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A Drama Club is planning a grand opening musical for the new auditorium! It can hold up to 1000 people. They plan on charging $6 for a student ticket (x) and $10 for an adult ticket (y). If they need to make $3500 to cover all of their expenses, answer the following:

a) Write an inequality to represent the number of tickets

b) Write an inequality to represent the amount of money brought in

c) Give ONE combination of student and adult ticket sales that would satisfy both inequalities

d) Give ONE combination of student and adult ticket sales that would satisfy ONE, but NOT both inequalities

1) The function is P(t) = 6.79e^ 0.0317t

2) There would be 8.18 million people in 2018

3) It would take 9 years to reach a population of 9 million

4) The doubling time is 22 years

We know that population growth has to do with the increase in the population of a place. Let us recall that population growth occurs exponentially and this would help us as we write the function for the population growth.

a) The population growth function is obtained as;

P(t) = 6.79e^ 0.0317t

t = Number of years since 2012.

b) In the year 2018, six years would have passed hence we have;

P(t) = 6.79e^ 0.0317 * 6

P(t) = 8.18 million people

c) The population would be 9 million when;

9 =  6.79e^ 0.0317t

9/6.79 =e^ 0.0317t

1.33 = e^ 0.0317t

ln(1.33) = 0.0317t

t = ln(1.33)/0.0317

t = 9 years

d) The doubling time would be;

2(6.79) =6.79e^ 0.0317t

2(6.79)/6.79 = e^ 0.0317t

ln 2 =  0.0317t

t = ln 2 / 0.0317

t = 22 years

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Answer:

17.5%

Step-by-step explanation:

We know that there are 35 out of 200 allergic to peanut

So we take

35 divided by 200, then times 100% = 17.5%

So, 17.5  of children are allergic to peanut

The graph that represents the function f(x) = 4[x] is option C.

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 4 [x]

[x] is the greatest integer function.

We see that,

f(0) = 4 [0] = 0

f(0.5) = 4 [0.5] = 4 x 0 = 0

f(x) = 0 for 0 ≤ x < 1

f(1) = 4 [1] = 4

f(1.5) = 4 [1.5] = 4 x 1 = 4

f(x) = 4 for 1 ≤ x < 2

f(2) = 4 [2] = 4 x 2 = 8

f(2.5) = 4 [2.5] = 4 x 2 = 8

f(x) = 8 for 2 ≤ x < 2

Thus,

The graph on option C has the required coordinates.

f(x) = 0 for 0 ≤ x < 1

f(x) = 4 for 1 ≤ x < 2

f(x) = 0 for 2 ≤ x < 2

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Answer:

No correlation

Step-by-step explanation: If the graph  shows a positive correlation, the correlation would be linear, if its showing a negative correlation , then the correlation would also be linear, but going in a downward slope

The required mean of 2 and 12 is 7.

One kind of average is the mean.

It is calculated by dividing the total number of values in a list of values, such as measurements or numbers, by the total number of values in the list.

Add up each value in the set to determine the mean.

So, we have the values:

2 and 12

Mean formula: Sum of terms / Number of terms

Now, solve for the mean of the 2 values using the formula as follows:

Mean: Sum of terms / Number of terms

Mean: 14 / 2

Mean: 7

Therefore, the required mean of 2 and 12 is 7.

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Answer:

C. Substitution

Step-by-step explanation:

Substitution is the final answer to an equation. So, the answer is C

Answer: C. Substitution

The nature of roots of the given quadratic equation is "real and unequal".

Nature of Roots:

Root type simply means the category to which the root belongs. Roots can be imaginary, real, unequal, or equal. If the discriminant is negative, the root is imaginary.

Depending on the value of the discriminant, we discuss the following cases for the nature of the root:

Case 1: D = 0

If the discriminant is zero (b2 – 4ac = 0), a, b, and c are real, and a≠0, the root of the quadratic equation is ax2 + bx + c = 0 is Real and equal. In this case the root is x = -b/2a. A graph of the equation is tangent to the x-axis at a point.

Case 2: D > 0

If the discriminant is greater than zero (b2 – 4ac > 0), then a, b, and c are real and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is real and not equal. The equation graph touches the x-axis at two different points.

Case 3: D < 0

If the discriminant is less than zero (b2 – 4ac < 0), a, b, and c are real, and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is Imaginary and not equal. Roots exist in conjugate pairs. The equation graph does not touch the x-axis.

Case 4: Perfect Square with D > 0

If D > 0 and Perfect Square, the roots of the quadratic equation are real, unequal, and rational.

Case 5: D > 0 and Not Perfect Square

If D > 0 and not perfect square, the roots of the quadratic equation are real, unequal, and irrational.

