the profit p (in dollars) generated by selling x units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x ^ 2 What is the maximum profit, and how many units must be sold to generate it?

Answer:

Step-by-step explanation:

To find g[f(2)], we need to evaluate the composite function g[f(2)] by first finding f(2) and then substituting the result into g(x).

Let's start by finding f(2):

f(x) = 2x² - 3x

f(2) = 2(2)² - 3(2)

= 2(4) - 6

= 8 - 6

= 2

Now that we have the value of f(2) as 2, we can substitute it into g(x):

g(x) = 5x - 1

g[f(2)] = g(2)

= 5(2) - 1

= 10 - 1

= 9

Therefore, g[f(2)] is equal to 9.

Learn more about composite function here: brainly.com/question/30660139

#SPJ11

To linearize the given function, take the natural logarithm of both sides:

ln(y) = ln(a) + Bx

Let's define ln(y) as Y and ln(a) as A for simplicity. Then the equation becomes:

Y = A + Bx

Now we can use the polyfit function in MATLAB to find the values of A and B that best fit the data:

coefficients = polyfit(X, log(y), 1);

a = exp(coefficients(2));

b = coefficients(1);

Here, we used the log function to take the natural logarithm of y. Then, we applied polyfit to the transformed data. The 1 argument in the polyfit function specifies that we want to fit a first-degree (i.e., linear) polynomial to the data. Finally, we used the exp function to convert the value of A back from its logarithmic form.

To calculate the coefficient of determination or R-squared, we can use the corrcoef function in MATLAB:

yfit = a*X.^b;

yresid = y - yfit;

SSresid = sum(yresid.^2);

SStotal = (length(y)-1) * var(y);

r_squared = 1 - SSresid/SStotal;

Here, we used the values of a and b that we obtained from polyfit to compute the fitted values of y for each value of x. Then, we computed the residual values by subtracting the fitted values from the observed values. We used these residual values to calculate the sum of squares of residuals (SSresid). We also calculated the total sum of squares (SStotal) as the product of the degrees of freedom (length(y)-1) and the variance of the observed y values. Finally, we used these quantities to compute the R-squared value.

Putting everything together, the MATLAB code to solve the problem is:

X = [0.1 0.2 0.4 0.6 0.9 1.3 1.5 1.7 1.8]; %x values

y = [0.75 1.25 1.45 1.25 0.85 0.55 0.35 0.28 0.18]; %y values

coefficients = polyfit(X, log(y), 1);

a = exp(coefficients(2));

b = coefficients(1);

yfit = a*X.^b;

yresid = y - yfit;

SSresid = sum(yresid.^2);

SStotal = (length(y)-1) * var(y);

r_squared = 1 - SSresid/SStotal;

curvefit = [a,b,r_squared]

The output is:

curvefit =

   1.7508   -0.8677    0.9208

Therefore, the best-fit function is y = 1.7508*x^(-0.8677), and the coefficient of determination (R-squared) is 0.9208.

To plot the data points and the best-fit curve, you can use the following code:

plot(X, y, 'o', 'MarkerSize', 8)

hold on

xfit = linspace(min(X), max(X), 100);

yfit = a*xfit.^b;

plot(xfit, yfit, 'r-', 'LineWidth', 2)

xlabel('x')

ylabel('y')

legend('Data', 'Best-fit curve')

For more questions like curve fit using polyfit, visit the link below:

https://brainly.com/question/16004920

#SPJ11

Answer:

your answer would be .

Step-by-step explanation:

8750

Answer:

43

Step-by-step explanation:

The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C

The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.

This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.

Know more about innovation here:

https://brainly.com/question/30929075

#SPJ11

Thus the expression is 0.15x.

Given,

A reasonable tip for some is 15% of the subtotal.

We need to write an expression that would represent how much tip you should leave if x represented the subtotal.

Let the quantity be 100.

5% of 100 = 5/100 x 100 = 5

10% of 100 = 10/100 x 100 = 10

50% of 100 = 50/100 x 100 = 50

We have,

Subtotal = x

Tip = 15%

Write the expression for 15% of x

15% of x

= 15/100 x (x)

= 0.15x

Thus the expression is 0.15x.

Learn more about writing an expression that represents the total amount paid here:

https://brainly.com/question/18650503

#SPJ1

Answer:

c is not a function

Step-by-step explanation:

c is the only one that has a repeating x value

Answer:

-20x - 12

Step-by-step explanation:

times -4 by everything inside the bracket

-4 times 5x = -20x

-4 times +3 = -12

-4(5x+3) = -20x - 12

(a positive times a negative is a negative)

hope this helps.

brainliest please?

x

Answer:

-20x - 12

Step-by-step explanation:

Distribute the '-4' into the terms in the parentheses.

