Q2A: What is the value of n?*

Nash equilibrium describes a situation in which no firm can improve its outcome by independently changing its course of action.

In the context of oligopoly, a Nash equilibrium refers to a situation in which no firm can improve its outcome by unilaterally changing its course of action, given the actions of other firms.

In other words, each firm is choosing its best response to the actions of other firms, and no firm has an incentive to deviate from its chosen strategy.

Nash equilibrium is a concept derived from game theory, which is the study of strategic decision-making in competitive situations. It helps to predict the behavior and outcomes in situations where multiple players or firms are interdependent.

Hence the correct option is Nash equilibrium.

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Answer:

Answer:

The prime polynomials are

x² + 9

x² + 3x + 9

Step-by-step explanation:

The system of equations for this problem is:
Basic: 1x + 1.5y + z = 75.7
Homeowner: 4x + 1.7y + 1.6z = 57.9
Pro: 3x + 1.5y + 1.4z = 46.6

To solve this problem using inverse matrices, we first need to create the matrices of coefficients and constants:
Coefficient Matrix:
[[1, 1.5, 1],
[4, 1.7, 1.6],
[3, 1.5, 1.4]]

Constant Matrix:
[[75.7],
[57.9],
[46.6]]

Next, we can use inverse matrices to find the solution:
Inverse of Coefficient Matrix =
[[-9.38, 7.81, 3.2],
[4.69, -3.81, -1.6],
[3.46, -2.81, -0.8]]

Solution =
[[-9.38*75.7 + 7.81*57.9 + 3.2*46.6],
[4.69*75.7 - 3.81*57.9 - 1.6*46.6],
[3.46*75.7 - 2.81*57.9 - 0.8*46.6]]

Therefore, the manufacturer can produce
Basic sets,
Homeowner sets and
Pro sets per day

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-18 + x = -11

Let's add 18 to both sides

x = 7

Answer:

7

Step-by-step explanation:

Step 1:

- 18 + x = - 11

Step 2:

x = - 11 + 18

Answer:

x = 7

Hope This Helps :)

Answer:

2 × pi × radius

..................

Answer:

Find the asymptotes.

Vertical Asymptotes:

x

=

−

2

Horizontal Asymptotes:

y

=

0

No Oblique Asymptotes

The equation of the  circle , with diameter  DEis (x - 5)² + (y - 7)² = 80

An equation is an expression that appears as the relationship between two or more variables and numbers. since the  standard equation  for a circle  is (x - h)² + (y - k)² = r², where    (h, k)  is the center of the circle and r is the radius. It is given that the diameter of the circle is at D(-3, 3) and E(13, 11). So the coordinate of the center is:

h = (13 + (-3))/2 = 5

k = (3 + 11)/2 = 7

(h, k) = (5, 7) and the  Radius is diameter / 2 = 8√5 ÷ 2 = 4√5.

the equation will be : (x - 5)² + (y - 7)² = (4√5)² => (x - 5)² + (y - 7)² = 80

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Answer:

(x - 5)² + (y - 7)² = 80

Step-by-step explanation:

Answer:

-8.2

Step-by-step explanation:

? =-4.9 - 3.3

?= -8.2

Answer:

\(27^{\frac{1}{3}} \quad 125^{\frac{2}{3}} \quad 9^{\frac{3}{2}}\)

Step-by-step explanation:

Rewrite 9 as 3²:

\(\implies 9^{\frac{3}{2}}=\left(3^2\right)^{\frac{3}{2}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 3^{(2 \cdot \frac{3}{2})}=3^3\)

Therefore:

\(\implies 3^3= 3 \cdot 3 \cdot 3=27\)

---------------------------------------------------------

Rewrite 27 as 3³:

\(\implies 27^{\frac{1}{3}}=\left(3^3\right)^{\frac{1}{3}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 3^{(3 \cdot \frac{1}{3})}=3^1\)

Therefore:

\(\implies 3^1=3\)

---------------------------------------------------------

Rewrite 125 as 5³:

\(\implies 125^{\frac{2}{3}}=\left(5^3\right)^{\frac{2}{3}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 5^{(3 \cdot \frac{2}{3})}=5^2\)

Therefore:

\(\implies 5^2=5 \cdot 5=25\)

---------------------------------------------------------

Solution

In order, from smallest to largest:

\(27^{\frac{1}{3}} \quad 125^{\frac{2}{3}} \quad 9^{\frac{3}{2}}\)

The weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

To determine the percentage of newborn African lions that weigh less than 3 pounds and the percentage that weigh more than 3.8 pounds, we would need statistical data on the weight distribution of newborn African lions. Since we don't have that information, we cannot provide the exact percentages.

However, if we assume that the weights of newborn African lions follow a normal distribution, we can use the properties of the standard normal distribution to make an estimation.

For the percentage of newborn African lions weighing less than 3 pounds:

We would need to know the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3 pounds and then find the corresponding percentage using a standard normal distribution table. Without this information, we cannot provide an accurate estimation.

