a) Write a linear system to model the situation:
For the school play, the cost of one adult ticket is $6 and the cost of one student ticket is $4. Twice as many student tickets as adult tickets were sold. The total receipts were $2016.

b) Use substitution to solve the related problem:
How many of each type of ticket were sold?​

The extreme of the function is Absolute minimum

y = -2

x-intercept = 3

A discontinuous function is a mathematical function that has one or more points in its domain where the function fails to be continuous.

In other words, at these specific points, the function exhibits a discontinuity, indicating a break or jump in the graph.

In the graph, there was discontinuities at points

x = -2, and x = 2

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The solutions to the equation (cosec(x)+2)(2cos(x)-1) are x = -π/6 + 2πn, 7π/6 + 2πn, x = π/3 + 2πn, 5π/3 + 2πn.

To solve the given equation, we can make use of zero-product property. The zero-product property states that if the product of the two factors is equal to zero, then one of the factors has to be equal to zero. So, now we will equate each factor to zero to find the solution.

1. (cosec(x)+2) = 0

 = cosec(x) = -2

 Taking reciprocal on both the sides:

 = 1/cosec(x) = -1/2

 = sin(x) = -1/2

The solutions for sin(x) = -1/2 occur when x = -π/6 + 2πn and 7π/6 + 2πn, where 'n' is an integer.

2. (2cos(x)-1) = 0

 = 2cos(x) = 1

 = cos(x) = 1/2

The solutions for  cos(x) = 1/2 occur when  x = π/3 + 2πn and 5π/3 + 2πn, where 'n' is an integer.

Therefore, the solutions to the equation (cosec(x)+2)(2cos(x)-1) are x = -π/6 + 2πn, 7π/6 + 2πn, x = π/3 + 2πn, 5π/3 + 2πn.

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The complete question is: Find out the possible solutions of the equation (cosecx+2)(2cosx-1)=0.

Answer:

[tex] \sqrt{9} \sqrt{9} = 9[/tex]

Answer:25.12

Step-by-step explanation:

Use the second equation

C = 8(3.14) = 25.12

Answer:

Area = 50.24 feet²

Circumference = 25.12 feet

Step-by-step explanation:

If the circle's diameter is 8 feet, then the radius will be 4 feet.

A=4²(3.14)

=16(3.14)

=50.24

C=2π(4)

C=8π

C≅25.12

Answer:

be more clear of what u mean edit the question so we can tell what u mean and answer correctly

Step-by-step explanation:

no explanation

The height of the isosceles triangle is approximately 9.70 meters.

To find the height (y) of an isosceles triangle given its slant height and two angles, we can use trigonometry. Here are the steps to solve this problem:

Start by drawing a sketch of the isosceles triangle. Label the base as "b," the height as "y," and the slant height as "s."

Since the triangle is isosceles, the two base angles are congruent, meaning each angle measures 57 degrees. Label one of these angles as "θ."

We know that the slant height (s) is given as 11.5 m.

Apply the sine function to relate the slant height (s) to the angle (θ) and the height (y) of the triangle. The sine of an angle is defined as the ratio of the opposite side (y) to the hypotenuse (s). So, we have sin(θ) = y/s.

Substitute the given values into the equation: sin(57 degrees) = y/11.5.

Solve the equation for y by multiplying both sides by 11.5: y = 11.5 * sin(57 degrees).

Use a calculator to find the value of sin(57 degrees) and multiply it by 11.5 to obtain the height (y) of the triangle.

Performing the calculation, y = 11.5 * sin(57 degrees) ≈ 9.70 meters (rounded to two decimal places).

Therefore, the height of the isosceles triangle is approximately 9.70 meters.

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Answer:

Step-by-step explanation:

add it then subtract the value

The probability of rolling a 6 with this die would be = 1/15.

To determine the possibility of the given event, the formula for probability should be used and it's given below as follows:

Probability= Possible outcome/sample space

where;

possible outcome= 1

sample space= 15

Probability = 1/15

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X = 4√6 because the tangent of 35 degrees is equal to X/8 in the first right triangle and 12/X in the second right triangle.

We have two right triangles with an angle of 35 degrees and side lengths of 8 units and 12 units.

