Answer:
If we are to make x small rugs, each of which takes 2 hours to dye, then the total time taken to dye the small rugs is 2x. Similarly for the y large rugs which each take 3 hours to dye, the total time for dyeing the large rugs is 3y. Therefore the total for all sizes of rugs is 2x + 3y. Finally, we have a maximum of 60 available hours for the dyeing, so the total time cannot exceed 60, and the final inequality is
2x + 3y < 60
Step-by-step explanation:
First, let's convert each line to slope-intercept form to better see the slopes.
Isolate the y variable for each equation.
2x + 6y = -12
Subtract 2x from both sides.
6y = -12 - 2x
Divide both sides by 6.
y = -2 - 1/3x
Rearrange.
y = -1/3x - 2
Line b:
2y = 3x - 10
Divide both sides by 2.
y = 1.5x - 5
Line c:
3x - 2y = -4
Add 2y to both sides.
3x = -4 + 2y
Add 4 to both sides.
2y = 3x + 4
Divide both sides by 2.
y = 1.5x + 2
Now, let's compare our new equations:
Line a: y = -1/3x - 2
Line b: y = 1.5x - 5
Line c: y = 1.5x + 2
Now, the rule for parallel and perpendicular lines is as follows:
For two lines to be parallel, they must have equal slopes.
For two lines to be perpendicular, one must have the negative reciprocal of the other.
In this case, line b and c are parallel, and they have the same slope, but different y-intercepts.
However, none of the lines are perpendicular, as -1/3x is not the negative reciprocal of 1.5x, or 3/2x.
<h3><u>B and C are parallel, no perpendicular lines.</u></h3>
Answer:
Any value of x
makes the equation true.
All real numbers
Interval Notation:
(−∞,∞)
Step-by-step explanation:
Any value of x makes the equation true.
So they need $125 to start a slime business.
To get money Carrie start to sell cupcakes for 0.50 cents
Juanita will be selling cards for $2.25
Juanita is selling cards for $2.25 and she is selling at least 35 of them
Carrie is selling cupcakes for 0.50 cents and the number of cupvakes is three times the number of cards so we will multiply 35 x 3=105 number of cupcakes
Then we will multiply 0.50 cents x 105= $53.2 on the cupcakes.
After that, we will multiply $2.25 x 35 for the cards = 78.5
Finally add them together
78.5
+53.3
---------
$ 131.8
So they will have $131.8 after selling cupcakes and cards.
Answer:
(a) $12,000. It is reasonable since profit is positive
(b) $6,000
Step-by-step explanation:
(a) The promoter's expected profit is given by the product of his potential earnings by the probability that it does not rain, minus the product of his potential losses by the probability of rain:
The promoter's expected profit is $12,000, it is a reasonable criterion since profit is positive.
(b) An insurance company should charge the product of the full potential losses by the probability of rain:
An insurance company should charge $6,000.
