The Rialto Theater sells balcony seats for $10 and main floor seats for


$25. One afternoon performance made $6250. The number of balcony


seats sold was 20 more than 3 times the number of main floor seats. Write


the system of equations to determine the number of main floor and


balcony seats.

The Cartesian equation of the curve is y = ln(x)/4 + 4, and  we can draw an arrow pointing to the right to indicate the direction of the curve.

(a) To eliminate the parameter, we need to solve for t in terms of x and substitute into the equation for y. From the equation x = e⁴ᵗ, we have t = ln(x)/4. Substituting into y = t + 4, we get y = ln(x)/4 + 4. Therefore, the Cartesian equation of the curve is y = ln(x)/4 + 4.

(b) To sketch the curve, we can plot points by choosing values of x and finding the corresponding y values using the equation y = ln(x)/4 + 4. As x increases, y increases but at a slower rate. This means that the curve is increasing but is becoming less steep.

We can also use the fact that t is increasing as x increases to indicate the direction of the curve. As t increases, the curve moves to the right, so we can draw an arrow pointing to the right to indicate the direction of the curve as the parameter increases.

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Answer:

12

Step-by-step explanation

60/100 to get the probability of success

0.6 * 20 attempts = 12

Regarding the second question, the management of Neat Upholsterers may determine whether a person has worked overtime by tracking their hours of work and comparing them to the standard working hours or the overtime policy defined in the employment contract or labor laws. This could involve using time cards, electronic systems, or other methods of tracking employee hours.

Whether this policy is fair or not depends on various factors, such as the specific overtime policy, the industry norms, the labor laws, and the bargaining power of the employees. If the overtime policy is reasonable, transparent, and consistent with the labor laws and the industry standards, and if the employees are compensated fairly for their extra work, then the policy could be considered fair. However, if the policy is exploitative, discriminatory, or violates the legal or ethical standards, then it could be considered unfair.

Yes, Mark is correct he believes that doubling one of the dimensions would double the volume of his toolbox.

Volume refers to the space occupied by a 3-Dimensional space. The volume of a cuboid is given by:

V = l * b * h

where l is the length

b is the breadth

h is the height

V = 9 * 6 * 7

= 378 cubic inches

If we double any of the dimensions, like

By doubling the 9 we get

V = 18 * 6 * 7

= 756 cubic inches

By doubling the 6 we get

V = 9 * 12 * 7

= 756 cubic inches

By doubling the 7 we get

V = 9 * 6 * 14

= 756 cubic inches

Then the volume of the toolbox is doubled as shown above.

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The complete equation of two squares to find the product of 22 and 18 is (22 + 18)(22 - 18) = 396

When we can interpret an expression as the difference of two perfect squares, i.e. a2-b2, we can factor it as (a+b)(a-b).

To use the difference of two squares to find the product of 22 and 18:

First, find the average of the two numbers:

(22 + 18) ÷ 2 = 20

Then, find the difference between the two numbers:

22 - 18 = 4

Now we can write:

(20 + 4)(20 - 4) = 24 × 16 = 384

But we need to add the extra 12 to get 396:

(20 + 4)(20 - 4) + 12 = 396

So the completed equation is:

(22 + 18)(22 - 18) = 396

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Answer:

B

Step-by-step explanation:

Lisa's first step is to distribute, so you have to distribute all numbers.

(3+6x)-2(x+1)+5

3(1+2x)-2)x+1)+5

Hope this helps! :)

The intervals where f is decreasing are given as follows:

None of the above.

Hence the decreasing intervals of the function are given as follows:

Which are none of the options given in the problem.

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(a) To minimize the area of the right triangle formed by the cable, ground, and building, we need to minimize the length of the cable. To do this, we can use the Pythagorean theorem:

c^2 = a^2 + b^2

where c is the length of the cable, a is the distance from the guidepost to the point where the cable is attached to the building, and b is the distance from that point to the ground.

Since we want to minimize c, we can differentiate the equation with respect to a and set the derivative equal to zero:

dc/da = 2a/c = 0

Solving for a, we get a = c/2. This means that the point where the cable is attached to the building should be halfway up the building, or 10 feet high.

