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
Marrrta [24]
3 years ago
13

The relationship between the selling price of an item and the cost of an item has been determined to be q=-20s+400 has been dete

rmined by a marketing firm, where q is the quantity sold in a year and s is the selling price. If the cost to produce the item is $12, what is the selling price that optimizes the year yearly profit?
Mathematics
1 answer:
MrMuchimi3 years ago
7 0
We are given with the variable cost which is:
q = -20s + 400

The selling price is 's'. So, the profit can be represented by:
P = qs - q(12)

Subsituting:
P = (-20s + 400)s - 12 (-20s + 400)
P = -20s^2 + 640s - 4800

To optimize this, we must differentiate the equation and equate it to zero, so:\
dP/ds = -40s + 640 = 0
Solving for s,
s = 16

So, the selling price should be $16 to optimize the yearly profit.
You might be interested in
1. Which of the following is NOT a true statement?
Andreas93 [3]

Answer:B

Step-by-step explanation: not cause you have trapeziums not c cause you have squares not d cause it just aint

4 0
3 years ago
Read 2 more answers
It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minute
NemiM [27]

Answer:

a) 10.93% probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 420 minutes.

b) 99.22% probability that the mean number of minutes of daily activity of the 5 lean people exceeds 420 minutes.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mildly obese

Normally distributed with mean 373 minutes and standard deviation 67 minutes. So \mu = 373, \sigma = 67

A) What is the probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 420 minutes?

So n = 5, s = \frac{67}{\sqrt{5}} = 29.96

This probability is 1 subtracted by the pvalue of Z when X = 410.

Z = \frac{X - \mu}{s}

Z = \frac{410 - 373}{29.96}

Z = 1.23

Z = 1.23 has a pvalue of 0.8907.

So there is a 1-0.8907 = 0.1093 = 10.93% probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 420 minutes.

Lean

Normally distributed with mean 526 minutes and standard deviation 107 minutes. So \mu = 526, \sigma = 107

B) What is the probability that the mean number of minutes of daily activity of the 5 lean people exceeds 420 minutes?

So n = 5, s = \frac{107}{\sqrt{5}} = 47.86

This probability is 1 subtracted by the pvalue of Z when X = 410.

Z = \frac{X - \mu}{s}

Z = \frac{410 - 526}{47.86}

Z = -2.42

Z = -2.42 has a pvalue of 0.0078.

So there is a 1-0.0078 = 0.9922 = 99.22% probability that the mean number of minutes of daily activity of the 5 lean people exceeds 420 minutes.

7 0
3 years ago
Over winter break, Raymond worked 12.5 hours at the library and 20.5 hours at a café. The library paid him $13 per hour. If he e
svet-max [94.6K]

Answer:

14.5

Step-by-step explanation:

the cafe paid him 14.5 an hr

6 0
3 years ago
Pls help I’ll brainlest
lora16 [44]

Answer:

8

Step-by-step explanation:

Jeremiah bought x toy sets for $20 each and then a video game for $60. Jeremiah spent a total of $220. How may toy sets did he buy?

To find our answer, we can solve the equation:

20x + 60 = 220

        -60    -60

20x = 160

/20    /20

x = 8

Jeremiah bought 8 toy sets!

I hope this helps :)

5 0
3 years ago
For the function y = f(x) = 3x -5<br> What is the y intersection
Jobisdone [24]

Answer:

The y-intercept is -5.

Step-by-step explanation:

In algebra, "y=" and "f(x)=" is basically the same thing. You don't have to write them both. Also, y=3x-5 is in slope-intercept form, which is: y=mx+b, where b is the y-intercept. That means "-5" is the y-intercept.

8 0
3 years ago
Other questions:
  • Larissa asked 40 students to name their favorite food. 10 students said their favorite food was pizza. What percent of the stude
    8·2 answers
  • How old am i if 500 reduced by 4 times my age is 184
    9·1 answer
  • Aubrey's dinner costed $85 she tips the waiter 30% how much did Aubrey tip for the waiter
    7·2 answers
  • Jack swam 8 taps. He swam 6 fewer laps than Lea.<br> How many laps did Lea swim?<br> pls quick
    5·1 answer
  • Find the coordinate of G' after a 90° counterclockwise rotation of the triangle about the origin.
    11·1 answer
  • Graph A
    9·1 answer
  • Help, ive been stuck on this for 2 hours
    13·1 answer
  • Which graph is likely to have a leading coefficient value of -1/8
    7·2 answers
  • Maddie'is working problems on her 250 problem test. She can work them
    8·1 answer
  • Three friends in Seattle each told you it’s rainy, and each person has a 1/3 probability of lying. What is the probability that
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!