solve the systems of equations by Elimination. Find the solution.

-x+y=9
x+2y=6

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.

Given the demand equations and the total cost function:

Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1

Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2

Total Cost: TC = 120 + 4Q

To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:

MR1 = MC:

16 - 0.2Q1 = 4

0.2Q1 = 12

Q1 = 60

MR2 = MC:

10 - 0.1Q2 = 4

0.1Q2 = 6

Q2 = 60

Substituting the quantities back into the demand equations, we find:

P1 = 16 - 0.1(60) = 10

P2 = 10 - 0.05(60) = 7

The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:

TR = P1 * Q1 + P2 * Q2

TR = (10 * 60) + (7 * 60)

TR = 600 + 420

TR = 1020

The total cost (TC) is given by the total cost function:

TC = 120 + 4Q

TC = 120 + 4(60 + 60)

TC = 120 + 480

TC = 600

Finally, the profit (π) can be calculated by subtracting total cost from total revenue:

π = TR - TC

π = 1020 - 600

π = 420

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

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Step-by-step explanation:

Hey, there!!

Here, one point is A(10,8) and P(8,5) is the midpoint.

Let B(x,y) be the another end point.

Now,

Using midpoint formulae,

\(p(x.y) = \frac{x1 + x2}{2} . \frac{y1 + y2}{2} \)

\(p(8.5) = ( \frac{10 + x}{2} . \frac{8 + y}{2} )\)

Since they are equal,equating with their corresponding elements we get,

\(8 = \frac{10 + x}{2} \)

or, 16 = 10 + x

or, x=16-10

Therefore, x = 6

Now,

\(5 = \frac{8 + y}{2} \)

or, 10 = 8 + y

or, y = 2

Therefore, The coordinates of another point are B(6,2)

Hope it helps .....

Answer:

         See below :)

Step-by-step explanation:

The solution is, 12 multiple-choice questions are on the test.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

The right answer for the question that is being asked and shown above is that:

m + f = 15 ---> 3m + 3f = 45

3m + 5f = 51

now, we have.

3m + 3f = 45

3m + 5f = 51

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

-2f = -6

f = 3

so, we get,

m + f = 15

m = 15 - 3

m = 12

So the correct answer is 12.

Hence, The solution is, 12 multiple-choice questions are on the test.

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Complete question:

Students are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. There are 15 questions on the test, and students are given 51 minutes to take it.

The system of equations shown can be used to find the number of multiple-choice questions, m, and the number of free-response questions, f, on the test.

m + f = 15

3m + 5f = 51

How many multiple-choice questions are on the test?

3

5

12

14

Work Shown:

7.12 = 7 + 0.12

7.12 = 7 + (12/100)

7.12 = 7 + (3/25)

7.12 = 7 & 3/25

The notation 7 & 3/25 means we have the whole part 7 and fractional part 3/25.

Answer:

x= -3,      x = 1

Step-by-step explanation:

Zeros are values of x, when f(x) = 0.

0=(x+3)(x-1)

x+3 = 0,  x - 1=0

x= -3,      x = 1

Answer:

x = -3, x = 1

Step-by-step explanation:

To determine the zeroes of the factored quadratic equation, we need to look back at its definition. The zeroes are a function are specific x-values that result in a y-value of 0.

In this case, we want the numbers inside of the parantheses to equal 0. If we substitute in x = -3, we get (0)(x - 1), and we know that is just 0. Similarly, if we substitute in x = 1, we get (x + 3)(0), and we know that is just 0.

As such, these are your solutions.

The exact values of the remaining trigonometric functions are listed below:

Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4

Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11

Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3

Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2

In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

Now we proceed to determine the exact values of the trigonometric functions:

Case 3: y = 4, √(x² + y²) = 5

x = √(5² - 4²)

x = 3

cos θ = 3 / 5

tan θ = 4 / 3

cot θ = 3 / 4

sec θ = 5 / 3

csc θ = 5 / 4

Case 4: x = 5, √(x² + y²) = 6

y = √(6² - 5²)

y = √11

sin θ = √11 / 6

tan θ = √11 / 5

cot θ = 5√11 / 5

sec θ = 6 / 5

csc θ = 6√11 / 11

Case 5: x = 8, √(x² + y²) = √73

y = √(73 - 8²)

y = 3

cos θ = 8√73 / 73

sin θ = 3√73 / 73

tan θ = 3 / 8

cot θ = 8 / 3

csc θ = √73 / 3

Case 6: x = √3, y = 1

sin θ = 1 / 2

cos θ = √3 / 2

tan θ = √3 / 3

sec θ = 2√3 / 3

csc θ = 2

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The expressions that represent the amount of chocolate chips Desmond used in his last batch are x+0.3x and 1.3x