For the percentage of newborn African lions weighing more than 3.8 pounds:

Similarly, we would need the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3.8 pounds and find the corresponding percentage using a standard normal distribution table. Without the required information, we cannot provide a specific estimation.

Please note that the weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

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Answer:

b value is 3

rise = 3 run = -2

another point could be (2,0)

Step-by-step explanation:

Answer:X=16*4=64

Soowwwyyy..

The solution of the linear equation 2.8y+6+0.2y=5y-14 is y=10.

Given linear equation 2.8y+6+0.2y=5y-14 and we have to find the solution of the equation.

An equation is relationship between two or more variables which is expressed in equal to form. It is solved in order to find the values of variables. Equation of two variables look like ax+ by=x.

The given linear equation is 2.8y+6+0.2y=5y-14 which can be solved as under:

2.8y+6+0.2y=5y-14

We have to add the coefficients of same variables. Coefficients are the numbers which are present with the variable.

3y+6=5y-14

We have to take same variables at one side.

3y-5y=-14-6

-2y=-20

y=-20/-2

y=10

Hence the solution of the linear equation 2.8y+6+0.2y=5y-14  is y=10.

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The first differential equation has a third-order derivative of y and the second differential equation has a fifth-order derivative of y.

The order of a differential equation refers to the highest derivative present in the equation. In the first differential equation, y' represents the first derivative of y, while y'' represents the second derivative of y. However, there is no term explicitly representing the third derivative of y, so the order of this equation is 0.

The second differential equation involves multiple derivatives. The term "dy/dx" represents the first derivative of y, "cos y" represents the function of y, and "x^3" represents the third power of x. The equation also includes various differentiation operators, such as dx^5/dx^3. When simplified, we find that the highest derivative present is the fifth derivative of y, represented as "d^5y/dx^5". Therefore, the order of this differential equation is 5.

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Answer:

25

Step-by-step explanation:

f(x) = 3(2)^2 + 1

f(x) = 3(8) + 1

f(x) = 24 + 1

f(x) = 25

You need to use A cube + B cube formula.

Answer: 21450

Step-by-step explanation:

That is the initial price.

The line cross the y axis at 21450.

The correct option is (C)

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Elise is buying a new car selling for $21,450.

The rate of depreciation on this type of car is 8% per year.

Using f(x) = A \((1+r)^x\)

A= $21,450.  and r = -8% (depreciated)

So, f(x) = A \((1+r)^x\)

f(x) = 21450 \((1- 8/100)^x\)

= 21450 x \((0.92)^x\)

Thus, the line cross the y axis at

= 21450 ( initial point)

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As per given value of card and its use , after first year relationship between the number of months and amount left on the card is given by an equation y = 25 - 2.50x , where x represents the number of months.

x is the independent variable and

y is the dependent variable.

As given in the question,

Starting value of the cash card = $25

For first year card is not in use then,

Every month value of card decrease by $2.50

Let x be the number of months and y be the total left amount on the card.

After first year:

Relationship between the number of months and the amount left on the card is :

y = 25 - 2.50x

y represents the dependent variable

x represents the independent variable

Therefore, for the given value of card and its use , after first year relationship between the number of months and amount left on the card is given by an equation y = 25 - 2.50x , where x represents the number of months.

x is the independent variable and

y is the dependent variable.

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Answer:

18.8 feet

Step-by-step explanation:

You have to use trigonometry for this question.

So, the basic measurements we have are:

1. The angle of elevation = 42 degrees

2. Base length of the triangle(ie. the shadow  on the floor) = 20 ft

Now, imagine a right angled triangle with the base length as the shadow height, the height of the triangle as the height of the tree and the hypotenuse as the sun ray that causes the shadow. Also, the angle opposite the height is the 42 degrees.

So, we know the Adjacent length and we want to know the opposite length ( in respects with the angle given)

So, the trig ratio that compares the two is ‘Tan’

Now, form the equation:

Tan (42) = Opposite/ Adjacent = O/ A = O/20

Rearrange to solve:

O/20 = Tan(42)

O = Tan(42) x 20

Key these into a calculator and you get the answer: 18.800808...

Round to a suitable degree of accuracy.

18.8 ( 3s.f)

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Therefore, the appropriate percent in the pie chart to represent the preference for Klean laundry detergent is 15%.

Percent is a way of expressing a fraction or a ratio as a portion of 100. The word "percent" means "per hundred." It is denoted by the symbol "%". Percentages are commonly used to express rates, proportions, or parts of a whole in various fields, such as mathematics, science, finance, and statistics. For example, an interest rate of 5% per annum means that for every 100 units of money, the lender will receive 5 units of interest each year.

Here,

To find the appropriate percent in the pie chart to represent the preference for Klean laundry detergent, we need to calculate the fraction of people who prefer Klean detergent, and then convert it to a percentage.

