Why is Dr. Craven surprised when he visits Colin?

Select 2 correct answer(s)
Question 1 options:

Colin wants to go outside.


Colin is laughing and sitting up straight.


Colin is reading with Mary.


Colin took his medicine.

Question 2 (1 point)
How are the children able to keep their plan to enter the garden a secret?

Question 2 options:

Mary will throw a temper tantrum, and when everyone comes to calm her, Dickon and Colin will sneak into the garden.


The children will sneak past the servants and gardeners, hiding behind the ivy on the Long Wall.


Colin tells Mr. Roach to make all the gardeners stay away from the walls when he goes out.


Dickon suggests that they go out into the garden at night when everyone is asleep.

Question 3 (1 point)
Which reason does Mr. Roach give for thinking that Dickon would be "as at home in Buckingham palace as at the bottom of a coal mine?"

Question 3 options:

Dickon always finds things to do and games to play.


Dickon likes every person and animal he meets.


Dickon is really a prince, even though he has been living on the moor.


Dickon is a fine person, who would be liked by anyone.

Question 4 (1 point)
Which passages show changes in Colin that are similar to changes that happened in Mary?

Select 3 correct answer(s)
Question 4 options:

He looked so strange and different because a pink glow of color had actually crept all over him - ivory face and neck and hands and all.


[The nurse] noticed that instead of lying like a log while his clothes were put on, [Colin] sat up and made some efforts to help himself, and he talked and laughed with Mary all the time.


Colin kept lifting his thin chest to draw [the wind] in, and his big eyes looked as if it were they which were listening - listening, instead of his ears.


The strongest footman in the house carried Colin down stairs and put him in his wheeled chair near which Dickon waited outside.

Question 5 (1 point)
What happens when Ben Weatherstaff tells Colin that he thinks Colin cannot walk?

Question 5 options:

Colin makes Ben Weatherstaff leave Misselthwaite Manor.


Colin throws a tantrum and runs out of the secret garden.


Colin cries and wishes to be brought back inside.


Colin is angry and gets out of his chair to prove he can stand.

Question 6 (4 points)
Match each vocabulary word to the sentence that it best completes.

Question 6 options:

The people ____________ the king and his tyrannical rule.


I understand that you're upset, but you don't need to _________________ him! Please, lower your voice.


Edgar Allen Poe's writing is often ___________, dealing with themes of death and suspense.


The leader of the group was punished harshly, but the followers were treated more ______________.

1.
detested

2.
leniently

3.
morbid

4.
harangue

If the exchange rate were 5 Egyptian pounds per US dollar, a watch that costs $25 US dollars would cost 125 Egyptian pounds.

The exchange rate is the price at which one currency can be exchanged for another. In this case, the exchange rate is 5 Egyptian pounds per US dollar. This means that one US dollar can be exchanged for 5 Egyptian pounds.

To find out how much a watch that costs $25 US dollars would cost in Egyptian pounds, we need to multiply the cost in US dollars by the exchange rate:

$25 x 5 = 125 Egyptian pounds

Therefore, if the exchange rate were 5 Egyptian pounds per US dollar, a watch that costs $25 US dollars would cost 125 Egyptian pounds.

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a) The firm’s long-run total, average, and marginal cost functions is:

C = wl + vk = (0.1w + 0.2v)q

AC = C/q = 0.1w + 0.2v

MC = dC/dq = 0.1w + 0.2v

b) The firm’s short-run total, average, and marginal cost functions:

C = wl + 10v = 0.1wq + 10v

AC = C/q = 0.1w + 10v/q

MC = dC/dq = 0.1w

c) This firm’s long-run and short-run average and marginal cost curves.

Long run cost:

AC = 0.3 + 0.2 = 0.5

MC = 0.3 + 0.2 = 0.5

Short run:

AC = 0.3 + 10/q

MC = 0.3

Cost function shows the relationship between the cost of production and the level of output. In the short run a portion of the total cost is fixed but, in the long run, all cost are variable. Average cost equals the cost per unit (i.e., total cost divided by output) and the marginal cost equals the change in cost per unit change in output.