To explain why X = 12, we can use the trigonometric ratio of tangent (tan). In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In the first right triangle, the side opposite to the angle of 35 degrees is X, and the adjacent side is 8 units. So, we have:

tan(35 degrees) = X / 8

Similarly, in the second right triangle, the side opposite to the angle of 35 degrees is 12 units, and the adjacent side is X. So, we have:

tan(35 degrees) = 12 / X

Since the tangent of an angle is the same regardless of the orientation of the triangle, we can equate the two ratios:

X / 8 = 12 / X

To solve for X, we can cross-multiply:

X^2 = 8 * 12

X^2 = 96

Taking the square root of both sides, we get:

X = √96

Simplifying, we have:

X = 4√6

Therefore, X is equal to 4 times the square root of 6.

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Answer:

Davis has a loss of $19

i.e -19

Step-by-step explanation:

On day 1, David lost 5.4 * 10 = $54

On day 2, David gained 5 * 7 = $35

Overall, his loss is greater than the profit

Total loss is $54 - $35 = $19

The row operation on the matrix [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex] is [tex]\left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

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

[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The row operation is given as

1/2R₁

This means that we divide the entries on the first row by 2

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

[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

Hence, the row operation on the matrix is [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

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Consider functions fand g below g(x)=-x^2+2x+4 is option D.As x approaches infinity, the value of f(x) decreases and the value of g(x) increases.

The limit of a function, as x approaches infinity, is defined as a certain value if the function approaches the same value as x approaches infinity from both sides. The behavior of a function, as x approaches infinity, is determined by the function's rate of increase or decrease and the value of the function at x = 0.

The value of f(x) and g(x) will both increase as x approaches infinity in situation C. This implies that the functions are continuously increasing without bound, i.e., the function's value at any given point will always be greater than the previous point. Consider the example of f(x) = x² and g(x) = 2x. As x approaches infinity, f(x) and g(x) will both continue to increase indefinitely.

This is because x² and 2x are both monotonically increasing functions.As x approaches infinity, the value of f(x) decreases and the value of g(x) increases in situation D. As the value of f(x) approaches infinity, it will eventually reach a point where its rate of increase slows and the function will start to decrease.

On the other hand, g(x) will continue to increase because its rate of increase is faster than f(x) and does not slow down as x approaches infinity. Consider the example of f(x) = 1/x and g(x) = x². As x approaches infinity, f(x) decreases towards zero while g(x) continues to increase without bound.The correct answer is d.

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The statement that is true is as x increases, the rate of change of g(x) exceeds the rate of change of f(x). Option B

First, let us determine the derivatives Let's first of the functions f(x) and g(x) to compare their rates of change:

The functions are given as;

f(x) = 1/50(3)

g(x) = 1/5(x²)

Since the derivative of a constant is zero, f'(x) = 0.

g'(x) = 2/5x

Then, we can say that the rate of change of g(x) increases faster than the rate of change of f(x) as x increases.

The rate of change of g(x) (2/5x) will grow as x increases, while the rate of change of f(x) stays constant.

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49.87 because I searched it up

The numerical value of x in the minor arc KU of the circle is 7.

The inscribed angle theorem states that an angle x inscribed in a circle is half of the central angle 2x that subtends the same arc on the circle.

It is expressed as:

Internal angle = 1/2 × ( major arc + minor arc )

From the diagram:

Internal angle = 122 degrees

Major arc = 194 degrees

Minor arc = ( 6x + 8 )

Plug these values into the above formula and solve for x:

Internal angle = 1/2 × ( major arc + minor arc )

122 = 1/2 × ( 194 + ( 6x + 8 ) )

Multiply both sides by 2:

122 × 2 = 2 × 1/2 × ( 194 + ( 6x + 8 ) )

122 × 2 =( 194 + ( 6x + 8 ) )

244 = 194 + 8 + 6x

244 = 202 + 6x

6x = 244 - 202

6x = 42

x = 42/6

x = 7

Therefore, the value of x is 7.

Option B) 7 is the correct answer,

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Answer:

80

Step-by-step explanation:

The range of the rational function in this problem is given as follows:

All real values. (fourth option).

From the graph of the function given by the image presented at the end of the answer, it assumes all values of y, hence the range is all real values.