The fraction of people who prefer Klean detergent is:

75/500 = 0.15

To convert this fraction to a percentage, we can multiply by 100:

0.15 x 100 = 15%

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From the proof of modular congruence below, it has been shown that;

41 ≡ 21 (mod 3).

We want to use the definition of modular congruence to prove that;

41 is congruent to 21 (mod 3) i.e if a ≡ b (mod m) then b ≡ a (mod m).

We are trying to prove that modular congruence mod 3 is a symmetric relation on the integers.

First, if we recall the definition of modular congruence:

For integers a, b and positive integer m,  

a ≡ b (mod m) if and only if m|a–b

Suppose 41 ≡ 21 (mod 3).

Then, by definition, 3|41–21, so there is an integer k such that 41 – 21 = 3k.

Thus;

–(41 – 21) = –3k

So

21 – 41 = 3(–k)

This shows that 3|21 – 41.

Thus;

21 ≡ 41 (mod 3) and the proof is complete

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Answer:

A.47

Step-by-step explanation:

Step-by-step explanation:

235 / 5 = 47

Hence there are 47 candles in each group (A).

Answer:

y=-x+2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)=(-5-1)/(7-1)=-6/6=-1

y-y1=m(x-x1)

y-1=-1(x-1)

y-1=-x+1

y=-x+1+1

y=-x+2

Answer:

y=-1x+2

Step-by-step explanation:

m=  

-5 - 1 over 7 - 1

(1,1). y=mx+b or 1=-1 × 1+b, or solving for b: b=1-(-1)(1). b=2.

(7,-5). y=mx+b or -5=-1 × 7+b, or solving for b: b=-5-(-1)(7). b=

It is worth noting that there are many other possible choices for a and b that satisfy ab=0. This is because there are many ways to construct matrices with a row or column of zeros, and many ways to choose the nonzero entries in the other positions.

To find nonzero 2x2 matrices a and b such that ab=0, we need to find matrices a and b whose product is the zero matrix. A matrix multiplication is a combination of dot products between rows and columns of the two matrices. In order for the product of two matrices to be zero, one or both of the matrices must have a row of zeros or a column of zeros.

One way to construct such matrices is to set one of the matrices to have a row of zeros and the other to have a column of zeros. Let a be a matrix with a row of zeros and b be a matrix with a column of zeros, but with a nonzero entry in a different position. For example, we could choose:

a = [0 0; 1 0]

b = [0 1; 0 0]

Then, the product ab is:

ab = [0 0; 1 0] * [0 1; 0 0] = [0 0; 0 0]

So, we have found two nonzero 2x2 matrices a and b such that ab=0.

It is worth noting that there are many other possible choices for a and b that satisfy ab=0. This is because there are many ways to construct matrices with a row or column of zeros, and many ways to choose the nonzero entries in the other positions.

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Answer:

(2,-8)

Step-by-step explanation:

(2,-8)

Answer:

Step-by-step explanation:

Given the height of the object covered by the ball modeled by the function;

h(x) = -16x^2 + 48x + 64

To determine the height covered by the ball after 1.2 secs, we will simply substitute x = 1.2s into the formula and find h(x) as shown;

h(1.2) = -16(1.2)^2 + 48(1.2) + 64

h(1.2) = -16(1.44) + 48(1.2) + 64

h(1.2) = -23.04 + 57.6 + 64

h(1.2) = 98.56m

This means that the ball have covered 98.56m in 1.2sseconds

Answer:

The Answer is D. 25ft

Step-by-step explanation:

Taking the quiz rn hope this helps:)

Solution

Given that:

The ratio of 10: 17 means

Since the sum of angles in a quadrilateral is 360

=> 121 + 185 + 10x + 17x = 360

=> 27x = 360 - 121 - 185 = 54

=> x = 54/27 = 2

Therefore, 10×2 = 20, and 17×2 =34

Hence, the measures of those two angles are 20 and 34 degrees.

The number of days would be 10 and the maximum percent of the population infected would be 25.752%.

What are exponential functions?

The exponential function, denoted by \(e^x\), is a mathematical function. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

\(p(t) = 7te^{-\frac{t}{10}}\)

percentage of infected people a maximum when p '(t) = 0

                    \(p '(t) = 7(1)e^\frac{-1}{10} +7te^\frac{-t}{10}(\frac{-1}{10})\\\\p'(t)=e^{-\frac{t}{10}}(7 -\frac{7t}{10})\\\\e^{-\frac{t}{10}}(7 -\frac{7t}{10})=0\\\\7 -\frac{7t}{10}=0\\\\t = 10\)

Hence percentage of infected people reaches a maximum after 10 days

maximum percent of the population infected = p(10)

    \(p(10) = 7(10)e^{-\frac{10}{10}}\\\\p(10)=\frac{70}{e}\\\\P(10)=25.752\%\)

Hence, the number of days would be 10 and the maximum percent of the population infected would be 25.752%.

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