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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The equivalent expression to the given one is -sin(pi/6).
<h3>
</h3><h3>
Which expression is equivalent to the given one?</h3>
The given expression is:
sin(7pi/6)
Where the argument is in radians.
Remember that:
sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)
Now we can rewrite:
sin(7pi/6) = sin(pi + pi/6)
Then we can use the above relation to rewrite:
sin(pi + pi/6) = sin(pi)*cos( pi/6) + sin(pi/6)*cos(pi)
And we know that:
sin(pi) = 0
cos(pi) = -1
Then we can write:
sin(7pi/6) = - sin(pi/6)
If you want to learn more about the sine function:
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Hello!
The equation for find the h when given volume and radius is
h is height
v is volume
r is radius
Put in the values you know
Since there is pi on the top and bottom we can get rid of it
multiply the 3 by the top number
the answer is 8m
Hope this helps!
Answer:
(a) 
(b) -6, 2
Step-by-step explanation:
Given: g(x) = x + 1
h(x) = (x + 6)(x - 2)
Therefore, 
(a) 
Therefore, g/h(3) = 4/9
(b) Values not in domain means we have to determine for which values of x the function becomes undefined.
This happens when the denominator becomes zero.
That means h(x) = 0
⇒ (x + 6)(x - 2) = 0
⇒ x = -6 or x = 2
Therefore, when x takes one or both of these values we can say that the function 
becomes undefined.
