Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets for $20. The venue has the capacity to hold
400 people. The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise $5,000 for her school:

How many Pre-sale Tickets tickets must she sell to make her goal?
A)400
B)300
C)250
D)100

Answer:

\(f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)\)

Step-by-step explanation:

The root -2 has a multiplicity of 2, and corresponds to a factor of \((x+2)^2\).

The root 1 has a multiplicity of 1, and corresponds to a factor of \((x-1)\).

The root 3 has a multiplicity of 1, and corresponds to a factor of \((x-3)\).

So, \(f(x)=a(x+2)^2(x-1)(x-3)\).

Since \(f(0)=10\),

\(10=a(0+2)^2(0-1)(0-3) \\ \\ 10=12a \\ \\ a=\frac{5}{6} \\ \\ \therefore f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)\)

Answer:

9.91%

Step-by-step explanation:

cost price= 400

selling price=444

profit made= 444-400

= 44

profit percentage= 44/444 ×100

=9.91%

Yes, both methods give the same result. The chain rule is used to differentiate a composite function, while the substitution method is used to differentiate a function after substituting a variable with its expression.

The chain rule is used to differentiate a composite function, which is a function of a function. To use the chain rule, we differentiate the inner function and multiply it by the derivative of the outer function. In this case, we would have

f(x) = (\(x^2 + 3x + 2\)) and

g(x) = \(2x^3 + 5\)

The derivative of f(x) would be 2x + 3 and the derivative of g(x) would be \(6x^2\). Taking the product of these two derivatives, we get

\(12x^3 + 18x^2\),

which is the answer we get using the chain rule. The substitution method involves substituting a variable in a function with its expression. In this case, we substitute x with (\(x^2 + 3x + 2\)). This gives us a new function that is a function of \(x^2 + 3x + 2\)instead of x. We then differentiate this new function and the answer we get is the same as the one we got using the chain rule. Therefore, both methods give the same result and agree with each other.

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Answer:

Below

Step-by-step explanation:

h = .4 p     <====== given     divide both sides of the equation by .4

h/.4 = p

2.5 h = p       p is 250 % of h    ( 2.5 is decimal for 250%)

Answer:

See below.

Step-by-step explanation:

We are given the value of an angle, and the hypotenuse.

x will equal 7.0

Using Trigonometry Functions, we can identify x.

\(\textsf{Trigonometry Functions:}\)

\(Sin = \frac{Opposite}{Hypotenuse}\)

\(Cosine = \frac{Adjacent}{Hypotenuse}\)

\(Tan = \frac{Opposite}{Adjacent}\)

\(\fbox{We should use Sin.}\)

Let's begin by solving for x.

\(\textsf{\underline{We should use;}}\)

\({Sin(23^{\circ})}\)

\(\textsf{\underline{Solve for x:}}\)

\(Sin(23^{\circ})=\frac{x}{18}\)

\(\textsf{\underline{Multiply by 18:}}\)

\(18 \times Sin(23^{\circ})={x}\)

\(x \approx 7.0\)

Answer:

\(x=\frac{9}{25}\)

x = 0.36

Step-by-step explanation:

5x/3 + 2/5 = 1

5x/3 + 2/5 - 2/5 = 1 - 2/5

\(\frac{5x}{3} = 0.6\)

5x/3 × 3 = 0.6 × 3

5x = 1.8

5x ÷ 5 = 1.8 ÷ 5

\(x=\frac{9}{25}\)

x = 0.36

If speed is important and the array is large, the a. Binary search algorithm should be used. This algorithm is designed to efficiently search through sorted arrays by repeatedly dividing the search interval in half.

