Seven pizzas require 3 bags of cheese.How many bags of cheese are needed to make 21 pizzas?

1. Yearly total dividends paid are $151,250.

2. The dividends per share are $1.25 for common stockholders

3.  The dividends per share are $4 for preferred stockholders.

We must calculate amount of dividends paid to the preferred stockholders in order to get dividends per share for common and preferred stockholders.

The per dividends paid to the preferred stockholders is:

= $50 par value x 8% guaranteed rate of return

= $4 per share

The total dividends paid to preferred stockholders:

=  $4 per share x 5,000 shares

= $20,000

The per dividends paid to those stockholder is calculated as:

= Common stock + Preferred stock

= $1.25 per share + $4 per share

= $5.25 per share

The total dividends paid to common stockholders:

= $5.25 per share x 25,000 shares

= $131,250.

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A stochastic process X(t) is called a martingale if the expected value of X(t) given all information available up to and including time s is equal to the value of X(s).

Thus, to show that the process X(t):=e^(t/2)cos(W(t)), 0 ≤ t ≤ T is a martingale w.r.t. any filtration for Brownian motion, we need to prove that E(X(t)|F_s) = X(s), where F_s is the sigma-algebra of all events up to time s.

As X(t) is of the form e^(t/2)cos(W(t)), we can use Itô's lemma to obtain the differential form:dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt

Taking the expectation on both sides of this equation gives:E(dX) = E(e^(t/2)cos(W(t))dW) - 1/2 E(e^(t/2)sin(W(t))dt)Now, as E(dW) = 0 and E(dW^2) = dt, the first term of the right-hand side vanishes.

For the second term, we can use the fact that sin(W(t)) is independent of F_s and therefore can be taken outside the conditional expectation:

E(dX) = - 1/2 E(e^(t/2)sin(W(t)))dt = 0Since dX is zero-mean, it follows that X(t) is a martingale w.r.t. any filtration for Brownian motion.

Now, let's represent X(t) as an Itô process on the interval [0,T]. Applying Itô's lemma to X(t) gives:

dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt= dM + 1/2 e^(t/2)sin(W(t))dt

where M is a martingale with M(0) = 0.

Thus, X(t) can be represented as an Itô process on [0,T] of the form:

X(t) = M(t) + ∫₀ᵗ 1/2 e^(s/2)sin(W(s))ds

Hence, we have shown that X(t) is a martingale w.r.t. any filtration for Brownian motion and represented it as an Itô process on any time interval [0,T], T > 0.

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Answer:

-11

Step-by-step explanation:

9+35=44. 34+21=55. - each other=-11

the first graph looks right

Answer:The answer is below

Step-by-step explanation:

The bottom of a river makes a V-shape that can be modeled with the absolute value function, d(h) = ⅕ ⎜h − 240⎟ − 48, where d is the depth of the river bottom (in feet) and h is the horizontal distance to the left-hand shore (in feet). A ship risks running aground if the bottom of its keel (its lowest point under the water) reaches down to the river bottom. Suppose you are the harbormaster and you want to place buoys where the river bottom is 20 feet below the surface. Complete the absolute value equation to find the horizontal distance from the left shore at which the buoys should be placed

Answer:

To solve the problem, the depth of the water would be equated to the position of the river bottom.

h is=380 or h=100

Step-by-step explanation:

Answer:

greater

Step-by-step explanation:

0.71 is more than 0.5 and 30 seconds is 0.5 a minute?

I have no idea how you are comparing the numbers lol

Answer:

Explanation:

Parameters:

Principal, P = $78,000

Interest rate, R = 9%

Time, T = 2 months OR 2/12 = 1/6 years

Interest = ?

The formula for simple interest is:

I = PRT/100

Answer:

in ratio 4:14

Step-by-step explanation:

The limit as x approaches -2 is equal to 0. The correct option is B.