(b) To minimize the length of the cable, we can use the principle of least action, which states that the path taken by the cable is the one that minimizes the integral of the tension along the cable.

Assuming that the tension in the cable is constant, we can use the law of sines to find the angle θ:

sin θ / 20 = sin (90° - θ) / c

where c is the length of the cable.

We want to minimize c, so we can differentiate the equation with respect to θ and set the derivative equal to zero:

d(c)/d(θ) = -20cos(θ) / sin^2(θ) + cos(θ) / sin(θ) * dc/d(θ) = 0

Solving for dc/d(θ), we get:

dc/d(θ) = 20c * tan(θ)

Substituting this into the original equation, we get:

-20cos(θ) / sin^2(θ) + cos(θ) / sin(θ) * 20c * tan(θ) = 0

Simplifying, we get:

cos(θ) / sin(θ) = tan(θ)

Solving for θ, we get:

θ = 45°

Therefore, to minimize the length of the cable, it should make an angle of 45° with the face of the building.

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The magnitude of vector v is:
|v| = 7

The magnitude of v is simply the length of the vector v, which can be found using the Pythagorean theorem. The vector v is given as v = 7i.

To find the magnitude of v (|v|), use the formula:
|v| = √(x² + y²)

where x and y are the components of the vector v. In this case, x = 7 (from 7i) and y = 0 (since there is no j component).

Now, plug in the values of x and y into the formula:
|v| = √(7² + 0²)
|v| = √(49 + 0)
|v| = √(49)
|v| = 7

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The bearing of U from T in the image is 32 degrees South by West of T

In mathematics, bearings refer to the direction of an object or location in relation to two points. It is determined by the angle between the line joining them and that of the north.

Measured typically in degrees, it follows a cardinal system where 0° or 360° signifies North; East stands for 90°, South denotes at 180° while West represents 270°.

Thus, it can be seen that the bearing of U from T in the image is 32 degrees South by West of T

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Ali's Gulf club account will have a future value of BD 101.93 at the end of the term on October 7. The calculation was done using the formula for future value of an annuity with monthly payments, interest rate of 8% per year, and a term of 2.9 months.

We can first calculate the number of months from July 11 to October 7: 2 months and 27 days (or approximately 2.9 months).

Then, we can use the formula for future value of a present sum with simple interest

FV = P(1 + rt)

where FV is the future value, P is the present sum (in this case, BD 100), r is the annual interest rate (8% = 0.08), and t is the time in years (2.9/12 = 0.2417 years).

Substituting the values, we get

FV = 100(1 + 0.08*0.2417)

= 100(1.01934)

= BD 101.93

Therefore, the future value of Ali's golf club account is BD 101.93.

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Answer:

9, 10, 11, 12, 13.

Step-by-step explanation:

All possible values for the number of tables that the store must sell in order to meet the requirements are 9, 10, 11, 12, 13

For the following expression arcsin (sin (-57π/10)) is 3π/10.

The function arcsin(x) gives the angle in radians whose sine is x.

In this problem, we need to find the angle whose sine is equal to the sine of -57π/10.

First, we need to simplify -57π/10 to an angle in the range [-π/2, π/2] since the sine function has a range of [-1, 1]. To do this, we use the fact that sine has a period of 2π,

which means that sin(-57π/10) = sin((-57π/10) + 4π) = sin(3π/10).

So we need to find the angle θ such that sin(θ) = sin(3π/10).

Since sine is an odd function, we know that sin(-θ) = -sin(θ), so we can also say that sin(θ) = sin(-3π/10).

Therefore, there are two possible angles that satisfy the equation: θ = 3π/10 or θ = -3π/10.

However, since the range of the arcsine function is [-π/2, π/2], only the angle in that range that satisfies the equation is θ = 3π/10.

Therefore, we can write:

arcsin(sin(-57π/10)) = arcsin(sin(3π/10)) = 3π/10

The answer is 3π/10.

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Keegan will have approximately $878.85 in the account after 5 years.

What is Compound interest ?

Compound interest is the interest that is earned not only on the initial amount of money invested (known as the principal), but also on any interest earned on that principal over time. In other words, compound interest is interest on interest.