The producer used k and l such that 5k = 10l

The output q, then, is

q = 5k = 10l

i.e., k = 1/5q = 0.2q and l = 1/10q = 0.1q

Long run cost:

C = wl + vk = (0.1w + 0.2v)q

AC = C/q = 0.1w + 0.2v

MC = dC/dq = 0.1w + 0.2v

b) Suppose that k is fixed at 10 in the short run. Calculate the firm's short-run total, average and marginal cost functions.

b) K= 10,

Short run cost:

C = wl + 10v = 0.1wq + 10v

AC = C/q = 0.1w + 10v/q

MC = dC/dq = 0.1w

c) Long run cost:

AC = 0.3 + 0.2 = 0.5

MC = 0.3 + 0.2 = 0.5

Short run:

AC = 0.3 + 10/q

MC = 0.3

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The function that is represented in the diagram is y/-1 = f(x + 5).

As per the information provided, it is given that there are two graphs

There are two diagrams available in black and white.

Let the graph of the function is y = f(x).

If the function is shifted vertically to the left, then the function can be rearranged as,

y = f(x + k), k > 0.

The function is shifted vertically 5 units to the left.

Therefore, the function can be rewritten as,

y = f(x + 5).

Now, the red part of the function is symmetric about the x-axis with respect to y.

Therefore, the function can be rewritten as,

y/-1 = f(x + 5).

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The complete question:

The black graph is the graph of y = f(x). Choose the equation for the red graph. A. y - 5 = f() B. = f(x + 5) C. = f(x - 5) D. y + 5 = f(x/-1)​

The slope of the line is a positive slope. The value of the slope is 2/3.

From the question, we are to determine if the slope of the line is positive, negative, undefined, or zero

First, we will calculate the slope of the line ,

Using the formula,

Slope = (y₂ - y₁) / (x₂ - x₁)

Pick two points: (0, -3) and (3, -1)

Thus,

Slope = (-1 - (-3)) / (3 - 0)

Slope = (-1 + 3)) / (3)

Slope = (2) / (3)

Slope = 2/3

Since the value of the slope is positive, the slope is a positive slope.

Hence,

The slope is positive.

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His record should not be changed. The correct option is A

An individual who works for an employer pursuant to an employment contract, whether it be written or verbal, is referred to as an employee.

David is an hourly worker, and since his compensation is remaining the same, his employee earnings record shouldn't be altered. Even if he transfers to a different department, his hourly rate and rate of pay need to stay the same. The employee's record's department or job code may be the only thing to change in this scenario, but the earnings record itself is unaffected.

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the line segment after a 90 counterclockwise rotation about the origin is attached accordingly.

A rotation is a sort of transformation  that rotates each point in a figure a specific number of degrees around a particular  point.

To do a 90-  degree counterclockwise rotation about  the origin, we can use the following rotation  formula

x ' = x *  cos( θ) - y * sin(θ)

 y' =  x * sin(θ )+ y * cos( θ)

where   (x, y) are the original coordinates and (x ', y') are the coordinates after the rotation.

Applying this

For   point A (- 5, -3) we have

x' = (-5) * cos(90°) - ( -3) * sin(90 °) = 3

y' = (-5) * sin(90°)+ (-3) * cos(90°) =  -5

So the new coordinates after the 90-degree counterclockwise rotation about the origin for point A are (3, -5).

 point B (1  , -2)

x' =  (1 ) * cos(90°) - (-2) * sin(90°) = 2

y ' = (1 ) * sin ( 90°) + ( - 2) * cos (90 °) = 1

So the new coordinates after the 90-degree counterclockwise rotation about the origin   for point B are (2, 1).

The line segment after a 90-degree counterclockwise rotation about the origin would connect point A' (3, -5) to point B' (2, 1).

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Part A) Local minimum value of 19 at (1, 0). A= -2 B= 20. Part B) local maximum value of 15 at the point (3, 4) A= 56 B= 6 C= 8.

To find A and B such that f(x,y) has a local minimum at (1,0) with a value of 19, we need to use the second derivative test.

