Answer:
The answer to the question: "Will Hank have the pool drained in time?" is:
- <u>Yes, Hank will have the pool drained in time</u>.
Step-by-step explanation:
To identify the time Hank needs to drain the pool, we can begin with the time Hank has from 8:00 AM to 2:00 PM in minutes:
- Available time = 6 hours * 60 minutes / 1 hour (we cancel the unit "hour")
- Available time = 360 minutes
Now we know Hank has 360 minutes to drain the pool, we're gonna calculate the volume of the pool with the given measurements and the next equation:
- Volume of the pool = Deep * Long * Wide
- Volume of the pool = 2 m * 10 m * 8 m
- Volume of the pool = 160 m^3
Since the drain rate is in gallons, we must convert the obtained volume to gallons too, we must know that:
Now, we use a rule of three:
If:
- 1 m^3 ⇒ 264.172 gal
- 160 m^3 ⇒ x
And we calculate:
(We cancel the unit "m^3)- x = 42267.52 gal
At last, we must identify how much time take to drain the pool with a volume of 42267.52 gallons if the drain rate is 130 gal/min:
- Time to drain the pool =
(We cancel the unit "gallon") - Time to drain the pool = 325.1347692 minutes
- <u>Time to drain the pool ≅ 326 minutes</u> (I approximate to the next number because I want to assure the pool is drained in that time)
As we know, <u><em>Hank has 360 minutes to drain the pool and how it would be drained in 326 minutes approximately, we know Hank will have the pool drained in time and will have and additional 34 minutes</em></u>.
We subtract 28 - 16 and get the number of girls
so lets do that
28 - 16 = 12
now we know the unsimplified ratio os 12 to 16
simplifed girls 12 ÷ 4 = 3
simplified boys 16 ÷ 4 = 4
since it says (girls to boys) we put girls first then boys
so it would become 3 : 4
Or the answer is B.) 3 : 4
Step 
<u>Find the length of the side MN</u>
we know that
Applying the Pythagorean Theorem

Solve for MN

in this problem

Substitute in the formula above



Step 
<u>Find the value of cos (M)</u>
we know that
in the right triangle MNL


Substitute



therefore
The answer is
The value of cos(M) is equal to 
The number of large boxes is 4 and the number of small boxes is 14.
<u><em>Explanation</em></u>
Suppose, the number of large boxes is
and the number of small boxes is 
As, the total number of boxes is 18, so the first equation is....

The large boxes hold 35 books, and the small ones hold 20 books and the total number of books is 420. So the second equation will be .....

Now solving equation (1) for
itself , we will get....

We will plug this
into equation (2). So.....

Now plugging this
into the equation
.......

Thus, the number of large boxes is 4 and the number of small boxes is 14.