The compound interest formula is given by:

A = P[tex](1 + r/n)^{nt}[/tex]

where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, Keegan deposited $675, the annual interest rate is 4.8%, the interest is compounded quarterly, and the investment is for 5 years. Therefore, we can plug in these values into the formula to get:

A = 675[tex](1 + 0.048/4)^{20}[/tex]

A = 675[tex](1.012)^{20}[/tex]

A ≈ $878.85

Therefore, Keegan will have approximately $878.85 in the account after 5 years.

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The value of the given expression is 44. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four basic operations, also referred to as "arithmetic operations," are thought to explain all real numbers. Operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference in mathematics.

We are given an expression as [tex]\frac{1}{2}[/tex] (7) (4) + 6 (5).

We know that when there is no sign in between two numbers, it denotes multiplication.

So, we get

⇒  [tex]\frac{1}{2}[/tex] * (7)  * (4) + 6 * (5)

⇒ 14 + 30

⇒ 44                                            (Using addition operation)

Hence, the value of the given expression is 44.

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The marked points are (-2,-4), (-2,-1), (0,-2), (2,-1), and (2,-4), under the condition that they are on the same coordinate plane having (A) y=x-2, (B) y=-x-2, (C) y=|x|-2.

In the given graph points on the coordinate plane, we have to plot the points (x,y)
Here
x = horizontal axis
y = vertical axis.

In the given point A, y=x-2, we can continue at the origin (0,0) and move 2 units go down on the y-axis and 2 units right on the x-axis to plot point A at (2,0).

In the given point B, y=-x-2, we can continue at the origin (0,0) and transfer 2 units down on the y-axis and 2 units left on the x-axis to plot point B at (-2,0).

In the given point C, y=|x|-2, we can continue plotting two points for this equation.
When x is considered negative, we can procees at the origin (0,0) and transfer 2 units down on the y-axis and 2 units left on the x-axis to plot point C at (-2,0).
When x is positive, we can start at the origin (0,0) and move 2 units down on the y-axis and 2 units right on the x-axis to plot point C at (2,0).

Then, all points (x,y) such that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2 are (-2,-4), (-2,-1), (0,-2), (2,-1), and (2,-4).
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The interest he had received in total after eight years is 1396.59 kroner

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

Principal, P = 7000

Rate, r = 2.3%

Time, t = 8

The interest he had received in total after eight years is calculated as

I = P(1 + r)^t - P

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

I = 7000(1 + 2.3%)^8 - 7000

Evaluate

I = 1396.59

Hence, the total interest is 1396.59 kroner

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The farmer would have made a profit of 5% if he had sold the goat for 2100 shillings.

Let's use the given terms and find out the percentage profit if the farmer had sold the goat for 2100 shillings.
Calculate the cost price of the goat
We know that the farmer made a loss of 28% by selling the goat for 1440 shillings. Let's represent the cost price as "CP".

We can write the equation:
[tex]CP \times  (1 - loss% ) = selling price (SP)[/tex]
[tex]CP \times  (1 - 0.28) = 1440[/tex]
Solve for CP
[tex]CP \times 0.72 = 1440[/tex]
CP = 1440 / 0.72
CP = 2000 shillings
Calculate the percentage profit
Now we want to find out the percentage profit if the farmer had sold the goat for 2100 shillings.

We can write the equation:
[tex](SP_{new - CP)} / CP \times  100 = profit[/tex]
[tex](2100 - 2000) / 2000 \times  100 = profit%[/tex]
[tex]100 / 2000 \times  100 = profit%[/tex]
5% = profit%.

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19. The triangle with sides 3, 4, 6 is obtuse triangle.

20. The triangle with sides 9, 11, 16 is acute triangle.

In a triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side for the triangle to be considered "non-degenerate," which means it is a valid triangle with a positive area.

19. We have sides of 3, 4, and 6. We can check whether this triangle is non-degenerate using the above formula:

3² + 4² = 9 + 16 = 25, which is less than 6² = 36.

Therefore, this triangle is non-degenerate and we can classify it based on the size of its angles.

To do so, we can use the Pythagorean Theorem to find that the longest side (6) is opposite the largest angle, which is obtuse. Therefore, triangle #19 is an obtuse triangle.