Taking the partial derivatives of f with respect to x and y, we get 2x + A and 2y, respectively. Evaluating these at (1,0) gives 2 + A and 0. Since f has a local minimum at (1,0), both of these partial derivatives must be zero, so A = -2.

To find B, we use the fact that f(1,0) = 19, which gives 1 + A + B = 19. Substituting in A = -2 and solving for B, we get B = 20.

For the second part of the question, we again use the second derivative test. Taking the partial derivatives of f with respect to x and y, we get -2x + B and -2y + C, respectively.

Evaluating these at (3,4) gives -6 + B and -8 + C. Since f has a local maximum at (3,4), both of these partial derivatives must be zero, so B = 6 and C = 8.

To find A, we use the fact that f(3,4) = 15, which gives A - 9 - 32 = 15. Solving for A, we get A = 56. Therefore, the values of A, B, and C that give f a local maximum of 15 at (3,4) are A = 56, B = 6, and C = 8.

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The fraction of the area of circle T occupied by sector BTC is S / (2π).

To find the fraction of the area of circle T that is occupied by sector BTC, we need to calculate the ratio of the area of sector BTC to the total area of circle T.

The total area of a circle is given by the formula A = πr², where r is the radius of the circle.

The area of sector BTC is a fraction of the total area of the circle, and this fraction is determined by the central angle of the sector, which is measured in radians. Let's call this central angle θ.

The formula to calculate the area of a sector is A_sector = (θ/2π) * πr², where θ is the central angle in radians.

In this case, we are given that the measure of BC (which is the same as the central angle θ) is S radians.

Therefore, the area of sector BTC is A_sector = (S/2π) * πr² = (S/2) * r².

The fraction of the area of circle T occupied by sector BTC is:

Fraction = (Area of sector BTC) / (Total area of circle T)

= ((S/2) * r²) / (πr²)

= S / (2π)

Hence, the fraction of the area of circle T occupied by sector BTC is S / (2π).

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Dr. Toming ran a regression analysis to settle the debate between L. Wood and H. Wood about whether to invest in large houses or large lots. She included all variables collected by the Woods and controlled for house size and lot size, which tend to correlate highly with each other. The output showed that the mean sale price is over $200,000. To determine whether this is a valid model, additional information is needed, such as the significance level and the R-squared value. Without this information, it is impossible to determine the validity of the model.

Dr. Toming's regression analysis controlled for both house size and lot size, which is important because they tend to correlate highly with each other. This means that the analysis accounted for the fact that larger houses tend to be on larger lots, and vice versa. However, the mean sale price alone does not provide enough information to determine the validity of the model. Additional information such as the significance level and the R-squared value would be necessary to make a determination.

Without additional information about the significance level and R-squared value, it is impossible to determine the validity of Dr. Toming's regression analysis. While controlling for house size and lot size is important in this case, more information is needed to evaluate the overall effectiveness of the model.

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Answer: c = 10, d = 7

Step-by-step explanation:

To solve this system using the linear combination method, we want to eliminate one of the variables, either c or d, by adding or subtracting the two equations. One way to do this is to add the two equations together, which will cancel out the d terms:

(c + d) + (c - d) = 17 + 3

2c = 20

c = 10

Now we can substitute this value of c into either equation to solve for d:

c - d = 3

10 - d = 3

d = 7

Therefore, the solution to the system is:

c = 10, d = 7.

Answer:

c=10 and d=7

Step-by-step explanation:

Use linear combination to solve the following system of equations.

Linear combination is synonymous with the method of elimination. The goal of elimination is to "eliminate" one of the variables so that we may solve for the other.

[tex]\left\{\begin{array}{ccc}c+d=17\\c-d=3\end{array}\right[/tex]

Notice how the "d" term has opposite signs in the system. We can add these two equations together to "eliminate" d.

[tex](c+d=17)+(c-d=3)=\boxed{2c=20}\\\\\therefore \boxed{\boxed{c=10}}[/tex]

We now know what "c" equals, plug this value into either of the equations and solve for "d."

