if 18 is an even number, then it is divisible by 2. and if 18 is divisible by 2, then it is a rational number. therefore, if 18 is an even number, then it is a rational number.

The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

Answer:

C

Step-by-step explanation:

Volume of a pyramid = 1/3 base area * height

                                   = 1/3 (8 * 10)(12)

Answer:-11

Step-by-step explanation:

Using the simplex method, the maximum value of Z=5A+4B is found to be 19.2 when A=3.6 and B=1.2. The calculations can be confirmed by using any software that solves linear programming problems.

To solve the given linear programming problem using the simplex method, we start by converting the problem into standard form. We introduce slack variables to convert the inequalities into equations.The initial tableau is as follows:

      | A | B | S1 | S2 | S3 | S4 |   RHS

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

 Z    | -5 | -4 | 0  | 0  | 0  | 0  |    0

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

 S1   |  6 |  4 | 1  | 0  | 0  | 0  |   24

 S2   |  1 |  2 | 0  | 1  | 0  | 0  |    6

 S3   | -1 |  1 | 0  | 0  | 1  | 0  |    1

 S4   |  0 |  1 | 0  | 0  | 0  | 1  |    2

We perform the simplex iterations until the optimal solution is reached. After applying the simplex method, the final tableau is obtained as follows:

      |  A  |  B  |  S1  |  S2  |  S3  |  S4  |   RHS

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

 Z    |  0  | 1.8 | 0.2  | -1   | -0.4 |  0.4 | 19.2

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

 S1   |  0  |  0  |  0   | 1.5  | -1   |  1   |  3

 S2   |  1  |  0  | -0.5 |  0.5 |  0.5 | -0.5 | 1.5

 A    |  1  |  0  | 0.5  | -0.5 | -0.5 |  0.5 |  0.5

 S4   |  0  |  0  |  1   | -1   | -1   |  1   |  1

From the final tableau, we can see that the maximum value of Z is 19.2 when A=3.6 and B=1.2. This solution satisfies all the constraints of the problem. The calculations can be verified using any software that solves linear programming problems, which should yield the same optimal solution.

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Answer:

10 thats the answer

Step-by-step explanation:

3+2=5×2=10

Answer:

Y=COS X+1

Step-by-step explanation:

The function whose graph is given by is y = cos x + 1.

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The graph of the function y = cos(x) + 1 can be understood by analyzing its two component functions:

cos(x) and 1.

The function cos(x) is a periodic function that oscillates between -1 and 1, with a period of 2π.

The graph of cos(x) is a smooth curve that has its maximum value at x = 0 and its minimum value at x = π (or x = -π).

The function 1 is a constant function that takes on the value of 1 for all values of x.

The graph of 1 is a horizontal line that extends infinitely in both directions along the x-axis.

When we add the two functions together, we get the function:

y = cos(x) + 1.

This function shifts the graph of cos(x) upward by 1 unit, so that it oscillates between 0 and 2, with a maximum value of 2 when cos(x) = 1 and a minimum value of 0 when cos(x) = -1.

The resulting graph of y = cos(x) + 1 is a periodic curve that oscillates above and below the horizontal line y = 1, with a period of 2π.

It has its maximum value of 2 when x = 2nπ (where n is an integer), and its minimum value of 0 when x = (2n + 1)π (where n is an integer). The graph is symmetric about the line y = 1, which is the horizontal asymptote of the function.

Thus,

The function whose graph is given by is y = cos x + 1.

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Answer:

Where is the picture so we can see the angles and the triangles

Answer:

x = 2, y = -1

(x,y) = > (2,-1)

Step-by-step explanation:

2x + 5y = -1

3x + 2y = 4

-3(2x + 5y = -1) = > -6x - 15y = 3

2(3x + 2y = 4) = > 6x + 4y = 8

-6x - 15y = 3

6x + 4y = 8

-11y = 11

/-11  /-11

y = -1

2x + 5y = -1

2x + 5(-1) = -1

2x -5 = -1

   +5   +5

2x = 4

/2   /2

x = 2

(x,y) = > (2,-1)

Hope this helps!

