The owner of the theater where the ticket price for an adult is $10 and the ticket price for a child is $7 wants to make at least $300 when a movie is shown. Choose the inequality that shows the numbers of tickets that must be sold.

A. 10x + 7y > 300
B. 10x + 7y < 300
C. 10x + 7y ≥ 300
D. 10x + 7y ≤ 300

Answer:

The values are k = -2 and c = 1

Step-by-step explanation:

Since it's a division of polynomials we can calculate "c" and "k" by using the inverse operation, which is the product. We need to multiply "x + k" with "3x + 1" and sum it with 3, that should be equal to "3x² - 5x + c". We have:

\(3x^2 - 5x + c = (x + k)*(3x + 1) + 3\\3x^2 - 5x + c = 3x^2 + x + 3kx + k + 3\\3x^2 - 5x + c = 3x^2 + (1 + 3k)x + (k+3)\)

In order for two polynomials to be equal, every coefficient must be equal, therefore:

\(-5 = 1 + 3k\\1 + 3k = -5\\3k = -5 -1\\3k = -6\\k = -2\)

\(c = k + 3\\c = -2 + 3\\c = 1\)

In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.

The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.

A place value chart can be used to understand the value of a digit in a number.

Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.

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Neville's method is a mathematical technique used for polynomial interpolation and approximation. It was developed by Edward Neville in the early 20th century as an alternative to the Lagrange interpolation method.

Neville's method offers several advantages. Firstly, it provides a straightforward and efficient way to interpolate data points and approximate functions using a polynomial. It avoids the need to explicitly construct the Lagrange polynomial, which can be computationally expensive for large data sets. Additionally, Neville's method allows for the interpolation of data points at arbitrary locations within the given range, making it a flexible interpolation technique.

When comparing Neville's method with the Lagrange interpolation polynomial, both techniques aim to approximate a function using a polynomial. However, the main difference lies in the construction of the interpolating polynomial. While the Lagrange method constructs a single polynomial that passes through all the given data points, Neville's method constructs a table of polynomials. This table allows for the calculation of intermediate polynomial values at any desired point, providing a more efficient way to interpolate and approximate functions.

To approximate √3 using Neville's method with the given data points (Xo = -2, x₁ = -1, x₂ = 0, x₃ = 1, and x₄ = 2) and f(x) = 3, we can follow the steps of Neville's algorithm. By constructing the Neville's table and evaluating it at x = 3, we obtain the approximation for √3.

To determine the exact error of the approximation, we compare the obtained approximation to the actual value of √3. The difference between the two values provides an indication of the accuracy of Neville's method in this specific case.

References:

Neville's Algorithm for Polynomial Interpolation. Retrieved from [insert reference here].

Neville's Method: An Overview. Retrieved from [insert reference here].

Numerical Analysis - Mathematics of Scientific Computing (Chapter 3). Retrieved from [insert reference here].

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multinv(x*y) = (multinv x) * (multinv y) {proved}

To prove that for all nonzero real numbers x and y, multinv(x*y) = (multinv x) * (multinv y), we will follow these steps:

Step 1: Understand the terms
Multinv(x) refers to the multiplicative inverse of x, which is the reciprocal of x (1/x).

Step 2: Write down the given equation
We are given that multinv(x*y) = (multinv x) * (multinv y).

Step 3: Replace the terms with their definitions
The multiplicative inverse of x*y is 1/(x*y). Similarly, the multiplicative inverse of x is 1/x, and the multiplicative inverse of y is 1/y.

Step 4: Plug in the definitions
1/(x*y) = (1/x) * (1/y)

Step 5: Verify if both sides of the equation are equal
Using the properties of fractions, we know that (1/x) * (1/y) is equal to 1/(x*y).

Thus, the given equation holds true:
multinv(x*y) = (multinv x) * (multinv y)

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Answer:

B. Is the answer of your question

The number sets to which each number belong are:

1. Rational.

2. Whole.

3. Irrational.

4. Whole.

5. Integer.

6. Irrational.

It is a terminating decimal, hence it is a rational number.