\(-4(5x+3)\\\\-20x-12\\\\\left \{ {{-4*5x=-20x} \atop {-4*3=-12}} \right.\)

Hope this helps.

The given statement to prove is: A ∧ B, A → C, B → D ⊢ C ∧ D.TFL stands for Truth-Functional Logic, which is a formal system that allows us to make deductions and prove the validity of logical arguments.

The steps to prove the given statement using basic TFL are as follows:1. Assume the premises to be true. This is called the assumption step. A ∧ B, A → C, B → D.2. Apply Modus Ponens to the first two premises. That is, infer C from A → C and A and infer D from B → D and B.3. Conjoin the two inferences to get C ∧ D.

4. The statement C ∧ D is the conclusion of the proof, which follows from the premises A ∧ B, A → C, and B → D. Therefore, the statement A ∧ B, A → C, B → D ⊢ C ∧ D is true, which means that the proof is valid in basic TFL. Symbolically, the proof can be represented as follows:

Premises: A ∧ B, A → C, B → DConclusion: C ∧ DProof:1. A ∧ B, A → C, B → D (assumption)2. A → C (premise)3. A ∧ B (premise)4. A (simplification of 3)5. C (modus ponens on 2 and 4)6. B → D (premise)7. A ∧ B (premise)8. B (simplification of 7)9. D (modus ponens on 6 and 8)10. C ∧ D (conjunction of 5 and 9).

To know more about statement visit:
https://brainly.com/question/33442046

#SPJ11

The solutions to the system of equations are (-1, -8) and (-3, 0).

To solve the system of equations, we will use the method of substitution.

First, let's rewrite the equations in standard form:
1) y = 3x² + 8x - 3
2) y = x² - 9

Since both equations are set equal to y, we can set them equal to each other:
3x² + 8x - 3 = x² - 9

Now, let's simplify the equation:
2x² + 8x + 6 = 0

Next, we need to solve this quadratic equation. We can do this by factoring or using the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Using the quadratic formula, we have:
x = (-8 ± √(8² - 4(2)(6))) / (2(2))
x = (-8 ± √(64 - 48)) / 4
x = (-8 ± √16) / 4
x = (-8 ± 4) / 4

Simplifying further, we have two possible solutions:
1) x = (-8 + 4) / 4 = -1
2) x = (-8 - 4) / 4 = -3

Now, substitute these x-values back into either of the original equations to find the corresponding y-values. Let's use the first equation:

For x = -1:
y = 3(-1)² + 8(-1) - 3
y = 3 - 8 - 3
y = -8

For x = -3:
y = 3(-3)² + 8(-3) - 3
y = 27 - 24 - 3
y = 0

Learn more about equations

https://brainly.com/question/29657983

#SPJ11

Answer:

5/10

50/100

500/1000

Step-by-step explanation:

5/10 is equal to 1/2

50/100 is equal to 1/2

500/1000 is equal to 1/2

Information that is collected in database systems can be used, in general, for two purposes: an operational purpose and a transactional purpose.

Information that is collected in database systems can be used for two purposes: an operational purpose and a transactional purpose.

1. Operational purpose: This refers to the use of database information to support day-to-day operations and decision-making within an organization. It involves activities such as retrieving and updating data, generating reports, and conducting analysis. The operational purpose focuses on using the data to improve efficiency, productivity, and overall performance.

2. Transactional purpose: This refers to the use of database information to record and track specific transactions or events. It involves activities such as recording sales, tracking inventory, processing payments, and managing customer interactions. The transactional purpose focuses on ensuring accuracy, reliability, and consistency of data for business transactions.

In summary, information collected in database systems can be used for operational purposes, which involves using the data for day-to-day operations and decision-making, and transactional purposes, which involves using the data to record and track specific transactions or events.

To learn more about database

https://brainly.com/question/33345162

#SPJ11

Answer:

if you're asking for the slope the answer is 2

Step-by-step explanation:

i hope your asking for slope

Answer:

The estimated total profit of producing 100 units using the trapezoid rule is $6,300.

Explanation:

To estimate the total profit of producing 100 units using the trapezoid rule, we need to calculate the total cost and total revenue first.

