B, C, and D are all correct.
Answer:
![[6\frac{1}{6},6\frac{1}{3},6\frac{1}{2},6\frac{2}{3},6\frac{5}{6}]](https://tex.z-dn.net/?f=%5B6%5Cfrac%7B1%7D%7B6%7D%2C6%5Cfrac%7B1%7D%7B3%7D%2C6%5Cfrac%7B1%7D%7B2%7D%2C6%5Cfrac%7B2%7D%7B3%7D%2C6%5Cfrac%7B5%7D%7B6%7D%5D)
Step-by-step explanation:
we have the compound inequality
where
x is a mixed number
so
The solution for the compound inequality are the numbers
![[6\frac{1}{6},6\frac{2}{6},6\frac{3}{6},6\frac{4}{6},6\frac{5}{6}]](https://tex.z-dn.net/?f=%5B6%5Cfrac%7B1%7D%7B6%7D%2C6%5Cfrac%7B2%7D%7B6%7D%2C6%5Cfrac%7B3%7D%7B6%7D%2C6%5Cfrac%7B4%7D%7B6%7D%2C6%5Cfrac%7B5%7D%7B6%7D%5D)
Simplify the numbers
1. the answer is 24. think of x as the original amount, and y as the new amount. y times 1.5 is x, and y+12 is x. reverse that to figure out y, which is what we need, and you have x/1.5 = y as well as x-12 = y. Use the equal values method and make an equation x/1.5=x-12. solve this equation to get x, which is 36. to figure out the new amount, y, you need to subtract 12, which would help you get 24 as your final answer.
2. once again, create an equation. let's call team 1 x and team 2 y. team one has 1/4th as many as team 2, so that would be x=1/4y. An easier way to write that is 4x=y. after 6 people quit team two, that would be y-6. after the transfer, that would be y-6-12, and x+12 for the teams. they are equal after these, so y-6-12=x+12. solve this equation to get y-18= x+12. if you recall earlier, y was 4 times x, so substitute that into y to get 4x-18=x+12. Solve the equation to get 10 people on team one originally. your final answer is 10 people.
Answer:
3:11
Step-by-step explanation:
3x=11y
<u>Rearrange to the format of the ratio.</u>
11y = 3x
<u>Let's find </u><u>y/x</u><u>. </u><u>y/x</u><u> is </u><u>y:x.</u>
11y = 3x
<u>Divide both sides by </u><u>11</u><u>.</u>
11y/11 = 3x/11
y = 3x/11
<u>NOW LET'S DIVIDE BOTH SIDES BY </u><u>x</u><u> TO GET </u><u>x</u><u> AS THE DENOMINATOR OF </u><u>y</u><u>.</u>
y = 3x/11
y/x = (3x/11)/x
y/x = (3x/11) * 1/x
y/x = 3/11
Therefore, y:x = 3:11
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Answer:
Step-by-step explanation:
<u>We know that:</u>
- Area of shaded region = Area of square - Area of circles
- Radius of circle = 3 in
- Area of circle = πr²
- Area of square = s²
<u>Solution:</u>
- Area of shaded region = Area of square - Area of circles
- => Area of shaded region = (12²) - 4(22/7 x 3 x 3)
- => Area of shaded region = (144) - 4(22/7 x 9)
- => Area of shaded region = (144) - 4(198/7)
- => Area of shaded region = 144 - 792/7
- => Area of shaded region = 144 x 7/7 - 792/7
- => Area of shaded region = 1008/7 - 792/7
- => Area of shaded region = 1008/7 - 792/7
- => Area of shaded region = 216/7 in²
