A firm in perfectly competitive market has a cost function of the form C = 5000 10Q + Q2 . Find the profit maximizing quantity for the firm if the market price P is N100. Calculate the profit as a function Q

Answer:

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Factorize as below and find roots:

Answer:

[tex]x=-1, \quad x=\dfrac{1}{2}, \quad x=-\dfrac{2}{3}[/tex]

Step-by-step explanation:

Given polynomial:

[tex]f(x)=6x^2+7x^2-x-2[/tex]

[tex]\boxed{\begin{minipage}{6 cm}\underline{Factor Theorem}\\\\If $f(x)$ is a polynomial, and $f(a) = 0$,\\ then $(x-a)$ is a factor of $f(x)$.\\\end{minipage}}[/tex]

Since the constant of the given polynomial is -2, the possible factors are ±1 and ±2.

Apply the Factor Theorem to check the possible values:

[tex]f(1)=6(1)^3+7(1)^2-(1)-2=10 \neq 0[/tex]

[tex]f(-1)=6(-1)^3+7(-1)^2-(-1)-2=0[/tex]

[tex]f(2)=6(2)^3+7(2)^2-(2)-2=72 \neq 0[/tex]

[tex]f(-2)=6(-2)^3+7(-2)^2-(-2)-2=-20 \neq 0[/tex]

Therefore, (x + 1) is a factor of the polynomial:

[tex]f(x)=(x+1)(ax^2+bx+c)[/tex]

Compare with the original function to find the coefficients of the quadratic:

[tex]6x^3=ax^3 \implies a=6[/tex]

[tex]7x^2=(b+a)x^2 \implies b=1[/tex]

[tex]-2=c \implies c=-2[/tex]

Therefore:

[tex]f(x)=(x+1)(6x^2+x-2)[/tex]

Factor the quadratic:

[tex]f(x)=(x+1)(6x^2+4x-3x-2)[/tex]

[tex]f(x)=(x+1)[2x(3x+2)-1(3x+2)][/tex]

[tex]f(x)=(x+1)(2x-1)(3x+2)[/tex]

Set the polynomial function to zero:

[tex](x+1)(2x-1)(3x+2)=0[/tex]

Apply the zero product property:

[tex](x+1)=0 \implies x=-1[/tex]

[tex](2x-1)=0 \implies x=\dfrac{1}{2}[/tex]

[tex](3x+2)=0 \implies x=-\dfrac{2}{3}[/tex]

Therefore, the solutions are:

[tex]x=-1, \quad x=\dfrac{1}{2}, \quad x=-\dfrac{2}{3}[/tex]

Answer:

1/8  =  0.12500

Step-by-step explanation:

23   divided by   26   = 2(3 - 6) = 2(-3) = 1/23

Work Shown:

7 AM, temp = 5

8 AM, temp = -10

9 AM, temp = -25

10 AM, temp = -40

Shortcut: 5 - 3*15 = 5 - 45 = -40

I recommend drawing a vertical number line to see what's going on.

Side note: -40 degrees Celsius = -40 degrees Fahrenheit

300 Hours will be the Interquartile range for the batteries of type A

In the given data there is a total number of 11 terms for Hours. We have to calculate the median value of Hours by using the formula :

  => Median =  [tex]\frac{n+1}{2}[/tex], and we know that Q2 = Median so Q2 can be calculated by Q2 = [tex]\frac{n+1}{2}[/tex]  => Q2 = 6 => 6th term Will be the Median.

Median = Q2 = 1300 Hours.

Now we have to Calculate Lower Quartile Q1 & Upper Quartile Q3. Since We have our Median 1300 Hours. So, the lower quartile will be :

Q1 = 1100 Hours

and, the Upper Quartile will be Q3 = 1400 Hours.

We have our Upper and Lower Quartiles. We can Calculate Interquartile Range be using the formula Q3 - Q1

   => IQR = Q3 - Q1

Putting values of Q3 and Q1, We get :

  => IQR = 1400 - 1100  => IQR = 300 Hours

Hence, the Interquartile Range IQR is 300 Hours.

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The present ages of Ann and Julie are 12 years and 8 years, respectively.

Let x, y are the current ages of Ann and Julie, whose features are synthetized in the following linear equations:

Ann is 4 years older than Julie;

x = y + 4

x - y = 4                                (1)

4 years ago, Ann was twice as old as Julie;

x - 4 = 2 · (y - 4)

x - 4 = 2 · y - 8

x - 2 · y = - 4                         (2)

Now we proceed to determine the ages of Ann and Julie by solving the system of linear equations;

(x, y) = (12, 8)

Hence, The present ages of Ann and Julie are 12 years and 8 years.

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Answer:12

Step-by-step explanation:

Suppose that today the exchange rate between the u.s. dollar and the chinese yuan is $1 =.12 yuan. if next week the exchange rate is $1 = .20 yuan, it is clear that yuan has depreciated relative to dollar.

