The least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.
<h3>What is inequality?</h3>
It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
A clothing manufacturer produces one type of sweater that earns $4 profit for each one sold.
Let x be the number of sweaters that must be produced each hour to earn a profit of at least $100
Total selling price if earns $4 profit for each one sold = 4x
The expenses for running the machine are $45 per hour.
4x - 45 ≤ 100
4x ≤ 145
x ≤ 145/4
x ≤ 36.25
Number of sweater(estimate value) = 37
Thus, the least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.
Learn more about the inequality here:
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When adding or subtracting fractions that have a common denominator, simply subtract the numerators (top numbers) by each other. However, to subtract fractions with unlike denominators, find the LCD or "least common denominator". That is the lowest number both denominators can equate to.
![\frac{13}{18} - \frac{5}{8} [tex] (\frac{13}{18})( \frac{4}{1} ) - (\frac{5}{8})( \frac{9}{1}) ](https://tex.z-dn.net/?f=%20%5Cfrac%7B13%7D%7B18%7D%20-%20%5Cfrac%7B5%7D%7B8%7D%20%5Btex%5D%20%28%5Cfrac%7B13%7D%7B18%7D%29%28%20%5Cfrac%7B4%7D%7B1%7D%20%29%20-%20%28%5Cfrac%7B5%7D%7B8%7D%29%28%20%5Cfrac%7B9%7D%7B1%7D%29%20%20%0A)
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The LCD of 8 and 18 is 72.
Some of the multiples of 8 are: 8, 16, 24, 32, 64, 72, 80, 88, 96, 104...
The multiples of 18 are: 18, 36, 54, 72, 90
The lowest common multiple is 72.
Multiply each fraction by what it takes for the denominator to equal 72.
8 multiplied by what number = 72
8*9=72
18 multiplied by what = 72
18*4=72
Multiply both fractions respectively
13/18*4= 13*4/72
5/8*9 = 5*9/72
52/72 - 45/72
Simplify
52-45/72
7/72
This being the answer for the original expression
I hope this helps! If you have any question feel free to ask!
Answer:
The maximum length of the second piece is 61.5 ft.
Step-by-step explanation:
We know that the rope is 100 ft long.
There are three pieces that make up the 100 ft. The first is length x, the second is three times as long as the first, so it would be 3x, and the third is 18ft.
So if we were to write this as an equation it would look something like this: x + 3x + 18 = 100. We can simplify this some more.
4x + 18 = 100
4x = 82
x = 20.5
Now that we know the length or the first piece / x. We can easily find the length of the second (3x) by plugging in 20.5 for x.
We find that the maximum length of the second piece of rope is 61.5 feet.
Good luck, hope that helps!
Answer: 
Step-by-step explanation:
<u>Given information</u>
∡1 = 35°
∡b = ?
Total Angle = 180° (Supplementary Angle)
<u>Derived formula from the given information</u>
∡1 + ∡b = Total Angle
<u>Substitute values into the given formula</u>
(35) + b = 180
<u>Subtract 35 on both sides</u>
35 + b - 35 = 180 - 35

Hope this helps!! :)
Please let me know if you have any questions