A theatre contains 457 seats and the ticket prices for a recent play were ​$54 for adults and ​$17 for children. If the total proceeds were ​$14,984 for a​ sold-out matinee, how many of each type of ticket were​ sold?

The correct option is A, the inequality is:

2.75x + 1.95y ≤ 750

Let's define the variables we will be using:

x = number of chicken sandwiches

y = number of hamburgers.

We know that the budget is $750, and the chicken sandwich costs $2.75 to make and the hamburger costs $1.95 to make, then we can write the inequality:

"Total cost equal to or smaller than 750"

2.75x + 1.95y ≤ 750

That is what we can see in option A, so that is the correct one.

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Answer:

Billy has £20, Liam has £40, and Nicola has £120. The total amount of money they have is £180, as given in the problem.

Step-by-step explanation:

Let's start by defining the variables:

Billy's money: x pounds

Liam's money: 2x pounds (twice as much as Billy)

Nicola's money: 3(2x) = 6x pounds (three times as much as Liam)

The total amount of money they have is £180, so we can write an equation:

x + 2x + 6x = 180

Simplifying the left side of the equation:

9x = 180

Solving for x:

x = 20

Now we can find out how much money each person has:

Billy: x = 20 pounds

Liam: 2x = 2(20) = 40 pounds

Nicola: 6x = 6(20) = 120 pounds

The length of a person’s forearm if the length of their foot is 8 inches.

A linear equation is an equation that describes a straight line on a graph. It is an algebraic equation that involves two variables, usually x and y, and can be written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.

The slope of a line is the measure of the steepness of the line, or how much it rises or falls for a given change in x. It can be calculated as the change in y divided by the change in x between any two points on the line.

The y-intercept is the point where the line crosses the y-axis, or the value of y when x is zero.

Let

x ----> Length of Foot in inches

y ----> Length of Forearm in inches

we have

y=1.11x-0.83

For x=8 in

To find y, change the value of x in the linear equation.

y=1.11(8)-0.83=8.05in

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The complete question is :

The data on the graph show the foot lengths and forearm lengths for a group of people. The line of best fit for the data is shown. Use the equation of the line of best fit to predict the length of a person’s forearm if the length of their foot is 8 inches.

A graph is labeled as Foot Length versus Forearm Length. The horizontal axis is labeled as Length of Foot left parenthesis inches right parenthesis and the vertical axis is labeled as Length of Forearm left parenthesis inches right parenthesis. The values on the horizontal axis range from 0 to 15 in increments of 1 and the values on the vertical axis range from 0 to 15 in increments of 1. Several points are scattered throughout the graph and a line is shown which passes between these points and the equation of the line is labeled as y equals 1 decimal point 1 1 x minus 0 decimal point 8 3.

A.8.88 inches

B.6.94 inches

C.9.16 inches

D.8.05 inches

The indicated value h(-1)  has a value of 0 when evaluated

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

f(x) = - 2x ^ 2

g(x) = x - 3

h(x) = 2f(x) - g(x)

The indicated value of the function is

h(-1)

This means that

h(-1) = 2f(-1) - g(-1)

Calculate g(-1)

So, we have

g(-1) = -1 - 3

g(-1) = -4

Calculate f(-1)

So, we have

f(-1) = -2 * (-1)^2

f(-1) = -2

Recall that

h(-1) = 2f(-1) - g(-1)

Substitute the known values in the above equation, so, we have the following representation

h(-1) = 2 * -2 + 4

Evaluate

h(-1) = 0

Hence, the value is 0

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The quadratic functions that have a graph with x-intercepts of -8 and 2 are:

y = (x + 8)(x - 2)

f(x) = -7(x + 8)(x - 2)

Options A and C are the correct answer.

We have,

To find the quadratic functions that have a graph with x-intercepts of -8 and 2, we can start by using the fact that the x-intercepts occur when y = 0.