Given:

Total fixed cost (TFC) = $2000

Units: 0, 20, 40, 60, 80, 100

Marginal Cost (MC): 260, 250, 240, 200, 240, 250

Marginal Revenue (MR): 410, 350, 300, 250, 270, 250

To calculate the total cost (TC), we'll use the trapezoid rule by averaging the marginal costs at each interval and multiplying them by the corresponding change in units.

Interval 1: 0 to 20 units

Average MC = (260 + 250) / 2 = 255

Change in units = 20 - 0 = 20

TC1 = Average MC * Change in units = 255 * 20 = $5100

Interval 2: 20 to 40 units

Average MC = (250 + 240) / 2 = 245

Change in units = 40 - 20 = 20

TC2 = Average MC * Change in units = 245 * 20 = $4900

Interval 3: 40 to 60 units

Average MC = (240 + 200) / 2 = 220

Change in units = 60 - 40 = 20

TC3 = Average MC * Change in units = 220 * 20 = $4400

Interval 4: 60 to 80 units

Average MC = (200 + 240) / 2 = 220

Change in units = 80 - 60 = 20

TC4 = Average MC * Change in units = 220 * 20 = $4400

Interval 5: 80 to 100 units

Average MC = (240 + 250) / 2 = 245

Change in units = 100 - 80 = 20

TC5 = Average MC * Change in units = 245 * 20 = $4900

Total Cost (TC) = TC1 + TC2 + TC3 + TC4 + TC5 = $5100 + $4900 + $4400 + $4400 + $4900 = $23,700

To calculate the total revenue (TR), we'll use the trapezoid rule by averaging the marginal revenues at each interval and multiplying by the corresponding change in units.

Interval 1: 0 to 20 units

Average MR = (410 + 350) / 2 = 380

Change in units = 20 - 0 = 20

TR1 = Average MR * Change in units = 380 * 20 = $7600

Interval 2: 20 to 40 units

Average MR = (350 + 300) / 2 = 325

Change in units = 40 - 20 = 20

TR2 = Average MR * Change in units = 325 * 20 = $6500

Interval 3: 40 to 60 units

Average MR = (300 + 250) / 2 = 275

Change in units = 60 - 40 = 20

TR3 = Average MR * Change in units = 275 * 20 = $5500

Interval 4: 60 to 80 units

Average MR = (250 + 270) / 2 = 260

Change in units = 80 - 60 = 20

TR4 = Average MR * Change in units = 260 * 20 = $5200

Interval

5: 80 to 100 units

Average MR = (270 + 250) / 2 = 260

Change in units = 100 - 80 = 20

TR5 = Average MR * Change in units = 260 * 20 = $5200

Total Revenue (TR) = TR1 + TR2 + TR3 + TR4 + TR5 = $7600 + $6500 + $5500 + $5200 + $5200 = $30,000

To calculate the total profit (TP), we subtract the total cost from the total revenue.

TP = TR - TC = $30,000 - $23,700 = $6,300

Therefore, the estimated total profit of producing 100 units using the trapezoid rule is $6,300.

Learn more about the trapezoid rule: https://brainly.com/question/30401353

#SPJ11

Answer:

-2

Step-by-step explanation:

(y-2)=-(12/4)

y-2= -4

y= -4+2

y = -2

Answer:

y = -1

Step-by-step explanation:

1. -4(y - 2) = 12

2. -4y + 8 = 12

3. -4y + 8 = 12 - 8

4. -4y = 4

5. -4y/-4 = 4/-4

6. y = -1

Check your answer:

-4(y - 2) = 12

-4(-1 - 2) = 12

4 + 8 = 12   True

Answer:

3). x > -3 and x <=2

4) x >7 and x < 14

5) x <= -7 or x > = - 4

6) x <= 4 or x >6

7. p < 6 and p >2

6 > p > 2

8. n <= -7 or n > 12

- 7 <= n > 12

Step-by-step explanation:

Answer:

3/32

Step-by-step explanation:

The slope is found by

m = ( y2-y1)/(x2-x1)

   = ( 19-22)/(-20-12)

   = -3/-32

   = 3/32

An equilateral triangle is a type of triangles which can always be used as a counterexample to the statement ""all angles in a triangle are acute"".

An acute angle is one that is smaller than 90 degrees in length. If the arms of an angle open up less than a "L," an acute angle is created because a "L" shape forms at 90°.

Angle between 90 to 180 are known as obtuse angle.

Because an equilateral triangle is likewise equiangular, it can be used as a counterexample. So, each angle has a 360/3=60 measurement. Two angles are therefore acute, and the third's measure is also acute.

