Answer:
4 containers.
Step-by-step explanation:
Since Noelle collected 3 quarts 1 pint of liquid from the first table, the amount of liquid collected in quarts is 3 quarts + 1 pint = 3 quarts + 1 pint × 1 quarts/2 pints = 3 quarts + 0.5 quarts = 3.5 quarts.
She also collected 4 quarts from the second table, 2 quarts from the third table.
Finally, she collected collected 3 quarts 1 pint of liquid from the fourth table, the amount of liquid collected in quarts is 3 quarts + 1 pint = 3 quarts + 1 pint × 1 quarts/2 pints = 3 quarts + 0.5 quarts = 3.5 quarts.
So, the total amount of liquid she collected in quarts is V = 3.5 quarts + 4 quarts + 2 quarts + 3.5 quarts = 7.5 quarts + 5.5 quarts = 13 quarts
We now convert this value to gallons to know the amount of containers Noelle needs since she has one gallon containers.
13 quarts = 13 × 1 quarts = 13 quarts × 1 gallon/4 quarts = 13/4 gallons = 3.25 gallons
Since the total amount of liquid is 3.25 gallons = 3 gallons + 0.25 gallons, Noelle would need 4 containers since 3 containers would contain the first 3 gallons and the fourth container would contain the remaining 0.25 gallons.
So, Alyssa would need 4 containers.
Answer:
$0.94 per pound
Step-by-step explanation:
To find the unit rate, make an equation and simplify it.
<em>2 pounds = $1.88</em>
<em>1 pound = ($1.88 ÷ 2) $0.94</em>
Hence, It costs <em>$0.94 per pound</em>
Answer: ![-\frac{240}{289}](https://tex.z-dn.net/?f=-%5Cfrac%7B240%7D%7B289%7D)
=========================================================
Explanation:
Use the pythagorean trig identity
and plug in the fact that ![\cos(\theta) = \frac{8}{17}\\\\](https://tex.z-dn.net/?f=%5Ccos%28%5Ctheta%29%20%3D%20%5Cfrac%7B8%7D%7B17%7D%5C%5C%5C%5C)
Isolating sine leads to
. I'm skipping the steps here, but let me know if you need to see them.
The result is negative because we're in quadrant 4, when y < 0 so it's when sine is negative.
Therefore,
![\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\\\\sin(2\theta) = 2*\left(-\frac{15}{17}\right)*\left(\frac{8}{17}\right)\\\\\sin(2\theta) = -\frac{240}{289}\\\\](https://tex.z-dn.net/?f=%5Csin%282%5Ctheta%29%20%3D%202%5Csin%28%5Ctheta%29%5Ccos%28%5Ctheta%29%5C%5C%5C%5C%5Csin%282%5Ctheta%29%20%3D%202%2A%5Cleft%28-%5Cfrac%7B15%7D%7B17%7D%5Cright%29%2A%5Cleft%28%5Cfrac%7B8%7D%7B17%7D%5Cright%29%5C%5C%5C%5C%5Csin%282%5Ctheta%29%20%3D%20-%5Cfrac%7B240%7D%7B289%7D%5C%5C%5C%5C)
Answer:
the think the answer is b.
Step-by-step explanation:
The quantity 5 more than a number t is labeled as (5+t)
Product of 9 and the quantity is labeled as = 9(5+t) which equals 45+9t
Result is less than 6 so the equation becomes
45+9t < 6