It is a non-negative non-decimal number, hence it is a whole number.

pi is an irrational number, as it is a non-terminating decimal, hence 2pi is also an irrational number.

It is a non-negative non-decimal number, hence it is a whole number.

The square root of 16 is 4, hence -√16 = -4, which is a negative non-decimal number, hence it is an integer.

The square root of 24 is non-exact, hence it is a non-terminating decimal , so an irrational number.

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Answer:

it should be (5,4)

Step-by-step explanation:

♊♊♊

Answer:

A would be reflected across to (5,-4), so, the bottom answer.

Step-by-step explanation:

For reflections across an axis, all I really do is count how many units a point is from the axis you are reflecting across, and then count the many on the other side of the axis. On this problem, A was 4 units above the x-axis, and 5 from the y-axis. I just counted 8 units down, or, 4 units down from the x-axis, and since I didn't change where my point was on the y-axis, it landed on the point (5,-4).

The probability of getting an order that is not accurate or is from Restaurant C is 0.345.

The events of selecting an order that is not accurate and selecting an order from Restaurant C are not disjoint events because it is possible to pick an order that is not accurate and from restaurant C (i.e., both events can occur at the same time).

The probability of getting an order that is not accurate or is from Restaurant C can be found using the addition rule of probability:

P(not accurate or from C) = P(not accurate) + P(from C) - P(not accurate and from C)

From the table, we have:

P(not accurate) = (37+50+33+16)/(315+273+248+135+37+50+33+16) = 0.170

P(from C) = 248/(315+273+248+135+37+50+33+16) = 0.209

P(not accurate and from C) = 33/(315+273+248+135+37+50+33+16) = 0.034

Therefore,

P(not accurate or from C) = 0.170 + 0.209 - 0.034 = 0.345

So, the probability of getting an order that is not accurate or is from Restaurant C is 0.345.

The events of selecting an order from Restaurant C and selecting an inaccurate order are not disjoint events because it is possible to pick an order that is both from Restaurant C and not accurate.

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Answer:

(3a-7)²

Step-by-step explanation:

Sum=-42

Prodect=441

9a²-21a-21a+49

3a(3a-7)-7(3a-7)

(3a-7)(3a-7)

=(3a-7)²

The probability that the coin did not turn up heads two times in a row when flipped 8 times is 0.0390625 or about 3.91%.

To find the probability that the fair coin did not turn up heads two times in a row when flipped 8 times, follow these steps:

Identify the possible outcomes.

Determine the sequences that do not have two heads in a row.
Valid sequences are:

HTH, HTHT, HTHTH, HTHTHT, HTHTHTH, THTHTHT, THTHT, THTHTH, THTHTHT, and THTHTHTH.

Calculate the probability of each sequence.
Since it is a fair coin, the probability of getting heads (H) or tails (T) is 0.5 each. Therefore, the probability of each sequence is

(0.5)⁸ = 0.00390625.
Count the number of valid sequences.
There are 10 valid sequences without two heads in a row.Calculate the overall probability.
Multiply the probability of each sequence by the number of valid sequences:

0.00390625ˣ10 = 0.0390625.

So, the probability that the coin did not turn up heads two times in a row when flipped 8 times is 0.0390625 or about 3.91%.

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Let A be the event that a student did well on the midterm, and B be the event that a student went bar hopping the weekend before the midterm.What is the probability that a randomly selected student did well on the midterm and also went bar hopping the weekend before the midterm.

The probability that a student did well on the midterm and also went bar hopping the weekend before the midterm is given by:P(A ∩ B) = 30/200 = 0.15What is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the midterm? The probability that a student did well on the midterm or went bar hopping the weekend before the midterm is given by:P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = (80/200) + (30/200) - (30/200) = 0.55What is the probability that a randomly selected student who went bar hopping did well on the midterm.

The probability that a randomly selected student who went bar hopping did well on the midterm is given by:P(A | B) = P(A ∩ B) / P(B) = 0.15 / 0.30 = 0.5What is the probability that a randomly selected student went bar hopping?The probability that a randomly selected student went bar hopping is given by:P(B) = (30+70)/200 = 0.5What is the probability that a randomly selected student did well on the midterm?The probability that a randomly selected student did well on the midterm is given by:P(A) = 80/200 = 0.4

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The mean number of particles emitted per minute is approximately 2.0026.