It has a time complexity of O(log n), which means that as the size of the array increases, the time it takes to search for an item will not increase at the same rate.
On the other hand, ascending bubble sort and other sorting algorithms such as selection sort and insertion sort have a time complexity of O(n^2), which means that as the size of the array increases, the time it takes to sort the array will increase exponentially. Therefore, these algorithms are not efficient for large arrays and should not be used if speed is important.
In summary, when dealing with large arrays and speed is important, binary search is the best algorithm to use for searching, while ascending bubble sort and other sorting algorithms with a time complexity of O(n^2) should be avoided.

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The given data sample contains all integers from 530 to 380 and all integers from 379 to 531. This means that the sample includes 152 integers in total. To find the mean of the sample, we need to add up all the numbers and divide by the total number of integers.

To do this, we can take the average of the two endpoints (530 and 380), which is 455. Then we can add the sum of the integers between 380 and 530, which is (530-381+1) + (530-379) = 150 + 151 = 301. Finally, we divide the total sum by the number of integers, which is 152, and get:

Mean = (455 + 301) / 152 = 3.980263158

Therefore, the mean of the given data sample is approximately 3.9803.

In summary, we can find the mean of a sample by adding up all the numbers and dividing by the total number of items. In this particular sample, we first found the average of the two endpoints and then added the sum of all the integers between them to find the total sum. Finally, we divided the total sum by the number of integers to find the mean of the sample.

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Answer:

-15

Step-by-step explanation:

in 1950 it was 45 and in 1980 it was 30 so it is -15

The average rate of change can be define as the value of something is changing with respect to another thing is tinging. The average rate of change of the population between 1950 and 1980 is 500 per year. It means the population is decreasing with 500 per year.

The given graph shows the population of a city between the year 1900 to 2000.

The average rate of change can be define as the value of something is changing with respect to another thing is tinging.

Form the given graph,

The year 1950 is between the year 1940 and year 1960. The value at the y axis where the population (in thousand) shown is 45,000 for the year 1950.

The year 1980 is shown in graph at the x axis and the value of the population in the y axis is 30,000.

Thus the population is decreasing from year 1950 to 1980. The difference in the population of the year 1950 and 1980 is,

\(d=45000-30000\)

\(d=15000\)

Thus the change in the population between 1950 and 1980 is 15,000.

Average rate of change of the population between 1950 and 1980 -

As the population and the year both are changing. The rate of change for the population with respect to the year can be calculating by dividing the difference of the population between two year to the total years between the 1950 to 1980.

There is total 30 year from 1950 to 1980, thus the average rate of change is,

\(A(x)=\dfrac{15000}{30} \\ A(x)=500\)

Thus the average rate of change of the population between 1950 and 1980 is 500 per year. It means the population is decreasing with 500 per year.

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Answer:

C. 7.0 Liters

Step-by-step explanation:

You always start with the amount that was given to you. In this case it was 7.41 quarts. You then multiply it with the conversion factor (1 qt = 0.95L)

To convert quarts into liters, you must set up the problem so the quarts are able to cancel out, meaining one should be in the numerator and the ither should be in the denominator.

When the quarts are cancelled out, your answer will now be in liters.

Now you just multiply all the numerators and divide the denominators.

7.41 × 0.951 = 7.0395

7.0395/1 = 7.0395

Then you round the answer to 7.0

The domain and the range of the quadratic function in this problem are given as follows:

The function is defined for all real values, assuming values of -8 and greater, hence the domain and range are given as follows:

The problem asks for the domain and the range of the quadratic function in this problem.

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Answer:

No

If all 4 bags of flour are 35 pounds, then 4 bags would equate to 920 muffins, just below 1000.

Answer:

the answer is -14.2

Step-by-step explanation:

-10.7 + (-3.5)= -14.2

Answer:

-14.2

Step-by-step explanation:

When adding two negatives, simply add together as normal and put a negative sign on the answer.

-10.7 + (-3.5) = -14.2

The given statement is true because Time series models are statistical models that analyze and predict future values based on patterns and trends observed in historical data. Option A

The underlying assumption of time series analysis is that the future values of a variable can be predicted based on its past behavior. By examining the historical data, time series models identify patterns, trends, and seasonal variations that can help forecast future values.

