The supply function and the demand function for a product are linear and are determined by the tables that follow.
Supply Function
Price ($) Quantity
75 125
150 150
300 200
Demand Function
Price ($) Quantity
45 355
120 330
270 280
(a) Write an equation for the supply function's price p as a function of q.
p =
Write an equation for the demand function's price p as a function of q.
p =
(b)Find the quantity and price that give market equilibrium.
Market equilibrium is achieved with a product quantity of units at a price of $ per unit.

Answer: Susie is correct.

Step-by-step explanation:

Susie is correct, because the Pythagorean theorem does not work on this triangle. Since the Pythagorean theorem only works on right triangles, we can conclude that Susie is correct, and that this triangle is NOT a right triangle.

a²+b² = c²

a = 9

b = 12

c = 17

9² + 12² = 17²

==> 81 + 144 = 289

==> 225 = 289, This is not true

Therefore this triangle is not a right triangle.

Answer:

70

Step-by-step explanation:

When the area of the poster is 256 square inches, the measurements are 32 inch and 8 inch.

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.

Here,

let length be l and width be w.

l=3w+8

l*w=256

(3w+8)*w=256

3w²+8w=256

3w²+32w-24w-256=0

3w(w-8)+32(w-8)=0

(3w+32)(w-8)=0

w=-32/3, 8

w=8 inch

l=3*8+8

l=32 inch

The dimensions for the poster are 32 inch and 8 inch when area of the poster is 256 square inches.

To know more about area,

https://brainly.com/question/22469440

#SPJ1

a) The given function is [tex]$\frac{x^2-2x+2}{(x-1)^2(x+2)}$[/tex]. The series of this function is [tex]$\sum_{n=0}^{\infty}(-1)^n(n+1)x^n$[/tex]. Therefore, the series is alternating (-1).

b) The sum of the first four nonzero terms of the series is [tex]$-1x^1+2x^2-3x^3+4x^4$.[/tex]

c) The interval of convergence is [tex](-2, 1)[/tex]. This is because the denominator [tex]$(x-1)^2(x+2)$[/tex] has a zero at [tex]$x=-2$[/tex] and a zero at [tex]$x=1$[/tex], and the function is undefined at these two points. Therefore, the interval of convergence is the open interval  [tex]$(-2, 1)$[/tex].

Convergence is the process of two or more different entities coming together and becoming one. In mathematics, it can refer to a sequence converging to a limit, or the process of a function approaching a finite value as the number of trials approaches infinity. In technology, convergence can refer to the combining of different media types into a single medium, such as the combination of audio, video, and text into a multimedia presentation.

To learn more about limit, visit:

brainly.com/question/8533149

#SPJ4

Answer:

  x = 15

Step-by-step explanation:

You have ∆UVW with angles U=(3x-10)°, V=(6x+5)°, and W=(4x-10)°, and you want to know the value of x.

The angle sum theorem tells you the sum of angles in a triangle is 180°.

  U +V +W = 180°

  (3x -10)° +(6x +5)° +(4x -10)° = 180°

  13x -15 = 180 . . . . . . . divide by °, collect terms

  13x = 195 . . . . . . . add 15

  x = 15 . . . . . . . divide by 13

The value of x is 15.

The Null Hypothesis, H0 is "Marble color preference and income class are independent" and the Alternate Hypothesis, H1 is "Marble color preference and income class are dependent".

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample. Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses.

We can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypotheses. However, the hypotheses can also be phrased in a general way that applies to any test.

We are given that to test the claim that marble color preference and club membership are related.

Thus, the Null Hypothesis, H0 is "Marble color preference and income class are independent" and the Alternate Hypothesis, H1 is "Marble color preference and income class are dependent".

To learn more about hypotheses, visit brainly.com/question/13025783

#SPJ4

The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.

As per the given data,

we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.

We know that,

Probability(Event) =Number of Favorable Outcomes/Total number of

                                Outcomes = x/n.    

Total number of Outcomes is 52 (given)

So,  we will calculate Number of Favorable Outcomes as follows:

The total no. of King in deck of card is 4

The total no. of queen in deck of card is 4.