In this game, the pure best response equilibria (BNE) are when Anna bids 200 and Brian bids 100, or when Anna bids 100 and Brian bids 200. These equilibria occur because both players are playing their best response to the other player's strategy, resulting in a Nash equilibrium.

(a) The normal form of the game can be represented in a payoff matrix where the rows represent Anna's strategies (bids) and the columns represent Brian's strategies (bids):

scss

Copy code

            Brian

         |   100   |   200   |

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

 100 |  (300, 0) | (300, 0) |

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

 200 | (0, 100)  | (0, 200) |

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

In each cell, the first number represents Anna's payoff, and the second number represents Brian's payoff.

(b) To find all pure best response equilibria (BNE), we need to examine each player's strategy and determine if they have a best response to the other player's strategy.

For Anna:

If Brian bids 100, Anna's best response is to bid 200, as this guarantees a higher payoff of 300.

If Brian bids 200, Anna's best response is to bid 100, as this guarantees a higher payoff of 300.

For Brian:

If Anna bids 100, Brian's best response is to bid 200, as this guarantees a higher payoff of 0.

If Anna bids 200, Brian's best response is to bid 100, as this guarantees a higher payoff of 0.

Therefore, the pure best response equilibria (BNE) of this game are:

(Anna: 200, Brian: 100)

(Anna: 100, Brian: 200)

In both cases, both players are playing their best response to the other player's strategy, resulting in a Nash equilibrium.

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Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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The author of the book "Pilgrim Feet" argues that American society has benefited greatly from the diversity of cultures that exist within it, and this is evident in various aspects of American life.

In "Pilgrim Feet," the author examines the ways in which different cultural groups have contributed to American society and how their interactions have shaped the country's history. The author suggests that these cultural exchanges have led to a diverse and dynamic society that has benefited from the contributions of various ethnic and religious groups.

For instance, the author notes how immigrants from different parts of the world have brought their unique cuisines, music, and other forms of art to the United States, enriching American culture in the process.

Additionally, the author highlights the role of minority groups in promoting social justice and equality, noting how the struggles of these groups have led to significant social and political changes in the country. Overall, the book argues that the diversity of cultures within American society has been a source of strength, and it has contributed to the country's economic, political, and cultural success.

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Answer:

it is 108

Step-by-step explanation:

you know that the 53 angle is also inside the triangle and that 180-125 gives you the second angle 55. you than calculate that the last inner angle is 72 and substract that from 180.

Answer:

108 degrees

Step-by-step explanation:

lets imagine that pqr are the angles of the triangle

<rpq=53°(opposite<)

for <prq 180°-125°(< on a straight line)=55°

<pqr= a+b+c

= 55°+53°+c= 180°(< in a ∆)

= 108°+c =180°

collect like terms

c= 108°-108°

c= 72°

Therefore<pqr= 72°

for the unknown angle which is x

55+53=108( the two sides are facing the exterior <)

Answer:

Step-by-step explanation:

Since there are missing data, let's discuss some facts about regular polygons and their angles.

1) The sum of its Interior angles is given by:

\(S_i=180^{\circ}(n-2) \therefore \:for\: a\:pentagon\:S_i=180^{\circ}(5-2) =540^{\circ}\)

2) Since it is a regular pentagon, each interior angle is congruent:

Each interior angle:

\(Interior\:angle=\frac{540^{\circ}}{5} =108^{\circ}\)

3) If we trace an outside line, the external angle will be supplemental, i.e.

\(m\angle external= 180^{\circ}-108^{\circ} \therefore= 72^{\circ}\)

4) If we trace from each diagonal one line segment, in a regular pentagon that will form 3 triangles with one-third of 108º,i.e.,36º

As we can see, the in the picture below

Answer:

The measures are 22 and 68 degrees

Step-by-step explanation:

for a right triangle, the total angle measure gives 90

Let one of the acute angle be x and the other be y

The measure of one of the acute angle is 4 times the the difference of the measure of the other angle and 5

x = 4(y-5)

Also x + y = 90

Put i into ii

4(y-5) + y = 90

4y-20 + y = 90

5y-20 = 90

5y = 90 + 20

5y = 110

y = 110/5

y = 22

But;

x = 4(y-5)

x = 4(22-5)

x = 4(17)

x = 68

The sum of the acute angles in a right-angled triangle is 90.