According to the Question:

The given quadratic equation:

9x²-6x-2 = 0

Here, a = 9, b = - 6 and c = -2

To Find: the nature of roots of the given quadratic equation.

∴ Discriminant, D = b²-4ac

= (-6)² - 4×9×(-2)

= 36 -36(-2)

= 36 + 72

=108

Since,

D = 108 > 0, the roots are real and unequal.

Hence, the nature of roots of the given quadratic equation is "real and unequal".

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Answer:

Congruent means the same shape but perhaps moved or rotated or reflected

Similar means a shape that has been enlarged by a scale factor

Step-by-step explanation:

Answer: the height of this triangle is 55.4 mm

Step-by-step explanation:

[tex]\displaystyle\\Area\ of\ a\ triangle:\ A =\ \frac{ah}{2} \\\\Hence,\\[/tex]

Multiply both parts of the equation by 2:

[tex]2A=ah[/tex]

Divide both parts of the equation by a:

[tex]\displaystyle\\\frac{2A}{a} =h\\\\Thus,\ h=\frac{2A}{a} \\\\h=\frac{2(227.14)}{8.2} \\\\h=\frac{454.28}{8,2} \\\\h=55.4\ mm[/tex]

The point (2,-4), (x,y), A, and B all lie on the line. An equation relating x and y is m(x-2)=y+4.

The points (2, -4), (x, y) are lie on the line.

The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run. The slope formula uses two points, (x1, y1) and (x2, y2), to calculate the change in y over the change in x. Slope is a ratio that includes how y changes for every unit increase of x.

The slope formula,

m[tex](x_{2}-x_{1})= y_{2}-y_{1}[/tex]

Here, [tex]x_{1} = 2, x_{2}= x, y_{1}= -4[/tex] and [tex]y_{2}= y[/tex]

Now, we have to substitute the values in the formula,

[tex]m=\frac{y-(-4)}{x-2}[/tex]

[tex]m= \frac{y+4}{x-2}[/tex]

m(x-2)= y+4

Therefore, the equation is m(x-2)=y+4.

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can you give a more clearer image if possible, please?

Answer:

cowboys fan:0  im guessing lol

Step-by-step explanation:

cowboys aren't bad so i'm not complaining:)

The value of sinx is 1 - 3cosx

What is Trigonometry?

Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles. The topic arose in the Hellenistic civilization during the third century BC from geometric applications to astronomical research. Today, four varieties of trigonometry are used: core, plane, spherical, and analytic. The ratio of the sides and angles of a right triangle is the subject of core trigonometry.

Solution:

1/cosx - tanx = 3

we can write tanx as sinx/cosx

this is because we know that sinx = Perpendicular / Hypotenuse

and cosx = Base / Hypotenuse

so if we divide sinx by cosx we will find that it is equal to Perpendicular / Base which is nothing but tanx

1-sinx = 3cosx

sinx = 1 - 3cosx

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To find the median of a set of numbers, we need to first put the numbers in order from least to greatest. In this case, the ages of the Carnegie children are 3, 9, 18, and 24 years old. Since there are 4 numbers in this set, the median is the average of the middle two numbers, which are 9 and 18. The median of the ages of the Carnegie children is (9 + 18) / 2 = 27 / 2 = 13.5 years old.

To find the mean of a set of numbers, we need to add the numbers together and then divide the sum by the number of numbers in the set. In this case, the sum of the ages of the Carnegie children is 3 + 9 + 18 + 24 = 54 years old. Since there are 4 children, the mean age is 54 years / 4 children = 13.5 years old. Therefore, the mean of the ages of the Carnegie children is 13.5 years old.

Answer:

Median: 13.5

Mean: 13.5

Step-by-step explanation:

To get the median, take the middle value. Since there are two middle values, add them together and divide them by two.

To get the mean, add all the values together and divide the sum by the number of values. In this instance, mean and median are the same.

Answer:

m = 13

Step-by-step explanation:

(-9, -6) (-8,7)

The slope is rise/run or ( y2 - y1) / (x2 - x1)

We see the y increase by 13 and the x increase by 1, so the slope is

13/1 or 13

So, m = 13

The limit of h(x) as x approaches infinity is ∞, and as x approaches 0, is undefined due to division by zero.

x h(x)

1 2 + 2

2 1.41 + 1

4 2 + 0.25

8 2.83 + 0.125

16 4 + 0.0625

To find the limit of h(x) as x approaches infinity, we see that h(x) = √(x) + 2/x - 5. As x increases without bounds, the square root of x and 2/x both approach infinity, but the value of -5 is constant. Therefore, the limit of h(x) as x approaches infinity is infinite.

To find the limit of h(x) as x approaches 0, we see that h(x) = √(x) + 2/x - 5. As x approaches 0, the value of the square root of x approaches 0, and the value of 2/x approaches infinity. However, the value of -5 is constant. Therefore, the limit of h(x) as x approaches 0 is -5 + ∞, which is undefined.