[tex]c=10\\\\\Longrightarrow 10+d=17\\\\\therefore \boxed{\boxed{d=7}}[/tex]

Thus, the system is solved. c=10 and d=7.

The area between the functions f(x) = 2 · x + 6 and g(x) = 2 · x² + 2 is equal to 8.333 square units. (Right choice: C)

In this question we must determine the area between the functions f(x) = 2 · x + 6 and g(x) = 2 · x² + 2, this can be done by using the following definite integral:

A = ∫²₋₁ [f(x) - g(x)] dx

A = ∫²₋₁ f(x) dx - ∫²₋₁ g(x) dx

A = ∫²₋₁ (2 · x + 6) dx - ∫²₋₁ (2 · x² + 2) dx

A = x²|²₋₁ + 6 · x|²₋₁ - (2 / 3) · x³|²₋₁ - 2 · x|²₋₁

A = 2² - (- 1)² + 6 · [2 - (- 1)] - (2 / 3) · [2³ - (- 1)³] - 2 · [2 - (- 1)]

A = 1 + 18 - 14 / 3 - 6

A = 8.333  

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To find the area of the region enclosed by the curves y = 2cos(pix/2) and y = 4 - 4x^2, we first need to find the x-coordinates of the points of intersection between the two curves.

Setting the two equations equal to each other gives:

2cos(pix/2) = 4 - 4x^2

Dividing both sides by 2 and rearranging gives:

cos(pix/2) = 2 - 2x^2

Since the cosine function has period 2π, we can write:

cos(pix/2) = cos((2nπ ± x)/2)

where n is an integer.

Therefore, we have:

2 - 2x^2 = cos((2nπ ± x)/2)

Solving for x, we get:

x = ±2cos^-1(2 - cos((2nπ ± x)/2))/√2

Since we want the area of the region enclosed by the curves, we need to integrate the difference between the two functions with respect to x, over the interval of x-values for which the curves intersect.

The two curves intersect when 0 ≤ x ≤ 1, so the area of the region enclosed by the curves is:

A = ∫[0,1] (4 - 4x^2 - 2cos(pix/2)) dx

Using the identity cos(pix/2) = cos((2nπ ± x)/2), we can rewrite the integrand as:

4 - 4x^2 - 2cos((2nπ ± x)/2)

We can evaluate this integral using integration by substitution, with u = (2nπ ± x)/2. The limits of integration in terms of u are u = nπ and u = (n+1)π.

The integral becomes:

A = ∫[nπ,(n+1)π] (-4u^2 + 8) du

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If rxy = 0.83, we can conclude that x and y have a relatively strong positive linear relationship or correlation.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, in this case, x and y. The value of r ranges between -1 and 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other variable tends to increase as well.

In this case, with rxy = 0.83, the correlation coefficient is close to 1, suggesting a strong positive linear relationship. This means that when x increases, y also tends to increase, and vice versa. The closer the value of r is to 1, the stronger the linear relationship between x and y.

It is important to note that correlation does not imply causation. While a high correlation coefficient indicates a strong linear relationship, it does not provide information about the underlying cause or direction of the relationship between the variables. Other factors and variables may influence the relationship, and further analysis may be required to understand the nature of the relationship between x and y.

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Thus, the results of this bivariate correlation analysis suggest that there is little to no relationship between students' love of cats and their love of school.

A bivariate correlation analysis is a statistical tool that is used to determine whether there is a relationship between two variables. In this case, the analysis tests the relationship between students' love of cats and their love of school.

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About 11.90% of students scored 59.99 or lower on the exam and failed the course (since this is a proportion, we can multiply it by 100 to get the percentage).

To determine the percentage of students who failed the course, we need to find the proportion of students who scored 59.99 or lower on the exam, and then convert this proportion to a percentage.
First, we need to standardize the cutoff score of 59.99 using the formula:
z = (x - μ) / σ
where x is the cutoff score, μ is the mean, and σ is the standard deviation.
Plugging in the values given in the question, we get:
z = (59.99 - 73) / 11 = -1.18
Next, we look up the proportion of scores below a z-score of -1.18 in a standard normal distribution table (or use a calculator or software). This proportion is approximately 0.1190.
Therefore, about 11.90% of students scored 59.99 or lower on the exam and failed the course (since this is a proportion, we can multiply it by 100 to get the percentage).
In other words, roughly 12% of the students failed the course based on the given criteria.