20. For triangle #20, we have sides of 9, 11, and 16. Checking again with the above formula:

9² + 11² = 81 + 121 = 202, which is less than 16² = 256. So this triangle is also non-degenerate.

Using the same method as before, we can find that the longest side (16) is opposite the largest angle, which is acute. Therefore, triangle #20 is an acute triangle.

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Given the sequence an = n^7/n^4, The sequence is = divergent. So, the answer is that the sequence is divergent.

The sequence an = n^7/n^4 can be simplified by cancelling out the common factor of n^4 in the numerator and denominator. This yields an = n^3.

Therefore, the sequence is simply the cubes of the positive integers, or 1, 8, 27, 64, 125, 216, ... and so on. This sequence grows without bound, as n gets larger, so it does not converge to any finite limit. In other words, the sequence an does not have a limit, and it is divergent.

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The radius of the base of the cone is approximately 12.65 feet if The cone is formed from 3,200 ft of gravel.

Height of cone =  24 feet

The volume of the cone = [tex]3,200 ft^3[/tex]

To find the volume of the cone, the formula used here is:

V =π* [tex]r^2h[/tex]

Here, the values of V and H are known terms. we need to calculate the radius r of the cone.

π = 3.14 constant value

Substituting the values in the above equation, we get:

[tex]3,200 = (1/3)^2*(24)*[/tex] π

[tex]r^2[/tex]= 3,200 / (8π)

[tex]r^2[/tex] = 400 / π

r = 12.65

Therefore, we can conclude that the radius of the base of the cone is  12.65 feet.

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The result should be interpreted with caution and cannot be directly extrapolated to the real-world Fender's blue butterfly populations, and the simulation does not take these factors into account.

The result of the simulation suggests that in a hypothetical scenario where the Fender's blue butterfly population is restricted to stepping stones, and the leave prairie probability is set to 0.9, the population is likely to increase over time. However, it is important to note that the simulation represents an idealized scenario and may not reflect the complexity of real-world butterfly populations.

Furthermore, the absence of fires in the simulation may not reflect the natural habitat of Fender's blue butterfly, as fire is a crucial factor in maintaining prairie habitats. In the real world, fire suppression and habitat fragmentation are major threats to the survival of Fender's blue butterfly populations, and the simulation does not take these factors into account.

In summary, while the simulation result may provide insights into the potential effectiveness of using stepping stones to conserve butterfly populations, it should be interpreted with caution and cannot be directly extrapolated to the real-world Fender's blue butterfly population. Further research and monitoring of butterfly populations in their natural habitats are necessary to fully understand their dynamics and inform conservation efforts.

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The zero #1 is (-3, 0) and the zero #2 is (1, 0).

To find the zeros of the quadratic equation y = 2x² + 4x - 6, we need to solve for the values of x when y = 0.

We can start by setting y to zero:

0 = 2x² + 4x - 6

Next, we can divide both sides by 2 to simplify the equation:

0 = x² + 2x - 3

We can then factor the left-hand side of the equation:

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

Using the zero product property, we can set each factor equal to zero and solve for x:

x + 3 = 0 or x - 1 = 0

x = -3 or x = 1

So the zeros of the quadratic function are (-3,0) and (1,0).

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The final values is (fog)(x) = f(g(x)) = f(0) = -8.

In the given problem, we are given two functions, f(x) and g(x). The function f(x) is a polynomial function, and g(x) is a constant function equal to 0. We are asked to find the composition of these two functions, that is, (fog)(x) and (gof)(x).

The composition of two functions f(x) and g(x) is denoted by (fog)(x) and is defined as follows:

(fog)(x) = f(g(x))

This means that we first evaluate g(x) and then use the output of g(x) as the input of f(x) to get the final output of (fog)(x).

In this case, since g(x) = 0, we have:

(fog)(x) = f(g(x)) = f(0)

To evaluate f(0), we substitute x = 0 in the expression for f(x):

[tex]f(x) = 2x^2 - 6x^2 + 4x - 8[/tex]

[tex]f(0) = 2(0)^2 - 6(0)^2 + 4(0) - 8[/tex]

f(0) = -8

Therefore, (fog)(x) = f(g(x)) = f(0) = -8.