We know that the x-intercepts are -8 and 2, so we can set up two equations:

(x + 8) = 0 and (x - 2) = 0

Solving for x in each equation, we get:

x = -8 and x = 2

Therefore, the factors of the quadratic function that has x-intercepts of -8 and 2 are (x + 8) and (x - 2).

Now we can use these factors to determine which quadratic functions have a graph with these x-intercepts.

A.

y = (x + 8)(x - 2)

Expanding this quadratic function gives:

y = x² + 6x - 16

This function has x-intercepts of -8 and 2, so it is a valid option.

B.

y = (x - 8)(x - 2)

Expanding this quadratic function gives:

y = x² - 10x + 16

This function does not have an x-intercept of -8, so it is not a valid option.

C.

f(x) = -7(x + 8)(x - 2)

Expanding this quadratic function gives:

f(x) = -7x² - 42x - 96

This function does have x-intercepts of -8 and 2, so it is a valid option.

D.

f(x) = -2x² - 12x + 32

To find the x-intercepts of this quadratic function, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values from the given function, we get:

x = (-(-12) ± √((-12)² - 4(-2)(32))) / 2(-2)

x = (-(-12) ± √(144 + 256)) / (-4)

x = (6 ± √(100)) / 2

x = 3 ± 5

So the x-intercepts are -2 and 8, which means this function is not a valid option.

E.

y = x² - 5x + 8

To find the x-intercepts of this quadratic function, we can again use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values from the given function, we get:

x = (-(-5) ± √((-5)² - 4(1)(8))) / 2(1)

x = (5 ± √(9)) / 2

x = 4 or x = 1

So the x-intercepts are 4 and 1, which means this function is not a valid option.

F.

f(x) = x² - 8x + 2

To find the x-intercepts of this quadratic function, we can once again use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values from the given function, we get:

x = (-(-8) ± √((-8)² - 4(1)(2))) / 2(1)

x = (8 ± √(60)) / 2

x = 4 ± 2√(15)

So the x-intercepts are 4 + 2 √(15) and 4 - 2 √(15), which means this function is not a valid option.

Therefore,

The quadratic functions that have a graph with x-intercepts of -8 and 2 are:

A. y = (x + 8)(x - 2)

C. f(x) = -7(x + 8)(x - 2)

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200.96  is the circle's circumference .

What is a circle, exactly?

A circle is a closed, two-dimensional object in which the distances between every point in its plane and its centre are all equal. The creation of the reflection symmetry line is influenced by each line that crosses the circle.

                                     Additionally, any angle surrounding the centre exhibits rotational symmetry. A figure with a circular form that lacks both sides and edges is referred to as a circle. A circle can be referred to in geometry as a closed form, a two-dimensional shape, or a curved shape.

C = 2πr

C = 2 *π * 32

C = 2 x 3.14 x 32

C = 200.96

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Answer:

y=3+2 to the power of x +1

Step-by-step explanation:

The area of each triangle to the nearest square inch is approximately 95 square inches.

A triangle is a 2-dimensional geometric shape that consists of three straight sides and three angles. It is one of the basic shapes in geometry, and it is widely used in various fields such as mathematics, engineering, architecture, and art.

To find the area of an equilateral triangle with a radius of 12.7 inches, we can use the formula:

Area = [tex](\sqrt{(3)/4})[/tex] x [tex](side)^2[/tex]

where side is the length of one of the sides of the equilateral triangle.

We know that the radius of the equilateral triangle is 12.7 inches, which means that the distance from the center of the triangle to one of the corners (i.e., the length of one of the sides) is also 12.7 inches. To find the length of the side, we can use the formula for the height of an equilateral triangle:

and solve for side:

side = Height / ([tex]\sqrt{(3)/2[/tex]) = (2 x Height) / [tex]\sqrt{(3)[/tex]

Plugging in the value of the radius, we have:

side = (2 x 12.7 inches) / [tex]\sqrt{(3)[/tex] ≈ 14.67 inches

Now we can use the formula for the area of an equilateral triangle:

Area = ([tex]\sqrt{(3)/4}[/tex]) x [tex](side)^2[/tex]

Plugging in the value of the side, we have:

Area = ([tex]\sqrt{(3)/4[/tex]) x [tex](14.67 inches)^2[/tex] ≈ 94.71 square inches

Therefore, the area of each triangle to the nearest square inch is approximately 95 square inches.