The limit of the function f(x) = x² - 4 / x + 2 as x approaches 2 is equal to 0. This can be evaluated by plugging in x = -2 into the expression for f(x) and simplifying it:-

The limit of the function f(x) = x² - 4 / x + 2 as x approaches -2 is equal to 4. This can be evaluated by plugging in x = -2 into the expression for f(x) and simplifying it:

f(-2) = (-2)² - 4 / -2 + 2 = 4 - 4 / 0 = 0

So, the limit as x approaches -2 is equal to 0.

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Answer:

I plugged in your equation into Desmos and here are 5 points

Step-by-step explanation:

(-6,7)

(-5,6)

(-4,5)

(-3,6)

(-2,7)

Answer:

\( \huge{ \bold{ \boxed{ \sf{x = \frac{1}{3} }}}}\)

☪ First , Let's know about Exponential Equation :

⤿ Let's take an equation : \( \sf{ {2}^{x} = 8}\).

In this equation , the variable ' x ' is the exponent of the base 2. Such an equation in which variable appears as an exponent of a base is known as exponential equation. The following axioms are useful while solving the exponential equations :

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

☯ Now , Let's Solve :

\( \underline{ \sf{Given \: Exponential \: Equation \: : {8}^{x} = 2}}\)

In this equation , the variable 'x' is the exponent of the base 8 .Write \( \sf{ {8}^{x} }\) in exponential form with the base of 2

↦ \( \sf{ {2}^{3x} = 2}\)

Write the number 2 in exponential form with the base of 2.

↦ \( \sf{ {2}^{3x} = {2}^{1}} \)

Since the bases are same , cut 2 on both sides and set the exponents equal.

↦ \( \sf{ { \cancel{2}} \: ^{3x} = { \cancel{2} } \: ^{1} }\)

↦ \( \sf{3x = 1}\)

Divide both sides by 3

↦ \( \sf{ \frac{3x}{3} = \frac{1}{3}} \)

↦ \(\boxed{ \bold{ \sf{x = \frac{1}{3} }}}\)

And we're done!

Hope I helped!

Have a wonderful day! ツ

~TheAnimeGirl ♡

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The formula to find the distance between two points with coordinates (x₁,y₁) and (x₂,y₂) is:

Substitute x₁=-5, x₂=-5, y₁=-15 and y₂=-2 to find the distance between the given points:

Therefore, the distance between the points N and P is:

Answer:

12

Step-by-step explanation:

As the cuboid has six rectangular faces, the total surface area of the cuboid is calculated as follows: Assume that, l, w, h be the length, width, and height of the cuboid respectively. Therefore, the total surface area of the cuboid is 2 (lh + lw+ hw) square units.

David suggests that the median be used instead of the mean to o predict how many T-shirts your homeroom will sell because it gives a better estimate of the number of T-shirts the other homerooms sold.

The median is not affected by unusually high or low values, so it shows a more reliable prediction. From the data, the median number of T-shirts sold by the other homerooms is 1434.

How to distinguish between the median and the mean?

The median is the middle value of the data when you arrange it in order, while the mean is the average of all the values.

Example:

If we arrange the number in ascending order:

Mrs. Garcia: 740

Ms. Zang: 1368

Mrs. Ashe: 1434

Mr. Oliver: 1517

Mr. Jackson: 1696

Here, 1434 is the Median.

The median doesn't change much if there are some really big or small values, so it's better for data with unusual numbers.

However, the mean considers all the values, but it can be affected by extreme numbers.

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Thus, the number of adult tickets that were sold that day was 60.

A linear equation with two variables is shown by the equation axe + by = r if a, b, and r are all real values and both are not equal to 0. The equation's two variables are represented by the letters x and y. The coefficients are denoted by the numerals a and b.

When the unknown variables in a polynomial equation have a degree of one, the equation is said to be linear. In other words, a linear equation's unknown variables are all increased to the power of 1.