The limit of h(x) as x approaches 0 is undefined.

You could also say that the function is not defined at x = 0, meaning that the limit as x approaches 0 does not exist.

It's worth noting that the original function is not defined when x=0 as we are dividing by x, so it's impossible to calculate the limit of this function at that point.

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The solution of the equation 2x^2 + 5x + 3 = 0 is x = -3 and x = -1/2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions are x = (-b +/- sqrt(b^2 - 4ac))/2a.

The solution of the equation 2x^2 + 5x + 3 = 0 can be found by using the Quadratic Formula. The Quadratic Formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions are x = (-b +/- sqrt(b^2 - 4ac))/2a. By substituting the given coefficients a = 2, b = 5, and c = 3 into this equation, we can solve for x. First, we calculate the discriminant b^2 - 4ac, which in this case is 25 - 24 = 1. Because the discriminant is positive, the equation has two real solutions. Next, we use the Quadratic Formula to calculate the solutions. To calculate the first solution, we substitute the given coefficients into the formula and solve for x: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -3 and -1/2.

Therefore, the solution of the equation 2x^2 + 5x + 3 = 0 is x = -3 and x = -1/2.

Discriminant: b^2 - 4ac = 25 - 24 = 1

Solution 1: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -3

Solution 2: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -1/2

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The median when the mean is 48 and the mode is 15 is 37.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

For instance, what is the median of our data set if we know that we have a mean of 10 and a mode of 4?

Since the Mean - Mode is 3, we may state that 10 - 4 equals 3. (10 – Median).

According to some algebra, the median of our data is 8 because 2 = (10 - Median).

So, the values are:
Mean = 48

Mode = 15

Formula: Mean – Mode = 3(Mean – Median)

Now, calculate the median using the formula as follows:

48 – 15 = 3(48– Median)

33 = 144 - 3Median

3Median = 144 - 33

3Median = 111

Median = 111/3

Median = 37

Therefore, the median when the mean is 48 and the mode is 15 is 37.

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The statement that is true is there are no outliers in this distribution.

What is distribution ?

Selling and providing goods and services to customers is the process of distribution. The phrase is used to refer to marketing channels that are employed to contact clients in various contexts and geographical locations.

There are four different categories of distribution channels: direct selling, selling through middlemen, dual distribution, and reverse logistics networks.

The delivery of goods from manufacturers to end users is ensured by a network of distributors or intermediaries known as a distribution channel. It is also in charge of sending payments made by clients for purchases made by producers.

In this scenario, the noticeable outliers in the data sets are 200 and 210. Thus, a statement which is not true about the data provided in the box plot above, is that there are no outliers in this distribution

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the function is [tex]f(x) = x^2.[/tex] The graph is what is known as the basic parabola. Take note of the graph's symmetry about the y-axis. The symmetry axis of this function is known as the y-axis.

Something bowl-shaped at the intersection of a right circular cone and a plane parallel to an element of the cone: a plane curve produced by a moving point so that its distance from a fixed point is equal to its distance from a fixed line (such as an antenna or microphone reflector). Any point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line. Conic section is a topic that includes parabola, and this article covers all of its principles.

equation of tangent line = [tex]y - y1 = m (x - x1)[/tex]

equation of a circle =  [tex]x^2 + y^2 + 2gx + 2fy + c = 0[/tex]

equation of hyperbola =  [tex][(x2/a2) - (y2/b2)] = 1[/tex]

equation of a line = [tex]y = mx + c[/tex]

equation of slope = [tex]m= \frac{y_2 - y_1}{x_2 - x_1}[/tex]

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Answer:

Right angle triangles

Step-by-step explanation:

the only type of triangles that can be solved with pythagorem theorem is right angle triangles. otherwise you would need to use a different formula

The roots of the graph of f(x) = (x+4)⁶(x+7)⁵ crosses the x axis at  x = -7 .

The Roots of the Graph of the equation is defined as the point at which the curve crosses the x axis , and also the roots satisfy the equation .

the function is given as : f(x) = (x+4)⁶(x+7)⁵ ;

let the function be denoted by y = f(x) .

If the graph crosses  x - axis , then the value of y is 0 .

that means ; (x+4)⁶(x+7)⁵ = 0   ;

which implies that , (x + 4) = 0   (x + 7) = 0 ,

simplifying ,

we get ; x = -4 and x = -7 .

we know that if the power of function is even the function bounces from the x axis ,

and if the power of function is odd the function crosses the x axis ,

Therefore , the graph crosses the x axis at  x = -7 .