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The volume of the composite figure is 3300 cubic feet.

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

The composite figure that has:

The volume V of a cuboid is given by the formula:

V = l × w × h

Therefore, the volume is:

Volume = 24 ft × 5 ft × 25 ft + 4 ft * 3 ft * 25 ft

V = 3300 cubic feet

So the volume is 3300 cubic feet.

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In the equation , cost of both companies will be same to rent a car is 6 days.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the deposit for the rent car in Wreck = $30

Cost for renting in Wreck = $15 per day

Cost for renting in Barely = $20 per day.

Here let us take the number of days as x.

Then, Cost for renting in Wreck = 15x+30

Cost for renting in Barely = 20x

To rent a car , if cost of both companies is same then the equation is,

=> 15x+30 = 20x

=> 20x-15x = 30

=> 5x = 30

=> x = 30/5 = 6

Hence We have to rent a car for 6 days  the cost of both companies to be the same.

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1) The value of given random variable having mean 20 and variance 25 is (a) 0.1587, (b) 0.0228 and (c) 0.5328.

2) The z-score corresponding to a probability of a) 0.95 is 1.645, b) 0.05 is -1.645 and c) 0.1515 is -1.04.

The mean is a measure of central tendency, which represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the total number of values.

1) (a) We can standardize the random variable X using the formula z = (X - μ) / σ, where μ is the mean and σ is the standard deviation. Therefore,

z = (15 - 20) / 5 = -1

Using a standard normal distribution table or calculator, we can find P(Z < -1) = 0.1587.

(b) Similarly, we have

z = (30 - 20) / 5 = 2

Using the standard normal distribution table or calculator, we can find P(Z > 2) = 0.0228.

(c) To find P(18 ≤ X ≤ 25), we can again standardize the random variable:

z1 = (18 - 20) / 5 = -0.4

z2 = (25 - 20) / 5 = 1

Then we can use the standard normal distribution table or calculator to find P(-0.4 ≤ Z ≤ 1) = 0.5328.

2) (a) Since we are given that X is a standard normal random variable, we can use the standard normal distribution table or calculator to find the value of a such that P(X < a) = 0.95. From the table, we find that the z-score corresponding to a probability of 0.95 is 1.645. Therefore,

a = μ + σ * z = 0 + 1 * 1.645 = 1.645

(b) Similarly, we can find the value of b such that P(X ≤ b) = 0.05 using the standard normal distribution table or calculator. From the table, we find that the z-score corresponding to a probability of 0.05 is -1.645. Therefore,

b = μ + σ * z = 0 + 1 * (-1.645) = -1.645

(c) We want to find the value of c such that P(X > c) = 0.8485. Since the normal distribution is symmetric about the mean, we know that P(X > c) = 1 - P(X < c), so we can find the value of c such that P(X < c) = 1 - 0.8485 = 0.1515. From the standard normal distribution table, we find that the z-score corresponding to a probability of 0.1515 is -1.04. Therefore,

c = μ + σ * z = 0 + 1 * (-1.04) = -1.04.

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The inequality that represents the sentence that the absolute value of x is greater than 6 is given as follows:

|x| > 6.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The absolute value of x is represented as follows:

|x|.

The inequality that represents the absolute value being greater than six is gjven as follows:

|x| > 6.

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Answer:

|x| > 6

Step-by-step explanation:

The correct statement is: |x| > 6.

This means that the distance between x and 0 on the number line is greater than 6 units, so x can be any number greater than 6 or less than -6.

