find the axis of symmetry for f(x)=x^{2}+12x+31

Answer:

6 x (9 + 9), (6 x 9) + (6 x 9), 54 + 54 = 108

Those are the answers for the blanks, hope this helped! :)

Answer:

Exponential notion makes a big number easier to write and read.

Step-by-step explanation:

By using Venn diagram the following probabilities are 0.75,0.25,0.9 and 0.625.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

Number of clients= 200

Number of television= 150

Magazines=80

Both magazine and television=50

Now,

To complete the diagram, we can fill in the following values:

The size of T is 150.

The size of M is 80.

The size of TM (the overlap between T and M) is 50.

The size of C (the total number of clients who use either T or M) is 150 + 80 - 50 = 180.

The size of U (the number of clients who use neither T nor M) is 200 - 180 = 20.

Now we can use the Venn diagram to answer the following probabilities:

i. P(T) is the probability that a randomly selected client uses television. This is the size of T divided by the total number of clients, which is 150/200 = 0.75.

ii. P(T ∩ M) is the probability that a randomly selected client uses both television and magazines. This is the size of TM divided by the total number of clients, which is 50/200 = 0.25.

iii. P(T ∪ M) is the probability that a randomly selected client uses either television or magazines (or both). This is the size of C divided by the total number of clients, which is 180/200 = 0.9.

iv. P(T|M) is the probability that a randomly selected client uses television given that they use magazines. This is the size of TM divided by the size of M, which is 50/80 = 0.625.

Therefore, by probability the answer will be 0.75,0.25,0.9 and 0.625.

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The integer to represent the profit of php 100.00 is +100.

Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.

Given that, a profit of php is 100.00​.

The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.

So, here the integer is +100

Therefore, the integer to represent the profit of php 100.00 is +100.

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Answer:

answer is 5

Step-by-step explanation:

2x=5×2

so 2x=10

10-5=5

so 2x-5=5

Answer:

5

Step-by-step explanation:

2x - 5 first, substitute

2(5) - 5 then, multiply

10 - 5 = 5

Answer:404087

Step-by-step explanation:

use the calculator frfr

Answer:

404087

Step-by-step explanation:

One change that Pedro can make to his plan to ensure that he meets his daily running goal is to increase the estimated number of steps per mile.

If Pedro overestimates the number of steps in a mile, he will end up taking more steps than he initially planned for, which can help him reach his daily goal.

For example, if Pedro increases his estimate from 2,000 steps per mile to 2,500 steps per mile, he will need to run approximately 4 miles per day to reach his goal of 10,000 steps. This will make it more likely for him to reach his daily goal within the 4 hours of running over the 5 days.

Alternatively, Pedro can increase his running speed to cover more distance in a shorter period of time. For instance, if he increases his running speed from 6 miles per hour to 8 miles per hour, he will need to run for only about 2.5 hours per day to reach his goal of 10,000 steps.

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The inequalities that are represented by the given graph are expressed as;

y - x > 0 and y ≥ 1

Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

For the dashed line, shading is above the line, the y-intercept is 0.

Slope is 1. Thus, equation is;

y - x > 0

For the horizontal line, the inequality is expressed as;

y ≥ 1

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The constant percent rate of change per unit interval is approximately 0.0305 or 3.05%.

What is the exponential functions?

An exponential function is a mathematical function of the form:

[tex]f(x) = a^x[/tex]

The given formula for the number of visitors to the county parks system is:

[tex]A = 20.6(1.03)^t[/tex]

where t is the number of years after 2010 and A is the number of visitors in thousands.

To find the constant percent rate of change per unit interval, we can take the derivative of A with respect to t:

[tex]dA/dt = 20.6(1.03)^t * ln(1.03)[/tex]

The constant percent rate of change per unit interval is given by the expression:

r = (dA/dt) / A

Substituting the values of dA/dt and A, we get:

[tex]r = [20.6(1.03)^t * ln(1.03)] / [20.6(1.03)^t]\\r = ln(1.03)\\r = 0.0305[/tex]

Hence, the constant percent rate of change per unit interval is approximately 0.0305 or 3.05%.

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The expected number of not blue is 54

From the question, we have the following parameters that can be used in our computation:

Spinner

Using the above as a guide, we have the following probability

P(Not Blue) = Not Blue/Total

So, we have

P(Not Blue) = 6/9

When it is spun 81 times, the expected number of times is

Times = 6/9 * 81

Evaluate

Times = 54

Hence. the number of times is 54

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Schedule K-1 (Form 8865) is used to report the partner's share of income, deductions, credits, and other items for the tax year of a foreign partnership.

Identification information: Fill out the partnership's name, employer identification number (EIN), and address.

Partner's identifying information: Fill out the partner's name, identifying number (usually their taxpayer identification number or TIN), address, and their percentage of ownership in the partnership.

Income items: Report the partner's share of ordinary income, net rental income, gain or loss from the sale of property, and other income items on lines 1-7. Make sure to also include any foreign source income or deductions.

Deductions: Report the partner's share of partnership deductions, such as business expenses, depreciation, and depletion, on lines 8-15.

Credits: Report the partner's share of any foreign taxes paid or other credits on lines 16-21.

Other items: Report any other items that are required to be reported on Schedule K-1, such as guaranteed payments, charitable contributions, and Section 743(b) adjustments, on lines 22-27.

At-risk limitation: If the partnership is engaged in an activity subject to the at-risk rules, report the partner's share of the at-risk limitation on line 28.

Passive activity limitation: If the partnership is engaged in a passive activity, report the partner's share of the passive activity limitation on line 29.

P.S Your question is incomplete, so I gave a general overview of the tax form for better understanding.

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The exponential function that passes through (-2,6) and (3,1) is y = 2.93(0.6988)ˣ

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

An exponential equation is in the form:

y = abˣ

where a is the initial value and b is the multiplier.

Given that an exponential function that passes through (-2,6) and (3,1). At the point (-2, 6):

6 = a(b)⁻²

a/b² = 6

a = 6b²   (1)

At the point (3, 1):

1 = ab³

substitute a = 6b²:

1 = 6b²(b³)

1/6 = b⁵

b = 0.6988

a = 6(0.6988)²

a = 2.93

The exponential function is y = 2.93(0.6988)ˣ

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Answer:

Let's use A to represent the number of adult tickets sold and C to represent the number of children's tickets sold.

We know that A + C = 166, since the total number of tickets sold is 166.

We also know that the revenue earned from adult tickets is $5A and the revenue earned from children's tickets is $3C. Since the total revenue earned is $718, we can write:

5A + 3C = 718

Now we have two equations with two variables:

A + C = 166

5A + 3C = 718

We can solve for A in the first equation to get:

A = 166 - C

Then we can substitute this expression for A into the second equation:

5(166 - C) + 3C = 718

Simplifying and solving for C, we get:

830 - 2C = 718

2C = 112

C = 56

So 56 children's tickets were sold. We can substitute this value back into the first equation to solve for A:

A + 56 = 166

A = 110

Therefore, 110 adult tickets were sold.

Answer:

Step-by-step explanation:

Let's use the following variables:

a = number of adult tickets sold

c = number of children tickets sold

We know that:

a + c = 166 (total number of tickets sold)

5a + 3c = 718 (total revenue)

We can solve this system of equations by substitution or elimination. Here, we'll use elimination:

Multiply the first equation by 3: 3a + 3c = 498

Subtract the second equation from the first: 2a = 220

Solve for a: a = 110

So 110 adult tickets were sold. We can find the number of children's tickets by substituting a = 110 into either of the original equations:

c = 166 - a = 166 - 110 = 56

Therefore, 110 adult tickets and 56 children's tickets were sold.

Answer:

Sum: not present

Term: 4(2x + 3), 5y

Product: 4 and (2x + 3), 4 and 2x, 4 and 3, 5 and y

Factor: 4, 2x, 3, 5, y

Quotient: (4(2x + 3)) ÷ 5y

Coefficient: 4, 5

Step-by-step explanation:

The calculation of volume for the different kind of prisms are:

Rectangular Prism- 1 dm³

Tall triangular prism- 1 dm³

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

Rectangular prism: A rectangular prism that is not a cube can have dimensions of 0.5 dm x 0.5 dm x 4 dm.

This gives a volume of:

0.5 dm x 0.5 dm x 4 dm = 1 dm³

The rectangular prism has six faces, all of which are rectangles.

Tall triangular prism: A tall triangular prism can have a triangular base with sides of length 1 dm, 1 dm, and 2/√3 dm, and a height of 2√3/3 dm. This gives a volume of:

(1 dm x 1 dm x 2/√3 dm) x (2√3/3 dm) = 1 dm³

The tall triangular prism has five faces, one of which is a parallelogram and the other four are triangles.

To prove that each of these prisms has a volume of 1 dm³, we can use the formula for the volume of a prism, which is:

Volume = Base Area x Height

For each of the prisms above, we have calculated the base area and height such that their product equals 1 dm³.

Therefore, each prism has a volume of 1 dm³.

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Answer: (see attached file/screenshot)

Step-by-step explanation: You didn't specify the question so im guessing we solve with the quadratic formula

These two situations are examples of poor conflict resolution because they do not offer a space for dialogue between the individuals involved, but rather there is only judgment by law without any mediation.

Conflict resolution is a term that refers to the ability of individuals to resolve conflicts or differences with others in a peaceful manner agreed upon by all parties involved. In this case, these two examples are not examples of good conflict resolution because there is no space for dialogue between students and teachers, but rather there is only aggression and prosecution before the entities in charge of justice in each country.

Due to the above, we believe that some strategies to end the culture of violence in schools is to spread messages of dialogue and conflict resolution in a peaceful manner. Also, offer workshops for parents so that from home conflict resolution is reinforced through dialogue.

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The domain and the range of h(n) consist of all possible sets of whole numbers.

Other answers are listed below

How to determine the domain and the range of h(n)

From the question, we know that:

h(n) is the number of houses

n and h(n) can only take whole numbers as its values

So, we have

Thus, the domain and range consist of all possible sets of whole numbers.

How to determine h(5) and h(11)

From the figure, we can see that

The number of houses is the same as the figure number

This means that

h(5) = 5 and h(11) = 11

How to represent the explicit function of h(n)

By the computations above, we have the formula of h(n) to be:

h(n) = n

The values of s(4) and s(7)

Here, we have

s(n) is the number of segments

From the figure, we can see that

The number of segments is twice the the figure number

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

Recall that:

The number of segments is twice the the figure number

This means that

The growth pattern of s(n) is linear, with a constant rate of change

The explicit function of s(n)

Above, we have

The number of segments is twice the the figure number

Mathematically, this can be expressed as

s(n) = 2n

How to complete the table for f(5) and f(7)

From the table, we can see that

The division of a term by 2 gives the next term

So, we have

f(5) = 2/2 = 1

f(7) = 1/2/2 = 1/4

How to determine the domain of f(n)

The possible values of n are real numbers

Thus, the domain consist of all possible sets of real numbers.

The observation of the function

Above, we have

The division of a term by 2 gives the next term

This represents the observation

How to determine the value of g(4)

From the question, we have

This means that

g(n) = 2(9)^n-1

So, we have

g(4) = 2(9)^3

g(4) = 1458

How to complete the statements

The function is a doubling function

So, we have

g(n) = g(n - 1) * 2, g(n) = g(n - 2) * 4 and  g(n) = g(n - 3) * 8

How to determine the value of g(24)/g(21)

Recall that

g(n) = 2(9)^n-1

So, we have

g(24) = 2(9)^23

g(21) = 2(9)^20

When the equations are divided, we have

g(24)/g(21) = 2(9)^23/2(9)^20

Evaluate

g(24)/g(21) = 729

Hence, the value is 729

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Answer:

492

Step-by-step explanation:

The GCF is found through p.i.g method.

6-2=3

Answer:4,383,900

Step-by-step explanation:

4,383,900

The correct statements regarding the translation are given as follows:

A translation changes only the position of the figure, keeping angle measures and orientation correct, hence the second and the third options are correct.

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The table that can be constructed with the following equation has vales x: 0, 1, 2, 3 and y = 0, 8, 16, 24.

When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0.

The slope of the linear relationship is eight. The solution is below, along with a picture of the line.

Substitute different values of x to obtain value of y:

The table is given below:-

x  I  y

-------

0  I  0

1  I  8

2  I 16

3  I 24

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The complete question is:

Answer:

Modus Tollens

Step-by-step explanation:

Consider the following argument: If we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase, the bookcase collapses. We do not put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase. Hence, the bookcase does not collapse.

The logical form of this argument is Modus Tollens.

Modus Tollens is a mode of argumentation that involves affirming the consequent of a conditional statement. In this argument, the conditional statement is "If we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase, the bookcase collapses." The antecedent of this statement is "we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase," and the consequent is "the bookcase collapses."

Modus Tollens is used to prove the negation of the consequent by negating the antecedent. In other words, if the consequent is not true, then the antecedent must also not be true. Thus, in this argument, since we know that the bookcase does not collapse, we can conclude that we did not put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase.

Therefore, the logical form of this argument is Modus Tollens.

The solution for the function at the different values of x are,

f(-10) = 20001

f(2) = 49

f(3) = 214

In mathematics, functions are often represented by equations or formulas, and take one or more input values to produce an output value. They can be used to model a wide variety of phenomena, from physical systems to economic behavior to social dynamics.

The given function is f(x) = 2x⁴ + x² - 10x + 1. The output of the function at the different values of x will be calculated as,

At x = -10,

f(x) = 2x⁴ + x² - 10x + 1

f(-10) = 2(-10)⁴ + (-10)² - 10(-10) + 1

f(-10) = 20001

At x = 2,

f(x) = 2x⁴ + x² - 10x + 1

f(2) = 2(2)⁴ + (2)² + 10(2)  + 1

f(2) = 49

At x = 3,

f(x) = 2x⁴ + x² - 10x + 1

f(3) = 2(3)⁴ + (3)² + 10(2) + 1

f(3) = 214

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We can say that line $p$ passes through point $H$, which is also enough information to uniquely determine line $p$.

What is Line point postulate ?

The line-point postulate, also known as the incidence postulate, is a fundamental axiom in geometry that states that for any two points in a plane, there exists exactly one line that contains both points.

In other words, the line-point postulate asserts that a line can be uniquely determined by two distinct points that lie on it. This is one of the most basic and intuitive principles in geometry, and it is essential for building a foundation for more advanced concepts such as angles, triangles, circles, and more.

The Line-Point Postulate states that a line can be uniquely determined by any two distinct points on the line. In this diagram, we can see an example of this postulate in action.

For instance, we can say that line $q$ passes through points $J$ and $K$, so according to the Line-Point Postulate, this is enough information to uniquely determine the line $q$. Similarly,

Therefore, we can say that line $p$ passes through point $H$, which is also enough information to uniquely determine line $p$.

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The slope of the line of fit is 7.5% per hour.

In mathematics, slope refers to the measure of steepness or incline of a line. It is the ratio of the vertical change between two points on the line (the rise) to the horizontal change between the same two points (the run).

To find the slope of the line of fit, we need to use the formula:

slope = change in y / change in x

In this case, the change in y represents the change in the predicted grade on the test, and the change in x represents the change in the number of hours studied. From the given data, we can see that:

The predicted grade for a student who studies for 0 hours is 80%.

The predicted grade for a student who studies for 1 hour is 90% (80% + 10%).

The predicted grade for a student who studies for 2 hours is 95% (90% + 5%).

Using this information, we can calculate the slope of the line of fit:

slope = (95% - 80%) / (2 hours - 0 hours) = 15% / 2 hours = 7.5%/hour

The slope of the line of fit is 7.5% per hour. This means that for each additional hour a student studies, their predicted grade on the test is expected to increase by an average of 7.5%. The slope represents the rate of change of the predicted grade with respect to the number of hours studied. In this case, a positive slope indicates that there is a positive correlation between the number of hours studied and the predicted grade on the test. The higher the slope, the steeper the line of fit, and the greater the impact of studying on the predicted grade.

Therefore, the slope of the line of fit is 7.5% per hour

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The company is searching for a fill amount of  12.305 ounces to identify the highest 1.5% of fill amounts poured by the filling machine.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given mean of 12.23 ounces and a standard deviation of 0.04 ounces.

To find the fill amount for the highest 1.5% of the fill amounts

we need to find the z-score corresponding to the 98.5th percentile

Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 98.5th percentile is  1.81.

The formula for converting a z-score to a raw score is:

x = μ + zσ

where x is the raw score we want to find, μ is the mean, z is the z-score, and σ is the standard deviation.

x = 12.23 + 1.81(0.04)

x = 12.305 ounces

Therefore, the company is searching for a fill amount of  12.305 ounces to identify the highest 1.5% of fill amounts poured by the filling machine.

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Answer:

The correct equation is y = -2x - 4.

PART 1: (a)The value of x in the pie graph is x = 30°

PART 2: (a)The value of x is 36°

(c) percentage of students for soccer is 25%

PART 3: (a)The value of Art is 165°

PART 1

(a) The value of x in the pie graph can be found by subtracting the other values from 360° because the sum of angles in a circle is 360°. That is:

x = 360 - 180 - 60 - 45 - 45 = 30°

(b) frequency = (angle of the part)/360 * 20

Baksket ball = 162/360 * 20 = 12

Bus        12

Car         4

Train       3

Walk       2

Bicycle   3

PART 2

(a) The value of x can be found by subtracting the other values from 360° because the sum of angles in a circle is 360°. That is:

x = 360 - 150 - 45 = 36°

(b) frequency = (angle of the part)/360 * 24

Basketball = 180/360 * 24 = 9

Basketball  9

Tennis        2

Hurling       4

Soccer       5

(c) percentage of student for soccer = 5/20 * 100 = 25%

PART 3

(a) The value of Art can be found by subtracting the other values from 360° because the sum of angles in a circle is 360°. That is:

Art = 360 - 162 - 90 - 72 = 165°

(b) frequency = (angle of the part)/360 * 120

Technology = 150/360 * 120 = 50

Technology  50

Music            15

Art                 55

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The equation of the new graph is:

f(x) = e^(x-6)

The graphs of the two functions f(x) = e^x and f(x) = e^(x-6) are shown below

From the question, we are to determine the equation of the new graph.

If the graph of the function f(x) = e^x is shifted 6 units to the right, the equation of the new graph can be found by replacing x with (x - 6) in the original equation.

This is because a horizontal shift of a function f(x) to the right by c units can be achieved by replacing x with (x - c) in the equation of the function. So, for the given function, a shift to the right by 6 units would be achieved by replacing x with (x - 6) in the original equation f(x) = e^x.

Therefore, the equation of the new graph is:

f(x) = e^(x-6)

This can also be written as:

f(x) = e^x / e^6

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