There are various types of time series models, including autoregressive integrated moving average (ARIMA), exponential smoothing models, and seasonal decomposition of time series (STL). These models use different mathematical techniques to capture and analyze different aspects of the time series data.

The main goal of time series analysis is to make accurate predictions or forecasts of future values. By leveraging the patterns and trends observed in the historical data, these models provide insights into potential future outcomes.

Time series models are widely used in fields such as economics, finance, meteorology, stock market analysis, and demand forecasting, among others.

Option A

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t distributions tend to be flatter and more spread out than the normal distribution.

This is due to the fact that in the formula, the denominator is s rather than σ.

The distribution of the sample mean is normal if some samples are taken from a normal population with known variance. However, if the population variance is unknown, the distribution is not normal but Student-t with long tails. This means that sample means tend to be extreme when the population variance is unknown. Using the normal distribution instead of the t distribution to test the hypothesis increases the chance of error.

Note that there is a different t-distribution for each sample size. That is, the class of distributions. When talking about a particular t-distribution, we need to specify the degrees of freedom. The degrees of freedom for this t-statistic is given by the sample standard deviation s in the denominator of Equation 1. The spread is larger than the standard normal distribution. This is because the denominator of equation (1) is s, not σ. Because s is a random variable that changes from sample to sample, t becomes more volatile and more spread out.

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Answer:

the first one

Step-by-step explanation: it worked for me i passed it

Answer:

A. y = 1.5x

B. y = -x + 1

C. x - y = 4

D. 2x + 3y = 7

Step-by-step explanation:

To identify if a given doublet is a solution to the equation you can substitute the x and y values to check if they satisfy the equation.

Answer:−7x^4y^4z^2

Step-by-step explanation:

Comparing experiment data to public opinion polls helps evaluate media accuracy, detect biases, and understand the influence on public opinion, while describing data trends and comparing theoretical and empirical probabilities aids in making informed decisions.

In conclusion, comparing the data collected from experiments to public opinion polls allows for the assessment of media accuracy and biases, while analyzing data trends and comparing theoretical and empirical probabilities provides valuable insights for decision-making.

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Answer:

Step-by-step explanation:

We know that cosx = sin(\(\pi\) - x)

We can apply it here:

sin(55°) = cosx

cos(\(\pi\) - 55°) = cosx

Now we apply the arccos to both sides:

x = \(\pi\) - 55° + 2k\(\pi\) or x = -\(\pi\) - 55° + 2k\(\pi\)

Answer:

(8 + 9) ÷ 3 = x

Step-by-step explanation:

You first need to add 8+9, so you put them in parenthesis for PEMDAS

Then you divide them by 3

Finally, you make the answer a variable as an algebraic expression involves variables and the answer is not given

The finite difference approximation for a Neumann boundary condition, \(\left(\frac{df}{dx}\right)\), at node \(n\) (right boundary) to \(O(h^2)\) is given by

\(\left(\frac{df}{dx}\right)_n \approx \frac{f_{n-2} - 4f_{n-1} + 3f_n}{2h}\),

where \(f_{n-2}\), \(f_{n-1}\), and \(f_n\) represent the function values at nodes \(n-2\), \(n-1\), and \(n\) respectively, and \(h\) represents the spacing between the nodes.

To derive this approximation, we start with the Taylor series expansion of \(f_{n-1}\) and \(f_n\) around \(x_n\):

\(f_{n-1} = f_n - hf'_n + \frac{h^2}{2}f''_n - \frac{h^3}{6}f'''_n + \mathcal{O}(h^4)\),

\(f_{n-2} = f_n - 2hf'_n + 2h^2f''_n - \frac{4h^3}{3}f'''_n + \mathcal{O}(h^4)\).