What is meant by the exchange rate?

Last week: $1 = 0.12 yuan

Therefore, for exchange of $1, 0.12 yuan will be given

Today: $1 = 0.2

Therefore, for exchange of $1, 0.2 yuan will be given.

So, yuan will be given for same amount of $. Thus yuan has depreciated.

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Answer:

perry da platypus

Step-by-step explanation:

Australia's short beaked platypus

Step-by-step explanation:

sorry if am wrong

Answer:

I believe its O x(yz)

Step-by-step explanation:

The terms of the expression are: -15h and 5y.

A term of an expression can be a constant, a variable multiplied by a constant, or a variable standing alone.

Given the expression, -9h + 5y - 6h, simplify the expression in order to determine the terms of the expression:

-9h + 5y - 6h

Combine like terms

-9h - 6h + 5y

-15h + 5y

Therefore, the terms of the expression are: -15h and 5y.

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Answer:

3 : 5 also = 0.6

Step-by-step explanation:

Yes, you are able to simplify the ratio into a decimal.

The measure of angle 1 from the given figure is an obtuse angle.

Given that, when you look at a pencil in water, it looks bent. This illusion is due to refraction, or the bending of light when it moves from one substance to the next.

Refraction is the "bending" of light (or any electromagnetic wave) when entering a different medium.

In the given figure, the three angles, are angle 1, angle 2 and angle 3.

Angle 1 and 2 are formed with the surface of the water. Angle 1 in the medium air and angle 2 is in the medium water.

From the figure, given below we can see that angle 1 is greater than 90° and less than 180°.

Therefore, the measure of angle 1 from the given figure is an obtuse angle.

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Answer:

[tex]x+y=27[/tex]

[tex]y=2x+6[/tex]

Step-by-step explanation:

Letting [tex]x[/tex] and [tex]y[/tex] represent the smaller and larger number, respectively we create these equations.

Answer:

1. { 1 , 3, 4, 6, 7, 0, 5, 2 }

2. { 6 ,7 ,0 }

3. { 9 ,2 ,4 ,3 ,0 ,7 ,6 }

4. { 1 ,8 ,5 ,9 ,11 }

5. { 1 ,8 ,6 ,7 ,3 ,4 ,11 }

6.

7 . { 0 }

8. { 0 }

9. { 6 ,7 ,0 ,2 }

Step-by-step explanation:

for the 6th one I'm not sure about that , that's why i didn't write the answer for it

please make my answer as brainelist

The ratio of blue balloons to the total number of balloons a. 1/2.

To find the ratio of blue balloons to the total number of balloons, firstly we need to find the number of blue balloons. Performing addition and subtraction for the same as follows -

Total number of balloons = Number of blue balloons + number of red balloons + number of white balloons

Number of blue balloons = 14 - (3 + 4)

Number of blue balloons = 14 - 7

Number of blue balloons = 7

Ratio = Number of blue balloons to the total number of balloons

Ratio = 7:14

Performing division of both digits by 7

Ratio = 1:2

Hence the ratio of blue balloons to the total number of balloons a. 1/2.

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Answer: -8/21

Step-by-step explanation:

-5/7= -15/21

1/3=7/21

-15/21+7/21= -15+7=18

(15-7=8)

-8/21

Simplified Solution:

[tex]-\frac{8}{21}[/tex]

Hope this helps!

Answer:

So,x=2/3

Step-by-step explanation:

6x-10=-8+3x

6x-3x=-8+10

3x=2

x=2/3

Hope its helpful for you

Answer:

[tex]6x - 10 = - 8 + 3x \\ 6x - 3x = - 8 + 10 \\ 3x = 2 \\ \boxed{x = \frac{2}{3}}[/tex]

8) The equation of the line in slope-intercept form is y = 5 · x - 8. (Correct choice: A)

10) The slope of the line is equal to 0. (Correct choice: A)

11) The equation for a graph that is a vertical line is 3 · x - 2 = 0.   (Correct choice: C)

Herein we must analyze and understand linear equations and their features. 8) The first exercise consists in looking for a linear equation in slope-intercept form with a slope of 5 and y-intercept of - 8, linear equations in slope-intercept form are defined by the following expression:

y = m · x + b

Where:

If we know that m = 5 and b = - 8, then the equation of the line in slope-intercept form is y = 5 · x - 8. (Correct choice: A)

10) The slope can be determined by the secant line formula:

m = (3 - 3) / [5 - (-4)]

m = 0

The slope of the line is equal to 0. (Correct choice: A)

11) Vertical lines on a Cartesian plane are of the form x = a or x - a = 0. Then, the equation for a graph that is a vertical line is 3 · x - 2 = 0.   (Correct choice: C)

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Answer:

