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pishuonlain [190]
3 years ago
9

Compare [3] and [ – 8|

Mathematics
1 answer:
mariarad [96]3 years ago
7 0

Answer:

3 > -8

Step-by-step explanation:

-8 -7 -6 -5 -4 -3 -2 -1 <u>0</u> 1 2 3 ....

-8< 3

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Keegan is priting and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total p
Damm [24]

Complete question is;

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

Answer:

Number of t-shirts to make maximum profit = 2790 shirts

Maximum profit = $12,209

Step-by-step explanation:

From the question, we are given that the profit function is;

p(x) = -x³ + 4x² + x

For the maximum value of the profit function,

(dp/dx) = 0 and (d²p/dx²) < 0

Since, p(x) = -x³ + 4x² + x

Then,

(dp/dx) = -3x² + 8x + 1

at maximum point (dp/dx) = 0, thus;

-3x² + 8x + 1 = 0

Solving this using quadratic formula, the roots are;

x = -0.12 or 2.79

Also, (d²p/dx²) = -6x + 8

Now, let's put the roots of x into -6x + 8 and check for maximum value conditon;

at x = -0.12

(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0

At x = 2.79

(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0

Maximum has to be d²p/dx² < 0

So, the one that meets the condition is -8.74 < 0 at x = 2.79

Thus, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousands) = 2790

Now, the maximum profits that corresponds to this number of t-shirts of 2.79(in thousands) is obtained by putting 2.79 for x in the profit function;

So,

p(2.79) = -(2.79)³ + 4(2.79²) + 2.79

p(x) = -21.7176 + 31.1364 + 2.79

p(x) = 12.2088 (in thousand dollars) ≈ $12,209

6 0
3 years ago
One student can paint a wall in 20 minutes. Another student can paint the same wall in 30 minutes. Working together, how long wi
Katarina [22]

1) in one minute for first  wiil be 1/20

the other 1/30, it means that  A paint in one minute  1/20 and B 1/30 then   A+B in one minute 1/20 + 1/30 = 3+2/60 = 5 / 60,  5/60 = 1/12

if in one min they make 1/12 then  in 12  min they  paint all the wall

5 0
3 years ago
When is 20% off better than 20$ off
Crazy boy [7]

Answer:

Price > 100$

Price > 150$

Step-by-step explanation:

Let us assume that x% off of price y$  is better than x$ off.

Hence, \frac{xy}{1000} > x  

Hence, y > 100

Therefore, when the price is more than 100$, then only x% off on the price is better than x$. (Answer)

Again, assume that 20% off on price y$ is better than 30$ off.

Hence, \frac{20y}{100} > 30

⇒ y > 150$

Therefore, when the price is more than 150$, then only 20% of on the price is better than 30$ off. (Answer)

7 0
3 years ago
Write (5.64) x 10-7 as a decimal.
Cloud [144]

Answer:

16.92

Step-by-step explanation:

5.64 x 3 = 16.92

<em>Hope that helps!</em>

3 0
3 years ago
Alex mows a lawn that measures 800 square feet in
Darina [25.2K]

First thing we gotta do is find the unit rate:

800 divided by 2.5 = 320

And now your problem is complete! The unit rate or square foot per hour is 320 square feet per hour!

Hope this helps, if not, comment below please!!!

5 0
3 years ago
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