The acute angles are 22 and 68 degrees

Let the acute angles be x and y, such that:

\(\mathbf{y = 4(x - 5)}\)

So, we have:

\(\mathbf{x + y = 90}\)

Substitute 4(x - 5) for y

\(\mathbf{x + 4(x - 5) = 90}\)

Open brackets

\(\mathbf{x + 4x - 20 = 90}\)

Add x and 4x

\(\mathbf{5x - 20 = 90}\)

Add 20 to both sides

\(\mathbf{5x = 110}\)

Divide both sides by 5

\(\mathbf{x = 22}\)

Recall that:

\(\mathbf{y = 4(x - 5)}\)

So, we have:

\(\mathbf{y = 4(22 - 5)}\)

\(\mathbf{y = 68}\)

Hence, the acute angles are 22 and 68 degrees

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It is to be noted that the scatter plot that represent the above data is attached accordingly.

A scatter plot is a graph in which the data of two variables are displayed along two axes, and any association is revealed by the pattern of the resultant dots.

Slope-intercept form is y = mx + b

m is the gradient of the line, determined by calculating "change of y divided by change of x"

To compute for the gradient (m) we say:

(60 - 32)/(8-2)

= 28/6

m = 4.667

Next we calculate for b

The point on the graph where the line crosses the vertical line is known as the y-intercept, or b. (y-axis).

Put one of the graph's points, say (2, 32), and the amount of m you just computed into the slope-intercept form to calculate b.

That is:

32 = m(2) + b

Recall that m = 4.667

Hence 32 = 4.667 * 2 + b

32 = 6.667 + b

b = 32 - 6.667

b = 25.33

Given that we have the figures for m and b,
Recall that the function is: y = mx + b; and that

If x = 14 years, then

y = 4.667 * 14 + 25.33

y = 90.668

y ≈ 91 kg.

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Answer:

$27.50

Step-by-step explanation:

55*50%

=55*1/2

=55/2

=27.5

Answer:

27.5

Step-by-step explanation:

50 divided into 2 is 20.50

5 divided by 2 is 2.50

Dilation and rotation transformation produces shapes that are not congruent.

Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.

Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.

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Answer:

goodgydudufjdjdjdjdururirurur7rigjfifut

Step-by-step explanation:

goodghdhfudjdjsdhydydbsjshhdvrjeiid

The characteristics of the given graph that can be used to find the

inequality are the y-intercept and the shaded region of the inequality.

Correct response:

Given:

From the given diagram, we have that the inequality is a linear inequality,

therefore, the inequality can be expressed as y ≤ m·x + c.

Where:

m = The slope

c = The y-intercept

From the graph, the y-intercept of the graph of the inequality is at the point (0, -1)

Therefore;

The shaded region which is to the right of the line with a positive slope

(the straight line increasing from left to right) indicates that the value of y is

less than the equation of the line of the inequality.

The solid line in the graph indicates that the inequality relationship is less

than or equal to (≤).

The inequality that has -1 as the y-intercept and a shaded region to the right of the solid line from among the given options is option j. 3·x - 1 ≥ y

The above inequality can be written as follows;

y ≤ 3·x - 1

Therefore;

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Answer:

c

Step-by-step explanation:

During the youth baseball season, Carter sold hamburgers and hot dogs at the Hillview baseball field and the price of a hamburger is $3, and the price of a hot dog is $4.2.

On Saturday, he sold 30 hamburgers and 25 hot dogs, earning $195 in total. On Sunday, he sold 15 hamburgers and 20 hot dogs, earning $120. The goal is to determine the price of a hamburger and the price of a hot dog.

Let's assume the price of a hamburger is represented by 'h' and the price of a hot dog is represented by 'd'. Based on the given information, we can set up two equations to solve for 'h' and 'd'.