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Answer:

math = 227.98

programming = 42.55

Step-by-step explanation:

Answer:

math = 227.98

programming = 42.55

Step-by-step explanation:

We have
3m + 4p = 854.14 -eq(1)

8m + 1p = 1866.39 -eq(2)

rq(2) x 4: 32m + 4p = 7465.56 -eq(3)

eq(3)-eq(1):

32m + 4p = 7465.56

- ( 3m + 4p = 854.14)

--------------------------------

29m = 6611.42

--------------------------------

⇒ m = 6611.42/29

m = 227.98

sub in eq(1)

3(227.98) + 4p = 854.14

4p = 854.14 - 683.94

4p = 170.2

p = 170.2/4

p = 42.55

Answer:

f^(-1)(x) = ±√(x - 5).

Step-by-step explanation:

Replace f(x) with y: y = x^2 + 5.

Swap the x and y variables: x = y^2 + 5.

Solve the equation for y. To do this, we'll rearrange the equation:

x - 5 = y^2.

Take the square root of both sides (considering both positive and negative square roots):

±√(x - 5) = y.

Swap y and x again to express the inverse function:

f^(-1)(x) = ±√(x - 5).

The area of the triangle in this problem is given as follows:

34 ft².

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The parameters for this problem are given as follows:

b = 10 ft, h = 6.8 ft.

Hence the area is given as follows:

A = 0.5 x 10 x 6.8

A = 34 ft².

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Answer:

x = - 2 , x = 4

Step-by-step explanation:

the x- intercepts are the points on the x- axis where the graph crosses

the graph crosses the x - axis at - 2 and 4 , then

x- intercepts are x = - 2 , x = 4

The insurance policy would cover up to $216,000 for the item or property.

If the replacement value of an item or property is $270,000 and your insurance policy provides coverage for 80% of the replacement value, it means that your insurance policy will cover up to 80% of the $270,000 in the event of a covered loss.

To calculate the coverage amount, you would multiply the replacement value by the coverage percentage:

Coverage Amount = Replacement Value * Coverage Percentage

In this case:

Coverage Amount = $270,000 * 0.80

Coverage Amount = $216,000

Therefore, your insurance policy would cover up to $216,000 for the item or property in question. Any losses exceeding this coverage amount would not be covered by your insurance policy.

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Answer:

Step-by-step explanation:

The measure of angle HFJ in the right triangle JFH is 43 degrees.

In the right triangle FGJ, first, we determine the hypotenuse FJ.

Angle GFJ = 43 degrees

Opposite of angle GFJ = 6

Hypotenuse FJ = ?

Using the trigonometric ratio, we can find the hypotenuse FJ:

sine = opposite / hypotenuse

sin( 43 ) = 6 / FJ

FJ = 6 / sin( 43 )

FJ = 8.7977

Now, we can find angle HFJ,

Angle HFJ = ?

opposite = 6

Hypotenuse FJ = 8.7977

Using the trigonometric ratio:

sin ( HFJ ) = 6 / 8.7977

sin ( HFJ ) = 6 / 8.7977

HFJ = sin⁻¹( 6 / 8.7977 )

HFJ = 43°

Therefore, angle HFJ measure 43 degrees.

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The interval notation (-3, 4) represents the set of real numbers r that are greater than -3 and less than 4, excluding -3 and 4.

The set builder notation {r | -3 < r < 4} can be expressed in interval notation as (-3, 4).

In interval notation, the parentheses indicate that the endpoints, -3 and 4, are not included in the set.

The interval (-3, 4) represents all the real numbers r that are greater than -3 and less than 4, but not including -3 and 4.

It can also be visualized on a number line as an open interval between -3 and 4, where the endpoints are not filled in.

The interval (-3, 4) can be interpreted as a range of values for r. Any real number between -3 and 4, excluding the endpoints, would satisfy the given set builder notations.

For example, -2, 0, and 3 are all included in the interval (-3, 4), but -3 and 4 themselves are not part of the set.

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The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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I can't really see the graph clearly but I think that the x-intercepts should be (-16/7, 0) and (32/7, 0).

Answer:

x-intercepts:  -2, 4

Step-by-step explanation:

The given graph shows a parabola that opens downwards.

The y-intercept is the point at which the curve crosses the y-axis, so when x = 0. From inspection of the given graph, we can see that the parabola crosses the y-axis when y = 8. Therefore, the y-intercept is (0, 8).

The x-intercepts are the points at which the curve crosses the x-axis, so when y = 0. From inspection of the given graph, we can see that the parabola crosses the x-axis when x = -2 and x = 4. Therefore, the x-intercepts are (-2, 0) and (4, 0).