By subtracting \(4f_{n-1}\) and adding \(3f_n\) from the second equation, we eliminate the first-order derivative term and retain the second-order derivative term. Dividing the result by \(2h\) gives us the desired finite difference approximation to \(O(h^2)\).

In conclusion, the finite difference approximation for a Neumann boundary condition, \(\left(\frac{df}{dx}\right)\), at node \(n\) (right boundary) to \(O(h^2)\) is \(\left(\frac{df}{dx}\right)_n \approx \frac{f_{n-2} - 4f_{n-1} + 3f_n}{2h}\). This approximation is obtained by manipulating the Taylor series expansion of \(f_{n-1}\) and \(f_n\) to eliminate the first-order derivative term and retain the second-order derivative term, resulting in a second-order accurate approximation.

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Using the properties of parallelograms and the given information, we proved that BAEC is equal to FABC. We utilized angle-angle similarity and the proportional relationships of corresponding sides in similar triangles to establish the equality.

To prove that BAEC = FABC, we will use the properties of parallelograms and the given information.

Given:

ABCD is a parallelogram.

BE is parallel to CD.

BF is parallel to AD.

To prove:

BAEC = FABC

Proof:

Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Let's denote the length of AB as a, BC as b, AD as c, and CD as d.

Since BE is parallel to CD and AD is parallel to BF, we have angle ABE = angle CDF and angle ADB = angle BFD.

By alternate interior angles, angle CDF = angle FAB.

Now, we have two pairs of congruent angles: angle ABE = angle CDF and angle ADB = angle BFD.

Using angle-angle similarity, we can conclude that triangle ABE is similar to triangle CDF and triangle ADB is similar to triangle BFD.

As the corresponding sides of similar triangles are proportional, we have the following ratios:

AB/CD = AE/CF (from triangle ABE and triangle CDF similarity)

AD/BC = BD/CF (from triangle ADB and triangle BFD similarity)

Cross-multiplying the ratios, we get:

AB * CF = CD * AE (equation 1)

AD * CF = BC * BD (equation 2)

Adding equation 1 and equation 2, we have:

AB * CF + AD * CF = CD * AE + BC * BD

Factoring out CF, we get:

CF * (AB + AD) = CD * AE + BC * BD

Since AB + AD = CD (opposite sides of a parallelogram are equal), we have:

CF * CD = CD * AE + BC * BD

Simplifying, we get:

CF = AE + BC

Therefore, we have shown that BAEC = FABC.

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The type of circuit that is represented above is a closed circuit that allows electrons to flow. That is option B

A circuit is defined as the electrical or electronic pathway that allows the flow of an electrical current.

There are two types of circuit that include the following;

The closed circuit is defined as the type of circuit that is complete and allow the flow of current

The open circuit is the type of circuit that is incomplete and that cannot allow complete flow of electrons.

The circuit shown above is a complete circuit that allows the build to turn on.

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The area of a rectangle is given by the product of its dimensions.

If this rectangle has a length of 2x + 7 and a width of x + 4, its area is:

The perimeter is the sum of all side lengths, so we have:

The given measurement in scientific notation as \(6\times10^9\). Therefore, option D is the correct answer.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as \(1.56\times10^7\).

The given distance is 6,000,000,000 miles.

There are 9 zeros in the given number

So, scientific notation is \(6\times10^9\)

Therefore, the number in scientific notation is \(6\times10^9\).

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Answer:

D

Step-by-step explanation:

see attachment

The density of an object is the ratio of the mass of the object to its volume. The height of the block of sugar maple is 6cm

The density of an object is the ratio of the mass of the object to its volume. Mathematically;

Density = mass/volume

Given the following

Mass of block = 82.8grams

Density = 0.69g/cm^3

volume = lwh
Volume = 20h

Substitute

0.69 = 82.8/20h
20h = 82.8/0.69
20h = 120

h = 6cm

Hence the height of the block of sugar maple is 6cm

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6cm

Step-by-step explanation i can confirm that the answer is 6 ;}