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, Desmond uses x ounces of chocolate chips, in his cookies, he wants to make the cookies more delicious, so he added 30% more chocolate chips in the batter of the cookies,

we need to find the expressions that represent the amount of chocolate chips Desmond used in his last batch,

Since, he is adding 30% more in x ounces,

Therefore, the total he will add = 30% of x + x

0.30x + x =

1.3x

Hence, the expressions that represent the amount of chocolate chips Desmond used in his last batch are x+0.3x and 1.3x

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Answer:

Step-by-step explanation:

If the side lengths are all different, none.

__

The following 7 combinations will form triangles:

  (5, 5, 5), (5, 5, 7), (5, 7, 7), (5, 15, 15)

  (7, 7, 7), (7, 15, 15)

  (15, 15, 15)

_____

Additional comment

The triangle inequality requires the sum of the two shortest lengths exceed the longest. Here, we have 5+7=12<15, so a triangle with all three lengths cannot be formed. We also note that 5+5=10<15, and 7+7=14<15, so isosceles triangles with only one side equal to 15 cannot be formed, either.

Answer:

none

Step-by-step explanation:

The length of DB, AD and AC are 24 m, 32 m, 42 m respectively. The measurement of ∠C = 67.38°.

What is a right angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Given that, in △BCD

BD = 24 m

DC = 10 m

BC = 26 m

△BCD is a right angle triangle.

The trigonometry ratio of sine is ratio of height to hypothenuse.

With respect to C, the height of △BCD is 24m and hypothenuse is 26m.

sin C = height/hypothenuse

sin C = 24/26

C = 67.38°

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Las edades de Andrea y Alejandro son 40 y 16 años, respectivamente.

En esta pregunta debemos traducir el enunciado en ecuaciones algebraicas y resolver el sistema resultante. Tras una lectura cuidadosa tenemos el siguiente sistema de ecuaciones:

\(y = \frac{2}{5}\cdot x\) (1)

\(x + y = 56\) (2)

Donde:

A continuación, procedemos a resolver el sistema:

(1) en (2):

\(x + \frac{2}{5}\cdot x = 56\)

\(\frac{7}{5}\cdot x = 56\)

\(7\cdot x = 280\)

\(x = 40\)

Por (1):

\(y = \frac{2}{5}\cdot 40\)

\(y = 16\)

Las edades de Andrea y Alejandro son 40 y 16 años, respectivamente.

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A student need a raw score of 36.

We can find the raw score (R) of the student by substituting A = 60 into the the formula and then solve for R. That is:

A = 10√R

√R = 60/10

√R = 6

R = 6²

R = 36

Thus, a student need a raw score of 36 to get a passing grade after her score is adjusted.

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The number that satisfies the given condition is 1 1/2 or 3/2.

The number that is less than 7/4 but greater than 9/8 is 1 1/2 or 3/2. To understand this, let's convert the fractions into a mixed number or a decimal.

7/4 is equal to 1 3/4, which means it is greater than 1.

9/8 is equal to 1 1/8, which means it is less than 2.

Therefore, the number we are looking for must be greater than 1 but less than 2.

In decimal form, 1 1/2 is equal to 1.5.

So, the number that satisfies the given condition is 1 1/2 or 3/2.

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Step1: Write the area of the circular Rug

The area of the circle is

From the question the diameter is 25feet, hence the radius is

Step2: substitute the value into the formula

Hence the area of the circular rug is 491.07 square feet

The will take approximately 491square feetyou

Answer:

\(144 cm^{2}\)

Step-by-step explanation:

Step 1: Find the true length of each side

We know that the perimeter is 56cm and the ratio of AD:AB:DC:BC is 5:12:6:5. It is safe to assume that this ratio is the simplified version, which means that if we multiply each of these numbers by a scale factor of \(x\), then we get the true length of each side, so we would get \(5x, 12x, 6x, 5x\) for the sides. We also know that when we add these numbers, we get the perimeter, which is 56. So, we can create the equation \(5x + 12x + 6x + 5x = 56\). Then, solve the equation for x, which would be 2, and go back and multiply each number with 2 to get the following:

AD = 5*2 = 10cm, AB = 12*2 = 24cm, DC = 6*2 = 12cm, BC = 5*2 = 10cm  

Step 2: Calculate the Height

Now we know the lengths of each side, lets take a look at the formula for the area of a trapezium: \(\frac{base_{1} + base_2}{2}*height\). So, the next step would be to calculate the height. We can draw the height by drawing a line straight down from the vertex D and another straight down from the vertex C. These lines are both the height, and will be the exact same length. We can calculate that the height is 8 because AB is 24 cm, but the length from the height at vertex D to the height at vertex C is 12 cm, so that means that the base of each triangle is 12/2 = 6 cm. Then we can use Pythagorean theorem to figure out that the height is 8cm.

Step 3: Calculate the Area

Lastly, we can calculate the area. The formula is \(\frac{base_{1} + base_2}{2}*height\). In this case, the numbers would be \(\frac{12 + 24}{2} * 8 = 144cm^{2}\)

I know this is a lot, so let me know if you have any questions!

Answer:

A = 189.25

Step-by-step explanation:

A = πr²

15 x 10 = 150

5 x 5 x 3.14 = 78.5

78/2 = 39.25

You divide by 2 because it's half of a circle.

150 + 39.25 = 189.25

Let me know if this helps!

Answer:

sadsadasdasxzc

Step-by-step explanation:

xzcxzcxz

Step-by-step explanation:

x=21

y=15

that is the answer

The term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.

Given,

In the question:

The quadratic sequence is :

3, 11, 25, 45, ...

To find the nth term of the quadratic sequence.

Now, According to the question;

The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.

The difference between the first and second terms can be calculated as follows:

11-3 = 8

The difference between the second and third terms can be calculated as follows:

25-11 = 14

The difference between the third and fourth terms can be calculated as follows:

45-25 = 20

The sequence is expressed as follows:

3,3+8,11+11,25+20,...

The difference between consecutive terms expands by 6.

Use the principle of mathematical induction.

6\((\frac{n(n+1)}{2} )\)

= 3n(n+1)

The sequence's nth term can be calculated as follows:

term = 3n(n+1) - 4n + 1

             = 3n² - n + 1

Hence, the term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.

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Here books can be arranged in: a) 39,916,800 ways b) 17,280 ways c) 86,400 ways d) 86,400 ways e) 30,240 ways

a) When the books can be arranged in any order, the total number of ways is given by 11!, which is the factorial of the number of books that is 39,916,800 ways. b) We have 2! ways to arrange the group and within the group, the math books can be arranged in 6! ways and the biology books can be arranged in 5! ways which is 17,280 ways.

c) The math books can be arranged in 6! ways, and the remaining books can be arranged in 5! ways that is 86,400 ways. d) If the math and biology books must alternate, we consider them as one group. Within this group, the math and biology books can be arranged in 6! ways that is 86,400 ways.

e) When none of the biology books can be next to each other, we consider the arrangements of the math books and the spaces between them. There are 7 spaces available for the biology books to be placed, and we use the permutation formula 7P5 to calculate the number of arrangements which can be 30,240 ways.

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We can say with 95% certainty that the genuine rate of all patients at this clinic who have high blood pressure is between 24% and 42%. 

To develop a 95% certainty interim for the rate of all patients at this clinic that have tall blood weight, we will utilize the equation:

CI = p ± z*(p*(1-p)/n))

where p is the sampling extent, z is the z-score related to the required certainty level (in this case, 1.96 for 95% certainty), and n is the test measure.

We are given that out of a test of 100 patients, 33 have high blood weight. In this manner, the test extent is:

p = 33/100 = 0.33

Utilizing the equation over, we will calculate the edge of the mistake:

Arduino

ME = z*(p*(1-p)/n)) = 1.96*(0.33*(1-0.33)/100)) ≈ 0.09

At that point, we are able to develop the 95% certainty interim:

CI = p ± ME = 0.33 ± 0.09 = (0.24, 0.42)

Hence, able to say with 95% certainty that the genuine rate of all patients at this clinic who have high blood weight is between 24% and 42%. 

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Answer:

26

Step-by-step explanation:

1/6 of 36 is 6

1/9 of 36 is 4

6+4=10

36-10= 26

Answer:

26 cakes

Step-by-step explanation:

36 divided by 6 = 6

30 - 6 = 24

36 divided by 9 = 4

6 + 4 = 10

36 - 10 = 26

Hopefully this helps you :)

pls give me brainlest  ;)

The expected value of the policy for the insurance company: $359.38

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The expected value of the policy for the insurance company can be calculated as follows:

Expected value = (Probability of survival) x (Annual payment)

= 0.999057 x $360

= $359.38

So, the expected value of the policy for the insurance company is $359.38.

