Find the degree of each algebraic expression
\(pq + {p}^{2} q - {p}^{2} {q}^{2} \)
\( {2y}^{2} z + 10yz\)
​

We need to use distributive property to find the missing factors:

"The distributive property of multiplication says that a multiplication fact can be broken up into the sum of two other multiplication facts."

because 5+2 = 7.

So the correct answer are:

7 X 3 = ( 5 X 3 ) + ( 2 X 3 )

Then

7 X 3 = ( 2 X 3 ) + ( 5 X 3 )

because:

( 5 X 3 ) + ( 2 X 3 ) = ( 2 X 3 ) + ( 5 X 3 )

Also :

7 X 3 = ( 1 X 3) + ( 6 X 3 )

Because 7 x3 = (6+1) x 3 = 1 X 3) + ( 6 X 3 )

The domain of the function will be [-4, 6). Then the correct option is B.

The complete question is attached below.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

\(f(x) = \left\{\begin{matrix}x+4, & if & -4\leq x < 3 \\\\2x-1, & if & 3 \leq x < 6 \\\end{matrix}\right.\)

Then the domain of the function will be [-4, 6).

Then the correct option is B.

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Answer:

The equation of the graph is   y = -lx - 4l - 1.

Step-by-step explanation:

As the values of y are same before and after (4, -1)

the slope of the graph is change on point (4, -1)

the equation of first line is

y - (-1) = 1 (x -4)

the equation of the second line is:

y - (-1) = -1 (x - 4)

As value of y should remain same in both equations

therefore: y - (-1) = - lx - 4l

y = - lx - 4l -1

The equation of the graph is   y = -lx - 4l - 1.

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12620256  different combinations of 31 balloons can be chosen

What are combinations?

Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.

From the question, we understand that; a combination of 31 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

n= 31 +8-1 = 38

r=31

Selection =  \(^{38}C_{31}\)

Use the formula:

\(^{n}C_{r}=\frac{n!}{(n-r)! r!}\)

= > \(^{38}C_{31}=\frac{38!}{(38-31)! 31!}\)

\(^{38}C_{31}=\frac{38!}{7! 31!}\)

         = \(\frac{38*37*36*35*34*33*32*31!}{7*6*5*4*3*2*1* 31!}\)

         = 12620256

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Answer:

C ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Answer:

A.47

Step-by-step explanation:

Step-by-step explanation:

235 / 5 = 47

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

Answer:

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation:

(−∞,∞)

Set-Builder Notation:

{y|y∈R}

Step-by-step explanation:

Answer:

0.125

Step-by-step explanation:

Hope this is helpful

Answer: If at least one constraint in a linear programming model is violated, the solution is said to be infeasible solution. Therefore,  it is the correct answer.

Step-by-step explanation:

In linear programming, an infeasible solution is a solution that does not satisfy all of the constraints of the problem. It means that there are no values of decision variables that simultaneously satisfy all the constraints of the problem.

An infeasible solution can occur when the constraints are inconsistent or contradictory, or when the constraints are too restrictive. In such cases, the problem has no feasible solution, and the optimization problem is said to be infeasible.

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The solution to the linear programming problem is:

Maximum value of z = 120

x₁ = 0, x₂ = 6

To solve the given linear programming problem using the graphical method, we first need to plot the feasible region determined by the constraints and then identify the optimal solution.

The constraints are:

x₁ + x₂ ≥ 12

x₁ + x₂ ≤ 6

x₁, x₂ ≥ 0

Let's plot these constraints on a graph:

The line x₁ + x₂ = 12:

Plotting this line on the graph, we find that it passes through the points (12, 0) and (0, 12). Shade the region above this line.

The line x₁ + x₂ = 6:

Plotting this line on the graph, we find that it passes through the points (6, 0) and (0, 6). Shade the region below this line.

The x-axis (x₁ ≥ 0) and y-axis (x₂ ≥ 0):

Shade the region in the first quadrant of the graph.

The feasible region is the overlapping shaded region determined by all the constraints.

Next, we need to find the corner points of the feasible region by finding the intersection points of the lines. In this case, the corner points are (6, 0), (4, 2), (0, 6), and (0, 0).

Now, we evaluate the objective function z = 15x₁ + 20x₂ at each corner point:

For (6, 0): z = 15(6) + 20(0) = 90

For (4, 2): z = 15(4) + 20(2) = 100

For (0, 6): z = 15(0) + 20(6) = 120

For (0, 0): z = 15(0) + 20(0) = 0

From the evaluations, we can see that the maximum value of z is 120, which occurs at the corner point (0, 6).

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The minimal point does not have x = 0.