The options given are:

Therefore, the correct statement is |x| > 6.

here's how to express the statement |x| > 6 as an inequality part 10a^2

| x | > 6

x^2 > 6^2

x^2 > 36

10x^2 > 360

10x^2 - 360 > 0

10x^2 - 360 > 0

Note that this inequality does not directly involve "a," as it is not mentioned in the original statement.

The third quartile  if the distribution is $22.08.

To find the third quartile, we need to find the value of the stock that separates the top 25% of days from the bottom 75%.

Since the distribution is uniform, we can find the third quartile by taking 75% of the range and adding it to the minimum value.

The range of the stock is:

$26.17 - $9.82 = $16.35

75% of the range is:

0.75 x $16.35 = $12.26

Adding this to the minimum value gives us the third quartile:

$9.82 + $12.26 = $22.08

So the third quartile is $22.08.

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The only possible solution is x = 2. Therefore, the three consecutive integers that form the sides of the right triangle are 2, 3, and 4.

Since they are consecutive integers, let's assume that the hypotenuse, which is the longest side of the right triangle, is x+2, as it is three units longer than the shortest side.

In a right triangle, the hypotenuse's square is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. We can thus write:

[tex](x+2)^2 = x^2 + (x+1)^2[/tex]

Expanding the squares, we get:

[tex]x^2 + 4x + 4 = x^2 + x^2 + 2x + 1[/tex]

Simplifying and rearranging terms, we get:

[tex]2x^2 - 2x - 3 = 0[/tex]

We can solve this quadratic equation by using the quadratic formula:

x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex]) / 2a

where a = 2, b = -2, and c = -3.

Plugging in these values, we get:

x = (-(-2) ± [tex]\sqrt{((-2)^2 - 4(2)(-3)))[/tex] / 2(2)

x = (2 ± [tex]\sqrt{(4 + 24))[/tex] / 4

x = (2 ± [tex]\sqrt28}[/tex] / 4

x = (2 ± [tex]2\sqrt{7}[/tex]) / 4

x = 1/2 ± [tex]\sqrt{7}[/tex]/2

The only option is x = 2, since x must be an integer. As a result, the numbers 2, 3, and 4 are the three consecutive integers that make up the sides of the right triangle.

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The equivalent value of the inequality is w ≥ 15

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

w/3 - 1 ≥ 4

On simplifying , we get

Adding 1 on both sides , we get

w/3 ≥ 5

Multiply by 3 on both sides , we get

w ≥ 15

Therefore , the value of w is greater than or equal to 15

Hence , the inequality is w ≥ 15

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There are no orange M&Ms in the bag, thus there is no probability of picking one.

An event is any subset of the sample space, which is the set of all potential results of a random experiment, according to probability theory. By dividing the number of favourable outcomes by the total number of possible outcomes, the probability of an event is determined.

Classical probability, empirical probability, and subjective likelihood are just a few of the several varieties of probability. Empirical probability is based on actual observations or experiments, as opposed to classical probability, which is predicated on the idea that all events are equally likely. On the other hand, subjective probability is dependent on opinion or conviction.

Picking a yellow M&M has a 4/20 chance, which drops to 1/5.

The likelihood of selecting a blue or green card M&M is the result of adding the odds of selecting a blue and a green:

To reduce to 1/2, 2/20 + 8/20 = 10/20.

The likelihood of choosing an orange M&M is zero because there are no orange M&Ms in the bag.

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The complete question is:

Answer: A

Step-by-step explanation: The distance for the ball to travel straight from Jose to Harlan is less than what it would be if she were to pass it to Alma first. You can use the distance formula to find this (find the distance between Jose and Harlan, and compare it to the sum of the distances between Jose and Alma and Alma and Harlan)

For the  given logarithmic expression the simplified result is given by option b.)  [tex]2 \log_b({x})-\frac{7}{3} \log_b({y) -\frac{8}{3} \log_b (z) \\\end{align*}[/tex].