It's important to note that this is just an estimate based on statistical probabilities and does not guarantee the outcome. The actual value could be higher or lower than this estimate, depending on the actual lifespan of the policyholder.

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Answer:

(-3, -4)

Step-by-step explanation:

Rotating a point that has the coordinates (x,y) 180° about the origin in a clockwise or counterclockwise direction, produces a point that has the coordinates (−x,−y). Ari's error was that she rotated "N" by 90 degrees instead of 180 degrees, as the rule for a 90 degree rotation is (-y, x). Therefore, the correct coordinated for N' can only be (-3,-4)

Answer:

A.

Step-by-step explanation:

remember, sine is the up/down distance from the center of the surrounding circle. cosine is the left/right sustenance from the center.

and for a triangle/circle different than the norm circle with radius = 1, we need to multiply all functions by the actual radius.

so, in this triangle

12 = cos(theta) × 20

cos(theta) = 12/20

The function r(x) is an example of a Pade approximation to f(x). it is not always possible to find such an approximation r(x). However,

It is not always possible to find an approximation r(x). However, the function r(x) is an example of a Pade approximation to f(x).

What is Pade approximation A Pade approximation is a technique for approximating a function using a ratio of two polynomials. This approximation is used to approximate functions that may be difficult to compute or solve exactly.

Pade approximations are often used in numerical analysis, scientific computing, and engineering to obtain accurate solutions to problems that are too complicated or expensive to solve exactly.How to find an approximation r(x) To find an approximation r(x), we need to find a ratio of two polynomials that approximates f(x).

The Pade approximation r(x) is given by the ratio of two polynomials: P(x) and Q(x). The P(x) and Q(x) are usually chosen to be of the same degree to minimize the error between the approximation and the exact value of f(x).Therefore, it is not always possible to find such an approximation r(x). However, the function r(x) is an example of a Pade approximation to f(x).

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Answer:

24

Step-by-step explanation:

Setting x as the number of salami sandwiches:

2/5 = x/60

Cross-multiplying: 5x = 2 × 60

Simplifying: 5x = 120

Division: x = 24

Given transfer function, the identified correct steady-state response ys(t) to the given input function is: y (t) = 27.116 Sin (1.5 t - 49.4°)

A transfer function is a mathematical link between a numerical input to a dynamic system and the subsequent output in statistical time-series analysis, signal processing, and control engineering.

Step 1

Recall that we are given T(s) = Ys)/F(s) = 75/(145 + 18)

⇒ T(Jw) = 75/ [18 + J14w]

This is called a steady state response to Sinusoidal input.

f(t) = [T(t) ↔T(jw)] → y(t A Sin (wi + φ)

Where A = A1 x [T(jw)] w= w1

⇒ A = A1 [T(jw1)]

And,

φ = θ + [T(jw)] w = w1

Step 2

Given, f(t) = 10 Sin 1.5t

A1 = 10, W1 = 1.5 red/see, θ = 0°

The Magnitude of T(jw) is

[T(jw)] = 75/√[(18²) + (14w)²

⇒ [T(jw] w = w1 = 1.5

= 75/√[(18²) + (141.5)²

⇒ [T(jw1)] = 2.7116

Hence,

A = A1 x [T(jw1)] =

10 x 2.7116

⇒ A = 2.116

⇒ Phase of T(jw) is,

[T(jw)] = - tan ⁻¹ (14w/18)

Hence, φ = 0° - Tan⁻1 (21/18)

φ = -49.4°

Hence,

y(t) = A sin (w1t + φ)

⇒ y (t) = 27.116 Sin (1.5 t - 49.4°)

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Answer:

4.32 francs

Step-by-step explanation:

45p × £/(100p) × 9.6 francs / £ = 4.32 francs

Answer:

its the first one

Step-by-step explanation:

t - 3 > -5

 +3  > +3

___________

t      >  -2

t is greater than -2 so the line should point to the right, and it should be an empty circle on -2 because it is not a greater than or equal to sign.

Answer:

t>-2

Step-by-step explanation:

Treat this like an equation and add -3 to both sides:

t>-2

The correct choice should be #1