For the given question:

Let the number of child tickets - x

Let the number of adult ticket - y

Price of each  child tickets - $6.10

Price of each adult ticket- - $9.40

Thus, the system of linear equation forms -

x + y = 136

x = 136 - y   ...eq 1

6.10x + 9.40y = 1027.60 ..eq 2

Put the value of x in eq 2

6.10x + 9.40y = 1027.60

6.10(136 - y) + 9.40y = 1027.60

829.6 - 6.10y + 9.40y = 1027.60

3.3y = 1027.60 - 829.6

3.3y = 198

y = 198/3.3

y = 60

x = 136 - 90

x = 46

Thus, the number of adult tickets that were sold that day was 60.

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The polynomial representing the area inside the fence is \(2x^4\) - 6x² + 6x - 6.

To calculate the area within the fence, multiply the width by the length. The width is specified as (2x² + 3x - 3) and the length as (x² - 2x - 2). As a result, the area within the barrier is,

A = (2x² + 3x - 3) × (x² - 2x - 2)

When we expand the product, we get:

A = \(2x^4\) + x³ - 7x² - 3x² + 6x + 6x - 6

When we combine like words, we get:

A = \(2x^4\) - 6x² + 6x - 6

As a result, the polynomial describing the area within the fence is \(2x^4\) - 6x² + 6x - 6.

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The equation that represents the equal distribution of ' d ' dumplings among Eli and Ana is -

x = nd/2.

Unitary method is used to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Given is a situation in which Eli and Ana are having dinner. They both have same number of dumplings to eat and each dumpling container contains 'd' dumplings.

Let's assume that there are 'n' containers of dumplings and both Eli and Ana got 'x' number of dumplings. Now -

In 1 container we have - 'd' dumplings

In 'n' containers, we will have -  n × d   dumplings.

Both Ana and Eli got same number of dumplings = x.

Therefore -

x + x = n × d

2x = nd

x = nd/2

Therefore, the equation that represents the situation is -

x = nd/2

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Answer:

This hypothesis test is a two-tailed test.

Step-by-step explanation:

When carrying out a hypothesis test, the null hypothesis and the alternative hypothesis are identified. The null hypothesis is generally the one that is initially assumed to be true, while the alternative hypothesis is the one that is being tested. The following are the hypotheses for the scenario presented in the question:

H0: p = 0.856

H1: p ≠ 0.856

To see if there is enough evidence to conclude that the proportion differs from the national percentage, a hypothesis test will be conducted with alpha = 0.01.

The null hypothesis in this case is that the proportion of undergraduates in the state is equal to the national percentage of 85.6 percent, while the alternative hypothesis is that the proportion differs from the national percentage. Therefore, the correct identification of the claim with the hypothesis is as follows:

H0: p = 0.856

H1: p ≠ 0.856

This hypothesis test is a two-tailed test because the alternative hypothesis is non-directional, indicating that the proportion may differ from the national percentage in either direction.

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Answer:-7.5

Step-by-step explanation:

If we take out the negative and make it 24 ÷ 3.2, it would be 7.5 since 3.2 would go into 24 7.5 times. But since we changed it to figure it out, we have to change it back with the rule that "a negative x negative is a positive" meaning that the

24 ÷ 3.2 = 7.5

would change to

24 ÷ (-3.2) = -7.5 OR

Positive ÷ negative = negative

(And this goes with any operation)

The equation sin(θ) = 0 has infinitely many solutions. Two solutions can be found at angles 0° and 180° in degrees, or 0 and π in radians.

The sine function, sin(θ), represents the ratio of the length of the side opposite the angle θ to the length of the hypotenuse in a right triangle. When sin(θ) = 0, it means that the side opposite the angle is equal to 0, indicating that the angle θ is either 0° or 180°.

In degrees, the solutions are 0° and 180°, as they are the angles where the sine function equals 0.

In radians, the solutions are 0 and π, which correspond to the angles where the sine function equals 0.

Therefore, two solutions of the equation sin(θ) = 0 are: 0°, 180° in degrees, and 0, π in radians.