The total no. of ace in  deck of card is 4.

The total no. of jack in deck of card is 4.

Therefore, the number of favorable outcomes is 4+4+4+4= 16

Now, putting values in the above stated formula of probability, we get:

Probability= 16/52=4/13

Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.

For more such questions on Probability:

https://brainly.com/question/25870256

#SPJ4

The equation of the function described as;  y = 7 sin ( 4x + π/2 ) + 3

The general equation of the sine curve can be written as;

y = a sin ( nx + α ) + b

where : a is the amplitude, n = 2π/period, b = shift in the direction of y

            α°= shift in the direction of x

We are Given period = π/2 the maximum value is 10, the minimum value is −4 and y-intercept of 10.

 Thus,

a = (maximum - minimum)/2 = (10 - -4)/2

a = 7

 n = 2π/period = 2π/(π/2)

n = 4

 b = maximum - a = 10 - 7

b= 3

To find α as y-intercept = 10

y = 10 at x = 0

Substitute in the general function;

y = a sin ( nx + α ) + b

10 = 7 sin ( 4*0 + α ) + 3

Thus, we have;

sin α = 1

α = π/2

So, the equation of the function described is;

 y = 7 sin ( 4x + π/2 ) + 3

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

It takes about 120 years for the graph to reach 100 million barrels per day whereas it takes 50 years to go from 100 million to 200 million.

As per the question the left axis indicates the amount of oil in the earth in trillions of barrels.

The right axis indicates the global consumption rate of oil in millions of barrels per day.

To the left of the red vertical line are model results that approximate reality whereas to the right are model-based predictions of the future.

The bottom axis is time in years.

The graph attached at the end of the solution.

Let the number of years of transition from using no oil to consuming 100 million barrels per day be a.

Let the number of years of transition from using 100 million to 200 million barrels per day be b.

From the given graph, we can see that initial consumption rate is low, and it takes 120 years for the graph to reach 100 million barrels.

But it takes 50 years to go from 100 million to 200 million.

This is known as exponential growth.

Therefore, the value of a is 120 and the value of b is 50.

For more questions on exponential growth

https://brainly.com/question/11487261

#SPJ4

(a) The differential Equation that is satisfied by y is dy/dt = k × y × (1 - y)   ,

(b) Solution of the differential equation assuming y(0) = c is y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .

In the question ,

Part (a)

let the fraction of people who heard the rumor is = y

So , the fraction who have not heard the rumor is = 1 - y .

the rate of rumor spread is ⇒ dy/dt = k×y(1 - y)

dy/y(1-y) = k.dt     ...where k is the constant of proportionality .

So , the differential equation is ..

dy/dt = k × y × (1 - y)

Part (b)

So , 1/y(1-y) = 1/y + 1/(1 - y)       ....equation(1)

integrating equation(1) , we get

∫dx/(1 + ax) = ㏑(1 + ax)/a     ,....where a is the constant

㏑y + ㏑(1-y)/(-1) = kt + d     ,.....where d is the constant

By using , ㏑a - ㏑b = ㏑(a/b) and taking exponential . we get ,

y/(1 - y) = c₁[tex]e^{k\times t}[/tex]

for t = 0 and y(0) = c

solving further , we get

c₁ = c/(1 - c)

So , y = (1-y)c₁[tex]e^{k\times t}[/tex]

y(1 + c₁[tex]e^{k\times t}[/tex]) = c₁[tex]e^{k\times t}[/tex]

y = c₁[tex]e^{k\times t}[/tex]/(1 + c₁[tex]e^{k\times t}[/tex])

taking c₁[tex]e^{k\times t}[/tex] common , and substituting the value of c₁ we get ,

the solution as , y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex]    .

Therefore , (a) the differential equation is dy/dt = k × y × (1 - y)   and

(b) the solution is y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex]   .

The given question is incomplete , the complete question is

One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor.

(a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.)

(b) Solve the differential equation. Assume y(0) = C.

Learn more about Differential Equation here

https://brainly.com/question/15188890

#SPJ4

The answers to find are 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30

When two triangles having congruent corresponding angles and the corresponding sides are in equal ratio, then the triangles are said to be similar triangles.