(a) Kuhn-Tucker conditions for the minimal value of fThe Kuhn-Tucker conditions are a set of necessary conditions for a point x* to be a minimum of a constrained optimization problem subject to inequality constraints. These conditions provide a way to find the optimal values of x1, x2, ..., xn that maximize or minimize a function f subject to a set of constraints. Let's first write down the Lagrangian: L(x, y, λ1, λ2, λ3) = f(x, y) - λ1(x+y-1) - λ2(xy-3) - λ3x - λ4y Where λ1, λ2, λ3, and λ4 are the Kuhn-Tucker multipliers associated with the constraints. Taking partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4 and setting them equal to 0, we get the following set of equations: 4x - 2y - λ1 - λ2y - λ3 = 0 2y - 2x - λ1 - λ2x - λ4 = 0 x + y - 1 ≤ 0 xy - 3 ≤ 0 λ1 ≥ 0 λ2 ≥ 0 λ3 ≥ 0 λ4 ≥ 0 λ1(x + y - 1) = 0 λ2(xy - 3) = 0 From the complementary slackness condition, λ1(x + y - 1) = 0 and λ2(xy - 3) = 0. This implies that either λ1 = 0 or x + y - 1 = 0, and either λ2 = 0 or xy - 3 = 0. If λ1 > 0 and λ2 > 0, then x + y - 1 = 0 and xy - 3 = 0. If λ1 > 0 and λ2 = 0, then x + y - 1 = 0. If λ1 = 0 and λ2 > 0, then xy - 3 = 0. We now consider each case separately. Case 1: λ1 > 0 and λ2 > 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have the following possibilities: x + y - 1 = 0, xy - 3 ≤ 0 (i.e., xy = 3), λ1 > 0, λ2 > 0 x + y - 1 ≤ 0, xy - 3 = 0 (i.e., x = 3/y), λ1 > 0, λ2 > 0 x + y - 1 = 0, xy - 3 = 0 (i.e., x = y = √3), λ1 > 0, λ2 > 0 We can exclude the second case because it violates the constraint x, y ≥ 0. The first and third cases satisfy all the Kuhn-Tucker conditions, and we can check that they correspond to local minima of f subject to the constraints. For the first case, we have x = y = √3/2 and f(x, y) = -1/2. For the third case, we have x = y = √3 and f(x, y) = -2. Case 2: λ1 > 0 and λ2 = 0From λ1(x + y - 1) = 0, we have x + y - 1 = 0 (because λ1 > 0). From the first Kuhn-Tucker condition, we have 4x - 2y - λ1 = λ1y. Since λ1 > 0, we can solve for y to get y = (4x - λ1)/(2 + λ1). Substituting this into the constraint x + y - 1 = 0, we get x + (4x - λ1)/(2 + λ1) - 1 = 0. Solving for x, we get x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4. We can check that this satisfies all the Kuhn-Tucker conditions for λ1 > 0, and we can also check that it corresponds to a local minimum of f subject to the constraints. For this value of x, we have y = (4x - λ1)/(2 + λ1), and we can compute f(x, y) = -3/4 + (5λ1^2 + 4λ1 + 1)/(2(2 + λ1)^2). Case 3: λ1 = 0 and λ2 > 0From λ2(xy - 3) = 0, we have xy - 3 = 0 (because λ2 > 0). Substituting this into the constraint x + y - 1 ≥ 0, we get x + (3/x) - 1 ≥ 0. This implies that x^2 + (3 - x) - x ≥ 0, or equivalently, x^2 - x + 3 ≥ 0. The discriminant of this quadratic is negative, so it has no real roots. Therefore, there are no feasible solutions in this case. Case 4: λ1 = 0 and λ2 = 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have x + y - 1 ≤ 0 and xy - 3 ≤ 0. This implies that x, y > 0, and we can use the first and second Kuhn-Tucker conditions to get 4x - 2y = 0 2y - 2x = 0 x + y - 1 = 0 xy - 3 = 0 Solving these equations, we get x = y = √3 and f(x, y) = -2. (b) Show that the minimal point does not have x=0.To show that the minimal point does not have x=0, we need to find the optimal value of x that minimizes f subject to the constraints and show that x > 0. From the Kuhn-Tucker conditions, we know that the optimal value of x satisfies one of the following conditions: x = y = √3/2 (λ1 > 0, λ2 > 0) x = √3 (λ1 > 0, λ2 > 0) x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4 (λ1 > 0, λ2 = 0) If x = y = √3/2, then x > 0. If x = √3, then x > 0. If x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4, then x > 0 because λ1 ≥ 0.

