.0357 in. or
`(357)/(10000)` in. each hour.

a) The change in the system per minute:

Quantity of water that leaks every 10 minutes = 3
`(1)/(2)` milliliters

The time for this quantity of water to leak = 10 minutes

The rate of leaking per minute = 3
`(1)/(2)` ÷ 10 = 0.35 or
`(7)/(20)` milliliters per minute

b) -2
`(1)/(6)` ÷ 7
`(4)/(5)`

We convert the mixed numbers into improper fractions:

-2
`(1)/(6)` gives -13/6

7
`(4)/(5)` gives 39/5

`-(13)/(6)` ÷
`(39)/(5)`

The reciprocal of
`(39)/(5)` is
`(5)/(39)`.

We now multiply as follows:

`-(13)/(6)` ​×
`(5)/(39)`

=
`-(65)/(234)`

= -0.278

Thus, -2
`(1)/(6)` ÷ 7
`(4)/(5)` =
`-(65)/(234)`, which is approximately -0.278.

c) The water level in the swimming pool =
`(12)/(35)` in.

The time of the decrease occurred between 11 p.m. and 9:36 a.m.

The number of minutes between 11 p.m. and 9:36 a.m. = 576 minutes (9 hours and 36 minutes) = 9.6 hours (576 ÷ 60)

The rate of decrease per hour = 0.0357 (
`(12)/(35)` ÷ 9.6) or
`(357)/(10000)` in. per hour