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The equation sin(θ) = 0 has infinitely many solutions. Two solutions can be found at angles 0° and 180° in degrees, or 0 and π in radians.

The sine function, sin(θ), represents the ratio of the length of the side opposite the angle θ to the length of the hypotenuse in a right triangle. When sin(θ) = 0, it means that the side opposite the angle is equal to 0, indicating that the angle θ is either 0° or 180°.

In degrees, the solutions are 0° and 180°, as they are the angles where the sine function equals 0.

In radians, the solutions are 0 and π, which correspond to the angles where the sine function equals 0.

Therefore, two solutions of the equation sin(θ) = 0 are: 0°, 180° in degrees, and 0, π in radians.

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Answer:

T ≥ 8x

50 ≥ 8x .......1

x ≤ 6

Liam can buy lunch for 6 people.

Step-by-step explanation:

Let x represent the number of people Liam can buy lunch for.

Given;

Lunch cost per person r = $8 per person

The total amount he has T = $50

The cost of buying lunch for c people is;

C = $8 × x

C = 8x

Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.

T ≥ C

Substituting C, we have;

T ≥ 8x

50 ≥ 8x ,.......1

Solving the inequalities;

8x ≤ 50

x ≤ 50/8

x ≤ 6.25

To the nearest whole number;

x ≤ 6

Liam can buy lunch for 6 people.

When using a risk-adjusted control chart to detect changes in a system, it is crucial to monitor both x and y variables. These variables represent the input/process parameters and output/performance measures, respectively.

To detect a change in the system using a risk-adjusted control chart, it is important to monitor x and y variables. These variables are typically associated with key performance indicators (KPIs) that provide valuable insights into the system's performance and potential variations. By monitoring x and y variables, we can effectively assess the system's stability, identify shifts or trends, and take appropriate actions to maintain control and improve performance.

The x variable represents the input or process parameter, while the y variable represents the output or performance measure. These variables are interconnected, as changes in the x variable can directly impact the y variable. Therefore, monitoring both variables provides a comprehensive understanding of the system and enables effective detection of any significant changes.

The choice to monitor x and y variables is based on the fundamental principle of understanding the cause-and-effect relationship within a system. By monitoring the x variable, we can observe variations or changes in the inputs or process parameters that might affect the system's performance. This allows us to proactively identify potential causes of any observed changes in the y variable.

Additionally, monitoring the y variable is essential as it reflects the actual performance or output of the system. By tracking the y variable, we can evaluate the system's performance against established targets or benchmarks. Deviations from the expected values or trends in the y variable can indicate a potential change or shift in the system that requires investigation and corrective actions.

Furthermore, employing a risk-adjusted control chart involves considering the inherent variability and potential risks associated with the process. Risk-adjustment allows for a more accurate assessment of system performance by accounting for various factors that may influence the output. By monitoring both x and y variables, we can better evaluate the system's stability while accounting for potential risks or confounding factors.

It is important to note that the choice of variables to monitor may vary depending on the specific context and objectives of the system. In some cases, additional variables such as z may be relevant and necessary to capture the complete picture of system performance. However, in general, monitoring x and y variables provides a solid foundation for detecting changes, understanding the underlying causes, and implementing appropriate control measures to maintain system stability and enhance overall performance.

In conclusion, when using a risk-adjusted control chart to detect changes in a system, it is crucial to monitor both x and y variables. These variables represent the input/process parameters and output/performance measures, respectively. By monitoring both variables, we gain a comprehensive understanding of the system, identify potential causes of variations, and effectively detect and respond to changes in the system.

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To test the claim that the standard deviation is greater than $16, we can perform a hypothesis test using the sample data. The null hypothesis (H0) assumes that the standard deviation is not greater than $16, while the alternative hypothesis (H1) assumes that the standard deviation is indeed greater than $16.

Let's define the hypotheses formally:

H0: The standard deviation is not greater than $16.