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Answer: a) 7        b) -4         c) 15         d) -1        e) -8

Step-by-step explanation:

7x + 9 = 58

     -9   -9

7x       =  49

÷7         ÷7  

  x      =   7

x/2 - 12 =  -14

      +12   +12

x/2       =   -2

×2          ×2  

  x      =    -4

-3x + 33 =  -12

       -33   -33

-3x         =  -45

÷-3         ÷-3  

  x         =   15

8x + 16 =    8

      -16   -16

8x        =   -8

÷8          ÷8  

  x      =    -1

2x - 2 = -18

     +2   +2

2x       = -16

÷2         ÷2  

  x      =  -8

Answer:

Vertex: (−3,−2)

Answer:
(-3, -2)

Step-by-step explanation:

The vertex of a graph of a quadratic function is the point where the graph reaches its minimum or maximum value, and it can be found by completing the square.

To find the vertex of the graph F(x) = |x+3| -2, we can rewrite the function as follows:

F(x) = (x+3) - 2, if x+3 ≥ 0

F(x) = -(x+3) - 2, if x+3 < 0

The first equation represents the portion of the graph where x+3 is positive, and the second equation represents the portion of the graph where x+3 is negative.

To find the vertex of the graph, we can find the average of the zeros of the function. The zeros of the function are the values of x that make the function equal to 0.

The zeros of the first equation are found by setting the expression equal to 0 and solving for x:

x+3-2 = 0

x = -1

The zeros of the second equation are found by setting the expression equal to 0 and solving for x:

-(x+3)-2 = 0

-(x+3) = 2

x = -5

The average of the zeros is (-1 + -5) / 2 = -3. This is the x-coordinate of the vertex of the graph.

To find the y-coordinate of the vertex, we can plug the x-coordinate into one of the equations and solve for y:

F(-3) = (-3+3) - 2 = -2

Therefore, the vertex of the graph F(x) = |x+3| -2 is (-3, -2).

Answer:

y=-2x+5

Step-by-step explanation:

Based on the information provided, only one of the independent variables can be an indicator (dummy) variable, which is:

- The player was traded in the last 5 years

Based on the information provided, only one of the independent variables can be an indicator (dummy) variable, which is:

- The player was traded in the last 5 years

This variable can take on a value of 0 or 1, where 0 represents that the player was not traded in the last 5 years, and 1 represents that the player was traded in the last 5 years. The other independent variables are continuous variables (e.g., player's age, player's height, career free throw percentage, average points per game) or categorical variables that do not need to be represented as dummy variables (e.g., the team had greater than 45 wins in the previous season).

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The main memory process that accounts for Shayla's ability to retain the vocabulary she learned in her first semester Spanish class is long-term memory.

Long-term memory is a type of memory storage that has a vast capacity and can store information for extended periods of time, ranging from minutes to years. It allows for the encoding, storage, and retrieval of information that can be retained for a long duration.

In Shayla's case, the vocabulary she learned in her Spanish class is stored in her long-term memory, enabling her to access and retain that information even after the class has ended. Long-term memory plays a crucial role in the consolidation and retention of learned knowledge and experiences, contributing to the long-term retention of information.

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Answer:

0.15

Step-by-step explanation:

Answer:

45 + 21e

3 (7e + 15)

Answer:

answer 2 I think.... hi fellow kpop stan

Step-by-step explanation:

❤

Given sides of the triangle:

We know that the perimeter of a triangle is the sum of all the sides of a triangle.

Perimeter of the triangle,

= 3x^2 + 8 + 2x^2 + x + x - 3

= 3x^2 + 2x^2 + x + x + 8 - 3

= 5x^2 + 2x + 5

Therefore, the perimeter of the triangle is 5x^2 + 2x + 5. Hence, the option A is the correct answer.

Answer:

13 is the answer.

Step-by-step explanation:

a^2+ b^2 = C^2  

13^2 + 5^2= c^2

169 = C^2

13=C

True. Selective distribution is a strategy in which a manufacturer limits the number of outlets at which its product is sold.

This strategy is often used for medium- and higher-priced products or stores that consumers don't expect to find on every street corner. By limiting the availability of the product, the manufacturer can maintain a premium image and prevent price erosion.

In contrast, products that are widely available and low-priced are more likely to be distributed through intensive distribution, in which the manufacturer tries to get the product into as many outlets as possible.

This strategy is effective for products with high turnover rates and where consumers prioritize convenience and accessibility over brand image.

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Answer:

Not all the means are equal.

Step-by-step explanation:

In an ANOVA table, a sum of squares for the independent variable divided by its respective degrees of freedom.

So if the omnibus null hypothesis is rejected it means that there is sufficient evidence to conclude that not all the means are equal.

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If the omnibus null hypothesis is rejected in a one-factor ANOVA, then, we can conclude that at least one of the population means is different from at least one other population mean.

ANOVA table gives us the total sum of squares ( TSS ), the residual sum of squares ( RSS ) and the estimated sum of squares ( ESS ).

It establishes the relation that:

ESS + RSS = TSS.

If we reject the omnibus null hypothesis, then it means that:

at least one of the population means is different from at least one other population mean.

Therefore, we get that, if the omnibus null hypothesis is rejected in a one-factor ANOVA, then, we can conclude that at least one of the population means is different from at least one other population mean.

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0, 1, 2, 4, 5, and 7.

So that would be 6 digits.

In mathematics, the only single symbol used to represent a number is a digit. For instance, there are two digits in the numbers 89: 8 and 9. As a result, in everyday life, digits like 0, 1, 2, 3, 4, 5, 6, 7, 8, and 0 are employed to represent groups of numbers and perform mathematical operations. A positional numeral system uses a single sign, such as "2," or a set of symbols, such as "25," to represent numbers. The word "digit" derives from the fact that the ten fingers of the hands, or digit in Latin, corresponding to the ten symbols of the decimal system, which uses the base-10 numeral system.

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The measure of an exterior angle of a regular 99-gon is approximately 3.6 degrees

We know that the sum of all the exterior angles in a polygon is 360 degrees.
Therefore, the measure of each exterior angle in a regular polygon of n sides is given by:measure of each exterior angle = 360/n
We have a 99-gon which is a regular polygon.
Hence, its measure of each exterior angle can be calculated as follows:measure of each exterior angle = 360/99measure of each exterior angle ≈ 3.6364
The measure of an exterior angle of a regular 99-gon is approximately 3.6364 degrees.
Rounding off to the tenth place, we get the required measure of an exterior angle of a regular 99-gon as 3.6 degrees.

Therefore, the measure of an exterior angle of a regular 99-gon is approximately 3.6 degrees.

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There are three major forms of linear equations:

Point slope form:

The point-slope form, as its name suggests, identifies a point on a line and its slope. Not frequently is this form provided to assist with line graphing. To get from a verbal or visual representation of a line to its slope-intercept or standard form, however, is where it is more frequently utilized.

Slope intercept form:

A line's slope and y-intercept are communicated using the slope-intercept form. Technically speaking, it is an exception to the point-slope form.

Standard form:

An equation's conventional form is as follows:

Ax+By=C

Where A is not a negative number and B, C, and all three are whole numbers.

Hence we get the required answer.

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Answer:

y = 28

Step-by-step explanation:

0.5y + y/ 3 = 0.25y + 7

1.5y / 3 = 0.25y + 7

y/2 = 0.25y + 7

y = ( 0.25y + 7)*2

y = 0.5y + 14

y - 0.5y = 14

0.5y = 14

y = 14/0.5

y = 28

None of the given functions (A, B, C, or D) have a horizontal asymptote at y = 3 since they are all linear functions, not exponential functions. Thus, the correct option is :

(E) None of these.

To determine which of the given exponential functions has a horizontal asymptote at y = 3, we need to examine the behavior of the functions as x approaches positive or negative infinity.

Let's analyze each option:

(A) f(x) = -3x + 3

This is a linear function, not an exponential function. It does not have an exponential growth or decay component and does not have a horizontal asymptote at y = 3.

(B) f(x) = -3x - 3

Again, this is a linear function, not an exponential function. It also does not have an exponential growth or decay component and does not have a horizontal asymptote at y = 3.

(C) f(x) = 3 - x + 3

This is not an exponential function. It is a linear function with a negative slope. It does not have an exponential growth or decay component and does not have a horizontal asymptote at y = 3.

(D) f(x) = 3 - x - 3

Similar to the previous options, this is not an exponential function. It is a linear function with a negative slope. It also does not have an exponential growth or decay component and does not have a horizontal asymptote at y = 3.

Thus, the correct option is :

(E) None of these.

The correct question should be :

Which of the following exponential functions has a horizontal asymptote at y=3 ？

(A) fx=-3x+3

(B) fx=-3x-3

(C) fx=3-x+3

(D) fx=3-x-3

(E) None of these.

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The OLS estimate of the return to an additional year of schooling is 0.074. This means that for every additional year of schooling, the individual's earnings will increase by 7.4%. This is statistically significant at the 5% level of significance because the t-value is 0.074/0.025 = 2.96, which is greater than the critical value of 1.96.

However, Sharon is not correct in thinking that this is the true return to schooling. This is because there may be other factors that affect earnings that are not included in the model, such as ability or family background. These omitted variables can bias the estimate of the return to schooling.

Sharon could use the information about the starting age and compulsory schooling age to obtain the true return to schooling. This is because these rules create exogenous variation in the amount of schooling that individuals receive. She could use this exogenous variation to estimate the causal effect of schooling on earnings by using an instrumental variables approach. By using the starting age and compulsory schooling age as instruments for years of schooling, she could obtain an unbiased estimate of the true return to schooling.

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