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Mathematics High School

The number of product units q assembled during one shift is a function of the number of employees, n. Suppose that this function is q=f(n)=60n−n3. The company profit p is a function of q, namely p=g(q)=43q−10000. Express the profit as a function of the number of employees n:

2 months ago

Solution 1

Guest #2391166

2 months ago

Answer:

2580n -43n^3 - 10000

Step-by-step explanation:

From the question:

q= assembled product

n = Number of employees

q(f) = 60n - n^3

p=g(q)= 43q - 10000

P(q)= 43(60n - n^3) - 10000

P(q) = 2580n - 43n^3 - 10000

📚 Related Questions

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Gym A charges a new member fee of $65 and $20 per month Gym B charges a new member fee of $25 and $35 per month but you get a discount of 20% monthly

Solution 1

Answer: it will take 5 months for both gyms to cost the same.

Step-by-step explanation:

Let x represent the number of months for which the total cost of gyms are the same.

Gym A charges a new member fee of $65 and $20 per month. This means that the cost of using gym A for x months would be

20x + 65

Gym B charges a new member fee of $25 and $35 per month but you get a discount of 20% monthly.

20% of 35 is 20/100 × 35 = 7

The monthly charge would be

35 - 7 = 28

This means that the cost of using gym A for x months would be

28x + 25

The number of months that it will take for the cost of both gyms to be the same would be

20x + 65 = 28x + 25

28x - 20x = 65 - 25

8x = 40

x = 40/8 = 5

Question

Greatest common factor of 6xy^2 and 8

Solution 1

Answer:

Step-by-step explanation:

6xy² = 1,2,3,6 ,x, y

8= 1,2,4,8

common factor =1.2

greatesst common factor = 2

Question

What is minus 7 minus minus 9

Solution 1

Answer:

Step-by-step explanation:the answer is 2

Solution 2

-7 - - 9.

- - = +

-7 - (-9)

-7 + 9

+9 - 7

9 - 7

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Question

(a) calculate the value of the correlation coefficient between sale price and size. (give the answer to three decimal places.) r = .701 correct: your answer is correct. (b) calculate the value of the correlation coefficient between sale price and land-to-building ratio. (give the answer to three decimal places.) r = -.3462 incorrect: your answer is incorrect. (c) if you wanted to predict sale price and you could use either size or land-to-building ratio as the basis for making predictions, which would you use?

Solution 1

Answer:

.701

Step-by-step explanation:

The reason for the option chosen is because the coefficient is closer to 1 which is the standard for correlation and also, the answer is rounded off to three decimal places as requested in the question.

Question

1 2 3 4 5 6 7 8 9 10 Time Remaining 59:45 Which statement best describes the use of a simulation to predict the probability that two randomly chosen people will both have their birthdays on a Monday? Randomly generate an integer from 1 to 2 seven times, and the probability is . Randomly generate an integer from 1 to 2 seven times, and the probability is . Randomly generate an integer from 1 to 7 two times, and the probability is . Randomly generate an integer from 1 to 7 two times, and the probability is . Mark this and return Save and Exit Next Submit

Solution 1

Answer:

Option D is correct.

That is,

Randomly generate an integer from 1 to 7 two times, and the probability is (1/7) ^2

Step-by-step explanation:

The probability of having birthday on a particular day of a week for anyone is 1/7. That is, 1 day out of the 7 days in a week.

Then for another person to have birthday on that same day is mathematically given as

(1/7) × (1/7) = (1/7)²

And this corresponds to option D. Therefore option D is the statement that best describes the use of a simulation to predict the probability that two randomly chosen people will both have their birthdays on a Monday.

Hope this helps!

Question

If there were 5 million births in a particular country and 3 comma 375 sets of naturally occurring triplets, what is the experimental probability of having triplets naturally?

Solution 1

Answer:

$Probablity =P=6.75*10^-^4$

Step-by-step explanation:

The experimental probability can be defined as the ratio of the number of times any particular event has occurred to the total number of times that event has taken place.