To find the mean number of particles emitted per minute, we can use the Poisson distribution formula for the probability of no particles being emitted in a one-minute time period, which is given by:

\(P(X=0) = e^(-λ) × (λ^0) / 0! = 0.1352\)

where λ is the mean number of particles emitted per minute, e is the base of the natural logarithm (approximately 2.718), and X is the number of particles emitted.

Step 1: Rearrange the formula to solve for λ:
\(e^(-λ) = 0.1352\)

Step 2: Take the natural logarithm of both sides:
\(-ln(λ) = ln(0.1352)\)

Step 3: Solve for λ:
λ = -ln(0.1352)

Step 4: Calculate the value:
λ ≈ 2.0026

The mean number of particles emitted per minute is approximately 2.0026.

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The player's batting average is 0.333.

The baseball player's batting average is found by dividing the number of hits by the number of times at bat. This number is then rounded to the nearest thousandth.

The question states that Cole Becker was at bat nine times with three hits.

To determine the player's batting average, divide the number of hits by the number of times at bat. A calculator can be used to compute this, and the result can be rounded to the nearest thousandth.

Batting Average = Number of hits/Number of times at bat

Batting Average = 3/9

Batting Average = 0.33333333...

Rounded to the nearest thousandth, the player's batting average is 0.333.

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Step-by-step explanation:

there, hope it helps! :)

Therefore, the components of vector E⃗ are Ex = 1 and Ey = -11. Thus, E⃗ = (1, -11).

To solve this equation, let's break it down component-wise. Given:

E⃗ = 2A⃗ + 3B⃗

We can write the equation in terms of its components:

Ex = 2Ax + 3Bx

Ey = 2Ay + 3By

We are also given the components of vectors A⃗ and B⃗:

Ax = 5

Ay = 2

Bx = -3

By = -5

Substituting these values into the equation, we have:

Ex = 2(5) + 3(-3)

Ey = 2(2) + 3(-5)

Simplifying:

Ex = 10 - 9

Ey = 4 - 15

Ex = 1

Ey = -11

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Answer:this

Step-by-step explanation:

Many regression models use linear combinations of predictors to forecast a variable. In contrast, autoregressive models use the variable's past values to determine the future value. AR(1) autoregressive processes depend on the value immediately preceding the current value.

Autoregressive modelling uses the earlier values of the variables using to predict the future in contrast to other models.

Autoregressive models are defined as the models which predicts the future values or nature of the variables based on the earlier or past values.

There are many approaches to forecast future behavior of the variables.

Linear regression models are the models which used one or more past values to predict the future.

Autoregressive models are a kind of linear regression models.

This only uses the past values to predict future but other forecasting approaches may not only use past values. They may use a linear combination of the predictors to find the future values.

Hence the difference is in the prediction of future values based on past values.

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According to survey data, approximately 90% of recruiters review the social profile of a candidate for a job.

This means that the majority of recruiters, about 90%, look at the social media accounts of potential candidates.

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Answer:

29 times

Step-by-step explanation:

Given :

Society C ;

Population = 100

Number of facts known = 10

Average fact known per person = known fact / population = 10 / 100 = 0.1

Society D:

Population = 19

Common fact = 5

Specialized fact = 5 * 10 = 50

Total facts = 55

Average fact known per person = 55 / 19 = 2.8947368 fact per person

Number of times society D is better :

2.8947368 / 0.1 = 28.947 times

Approximately 29 times

Answer 1:

\(y = \frac{9}{5} - \frac{6x}{5}\)

Answer 2:

\(y = 3 - \frac{8(x+7)}{7}\)

Note:

User stated an explanation was not needed.

We can express the solution to the original differential equation as:y2(x) = u(x) y1(x) = [c2 + c1 e x2/2 + C] e x

To verify that y1(x) = e x is a solution of (1), we will substitute y1(x) and its first and second derivatives into (1).y1(x) = e xy1′(x) = e xy1′′(x) = e xEvaluating the equation (x + 1)y ′′ − (x + 2)y ′ + y = 0 with these values, we get: (x + 1)ex − (x + 2)ex + ex = ex(1) − ex(x + 2) + ex(x + 1) = 0.