The given question is incomplete , the complete question is

At which root does the graph of f(x) = (x+4)⁶(x+7)⁵ cross the x axis ?

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-a/b=-5/3  is the slope of the line 5x 3y 15

for

ax+by=c

the slope is -a/b

the slope of paralell lines are the same

find slope

5x+3y=15

-a/b=-5/3

paralell as same slope

the slopes are:

L1: slope 3

L2: slope -3

L3: slope -1/3

So now multiply the slopes of each pair of lines:

L1 and L2: 3 * (-3) = - 9 => No, they are not perpendicular

L2 and L3: (-3) * (-1/3) = 1 => No, they are not perpendicular

L1 and L3: (3) *  (-1/3) = -1 => Yes, they are penpendicular.

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The line produced by the equation 3x + 4y=-12 has a slope of -3/4.

To find the slope of a line represented by the equation 3x + 4y = -12, you need to have the equation in the form y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).

To put the equation 3x + 4y = -12 in this form, you can start by isolating the y term on one side of the equation:

3x + 4y = -12

4y = -3x - 12

y = (-3/4)x - (12/4)

The slope of the line produced by the equation 3x + 4y=-12 is therefore -3/4.

The complete question is:-

What is the slope of the line given by the equation 3x +4y =- 12?

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The volume of the pyramid is one-third of the product of its height and the area of its base. That is volume of the pyramid is linearly proportional to its height and the area of its base.

A pyramid is a solid with a base and rectangle face on the edge of base meeting at a vertex. Generally we consider a right pyramid.

Consider a pyramid of base area A and height h, the volume of the pyramid is one-third of the product of its height and the area of its base, that is the volume formula of pyramid is

V = A × h/ 3

That is

V ∝ A and

V ∝ h

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The area henry' rectangular kitchen island top with length 35. 5 inches and width 46. 75 inches is 1659. 625 inch².

The word "area" means an open area. A shape's area is calculated using its length and width. Length is one-dimensional and measured in units such as feet (ft), yards (yd), and inches (in). Area is defined as the total space occupied by a planar (2-D) surface or shape of an object. It is measured in units such as square feet (ft²) and square inches (in²)

Let " l " be length of rectangular island top and "w" be width of it.

We have , l = 35.5 inches , w = 46.75 inches

We have to calculate the area if henry' rectangular kitchen iland top.

let "A" be area of rectangular island top .

As discuss above, Required Area , A = l × w

=> A = 35.5 inches × 46.75 inches

=> A = 1659.625 inch²

Hence, required area is 1659.625 square inches.

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In order to determine the  height of a box we can use the formula h = V/b or if the given box is a square box or a cube then we can calculate its height by finding the cube root of its volume.

In the formula , V = volume and b = base

Volume is calculated in three dimension , it is the measure of the space occupied by an object . Any given solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

There are various shapes in geometry and all of them have a specific formula to calculate the volume.

The SI unit of volume for a cube is m³.

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The required coordinates of point P, following the given coordinate points, are (5.5, -1).

Let's assume that point P has coordinates (x, y). We want to find the coordinates of point P along the directed line segment AB, such that the ratio of AP to PB is 1 to 4.

The coordinates of point A are (8, 0), and the coordinates of point B are (3, -2).

According to the ratio given, we have:

AP/PB = 1/4

Now, we can use the midpoint formula to find the coordinates of point P. The midpoint formula states that the coordinates of the midpoint M between two points (x₁, y₁) and (x₂, y₂) are given by:

Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Let's use the midpoint formula to find the coordinates of point P:

x = (8 + 3) / 2
  = 5.5

y = (0 + (-2)) / 2
  = -1

So, the coordinates of point P are (5.5, -1).

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Arithmetic mean of the data set 4, 5, 0, 10, 8 and 3  is '5'

As per the question the given data set is :

4 , 5 , 0 , 10 , 8 and 3

Number of observations in given data set are '6'

We have to determine the value of arithmetic mean of the data

Arithmetic Mean is simply the mean or average for a set of data or a collection of numbers.

Arithmetic mean is defined as the ratio of sum of all observations in given data set to the total number of values.

Arithmetic mean ( AM ) formula is

AM = (sum of all observations in given data set) ÷ (total number of observations)

Sum of all observations in given data set :

= 4 + 5 + 0 + 10 + 8 + 3

= 30

Arithmetic mean :

[tex]=\frac{30}{6}[/tex]

= 5

Therefore arithmetic mean of the given data set 4, 5, 0, 10, 8 and 3  is 5.

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A data set's mean can be estimated by dividing the sum of all the data points by the total number of data points in the data set.

How is the mean method calculated?

It is calculated by merely dividing the total number of values in a data collection by the sum of all the values in the data set. Both raw data and data that have been combined in a frequency table may be used in the calculation.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                 Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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