Given are the similar triangles,

1) Δ HJG ~ Δ CAB

Scale factor = 3:1

2) Δ NPM ~ Δ ABC

Scale factor = 1:2

3) KJML ~ CDAB

Scale factor = 1:2

4) 40/x = 20/5

x = 10

5) 18/x = 21/7

x = 6

6) 6/3 = x/15

x = 30

Hence, the answers are: 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30

For more references on similar triangles, click;

https://brainly.com/question/29191745

#SPJ1

Answer: x = 9/10 - 7/10

Step-by-step explanation:

a) A discrete random variable is a variable that can take only a countable number of distinct values, such as 0, 1, 2, 3, 4, and so on.

b) Examples of discrete random variables are the number of children in a family, the number of people who go to the cinema on Friday nights, etc.

c) E(x) = 1/p

Discrete Random Variable:

A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.

Discrete random variables are used to quantify the results of random experiments. A discrete random variable takes on an infinite number of possible outcomes. In general, discrete random variables can be counted as 0, 1, 2, 3, 4, ...

Geometric Distribution :

The geometric variate is the variate that specifies the number of consecutive failures before the first success in Bernoulli trials. The probability of success of a Bernoulli trial is given by p and the probability of failure is 1 - p.

The Geometric Random Variable can be written as X ~ G(p).

The probability mass function is P(X = x) = (1  - p)ˣ⁻¹ p

Learn more about Discrete Random Variable:

https://brainly.com/question/17238412

#SPJ4

The length of the building on the scale drawing is found as 16 centimeters.

For the given data in the question-

Dimensions of the building;

Dimensions of the drawing of the building;

Thus, taking ratios of Height to length

125/80 = 25/x

On simplification;

x = 80 x 25 / 125

x = 16

Thus, the length of building on the scale drawing is found as 16 centimeters.

To know more about the scale factor, here

https://brainly.com/question/25722260

#SPJ1

Answer: wutttttttttt

Step-by-step explanation: i jus need points

Answer:

Your answer is 416 + 13 [tex]\sqrt{5}[/tex].

Step-by-step explanation:

Answer:

x1,y16 is the rate of change

Step-by-step explanatI subtracted 13-32 which gives me 16, then I added 16 to 32 to be sure and it gave me 48 so the change on the Y axis is going up by 16 and x axis is going up by 1

The area enclosed by the curves f(x) and g(x) is  1/12

Integral calculus can be used to compute the area between two curves, which is the region between two intersecting curves.

When we are aware of the equation for two curves and the locations of their intersections, integration can be utilized to determine the area under the curves.

Let our given curves be :

f(x) = x² and g(x) = x³ within the interval [0,1]

Formula to calculate area under these curves is

=> A = [tex]\int\limits^{c}_{a} {|f(x) - g(x)| \, dx[/tex]

Interval is given from 0 to 1

Therefore ,

=> A = [tex]\int\limits^{1}_{0} {[x^2 - x^3]} \, dx[/tex]

Integrating,

=> [tex][\frac{x^3}{3} - \frac{x^4}{4}]^{1}_{0}[/tex]

=> 1/3 - 1/4

=> 1/12 is required area

The given question is incomplete So, I've answered the question in general

To know more about Area under curve here

https://brainly.com/question/15122151

#SPJ4

The ratio of rainy days to total days written as a percent will be 75%.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.

Since in the last 24 days, it rained 18 days.

Number of rainy days = 18.

Number of total days = 24

The ratio of rainy days to total days written as a percent will be:

= Number of rainy days / Total days × 100

= 18/24 × 100

= 3/4 × 100

= 75%

Therefore, the ratio is 3:4 which is 75%.

Learn more about ratio on:

brainly.com/question/2328454

#SPJ1

Answer:

0.25 − 3

=0.25 + −3

= −2.75

( a number line to help to)

Step-by-step explanation:

The change in temperature based on the information is 27°F.

It should be noted that temperature simply means the degree of coldness and hotness in a body. In this case, after a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F.

Let the change in temperature be represented by x.