Experimental probability = P = No. of event occurrences / total number of occurrences.

In our question statement,

No of naturally occurring triplets are = 3375

Total number of births = 5 million = 5,000,000

Putting values in equation.

$P=3375/5000000$

$P = 0.000675\\P=6.75*10^-^4$

Solution 2

Answer: 6.75

Step-by-step explanation:

You just divide by 3,375/500,000 and get 6,75

Question

Three distinct integers are chosen at random from the first 20 positive integers. Compute the probability that: (a) their sum is even; (b) their product is even.

Solution 1

Answer:

Step-by-step explanation:

There are first 20 positive integers 1,2...20. Three distinct integers are chosen at random.

Total no of ways of drawing 3 integers = $20C3 = 1140$

To Compute the probability that: (a) their sum is even

a) Sum can be even if either all 3 are even or 1 is even and 2 are odd.

There are in total 10 odd and 10 even.

Ways of sum even = $10C3 + 10C2 (10C1)\\= 120+45(10)\\= 570$

Prob = $\frac{570}{1140} =0.50$

b) their product is even

Here any one should be even or both

SO no of ways are

= $10C2 +10C2(10C1)\\= 45 +450\\=495$

Prob = $\frac{495}{1140} =0.4342$

Question

Given a data set, how do you know whether to calculate sigma or s? Choose the correct answer below. A. If the given data set contains a large number of entries, then s is calculated. If the data set contains a small number of entries, then sigma is calculated. B. When given a data set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a population, then sigma is calculated. If the data are a sample, then s is calculated. C. When given a data set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a population, then s is calculated. If the data are a sample, then sigma is calculated. D. If the given data set contains a large number of entries, then sigma is calculated. If the data set contains a small number of entries, then s is calculated.

Solution 1

Answer:

Step-by-step explanation:

S is the sample standard deviation, it is calculated when the observations represent a sample of the population. sigma is the population standard deviation, it is calculated when de observations are the whole population.

Question

Which of the following variables are qualitative and which are quantitative? If the variable is quantitative, then specify whether the variable is discrete or continuous. a. Points scored in a football game. Qualitative Quantitative; discrete Quantitative; continuous b. Racial composition of a high school classroom. Qualitative Quantitative; discrete Quantitative; continuous c. Heights of 15-year-olds. Qualitative Quantitative; discrete Quantitative; continuous

Solution 1

Answer:

a) Quantitative; discrete

b) Qualitative

c) Quantitative; continuous

Step-by-step explanation:

Quantitative and Qualitative:

Qualitative variables are the non-parametric variables.
Quantitative variables are the variables whose values are expressed in the form of number.
Qualitative is information about a variable where as quantitative describes the variable with the help of values.

Discrete and Continuous:

Quantitative variables whose values are expressed in the form of whole numbers are discrete variable.
Discrete variable cannot take all the values of an interval. They are counted not measured.
Quantitative variable whose values can be expressed in the form of decimals are continuous variable.
Continuous variable take all the values within interval. They are measured not counted.

a. Points scored in a football game.

Since the points are expressed in numerical. Thus, they are quantitative variable. Since points are always expressed in whole numbers and are always counted it is a discrete variable.

b. Racial composition of a high school classroom

This will include the categorical values and not expressed as numerical. Thus, it is qualitative variable.

c. Heights of 15-year-olds.

These values will be expressed with the help of numerical and can take any value within an interval. Also, height is always measured and not counted. Thus it is a continuous variable.

Question

the sales tax in bills state is 6% bill bought a scion on having a sales tax of $820 what was the cost of the car round to the nearest dollar

Solution 1

Tax paid = $820

Let the value = x.

Tax = 6%

6% of x = 820

(6/100)x = 820

0.06x = 820

x = 820/0.06

x ≈ `13666.67

Cost ≈ $13 666.67

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