Hence, y1(x) = ex is a solution of (1).

Let y2(x) = u(x) y1(x), where u = u(x)Differentiating y2(x) once, we get:y2′(x) = u(x) y1′(x) + u′(x) y1(x).

Differentiating y2(x) twice, we get:y2′′(x) = u(x) y1′′(x) + 2u′(x) y1′(x) + u′′(x) y1(x).

We can now substitute these expressions for y2, y2' and y2'' back into the original equation and we get:(x + 1)[u(x) y1′′(x) + 2u′(x) y1′(x) + u′′(x) y1(x)] − (x + 2)[u(x) y1′(x) + u′(x) y1(x)] + u(x) y1(x) = 0.

Expanding and grouping the terms, we get:u(x)[(x+1) y1′′(x) - (x+2) y1′(x) + y1(x)] + [2(x+1) u′(x) - (x+2) u(x)] y1′(x) + [u′′(x) + u(x)] y1(x) = 0Since y1(x) = ex is a solution of the original equation,

we can simplify this equation to:(u′′(x) + u(x)) ex + [2(x+1) u′(x) - (x+2) u(x)] ex = 0.

Dividing by ex, we get the following differential equation:u′′(x) + (2 - x) u′(x) = 0.

We can solve this equation using the method of integrating factors.

Multiplying both sides by e-x2/2 and simplifying, we get:(e-x2/2 u′(x))' = 0.

Integrating both sides, we get:e-x2/2 u′(x) = c1where c1 is a constant of integration.Solving for u′(x), we get:u′(x) = c1 e x2/2Integrating both sides, we get:u(x) = c2 + c1 ∫ e x2/2 dxwhere c2 is another constant of integration.

Integrating the right-hand side using the substitution u = x2/2, we get:u(x) = c2 + c1 ∫ e u du = c2 + c1 e x2/2 + CUsing the fact that y1(x) = ex, we can express the solution to the original differential equation as:y2(x) = u(x) y1(x) = [c2 + c1 e x2/2 + C] e x.

In this question, we have verified that y1(x) = ex is a solution of the given differential equation (1). We have also found another solution y2(x) of the differential equation by letting y2(x) = u(x) y1(x) and solving for u(x). The general solution of the differential equation is therefore:y(x) = c1 e x + [c2 + c1 e x2/2 + C] e x, where c1 and c2 are constants.

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The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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Answer:

11

Step-by-step explanation:

Answer:

Let the type A coffee be

Let the type B coffee be

Three times as many pounds of type B coffee as type A, will be represented below as

The cost of type A coffee is

The cost of type B is

The total cost of both coffee is

Hence,

The equation will be

Hence,

The number of pounds of type A coffee is = 32 pounds

(c) The student misses the bus by the difference between the total distances covered by the bus and the student.

(a) To determine the distance covered by the bus from the moment the student starts chasing it until the moment the bus passes by the stop, we need to consider the relative motion between the bus and the student. Let's break down the problem into two parts:

1. Acceleration phase of the student:

During this phase, the student accelerates until reaching the bus's velocity. The initial velocity of the student is zero, and the final velocity is the velocity of the bus. The time taken by the student to accelerate is given as 1.70 s.

Using the equation of motion:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the acceleration of the student:

a = (v - u) / t

  = (0 -\(v_{bus}\)) / 1.70

Since the student starts 200 m ahead of the bus, we can use the following kinematic equation to find the distance covered during the acceleration phase:

s = ut + (1/2)at^2

Substituting the values:

\(s_{acceleration}\) = (0)(1.70) + (1/2)(-\(v_{bu}\)s/1.70)(1.70)^2

              = (-\(v_{bus}\)/1.70)(1.70^2)/2

              = -\(v_{bus}\)(1.70)/2

2. Constant velocity phase of the student:

Once the student reaches the velocity of the bus, both the bus and the student will cover the remaining distance together. The time taken by the bus to cover the remaining distance of 200 m is given as 36 s - 1.70 s = 34.30 s.