Therefore, -10 + x = -17

x = 17 + 10

x = 27

The Temperature is 27°F.

Learn more about temperature on:

brainly.com/question/24746268

#SPJ1

After a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F. What was the change in temperature?

The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit

Now, According to the question:

The given sphere is of radius R.

Let h be the height and r be the radius of the cylinder inscribed in the sphere.

We know that:

Volume of cylinder

V = [tex]\pi R^2h[/tex]    .....(1)

In right Triangle OBA

[tex]AB^2 + OB^2 = OA^2[/tex]

[tex]R^2 + \frac{h^2}{4} = r^2[/tex]

So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]

Putting the value of [tex]R^2[/tex] in equation (1), We get

V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]

V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex]   ....(2)

dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)

For, Stationary point, dV/dh = 0

[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0

[tex](r^2 - \frac{3h}{4} )[/tex]   => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]

Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]

[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex]   = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0

Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]

Maximum volume is :

[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]

[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]

[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]

[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit

Learn more about Volume of Cylinder at:

https://brainly.com/question/16134180

#SPJ4

The adding property of equality should be used to satisfy the given equation.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

-15 + x/3 = 18

Add 15 on both sides of the equation

So, we have

45 + x = 18 × 3

x = 54 + 45

x = 99

To know more about equation:

https://brainly.com/question/29657983

#SPJ1

The solution of the equation written as an imaginary number is y =  3i or -3i

An imaginary number is a number of the form ai, where a is a real number and i is the square root of -1. Imaginary numbers are often denoted with the letter "i".

Given: y² + 11 = 2

y² + 11 = 2

y² = 2 - 11

y² = -9

y = ±√-9                      

y = ± 3i

y = 3i or -3i

(Note: √9 = 3 and √-9 = 3i)

Thus, the solution is y =  3i or -3i

Learn more about imaginary number on:

https://brainly.com/question/13039076

#SPJ1

1) The enrollment in 2016 will be 7500.

2) In 2026 year the enrollment reach 10,000.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function f(x) represents the number of enrollment.

Defined as;

⇒ F(x) = 250x + 6000

Where x represents year since 2010.

(1) Now for finding the enrollment in 2016;

Put x = 2016 - 2010 = 6 in the function

⇒ F(6) = 250x6 + 6000

          = 7500

Thus, The required number of enrollment = 7500

(2) Now we have to find the year in which enrollment reach 10,000;

i.e f(x) = 10,000

=> 250x + 6000 = 10000

=> 250x = 4000

=> x = 16

Thus, The required year = 2010 + 16

                                     = 2026 answer.

1) The enrollment in 2016 will be 7500.

2) In 2026 year the enrollment reach 10,000.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

A sample size of [214] to be within 5 % of the true proportion of women over age 55 who are widows and be 900 % confident.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

We are given that recent study Indicated that 27% of the 142 women over age 55 in the study were widows

Margin of error  = 0.05 = E

z-score = z/2 = 1.645

n = 0.27 x 0.73 (1.645/ 0.05)²

n = 213.343

n=214

To learn more about standard deviation visit:

brainly.com/question/23907081

#SPJ1

The probability of drawing 2 marbles of different colors would be 0.317.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:

Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81

Total number of ways to draw 2 marbles: 16 (4 marbles of each color)

Probability of drawing 2 marbles of different colors: 81/256 = 0.317

Hence, the probability of drawing 2 marbles of different colors would be 0.317.

To learn more about the probabilities, visit:

https://brainly.com/question/24756209

#SPJ1

The probability of drawing 2 marbles of different colors would be 0.317.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:

Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81

Total number of ways to draw 2 marbles: 16 (4 marbles of each color)

Probability of drawing 2 marbles of different colors: 81/256 = 0.317

Hence, the probability of drawing 2 marbles of different colors would be 0.317.

To learn more about the probabilities, visit:

brainly.com/question/24756209

#SPJ1

Answer:

Step-by-step explanation:

The equation 5x-8+7y=y-6 is linear because it contains only terms with the variables x and y raised to the power of 1. In a linear equation, the highest power of any variable is 1. Nonlinear equations contain exponents that are higher than 1 on one or more variables.