[tex]\begin\text{Given \;expression:} \quad & \log_b \sqrt[3]{\frac{x^6}{y^7 \cdot z^8}} \\[/tex]

[tex]\text{1: Simplify the expression inside the cube root:} \quad & \frac{(x^6)^{\frac{1}{3}}}{((y^7 \cdot z^8)^{\frac{1}{3}})} \\\\[/tex][tex]\text{2: Simplify the exponents:} \quad & x^{6 \cdot \frac{1}{3}} = x^2, \quad (y^7 \cdot z^8)^{\frac{1}{3}} = y^{\frac{7}{3}} \cdot z^{\frac{8}{3}} \\\\[/tex]

[tex]\text{3: Substitute the simplified expression back:} \quad & \log_b\frac{x^2}{y^{\frac{7}{3}} \cdot z^{\frac{8}{3}}} \\\end{align*}[/tex]

Now Using ,[tex]\log_c\frac{a}{b}} = \log_c a -\log_cb[/tex]

[tex]\text{4: Equation becomes:} \quad & \log_b({x^2})-\log_b({y^{\frac{7}{3}} \cdot z^{\frac{8}{3})}} \\\end{align*}[/tex]

Also,  [tex]\log_c{b^n}} = n\log_c b[/tex]

[tex]\text{5: Using property stated above, we get:} \quad &2 \log_b({x})-\frac{1}{3} \log_b({y^7 \cdot z^{{8}}) \\\end{align*}[/tex]

Finally,[tex]\log_c{a}\cdot{b}} = \log_c a +\log_cb[/tex]

[tex]\text{6:Making the final result:} \quad &2 \log_b({x})-\frac{7}{3} \log_b({y) -\frac{8}{3} \log_b (z) \\\end{align*}[/tex]

Thus, option b is the required result.

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Step-by-step explanation:

At low tide   depth =  (3)(-1) + 7  = 4

at HIGH tide  depth = (3) (+1)  + 7 =   10 feet

Answer:

(½,0),(1,0)

...............

Answer:

Step-by-step explanation:

To find the x-intercepts of a function, we set y = 0 and solve for x.

For the function 2x² - 3x + 1:

2x² - 3x + 1 = 0

We can use the quadratic formula to solve for x:

x = [ -(-3) ± sqrt( (-3)² - 4(2)(1) ) ] / (2*2)

x = [ 3 ± sqrt(1) ] / 4

x = 1/2 or x = 1

Therefore, the x-intercepts are (1/2, 0) and (1, 0).

For the function y = 2x² + 8x + 6:

2x² + 8x + 6 = 0

We can simplify this equation by dividing both sides by 2:

x² + 4x + 3 = 0

This equation factors as:

(x + 3)(x + 1) = 0

So the solutions are x = -3 and x = -1.

Therefore, the x-intercepts are (-3, 0) and (-1, 0).

For the coordinates (0.5, [?]).

To find the y-coordinate of the point (0.5, [?]), we can substitute x = 0.5 into the equation for the function:

y = 2(0.5)² + 8(0.5) + 6

y = 2(0.25) + 4 + 6

y = 5.5

Therefore, the coordinates are (0.5, 5.5).

For the coordinates ([ ], [ ]).

Without knowing the specific function, we cannot determine the x-intercepts or any other information about the graph. We would need to know the equation of the function or have additional information about the graph.

Answer:72

Step-by-step explanation:you would add the 9 to the other side and then it would give you the answer of x=72. You do this because it is -9 if it were say x+9 then you would subtract 9 from both sides

A simplification of the fractions (-5/8) ÷ (-3/4) is equal to: B. -20/24.

The step in which Johnetta made her error include the following: A. step 1.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, the division can be calculated as follows;

Fraction = (-5/8) ÷ (-3/4)

Fraction = -5/8 × (-4/3)

Fraction = -20/24

For Johnetta, we have:

Fraction = 7/9 ÷ 3/8

Fraction = 7/9 × 8/3

Fraction = 56/27

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Answer:

y=(x+8)^2/6 - 5/2

Step-by-step explanation:

Khan Academy

we should expect 4 of the next 20 pastries served to be bran muffins.