1) 38

2) 18

Step-by-step explanation:

1) 4m - 2t

m = 10

t = 2

(4 * 10) - (2 * 2)

40 - 4 = 36

Answer : 36

2) t + 2m - 4

m = 10

t = 2

2 + (2 * 10) - 4

22 - 4 = 18

Answer : 18

3) m/2t

m = 10

t = 2

10/(2*2) = 2.5

Answer : 2.5

The answer is 91

Step-by-step explanation:

Average Marks = (Total Marks) ÷ Total Tests

83 = (71 + 70 + 87 + 97 + 82 + x) ÷ 6

83 × 6 = 407 + x

498 = 407 + x

x = 498 - 407

x = 91

12 hours will it take to fill the given pool .

we can solve this problem using unitary method ,

10 hours is required to fill the full pool

1 hour is required to fill 1/10th of the pool

30 hours is required to empty the pool

1 hour is required to empty 1/30th of the pool

If two pipes are open then in 1 hour ( 1/10 - 1/30 = 2/30 = 1/15 ) pool will be filled .

The pool is 1/5th filled already as it is mentioned .

So , remaining is ( 1 - 1/5 = 4/5 )

If 1/15th is filled in 1 hour , then 4/5th will be filled in ( 15 × 4/5 ) hours = 12 hours

So, it will take 12 hors to fill the pool .

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Categorical data can be either numeric or nonnumeric.

Categorical data can be described as a type of data that can be divided into group and given labels or numerical value for the sake of identification.

Some examples of numerical data are age group, race, sex, educational level, among others.

For example, we can give numerical values like 1 for male, and 2 for female when categorizing people based on sex.

Therefore, categorical data can be either numeric or nonnumeric.

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The mean, which is a measure of central tendency for quantitative data should not be used for likert scale data values, which are ordinal (qualitative) data.

The use of the mean as a measure of central tendency for ordinal data may be encountered, in the customer satisfaction data analysis systems used in some banks

Ordinal data are a data form that specified categories that are scaled or have a set order.

However, ordinal scales are not standard, such that they cannot be manipulated quantitatively.

The mean specifies the average value, which the sum of the quantitative measurements, divided by the number of measurements

Therefore;

An example in real life where the mean could be used as a measure of central tendency of ordinal data is in customer satisfaction survey at the bank, where customers have five levels to select how happy they are with the bank services.

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To calculate average rate of change of a function f(x) over an interval between 2 points (a. f(a)) and (b, f(b)) is given by

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

The given function is [tex]h(x)= x^{2} -9x+18[/tex]

and the given interval is [tex]4\leq x\leq 11[/tex]

Now, h(b) = h(11) = [tex](11)^{2} -9(11)+18[/tex]

= [tex]121-99+18[/tex]

= [tex]40[/tex]

h(a) = h(4) = [tex](4)^{2} -9(4)+18[/tex]

= [tex]16 -36+18[/tex]

= [tex]-2[/tex]

The average rate of change between (4, -2) and (11, 40) is

= [tex]\frac{40-(-2)}{11-4}[/tex]

= [tex]\frac{40+2}{11-4}[/tex]

= [tex]\frac{42}{7}[/tex]

= [tex]42[/tex]

∴ The average rate of change between (4, -2) and (11, 40) is 42

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Step-by-step explanation:

direct variation means that

y = kx

that means it is a line with y-intercept = 0.

in other words, when x = 0, then y = 0 too.

for 2 given points the first part is automatically true. 2 points always define a line.

so, what we need to find out is, if (0, 0) is also on the line.

if not, it is not a direct variation.

the 2 points imply the equation

y = x + 2

as the y value is always larger than the x value by 2.

this has a y-intercept larger than 0 (2).

and so, (0, 0) is NOT on the line, and it is NOT a direct variation.

so, the 3rd answer option is correct.

Based on the transitive property of equality, m<MLI = 201°

181° + m<HAV = 287°, based on the substitution property of equality.

The transitive property of equality states that,  if d = e and e = f, then d = f.

Given that a = 3, if a + 5 = 8, then, based on the substitution property of equality, we would replace a with 3 into the equation as shown below:

3 + 5 = 8.

Based on the transitive property of equality, we are given that:

m<MLI = m<YGF

m<YGF = 201°

Then, we would have:

m<MLI = 201°

Also, we are given that:

m<CJW + m<HAV = 287°; and m<CJW = 181°.

Then, 181° + m<HAV = 287°, based on the substitution property of equality.

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The time it would take Joey is 3 years

Given that the formula for simple interest is;

I = PRT

Where;

Substitute into the formula

400 = 300 × 4 × t/ 100

cross multiply

4000 = 1200 t

Make 't' the subject

t = 4000/ 1200

t = 3. 3

t = 3 years in the nearest tenth

Thus, the time it would take Joey is 3 years

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