H1: The standard deviation is greater than $16.

We can use the chi-square test statistic to evaluate the hypothesis. The test statistic is calculated as:

χ² = (n - 1) * (s² / σ₀²)

Where:

n is the sample size (33 in this case).

s² is the sample variance (squared sample standard deviation).

σ₀ is the hypothesized standard deviation under the null hypothesis.

We will use a significance level of 0.05 (5%) for this test. The critical value for a one-tailed test (since we are testing for the standard deviation being greater) with 32 degrees of freedom at a 5% level of significance is approximately 48.05 (obtained from a chi-square table).

Let's calculate the test statistic:

χ² = (33 - 1) * (13² / 16²) ≈ 24.41

Since the calculated test statistic (24.41) is greater than the critical value (48.05), we fail to reject the null hypothesis. This means that there is not enough evidence to support the claim that the standard deviation is greater than $16.

The data does not provide sufficient evidence to conclude that the cost of the calculator varies significantly from store to store in terms of standard deviation.

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Yes, even if you don't know how many handshakes there were overall, you can be sure that there were at least two guests who had the same number.

Assume that the gathering will have n visitors. With the exception of oneself, each person may shake hands with n-1 additional individuals. For each guest, this means that there could be 0, 1, 2,..., or n-1 handshakes.

There will be the following number of handshakes if each guest shakes hands with a distinct number of persons (i.e., no two guests will have the same number of handshakes):

0 + 1 + 2 + ... + (n-1) = n*(n-1) divide by 2

The well known formula for the sum of the first n natural numbers . The paradox arises if n*(n-1)/2 is not an integer since we know that the actual number of handshakes must be an integer. The identical number of handshakes must thus have been shared by at least two other visitors.

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Percentiles provide information about the placement of data points in a quantitative dataset, histograms display the distribution of data, categorical data is grouped into categories, and ordinal data has an inherent order but no meaningful numerical differences.

Based on the terms you provided, we are looking for information about percentiles, histograms, categorical data, and ordinal data.
A percentile is a measure of placement in a sorted quantitative dataset.

It indicates the relative standing of a data point within the dataset.

For example, a score in the 80th percentile means that it is higher than 80% of the scores in the dataset.
A histogram is a graphical representation of the distribution of a dataset, typically used for continuous data.

The vertical axis of a histogram displays frequency or density, while the horizontal axis represents the data values divided into bins or intervals.
Categorical data is a type of data that can be divided into groups or categories, such as gender, ethnicity, or favorite color.

A numerical summary for categorical data usually involves counts or percentages for each category.
Ordinal data is a type of data where the order matters, but the difference between values is not meaningful, such as rankings or ratings.

A numerical summary for ordinal data can include measures of central tendency, such as the median or mode.

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Answer:

Step-by-step explanation:

m<MON = 8x - 13°

m<LOM = 7x - 17°

To find : m <MON

First, we have to find the value of x :

Create an equation

\( \mathrm{8x - 13 + 7x - 17 = 180}\) ( sum of angle in straight line )

Collect like terms

\( \mathrm{15x - 13 - 17 = 180}\)

Calculate

\( \mathrm{15x - 30 = 180}\)

Move constant to R.H.S and change its sign

\( \mathrm{15x = 180 + 30}\)

Calculate the sum

\( \mathrm{15x = 210}\)

Divide both sides of the equation by 15

\( \mathrm{ \frac{15x}{15} = \frac{210}{15} }\)

Calculate

\( \mathrm{x = 14}\)

Now, let's find the value of m<MON

\( \mathrm{8x - 13}\)

Plug the value of x

\( \mathrm{ = 8 \times 14 - 13}\)

Calculate the product

\( \mathrm{ = 112 - 13}\)

Calculate the difference

\( \mathrm{ = 99}\) °

Hope I helped!

Best regards!

Answer:

48

Step-by-step explanation:

because i say so

Answer:

Option A is the best deal for posters