How to solve the question?

To calculate the expected number of bran muffins out of the next 20 pastries served, we need to first determine the proportion of pastries that are bran muffins out of the total number of pastries observed.

The total number of pastries observed is 10 (1 poppy seed muffin + 3 cinnamon rolls + 2 bran muffins + 2 apple fritters + 2 croissants). Out of these, 2 are bran muffins. Therefore, the proportion of pastries that are bran muffins is 2/10 or 0.2.

To calculate the expected number of bran muffins out of the next 20 pastries served, we simply multiply the proportion of bran muffins by 20.

Expected number of bran muffins = 0.2 x 20 = 4

Therefore, we should expect 4 of the next 20 pastries served to be bran muffins.

It's important to note that this calculation assumes that the proportion of bran muffins served remains the same for the next 20 pastries. If there are any changes in the pastry selection or the proportion of each pastry, the expected number of bran muffins would also change.

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Your complete question is :-poppy seed muffins 1,cinnamon rolls 3,bran muffins 2,apple fritters 2,croissants 2

Considering this data, how many of the next 20 pastries served should you expect to be bran muffins?

The period of the sinusoidal equation of the graph is 4 months.

The amplitude of the sinusoidal equation of the graph is 84 degrees Celsius.

The period and amplitude are two important characteristics of a wave.

Period: The period of a wave is the time it takes for one complete cycle of the wave to occur. The period of a wave determines its frequency, which is defined as the reciprocal of the period.

Amplitude: The amplitude of a wave is the maximum displacement of the wave from its equilibrium position. In simpler terms, it represents the height or strength of the wave.

In then given graph, the period of the wave = 1 complete cycle in 4 months = 4 months/cycle = 4 months

Amplitude = 84 degrees Celsius.

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The system has the following solution: [tex]x_1=-4,\ x_2=3,\ x_3=1[/tex]. The vector xequals can be used to represent the answer.

A statement in mathematics demonstrating the equality of two expressions is called an equation. Two phrases with the same value are normally separated by the equals sign (=). Finding the area of a circle and predicting planetary motion are only two examples of the many practical issues that equations are used to address.

The linear system's augmented matrix, which is determined by the matrix equation A x = b is given by:

Aequals

[tex]\left[\begin{array}{ccc}1&-3&4\\2&-3&2\\-3&3&4\\-7&15&-4\end{array}\right][/tex]

Part 2:

Aequals

Write the system's solution as a vector after solving it.

We can use Gaussian Elimination to solve this system.

Step 1:

[tex]\left[\begin{array}{ccc}1&1&0\\2&-1&1\\-3&0&1\\-7&8&3\end{array}\right][/tex]

Step 2:

Aequals

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\3&1&0\\-4&3&1\end{array}\right][/tex]

The system's solution is [tex]x_1=-4,\ x_2=3,\ x_3=1[/tex]. The vector xequals represents the answer.

The matrix is,

[tex]\left[\begin{array}{ccc}-4\\3\\1\end{array}\right][/tex]

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Simplifying this equation, we get: PQ ≈ 6.93 and QR ≈ 8.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides.

To find the lengths of PQ and QR in triangle RPQ, we can use the law of sines:

sin(R) / RP = sin(P) / PQ = sin(Q) / QR

We are given R = 30° and P = 60°, so we can find Q:

Q = 180° - R - P

Q = 180° - 30° - 60°

Q = 90°

Now we can use the law of sines:

sin(30°) / 4 = sin(60°) / PQ = sin(90°) / QR

Simplifying this equation, we get:

PQ = (4 * sin(60°)) / sin(30°) ≈ 6.93

QR = (4 * sin(90°)) / sin(30°) = 4 * 2 ≈ 8

Therefore, PQ ≈ 6.93 and QR ≈ 8.

To learn more about triangle from the given link:

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Answer:

Once a person has identified the ways they are wasting money, there are several steps they can take to stop wasting money and start saving it:

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