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BlackZzzverrR [31]
3 years ago
6

Consider y=(x+3)^2-1

Mathematics
1 answer:
Rom4ik [11]3 years ago
7 0
The coefficient of x^2 is positive so it will have a minimum value

Its B
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6.7.37
posledela

Answer:

a. The start-up cost for the teenagers company is $50

b. The number of mugs the teenager must sell to break even are 5 mugs or 25 mugs

c. The number of mugs that will give maximum profit is 15 mugs

d. The profit if she sells 10 mugs is $30

Step-by-step explanation:

The given profit function for selling <em>x</em> number of mugs is presented as follows;

f(x) = -0.4·x² + 12·x - 50

a. The start-up cost in dollars is given by the value of the profit function at the start, where, x = 0, as follows;

Start-up cost = f(0) = -0.4×0² + 12×0 - 50 = -50

The negative sign represents amount put in the business

The start-up cost = (The initial) $50 put into the business.

b. The break even point is the point where, the revenue and costs are equal

At break even point; Revenue = Cost

∴ Profit, at break even point, f(x) = Revenue - Cost = 0

From the profit function, we get;

At the break even point, f(x) = 0 = -0.4·x² + 12·x - 50

Dividing by -0.4 gives;

0/(-0.4) = 0 = (-0.4·x² + 12·x - 50)/(-0.4) = x² - 30 + 125

0 = x² - 30 + 125

∴ (x - 25)·(x - 5) = 0

The number of mugs the teenager must sell before she breaks even, x = 5 mugs or x = 25 mugs.

c. From the general form of a quadratic equation,  which is; y = a··x² + b·x + c, the formula for the x-values at the maximum point is; x = -b/(2·a)

Comparing the profit function to the general form of the quadratic equation we have at the maximum point;

x = -12/(2×(-0.4)) = 15

Therefore, the number of mugs that will give maximum profit, x = 15 mugs.

d. The profit from selling 10 mugs, f(10) is given as follows;

f(10) = -0.4 × 10² + 12 × 10 - 50 = 30

The profit from selling 10 mugs, f(10) = $30

4 0
2 years ago
Is one side of a rectangular fish tank best represented by a point, line, plane, or ray?
Inessa05 [86]
<span>One side of a rectangular fish tank can be best represented by a plane because it is two dimensional.Whereas,point,line or a ray are all one dimensional and hence they cannot represent a rectangle as it has two dimensions.</span>
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3 years ago
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What is 71/5 written as a percent
ratelena [41]
Percent (%) = per 100

7 1/5 = 36/5 = 720/100 = 720%
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3 years ago
Find a constant c for which p(z ≥ c.= 0.1587. round the answer to two decimal places.
Vikki [24]
What you see in the z score table is P(z< a constant), for P( z≥ a number), subtract the probability from 1:
1-0.1587=0.8413
on the z score table, you will see that p(z<1.00)=0.8413
so c=1.00
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3 years ago
Jaron paid $2.70 for 6 juice boxes.How much should Jaron expect to pay for 18 juice boxes and how would I show work
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2.7/6=x/18
2.7 x 18 = 6x
48.6 = 6x
8.1= x

Jaron paid $8.10
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