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A: The expression is 3y(2x² - x - 8xy + 4y).

B: Completely factorized expression is 3y{x(2x - 1-8y) + 4y}.

Part A: To factor out the greatest common factor (GCF), we need to find the highest power of each variable that appears in all terms. In this expression, the variables are x and y.

The GCF of the coefficients is 3, and the GCF of the variables is xy.

Factoring out the GCF, we get:

3y(2x² - x - 8xy + 4y)

Part B: To factor the entire expression completely, we look for common factors among the terms and apply factoring techniques.

The given expression is:

6x²y − 3xy − 24xy² + 12y²

First, let's factor out the GCF of the coefficients, which is 3:

3y(2x² - x - 8xy + 4y)

Factor out x from the common terms,

3y{x(2x - 1-8y) + 4y}

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The 7th term of the sequence is 729. To find the 7th term, we notice that the sequence is formed by multiplying each term by 3. Therefore, the 4th term is 327=81, the 5th term is 381=243, the 6th term is 3243=729, and the 7th term is 3729=2187.

In this problem, we are given the first three terms of a sequence and asked to find the 7th term. A sequence is a list of numbers in a specific order, where each number is called a term. To find the next term in a sequence, we need to identify the pattern or rule that generates the sequence.

In this case, we notice that each term is obtained by multiplying the previous term by 3. That is, if a_1=3, a_2=9, a_3=27, then a_4=3a_3=81, a_5=3a_4=243, a_6=3a_5=729, and a_7=3a_6=2187.

Therefore, the 7th term is 2187. It is important to round to the nearest thousandth only when we are dealing with decimal numbers. Since the terms of this sequence are integers, we do not need to round.

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When testing the claim that μ > 25.6 with a sample size of n=51 and a level of significance of α=0.01, you should reject H₀ if the standardized test statistic is greater than the critical value.

To determine when to reject H₀ (the null hypothesis that μ=25.6), we need to calculate the standardized test statistic using the sample size (n=51) and level of significance (a=0.01).The appropriate critical value for a one-tailed test at a 0.01 level of significance is 2.33. Therefore, we should reject H₀ if the standardized test statistic is greater than 2.33.The formula for calculating the standardized test statistic is: [tex]$\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$[/tex], where [tex]$\bar{x}$[/tex] is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

With a sample size of 51, we can use the Central Limit Theorem to assume that the sample mean is normally distributed. We would calculate the standardized test statistic and compare it to the critical value of 2.33 to determine whether or not to reject H₀. In this case, the critical value can be found using a Z-table or calculator for a one-tailed test with α=0.01. The critical value is 2.33. Therefore, you should reject H₀ if the standardized test statistic is greater than 2.33.

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Answer:

[tex]1000( {1.1}^{5}) = 1610.51[/tex]

The correct answer is D.

Ashley's commute using normal distribution would be shorter than 37 minutes is approximately about 254 times out of 260 days.

Mean = 33 minutes

Standard deviation = 2 minutes

Sample size = 260 days

Use the properties of the normal distribution to find the number of times.

Ashley's commute would be shorter than 37 minutes.

First, we need to standardize the value 37 using the formula,

z = (x - μ) / σ

where x is the value we want to standardize,

μ is the mean of the distribution,

and σ is the standard deviation of the distribution.

Plugging in the values, we get,

z = (37 - 33) / 2

 = 2

Next, we need to find the probability that a standard normal variable is less than 2.

In a standard normal table to find that,

Attached table.

P(Z < 2) = 0.9772

This means that the probability of Ashley's commute being less than 37 minutes is 0.9772.

To find the number of times this would happen out of 260 days, multiply this probability by the total number of days,

0.9772 x 260 = 254.0 Rounding to the nearest whole number.

Therefore, the Ashley's commute would be shorter than 37 minutes about 254 times out of 260 days using normal distribution.