Now, to find (gof)(x), we need to evaluate g(f(x)). Since f(x) is a polynomial function, we can find its value for any value of x. However, since g(x) is a constant function equal to 0, its output is always 0 for any input x. Therefore, g(f(x)) = 0 for all values of f(x).

This means that (gof)(x) = g(f(x)) = 0 for all x.

In summary, we found that (fog)(x) = -8 and (gof)(x) = 0.

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Answer:

The answer is A

Step-by-step explanation:

To prove the trigonometric identity csc(x) - sin(x) - cos(x)cos(x), we will start by simplifying the left-hand side of the equation using trigonometric definitions and identities.

Recall that csc(x) = 1/sin(x). We will use this definition to rewrite the left-hand side of the equation:

1/sin(x) - sin(x) - cos(x)cos(x)

Now, we will find a common denominator for the terms in the equation. In this case, the common denominator is sin(x). To do this, we will multiply sin(x) to the second term:

(1 - sin^2(x) - cos(x)cos(x)sin(x)) / sin(x)

Next, we will use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to replace sin^2(x) in the expression:

(1 - (1 - cos^2(x)) - cos(x)cos(x)sin(x)) / sin(x)

Simplifying the expression, we get:

(cos^2(x) - cos(x)cos(x)sin(x)) / sin(x)

Now, we can factor out cos(x) from the numerator:

cos(x)(cos(x) - sin(x)) / sin(x)

This expression is equivalent to the given identity, so we have proven the trigonometric identity:

csc(x) - sin(x) - cos(x)cos(x) = cos(x)(cos(x) - sin(x)) / sin(x)

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The options that are statistical are:

how many pets do you have?

what time do you go to sleep?

how many siblings do you have?

The options that are non-statistical are:

what kind of dog does bruno have?

what is clara's brother's name?

what time did javed go to sleep?

A statistical question is defined as one that will obtain the data that will vary from one particular response to another. However, a non-statistical question is defined as one that will obtain data that is basically exact and then has only one response.

A question that will not provide a variety of different answers is referred to as not a statistical question. For example, we can say that 'how many siblings do I have?' is not referred to as statistical. The answer will definitely have just one response, and not many.

A non-statistical question in math is defined as a question that will not provide a variety of answers. Finally, non-statistical questions provide us with exact answers that do not change.

Thus, the options that are statistical are:

how many pets do you have?

what time do you go to sleep?

how many siblings do you have?

The options that are non-statistical are:

what kind of dog does bruno have?

what is clara's brother's name?

what time did javed go to sleep?

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Sin theta = -5/sqrt(26) Is the correct option , To find the six trigonometric functions of theta, we need to first find the values of x and y on the terminal side of theta. From the given equation, 5x + y = 0 and x ≥ 0, we can solve for y in terms of x:

y = -5x

Since x ≥ 0, we know that (x, y) lies in the fourth quadrant. We can now use the Pythagorean theorem to find the length of the hypotenuse:

r =[tex]sqrt(x^2 + y^2) = sqrt(x^2 + (-5x)^2) = sqrt(26x^2)[/tex]

Now we can find the six trigonometric functions:

sin(theta) = y/r = [tex]-5x/sqrt(26x^2) = -5/sqrt(26)[/tex]

cos(theta) = x/r =[tex]x/sqrt(26x^2) = 1/sqrt(26)[/tex]

tan(theta) = y/x = -5x/x = -5

csc(theta) = r/y = [tex]sqrt(26x^2)/(-5x) = -sqrt(26)/5[/tex]

sec(theta) = r/x = sqrt(26x^2)/x = sqrt(26)/1 = sqrt(26)

cot(theta) = 1/tan(theta) = -1/5

Therefore, the exact values of the six trigonometric functions of theta are:

sin(theta) = -5/sqrt(26)

cos(theta) = 1/sqrt(26)

tan(theta) = -5

csc(theta) = -sqrt(26)/5

sec(theta) = sqrt(26)

cot(theta) = -1/5

Answer: A. sin theta = -5/sqrt(26)

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