From Saturday's sales:

30h + 25d = 195

From Sunday's sales:

15h + 20d = 120

To solve this system of equations, we can use various methods such as substitution, elimination, or matrix operations. Let's use the method of elimination:

Multiply the first equation by 4 and the second equation by 3 to eliminate 'h':

120h + 100d = 780

45h + 60d = 360

Subtracting the second equation from the first equation gives:

75h + 40d = 420

Solving this equation for 'h', we find h = 3.

Substituting h = 3 into the first equation, we get:

30(3) + 25d = 195

90 + 25d = 195

25d = 105

d = 4.2

Therefore, the price of a hamburger is $3, and the price of a hot dog is $4.2.

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Answer:

51

Step-by-step explanation:

x + y + z  = 0   →-  -(x + y)  = z  →   z^3 =  - (x^3 + 3x^2y + 3xy^2 + y^3)

xyz  = 17

xy [ -(x + y) ]  = 17

xy (x + y)  = -17  →  x^2y + xy^2  = -17  →  3x^2y + 3xy^2  = -51

So......

x^3  + y^3  +  [ z^3 ]

x^3  + y^3  +  [ -  ( x^3 + 3x^2y + 3xy^2 + y^3) ]  =

-3x^2y - 3xy^2  =

-[ 3x^2y + 3xy^2]  =

- [-51]  =

51

please rate 5 stars

Answer: Each friend should bring 10 cups, 10 plates, and 20 napkins.

Sorry if this isn't the proper answer your looking for; I might not be understanding the context of the question.

The roots of the polynomial f(x) = x³ - x² - x - 15 are  3, -1 + 2i and -1 - 2i

A root of a polynomial is a value of x that makes the polynomial equal to zero. A polynomial is a mathematical expression that is made up of terms, each of which includes a variable (x) raised to a power, such as x^2, x^3, x^4, etc. The powers of x are called the degrees of the polynomial.

For example, the polynomial equation x^2 + 2x - 3 = 0 has two roots, x = -1 and x = 3.

The number of roots of a polynomial equation is determined by its degree. A polynomial equation of degree n has at most n roots. A polynomial equation of degree n can have n distinct roots, n-1 distinct roots, or even no roots at all.

f(x) = x³ - x² - x - 15

0 = x³ - x² - x - 15

The roots are 3, -1 + 2i and -1 - 2i

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Answer: 11

Step-by-step explanation:

The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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Answer:

I'll help u with #1 then u can do the others hopefully

Step-by-step explanation:

y=mx+b

1. slope=m

slope=1.5 so y=1.5x+b

y-intercept=b

y-intercept=5 (because (0, 5) means x is 0 and y is 5, which is that point)

Answer: y=1.5x+5

Answer:

some information is missing, so I looked for similar questions and found the attached image:

since each recipe requires ¹/₂ cup of butter, you are able to make 12 ÷ ¹/₂ = 24 recipes with one container of butter (assuming you have all the other ingredients).

One-half, ¹/₂, is a fraction that can also be written in decimal form as 0.5. Two times ¹/₂ is equal to 1, and similarly, twenty four times ¹/₂ is equal to 12.

The solution set of the given homogeneous system in parametric vector form is (x1,x2,x3)=(s,-2,-5)

Parametric vector form:

If there are m-free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors:

x = s1v1 + s2v2 + ··· + sm vm. This is called a parametric equation or a parametric vector form of the solution.

A common parametric vector form uses the free variables as the parameters s1 through sm

Given is a system of equations

We are to solve them in parametric form.

x1 + 3x2 + x3 = 0 --------(1)

-4x1 + 9x2 + 2x3 = 0 ---------(2)

-3x2 - 6x3 = 0--------(3)

From equation(3)

-3x2=6x3

x2=-2x3

substitute in equation(1) and equation(2)

x1+3(-2x3)+x3=0

x1-6x3+x3=0

x1-5x3=0

x1=5x3

So the solution in parametric form is (x1,x2,x3) = (s,-2,5) for all real values.

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Given:-

\( \: \)

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

hope it helps! :)