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For the graph:  y= -2cos (x+π/2)

period: 2π

phase shift: 0

Vertical shift: - 2

Reflection about x axis.

For the graph:  y= 1/2sin 2(x-π/4)

period: π

phase shift: 0

Vertical shift:

No any reflection.

For the graph: y= -1/2sin (x+π/2)-1

period: 2π

phase shift: 0

Vertical shift: -1

Reflection about x axis.

(1) For the given function,

Since the period of y = -2cos(x) is 2π,

So the period of y = -2cos(x + pi/2) is also 2π

To find the phase shift.

The phase shift of y = -2cos(x) is π/2,

so the phase shift of y = -2cos(x + π/2) is 0.

The vertical shift is -2, and there is a reflection about the x-axis.

(2) For the given function,

y= 1/2sin 2(x-π/4)

Since the period of y = 1/2sin(x) is 2π,

so the period of y = 1/2sin(2x) is π.

The phase shift of y = 1/2sin(x) is π/4,

so the phase shift of y = 1/2sin(2x - π/4) is 0.

There is no vertical shift, and there is no reflection.

(3) For the given function,

y= -1/2sin (x+π/2)-1

Since the period of y = -1/2sin(x) is 2π,

so the period of y = -1/2sin(x + π/2) is also 2π.

The phase shift of y = -1/2sin(x) is -π/2,

so the phase shift of y = -1/2sin(x + π/2) is 0.

The vertical shift is -1, and there is a reflection about the x-axis.

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The factored function is given as follows:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)[/tex]

The function for this problem is defined as follows:

[tex]y = x^4 + 2x^3 - 20x^2 + 64x - 32[/tex]

The zeros are given as follows:

Hence the function is factored as follows:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x - 2 + 2i)(x - 2 - 2i)[/tex]

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x^2 - 4x + 8)[/tex]

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = ax^4 + (-4 + b)x^3 + \cdots + 8c[/tex]

Hence the value of a is given as follows:

a = 1.

The value of b is given as follows:

-4 + b = 2

b = 6.

The value of c is given as follows:

8c = -32

c = -4.

Hence the factored expression is of:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)[/tex]

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$4500 was collected from the sale of adult tickets.

Let's say that x is the number of adult tickets sold and y is the number of student tickets sold.

We know that:

x + y = 1500 (because the auditorium has 1500 seats and it sold out)

y = 3x (because three times as many student tickets were sold as adult tickets)

We can substitute the second equation into the first equation to get:

x + 3x = 1500

4x = 1500

x = 375

So 375 adult tickets were sold.

The revenue from the sale of adult tickets can multiply the number of tickets sold by the price per ticket is $12:

Revenue from adult tickets = 375 × $12

= $4500

Assume that x represents the quantity of adult tickets sold and y represents the quantity of student tickets sold.

We are aware of:

Since there are 1500 seats in the auditorium, x plus y equals 1500.

y = 3x (because there were sold three times as many student tickets as adult tickets).

To obtain x + 3x = 1500, we simply insert the second equation into the first equation.

4x = 1500 x = 375

375 adult tickets were consequently sold.

The amount of money made from selling adult tickets may be calculated by multiplying the quantity sold by the $12 per ticket price:

Total revenue from adult tickets is $4500 ($375 x $12).

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If you randomly draw one card from the deck, there is about a 26.92% chance that you will get either a Jack or a Spade.

Since there is only one Jack of Spades, we have one favorable outcome for drawing a Jack. Additionally, there are 13 Spades in the deck, including the Jack of Spades. Therefore, the number of favorable outcomes for drawing a Spade is 13.

Total number of favorable outcomes = Number of Jacks + Number of Spades

= 1 + 13

= 14

Total number of possible outcomes

In a deck of 52 cards, each card is unique. Therefore, the total number of possible outcomes is equal to the total number of cards in the deck, which is 52.

Now that we have determined the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability using the following formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

Substituting the values we found:

Probability = 14 / 52

Simplifying the fraction:

Probability = 7 / 26

So, the probability of drawing a Jack or a Spade from a standard deck of 52 cards is 7/26, or approximately 0.2692, which can also be expressed as 26.92%.

