Answer: 
Step-by-step explanation:
By definition, a direct varition is expressed as following:

Then, <em>y </em>is directly proportional to <em>x </em>and <em>k</em> is the constant of variation.
Therefore, given the direct variation:

You must solve for the variable <em>y </em>as you can see below:

Therefore, as you can see, the constant of variation is the following:

Answer:
$1.50
Step-by-step explanation:
12/8 = 1.50
Answer:
(a)
(b)
(c)R'(5400)=$394
Step-by-step explanation:
Given that x is the quantity demanded and the speaker's unit price (in dollars) is p where:
p = −0.02x + 610 (0 ≤ x ≤ 20,000)
(a)Revenue function R.
Revenue = Price X Quantity Demanded
Therefore:
R(x)=xp

(b)Marginal revenue function R'(x)
If 
Then, the marginal revenue function

(c)We want to compute R'(5,400)

From the above, we can infer that the revenue that will be generated on the sales of the 5401st item is $394.
Answer:
m= -3/2
Step-by-step explanation:
First, we must find the slope of the line given. We are given the equation:
y-2/3x=2
We must get this equation in slope-intercept form: y=mx+b (where m is the slope and b is the y-intercept). In order to do this, we must get y isolated.
2/3x is being subtracted from y. We want to preform the inverse, so we should add 2/3x to both sides.
y-2/3x+2/3x=2+2/3x
y=2+2/3x
Rearrange the terms.
y= 2/3x+2
Now the equation is in slope intercept form. (y=mx+b). 2/3 and x are being multiplied, so we know that the slope is 2/3.
Now, we have to find the perpendicular slope. Perpendicular lines have negative reciprocal slopes.
1. Negative
m=2/3
Negate the slope.
m= -2/3
2. Reciprocal
m= -2/3
Flip the numerator (top number) and denominator (bottom number).
m= -3/2
The perpendicular slope is -3/2
Randy sells, in average, 460 vacuum cleaners per month.
<h3>How many vacuum cleaners does Randy sell each month?.</h3>
First, we know that Janice sells 690 units per year.
There are 12 months in a year, so the amount that she sells, in average, per month is:
J = 690/12 = 57.5
This means that Janice sells, in average, 57.5 units per month. And Randy sells 8 times as many, then we can solve the product:
R = 8*57.5 = 460
This means that Randy sells 460 units per month.
If you want to learn more about products:
brainly.com/question/10873737
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