The distance covered by the bus during this time is simply:

\(s_{constant}_{velocity} = v_{bus}\) * (34.30)

Therefore, the total distance covered by the bus is:

Total distance = s_acceleration + s_constant_velocity

              = -v_bus(1.70)/2 + v_bus(34.30)

Since the distance covered cannot be negative, we take the magnitude of the total distance covered by the bus.

(b) To determine the distance covered by the student during the 36 s, we consider the acceleration phase and the constant velocity phase.

1. Acceleration phase of the student:

Using the equation of motion:

s = ut + (1/2)at^2

Substituting the values:

\(s_{acceleration}\) = (0)(1.70) + (1/2\(){(a_student)}(1.70)^2\)

2. Constant velocity phase of the student:

During this phase, the student maintains a constant velocity equal to that of the bus. The time taken for this phase is 34.30 s.

The distance covered by the student during this time is:

\(s_{constant}_{velocity} = v_{bus}\) * (34.30)

Therefore, the total distance covered by the student is:

Total distance =\(s_{acceleration} + s_{constant}_{velocity}\)

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Hey there! I'm happy to help!

The greatest common factor is the largest factor that both numbers contain. Let's look at the factors of these terms.

12x²: 1, 12, 2, 6, 3, 4, x, x

15x³: 1, 15, 3, 5, x, x ,x

We see that both of these numbers contain a 3 and 2 x's, so our GCF would be 3x².

Have a wonderful day!

After solving the given expression → F = - m + B/q³  for  [B], we get -

B = q³(F + M).

We have the following equation -

F = - m + B/q³

We have the following equation -

F = - m + B/q³

On solving for [B], we get -

F + M = B/q³

B = q³(F + M)

Therefore, the given expression after solving for [B], we get -

B = q³(F + M).

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Answer:

0= -42

Step-by-step explanation:

Simplify then add 6 to both sides after simplify again and subtract 2x from both sides then finally combine like terms and simplify the expression.

Where the above conditions are given,  the correct option is: Plan 1 is a better deal for more than 5 cards purchased.

To determine   which pricing plan is a better deal,we need to compare the total cost for a certain number of game cards purchased.

Let's calculate the   total cost for different numbers  of game cards.

For Plan 1  -

- Admission fee  - $5 (fixed)

- Cost per game card  - $1

For Plan 2  -

- Admission fee  - $2.50 (fixed)

- Cost per game card  - $1.50

Now, let's compare the total cost for different numbers of game cards  -

1. If you purchase 1 game card  -

  - Plan 1  - $5 (admission fee) + $1 (cost per game card) = $6

  - Plan 2  - $2.50 (admission fee) + $1.50 (cost per game card) = $4

2. If you purchase 5 game cards  -

  - Plan 1  - $5 (admission fee) + $5 (cost for 5 game cards) = $10

  - Plan 2  - $2.50 (admission fee) + $7.50 (cost for 5 game cards) = $10

3. If you purchase 8 game cards  -

  - Plan 1  - $5 (admission fee) + $8 (cost for 8 game cards) = $13

  - Plan 2  - $2.50 (admission fee) + $12 (cost for 8 game cards) = $14.50

Based on these calculations, we can conclude that  -

- Plan 1 is a better deal for more than 5 cards purchased.

- Plan 2 is a better deal for more than 8 cards purchased.

Therefore, the correct option is  - Plan 1 is a better deal for more than 5 cards purchased.

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The best interpretation of these data is that there is a direct relationship between number of hours studied and the score on the test.

The correlation coefficient r measures the strength and direction of a linear relationship between two variables. In this case, the positive value of r = .59 indicates a direct (or positive) relationship between number of hours studied and the score on the test. This means that as the number of hours studied increases, the score on the test tends to increase as well.

Therefore, we can conclude that more study leads to a higher score on the test.

Option 1 and 2 are correct interpretations, while options 3 and 4 are incorrect. Option 3 implies a negative correlation coefficient, while option 4 implies an inverse relationship between the variables, which is not the case here.

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