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Answer:

(5,21)

Step-by-step explanation:

multiply the second equation by 4

=4x-20y=-400

now subtract the second from first

4x-4x = 0

-y-(-20y) = 19y

-1-(-400) = 399

19y = 399

divide equation by 19

399/19 = 21

y = 21

input 21 into any of the equations

4x-21=-1

4x=20

divide equation by 4

x=5

answer is (5,21)

The margin of error for the given values of c=0.95, s=5, and n=23 is approximately 0.9907.

To find the margin of error for the given values of c=0.95, s=5, and n=23, we can use the following formula:
Margin of error = c * (s / sqrt(n))

Substituting the given values, we get:
Margin of error = 0.95 * (5 / sqrt(23))
= 0.95 * (5 / 4.7958)
= 0.95 * 1.0428
= 0.9907

Therefore, the margin of error for the given values of c=0.95, s=5, and n=23 is approximately 0.9907.

This means that the actual value of the population parameter is expected to be within 0.9907 units of the sample estimate, with 95% confidence.

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The exact length of the curve is 8/3 (5sqrt(26) - 1).

To find the length of the curve, we can use the arc length formula:

L = ∫[tex][a,b]sqrt(dx/dt)^2 + (dy/dt)^2 dt[/tex]

where a and b are the starting and ending values of the parameter t, and dx/dt and dy/dt are the derivatives of x and y with respect to t, respectively.

Plugging in the given equations, we get:

[tex]dx/dt = 24t[/tex]

[tex]dy/dt = 24t^2[/tex]

Therefore,

[tex](sqrt(dx/dt)^2 + (dy/dt)^2) = sqrt((24t)^2 + (24t^2)^2) = sqrt(576t^2 + 576t^4)[/tex]

Substituting these expressions into the arc length formula, we get:

L = ∫[tex][0,2]sqrt(576t^2 + 576t^4) dt[/tex]

We can factor out 576t^2 from the square root:

L = ∫[tex][0,2]sqrt(576t^2(1 + t^2)) dt[/tex]

And then simplify the expression inside the square root:

L = ∫[tex][0,2]24t sqrt(1 + t^2) dt[/tex]

This integral can be evaluated using the substitution[tex]u = 1 + t^2, du/dt = 2t, dt = du/2t:[/tex]

L = ∫[tex][1,5]12 sqrt(u) du[/tex]

Now we can use the power rule of integration to evaluate this integral:

[tex]L = [8/3 u^(3/2)]_1^5 = 8/3 (5sqrt(26) - 1)[/tex]

Therefore, the exact length of the curve is 8/3 (5sqrt(26) - 1).

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The popcorn box would hold 168.75 cubic inches of popcorn when it is full. Rounded to the nearest tenth, the answer is 168.8 cubic inches.

To find the volume of the popcorn box, we need to multiply its length, width, and height. However, we need to make sure that all the dimensions are in the same units before we multiply them.

First, let's convert the mixed numbers to improper fractions:

3 3/4 = 15/4

7 1/2 = 15/2

Now, we have the dimensions in the same units (inches):

Length = 15/4 in

Width = 3 in

Height = 15/2 in

To find the volume, we multiply the three dimensions:

Volume = Length x Width x Height

Volume = (15/4) x 3 x (15/2)

Volume = 168.75 cubic inches

Therefore, the popcorn box would hold 168.75 cubic inches of popcorn when it is full. Rounded to the nearest tenth, the answer is 168.8 cubic inches.

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The function for the garden's perimeter in terms of the width "w" would be P(w) = 4w + 24

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's call the width of the rectangular garden "w".

According to the problem, the length of the garden is 12 feet longer than its width. So, the length would be w + 12.

The perimeter is the sum of all four sides of the rectangular garden. So,

Perimeter = w + w + (w + 12) + (w + 12)

Simplifying this expression, we get:

Perimeter = 4w + 24

Therefore, the function for the garden's perimeter in terms of the width "w" would be P(w) = 4w + 24.

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