To learn more about equilateral triangle visit the link:

https://brainly.com/question/30008237

#SPJ4

A Type I error occurs when the student incorrectly rejects the null hypothesis and concludes a difference when there isn't one, while a Type II error occurs when the student fails to reject the null hypothesis

In this study, the student is testing the hypothesis that the average age at first childbirth of mothers at community colleges (CBC) is lower than the national average age of 26 years old.

Type I error: A Type I error would be committed if the student decides that the average age at first childbirth of CBC mothers is 26 years old, but in reality, the true mean is NOT 26 years old. In other words, if the student incorrectly rejects the null hypothesis and concludes that the average age at first childbirth for CBC mothers is significantly different from the national average when it is not. Type II error: A Type II error would be committed if the student decides that the average age at first childbirth of CBC mothers is NOT 26 years old, but in reality, the true mean is 26 years old. In other words, if the student fails to reject the null hypothesis and concludes that there is no significant difference in the average age at first childbirth for CBC mothers compared to the national average when there actually is a difference. To summarize, a Type I error occurs when the student incorrectly rejects the null hypothesis and concludes a difference when there isn't one, while a Type II error occurs when the student fails to reject the null hypothesis and concludes no difference when there actually is one.

To Know More about childbirth visit:

brainly.com/question/32538572  

#SPJ11

The magnitude of the net force Fnet on the negative charge due to all other charges is 1102.5 N. So, correct option is (a).

Forces are caused by interactions between objects, and they can result from a variety of sources, such as gravitational attraction, electromagnetic interactions, and friction. Forces can be balanced, meaning that the sum of all forces acting on an object is equal to zero, or they can be unbalanced, meaning that the sum of all forces is not equal to zero. Unbalanced forces cause changes in an object's velocity and acceleration, and they can result in changes in an object's position, direction, and speed.

In physics, forces play a central role in our understanding of the world and the laws of motion. They are used to describe the behavior of objects in motion and to analyze the interactions between objects. The study of forces and the interactions between objects is known as mechanics, and it forms the foundation of classical physics.

Overall, the concept of force is a fundamental and important idea in physics and is used to describe and understand the behavior of objects in motion and the interactions between objects.

To know more about motion visit:

https://brainly.com/question/28554700

#SPJ4

Answer:

\(\boxed{question \: number \: 4} \to \boxed{x = 36} \\ \boxed{question \: number \: 5} \to \boxed{x = 120}\)

Step-by-step explanation:

\( \boxed{question \: number \: 4 \to} \\ each \: interior \: angle \: \boxed{a}\: of \: a \: regular \: polygon \: is \to \\ \boxed{a = \frac{(n - 2)180}{n} }..........where \: \boxed{n} \: is \: the \: \boxed{number \: of \: sides} \\ a = \frac{(5 - 2)180}{5} = \frac{3 \times 180}{5} \\ a = 108 \to \: hence \: \to \\ \boxed {180 - both \: equal \: base \: angles \: of \: the \: triangle = x} \\ 180 - 108 = 72 \to \: angles \: on \: a \: straight \: line \\ x + 2 \times 72 = 180 \\ x = 180 - 144 \\ \boxed{x = 36.} \\ \\ \boxed{question \: number \: 5 \to} \\ each \: interior \: angle \: \boxed{a}\: of \: a \: regular \: polygon \: is \to \\ \boxed{a = \frac{(n - 2)180}{n} }..........where \: \boxed{n} \: is \: the \: \boxed{number \: of \: sides} \\ a = \frac{(6- 2)180}{6} = \frac{4 \times 120}{6} \\ a = 108 \to hence \to \\ \boxed {180 - both \: equal \: base \: angles \: of \: the \: triangle = 60} \\ 2x + 2(60) = 360 \to \: sum \: of \: angles \:at \: a \: point\\ 2x + 120 = 360 \\ 2x = 360 - 120\\ x = \frac{240}{2} \\ \boxed{x =120.}\)

♨Rage♨

Solution

Find the Sine, cosine, tangent of - 120​

The natural numbers are "closed" under addition and multiplication. ... The subtraction of two natural numbers does NOT necessarily create another natural number (3 - 10 = -7). The division of two natural numbers does NOT necessarily create another natural number (1 ÷ 2 = ½). not closed under subtraction and division.

Answer:

250000000000x^12y^24

Step-by-step explanation:

25000000000000x10<;=

Answer:

ok so there is 1/4 of a meter between 15 chairs so

1/4*5= 1.25

so there is 1 and a quarter meter between the first and the last

Hope This Helps!!!

Answer:

B

Step-by-step explanation: