The Town Theater receives $4212 by selling 465 tickets to
the opening night of the revue. If the full price of a ticket is $10.00
and discount tickets for students and seniors are $8.00 each, how
many discounted senior/student tickets were sold?

There are only prime factors of the number 7 that are possible which are 1 and 7.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

Prime factorization is the process of expressing a number as the sum of all its prime factors. In prime factorization, each and every integer is a prime number.

Factors can be found using either division or multiplication. Rules of divisibility can also be used.

There are only prime factors of the number 7 that are possible which are 1 and 7.

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Answer:

no solutions

Step-by-step explanation:

y = -x + 4

y=-x+1

-x+1 = -x+4  ==> since y=-x+1 and y=-x+4, -x+1=-x+4

-x+1-1 = -x+4-1  ==> isolate x on one side by subtracting 1 on both sides

-x = -x+3

-(-x) = -(-x+3)

x = x - 3  ==> this isn't equal since a number won't have the same value if

                     you take away 3 from it.

Hence, there are no solutions.

Answer:

There is no solution

Step-by-step explanation:

y = -x + 4

y=-x+1

If we solve

-x + 4 = -x +1

Add x to both sides and it will be 0

So, there is no solution!

Answer:

(1) The answer is given in the paper.

(2) The answer is given in the paper.

(3) PT = 21.26 cm

Step-by-step explanation:

(1) the paper says the answer is 7.81 cm

(2) the paper says the answer is 42 cm

(3) The work is in the image that is attached to this response.

The solution of the given quadratic equation is  x = (- 7 ± √(65)) / (2)

The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given is a quadratic equation,

For this case, the first thing we must do is rewrite the polynomial:

x² + 7x - 4 = 0

We use the resolver to solve the problem using quadratic formula;

x = (- b ± √(b² - 4 × a × c)) / (2 × a)

Where,

a = 1

b = 7

c = -4

Substituting the values:

x = (- 7 ± √((7)² - 4 × (1) × (- 4))) / (2 × (1))

x = (- 7 ± √(49 + 16)) / (2×(1))

x = (- 7 ± √(65)) / (2)

Hence, The value of x is (- 7 ± √(65)) / (2)

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Answer:

the result of subtracting (3x^3 −2x^2 +6x−1) from the sum of (2x^3 −3x+2) and (5x^2 +4x−6) is −x^3 +3x^2 +7x−5.

Step-by-step explanation:

To find the result of subtracting (3x^3 −2x^2 +6x−1) from the sum of (2x^3 −3x+2) and (5x^2 +4x−6), we can first add the two given expressions to find the sum, and then subtract the third expression from that sum.

The sum of (2x^3 −3x+2) and (5x^2 +4x−6) is:

(2x^3 −3x+2) + (5x^2 +4x−6) = 2x^3 +5x^2 −3x+4x −6 = 2x^3 +5x^2 +x−6

Subtracting (3x^3 −2x^2 +6x−1) from this sum gives us:

(2x^3 +5x^2 +x−6) − (3x^3 −2x^2 +6x−1) = (2x^3 −3x^3) + (5x^2 −2x^2) + (x+6x) − (−1−6) = −x^3 +3x^2 +7x−5

Therefore, the result of subtracting (3x^3 −2x^2 +6x−1) from the sum of (2x^3 −3x+2) and (5x^2 +4x−6) is −x^3 +3x^2 +7x−5.

Sam spent two-fifth of his work day by answering email. He works for 9 hours.

Steps to translate and solve a word problem using algebraic expressions:

- Assign the unknowns to variables

- Translate the word into operators plus, less, multiply, or division

- Isolate the unknown

In the given problem, let p is the variable to express the total hours Sam worked yesterday.

He spent two-fifth of hi work day by answering email = 2/5 p

He spent 3.6 hours answering email yesterday, means:

2/5 p = 3.6

p = 5 x 3.6/2 = 9 hours

Hence, Sam worked for 9 hours.

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The documents needed for SSS loan sickness benefit are as follows :

                 - Driver’s License

                 - Passport

                 - Voter’s ID Card

                 - National Bureau of Investigation (NBI) Clearance

                 - Postal Identity Card

                 - Any other government-issued (secondary) ID      cards/documents

                 - Laboratory, X-ray, ECG, and other diagnostic results

                 - Operating room/clinical record that will support the diagnosis

For illnesses or injuries that occurred abroad, the issuing nation's official documentation must include an English translation and be properly authenticated by the Philippine Embassy or Consulate Office or properly certified by a notary public of the receiving nation.

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Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.

Following steps to graph inequalities on a calculator:

1) Press the [Y=].

2) Press [3] [X,T,θ,n] [+] [2] on Y1.

3) Press [◄] six times until the symbol to the left of Y1 is flashing.

4) Press [ENTER] [▼] to select the Line area.

5) Press [►] repeatedly until a triangle pointing to the lower part is displayed.

6) Press [▼] [ENTER].

7) This will change the graph style to shade below the function (this style was chosen because the solution set consists of all real numbers below the line of the y= equation).

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Answer: the tradition is to use (x, y) as the order of the coordinate pair locating a point on a plane

Step-by-step explanation: A two-axis system of east-west and north-south was defined using the algebra coordinate system created by mathematician René Descartes in the 1600s

The y-intercept is (0, 5). Hence, the intercepts of the equation 5x + 3y = 15 are (3,0) and (0,5).

To find the x-intercept we have to substitute y = 0 into the equation, as follows:

9x - 7*0 = -63

9x = -63

Dividing by 9 at both sides of the equation:

9x/9 = -63/9

x = -7

To find the y-intercept we have to substitute x = 0 into the equation, as follows:

9*0 - 7y = -63

-7y = -63

Dividing by -7 at both sides of the equation:

-7y/(-7) = -63/(-7)

y = 9

x-intercept: −7; y-intercept: 9

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the probability of risk increases with the extension of supply chain. The more we enlarge our business the more possibility of risk.

A supply chain refers a system of connection of the business elements such as raw materials, products, resources, profit, loss as well as all the activities of a running business organization.

the extent of possibility of occurring unexpected incident in a business. while going on with our business, we wish to extend our organization so as to earn reputation as well as gaining outstanding outcomes. But at the same time the chance of getting bad outcomes rises. It is termed as probability of risk.

hence, the above expression risk rises with increasing supply chain is true.

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AAA ( Angle - Angle - Angle) congruence rule is one of congruence postulate but not preferable, for showing the similarity in two triangles

Two triangles are said to be congruent if one can be superimposed on the other exactly by rigid body motion, and the congruence theorem gives the conditions under which this occurs.

AAA Congruence rule:

It is stands for angle-angle-angle Congruence rule. When all three angles of one triangle is equals to the corresponding angles of another triangle. but it is possible if and only if the corresponding sides of both triangles are equal and when all three sides of two triangles are equal to each other then we use SSS Congruence rule. So, it not considered as preferable congruence rule . For example, In ∆ABC and ∆PQR

all three angles of ∆ABC is equal to corresponding angles of ∆PQR. So,∆ABC and ∆PQR are congruent.

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Answer:

Elga is 22 years old

Step-by-step explanation:

Let A = Alvin's age

Let E = Elga's age

We have the equations:

A = E - 11

A + E = 33

Substitute A = E - 11 from the first equation into the second equation and solve for E

So, we have

A + E = 33

(E - 11) + E = 33

2E - 11 = 33

2E = 44

E = 22 years old

So, Alvin is 11 years old and Elga is 22 years old

The Median of 23 will be 23.

How to calculate the Median?

A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it. In a list of odd numbers, one would select the middle number with an equal number of numbers on either side of it to determine the median value. The numbers should be arranged in order, typically from lowest to highest, before calculating the median.

The middle pair must be identified, added, then divided by two in order to calculate the median value in a list of even integers. Once more, group the figures from lowest to highest.

The median will be the average of the two middle numbers, in our questions 23 and 23, the mean of which is 23 because there are an even number of values.

So the final answer will be 23.

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We divide the smaller number in HCF by the remaining after dividing the smaller number by the smaller number. Until there is no more remaining, we repeat the process.

For two or more numbers, HCF can be assessed. It is the most powerful factor for dividing any pair of numbers by either half or all of them. To illustrate: 15 is the biggest number that can divide both 60 and 75 perfectly, making it the highest common factor between those two numbers.

here

Step 1 is to divide the largest integer by the smallest number.

Step 2: Divide the first divisor by the first remainder, taking the divisor as the new dividend and the remainder as the new divisor.

Step 3: Continue until the remainder is 0 and the HCF of the given numbers is the last divisor.

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Test value for a test of the difference between these two population proportions would be 2.44

What is Proportion?

A proportion in math is when two ratios are equivalent, that means they are equal to each other.

To calculate the test value for the difference between the two population proportions, you will need to first calculate the sample proportions for each group.

The sample proportion for the group of students attending 2-year colleges is 105/300 = 0.35.

The sample proportion for the group of students attending 4-year universities is 20/225 = 0.089.

Next, you can use these sample proportions to calculate the test value using the following formula:

      test value =  [tex]\frac{p1-p2}{\sqrt{[(p1(1-p1)/n1) + (p2(1-p2)/n2)]} }[/tex]

where p1 is the sample proportion for the first group, p2 is the sample proportion for the second group, n1 is the sample size for the first group, and n2 is the sample size for the second group.

Plugging in the values from the problem, we get:

test value = [tex]\frac{(0.35 - 0.089)}{\sqrt{[(0.35(1-0.35)/300) + (0.089(1-0.089)/225)]} }[/tex]

Simplifying this expression gives us a test value of approximately 2.44. This is the test value for the difference between the two population proportions.

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Let x= the co-efficient of x^3-1. So the co-efficient of given function is x=1.

The term "coefficient" refers to a number or symbol that multiplies another number or symbol (used as a mathematical variable).

An amount multiplied by a variable is known as a coefficient. As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.

Let x= the co-efficient of x^3-1. So the co-efficient of given function is x=1.

The term multiplied with x^3 is the co-efficient of this expression. As there is not term with x^3 so it is 1.

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A three-term expression is called a trinomial.

Math is a powerful tool that can be used to solve a range of problems. From simple arithmetic to complex equations, math provides us with powerful tools to explore the world around us. One such tool is the trinomial, a three-term expression that can be used to represent a wide variety of mathematical problems. In this essay, we will explore the possibilities of trinomials, examining their structure, uses, and potential applications.

Trinomials are composed of three terms: a variable, a coefficient, and a constant. Each term can be used to represent a different aspect of a problem. The variable is typically either an x or a y, and is used to represent the unknown quantity in an equation. The coefficient is a number used to modify the variable, and the constant is a number that is not affected by the variable. Together, these three terms form a trinomial, which can be used to represent a wide range of mathematical problems.

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15 is the standard deviation of 225 .

What is explained by the standard deviation?

You can tell how skewed the data is by looking at the standard deviation. It gauges how far away from the mean each observed value is.

                      Any distribution will have roughly 95% of its values within two standard deviations of the mean. Think about the following data: 2, 1, 3, 2, 4. The average and the sum of squares representing the observations' variances from the mean will be 2.4 and 5.2, respectively.

Variance is simply the square of the standard deviation (v=σ2) .

          So if the variance is 225,

                        σ=√225 or 15.

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The mean formula in statistics for a set is defined as the sum of the observations divided by the total number of observations.

One of the most significant and often employed metrics of central tendency is the mean. In mathematics, there are various different kinds of means. In statistics, the mean is the product of all the values in a set of data divided by the total number of values in the data for a particular set of observations.

To put it another way, calculating the mean of a data set only requires adding up all the values and dividing the result by the total number of values.

However, depending on whether grouped or ungrouped data is provided, the basic approach and formulae change. Ungrouped data is a collection of random observations, whereas grouped data is a collection of individual observations of a variable aggregated into separate groups.

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To put it another way, all that is necessary to determine the mean of a set of data is to sum up all the values and divide the total by the number of values.

However, the fundamental approach and equations vary according on whether grouped or ungrouped data are presented. Ungrouped data is a collection of arbitrary observations, whereas grouped data is a collection of distinct groupings of individual observations of a variable.

7 pens are obtained by adding 5 and 2. We receive 5 back after subtracting 7 pens and 2 pens. The procedures of addition and subtraction are reversed in this case.

Given,

Inverse operations;

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.

Examples for inverse operations;

We get 7 pens when we mix 5 and 2. We now have 5 pens left after subtracting 7 pens and 2 pens. Addition and subtraction are inverse operations in this situation.

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The range() function outputs a list of numbers that starts at 0 by default, increases by 1 (by default), and ends before a given value .

The statistical range for a given data collection is the range of values between the highest and lowest values. Another way to show the range is to compare the top and lowest observation differences. The sample interval can be calculated by subtracting the highest number from the lowest. For continuous variables, the sample range is an essential measure of variability.

here ,

Python has a built-in method called range() that can be used to create a series of numbers.

The range() function accepts starting and ending values as inputs, which can be supplied by the user to construct a sequence .

The range() function outputs a list of numbers that starts at 0 by default, increases by 1 (by default), and ends before a given value .

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Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

AAS (Angle-Angle-Side) is the basic congruence criteria for proving the congruence ( similarity) of two triangles.

Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal.

The basic terms of the agreement are as follows.

Now let's talk about AAS Consensus Criteria.

AAS Congruence Criteria: AAS Criterion stands for Angle-Angle-Side Criterion. According to the AAS criterion, two triangles are congruent if any two angles and excluded sides of one triangle are equal to the corresponding angles and excluded sides of the other triangle.

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Answer:6 dollars

Step-by-step explanation:

1 dozen=12 oranges

3 dozen=36 oranges

36 divided by 6=6

6 times 1= 6 dollars

By analyzing and applying correct method we can solve for any given Y problem.

Analysis is the process of carefully examining something difficult in order to comprehend it or identify its key characteristics.

Explaining, rephrasing, or otherwise demonstrating your own understanding of something is the act of interpretation. An interpreter is a person who interprets from one language into another for the purpose of explaining what is being said to a non-native speaker.

Let any problem is represented as Y. We can solve Y problem by analyzing the situation that is presented in the problem and by applying right method or formula to get required solution of given problem.

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The graph of the function h(x) is attached below.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is h(x) = √(x-2) + 3

The radical function is always positive.

Therefore,

x - 2 ≥ 0

x ≥ 2

The domain of the function is [2, ∞)

The value of h(x) is at the lowest value of x that is x = 2.

h(2) = √(2-2) + 3

h(2) = 3

The range of the function is [3, ∞)

The starting point of the function is (2,3).

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By applying direct proportion, the value of y when x is 17 is equal to 68.

Mathematically, a direct proportion or direct variation can be represented the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

k = y/x

k = 156/39

k = 4

Now, we can calculate the value of y when x is 17;

y = kx

y = 4 × 17

y = 68.

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There are three terms  in the following expression 7x² 5x 5  This means that for every x in the expression, 5 will be multiplied by it

The coefficient of x in the expression 5x³ 7x² is 5. This means that for every x in the expression, 5 will be multiplied by it. To calculate the coefficient of x, we need to first expand the expression. The expanded form of the expression 5x³ 7x² is 5x³ + 7x². Here, we can see that 5 is multiplied by x three times and seven is multiplied by x twice. This indicates that the coefficient of x is 5. This can be understood by considering the following example:

Let's say we have the expression 5x³ 7x² = 5x³ + 7x².

Here, 5 is multiplied by x three times and seven is multiplied by x twice. This means that the coefficient of x is 5. This can be written as 5x³ + 7x² = 5x³ + 7x x 1 = 5x(x² + x). Hence, the coefficient of x in the expression 5x³ 7x² is 5.The coefficient of x in the expression 5x³ 7x² can be calculated using the following steps:

Expand the expression 5x³ 7x².

The expanded form of the expression is 5x³ + 7x².

Here, we can see that 5 is multiplied by x three times and seven is multiplied by x twice. This indicates that the coefficient of x is 5.

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