1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ehidna [41]
3 years ago
7

These are the cost and revenue functions for a line of trumpets sold at a music store:

Mathematics
1 answer:
Maslowich3 years ago
4 0

Answer:

168 trumpets for $1702

Step-by-step explanation:

Profit is the measure to be maximized.  We are given revenue and cost relationships as a function of units, x (trumpets).  Profit is the difference:

Profit = Revenue[R(x)] - Cost[C(x)]

Profit = (76x – 0.25x^2) - (-7.75x + 5,312.5)

Profit = 76x - 0.25x^2 + 7.75x - 5,312.5

Profit = 76x - 0.25x^2 + 7.75x - 5,312.5

Profit = - 0.25x^2 + 83.75x - 5312.5

At this point we can find the trumpets needed for maximum profit by either of two approaches:  algebraic and graphing.  I'll do both.

<u>Mathematically</u>

The first derivative will give us the slope of this function for any value of x.  The maximum will have a slope of zero (the curve changes direction at that point).  Take the first derivative and set that equal to 0 and solve for x.

First derivative:

d(Profit)/dx = - 2(0.25x) + 83.75

d(Profit)/dx = - 0.50x + 83.75

0 = - 0.50x + 83.75

0.50x = 83.75

x = 167.5 trumpets

<u>Graphically</u>

Plot the profit function and look for the maximum.  The graph is attached.  The maximum is 167.5 trumpets.

Round up or down to get a whole trumpet.  I'll go up:  168 trumpets.

<u>Maximum Profit</u>

Solve the profit equation for 168 trumpets:

Profit = - 0.25x^2 + 83.75x - 5312.5

Profit = - 0.25(168)^2 + 83.75(168) - 5312.5

<u>Profit = $1702</u>

You might be interested in
Find the measure of angle C of a triangle ABC, if: d m∠A = 60°+α, m∠B = 60°−α
sukhopar [10]

Answer:

C abc dm<a=60> o+a ,m(b=60o'a is equal to 150

7 0
3 years ago
Read 2 more answers
How to know if a problem is permutation or combination?
vredina [299]
If the order matters it is a permutation. For example: if you are selecting 3 people to be on a committee it doesn't matter what order you select them, but if you're selecting three people to be president, vice president, and secretary the order in which you choose them matters the first person being president, the second person being vice president, and the third person be secretary
6 0
3 years ago
Several years ago, the mean height of women 20 years of age or older was 63.7 inches. Suppose that a random sample of 45 women w
VikaD [51]

Since the p - value is less than significance level . So, we will accept the null hypothesis.

​(a) State the appropriate null and alternative hypotheses to assess whether women are taller today.

Definition of null hypothesis : The null hypothesis attempts to show that no variation exists between variables or that a single variable is no different than its mean. it is denoted

Alternative Hypothesis : In statistical hypothesis testing, the alternative hypothesis is a position that states something is happening, a new theory is true instead of an old one (null hypothesis).

We are given that The mean height of women 20 years of age or older was 63.7 inches.

So, null hypothesis :  H₀ : μ = 63.7

Alternative Hypothesis :  H₁ : μ > 63.7

b)The​ P-value for this test is 0.06.

The p-value represents the probability of getting a sample mean height of 20 years old women is  64.1 inches.

c) Write a conclusion for this hypothesis test assuming an alpha equals 0.10 level of significance.

p- value = 0.06

Since the p - value is less .

So, we will accept the null hypothesis

So,  

Hence The mean height is 63.7 inches

To learn more about hypothesis testing from the given link

brainly.com/question/12976831

#SPJ4

7 0
1 year ago
Which demical is less than 8.0
pochemuha

Answer:

any decimal under 8...

you can write it as:   x<8

x is less than 8

or your number is less than 8

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Can’t figure out how to figure out the diameter from the area..... Btw look at the image
julia-pushkina [17]

Answer:

2.26 in

Step-by-step explanation:

Given:  the area of the slice is 4 in^2.

The formula for the area of a circle is A = (pi)(r)^2, where r is the radius.

Therefore,

A = 4 in^2 = (pi)(r^2), or

   

         4 in^2

r^2 = ------------ = 1.273

             pi

Since the area of the slice is A = (pi)(r^2), and since (d/2)^2 = r^2 = d^2/4

A =  (4 in^2) = (pi)(d^2 / 4)

Solving for d^2, we divide both sides by pi/4, obtaining:

4 in^2

---------- = d^2  = 5.093 in^2

 pi/4

and so d = √5.093 = 2.26 in (to the nearest 100th)

7 0
3 years ago
Other questions:
  • in one baseball season, peter hit twice the difference of the number of home runs alice hit and 6. altogether, they hit 18 home
    10·1 answer
  • Help me or I’ll fail my math grade
    9·1 answer
  • Write the expression in terms of sine only sin 9x cos 9x
    5·1 answer
  • the populatipn of a school of fish increases at a rate of 18% a Month. There are currently 500 fish in the school.
    15·1 answer
  • What is six times six?​
    12·2 answers
  • Click on the picture thanks so much
    10·1 answer
  • 45/19 as a decimal rounded to the nearest tenth
    10·2 answers
  • Rose is fishing from a small boat. A fish swimming at the same depth as the hook at the end of her fishing line is 8 meters away
    6·1 answer
  • Can somebody help me out ?? please ..
    5·1 answer
  • In which step did John first make a mistake?<br> look at photos
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!