The income statement for the year 2021 of Buffalo Co contains the following information:

My courses >

My books

Expenses:

Revenues

$71000

Salaries and Wages Expense

$43500

Rent Expense

12500

My folder

Advertising Expense

10400

Supplies Expense

5800

2500

Utilities Expense

Insurance Expeme

1800

Total expenses

76500

Net income (loss)

$(5500)

At January 1, 2021, Buffalo reported retained earnings of $50500. Dividends for the year totalled $10600. At December 31, 2021, the

company will report retained earnings of

$23400

$34400

$45000

$39900

We can proceed with conducting a z-test for one proportion to test whether the true proportion of players who win the game differs from 0.10.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Yes, the conditions for inference are met for conducting a z-test for one proportion.

The random condition is met because the sample is chosen randomly from the large population of all players.

The 10% condition is also met since the sample size (100) is less than 10% of the entire population.

The large counts condition is met because both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the hypothesized proportion of players who win the game. In this case, np = 100 * 0.1 = 10 and n(1-p) = 100 * 0.9 = 90.

Therefore, we can proceed with conducting a z-test for one proportion to test whether the true proportion of players who win the game differs from 0.10.

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The correct that refers Facts, statistics, numerical data, quotations, specific examples, and expert opinions that support a claim are called evidence.

The term numerical data refers the data which is in the form of numbers, and not in any language or descriptive form.

Here we have to find the suitable term for the statement "Facts, statistics, numerical data, quotations, specific examples, and expert opinions that support a claim are called".

While we have looking into the given statement, we have identified the following from it,

When we look into the meaning of each one we have identified that each of them are acted as the proof to prove the thing is liable.

So, all these things are collectively called as evidence.

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taking a close look at the graph hmmm we can see that it has roots or solutions at -4 and 5, however, let's notice something, the graph touches the x-axis at -4 and 5 but it doesn't cross it, it simply bounces off of it, which means those roots have an even multiplicity, hmmm let's give it say 2.  Let's also notice the graph has a y-intercept at hmm 100, so the graph passes through (0 , 100).

\(\begin{cases} x=-4\implies &x+4=0\\\\ x=5\implies &x-5=0 \end{cases}\implies y=a\stackrel{"2" multiplicity}{(x+4)^2 (x-5)^2} \\\\\\ \textit{we also know} \begin{cases} x=0\\ y=100 \end{cases}\implies 100=a(0+4)^2 (0+5)^2 \\\\\\ 100=a(16)(25)\implies \implies \cfrac{100}{(16)(25)}=a\implies \cfrac{1}{4}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=\cfrac{1}{4}(x+4)^2 (x-5)^2~\hfill\)

Check the picture below.

For f(x) = cos(x) we have:

For a general cosine function, we have:

f(x) = A*cos(kx + p) + M

Where:

For the function:

f(x) = cos(x).

We can see that:

A = 1, M = 0, k = 1, p = 0.

So, the amplitude is equal to 1, and the midline is equal to zero.

Now we also need to get the period. By definition of the trigonometric functions sin(x) and cos(x), we know that the period of the two is equal to 2π.

Finally, we need to identify the graph of cos(x).

Notice that:

f(0) = cos(0) = 1.

So the graph of f(x) = cos(x) is the graph with an y-intercept equal to 1. Which is the bottom graph on the second image.

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Three rotational symmetries does  figure of  F have.

What is rotational symmetries?

Rotational symmetry is a type of symmetry where a shape or object can be rotated by a certain angle (less than 360 degrees) and still look the same as the original shape. In other words, it is a property of a shape or object that remains unchanged when rotated around a fixed point called the center of rotation.

The number of times a shape looks the same after being rotated by a certain angle is called the order of rotational symmetry. Shapes with higher order of rotational symmetry appear more symmetrical as they can be rotated by more angles and still retain their original form. Rotational symmetry is an important concept in mathematics, geometry, and physics, and it is used in many real-world applications, such as in designing objects, structures, and patterns.

To determine the number of rotational symmetries, we need to look for the number of times the figure looks the same after rotating it by some angle.

In the case of F, we can rotate it by 120°, 240°, and 360° and it will still look the same. Therefore, F has three rotational symmetries.

Option a) 1 at 360° is incorrect because F has additional rotational symmetries at 120° and 240°. Option c) 2 is incorrect because F has three rotational symmetries, not two.

Therefore, F has three rotational symmetries.

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Complete Question:

Answer:

70.4

Step-by-step explanation:

the aquare root of 40.96 is 6.4

so,64+6.4=70.4

The answer is Option C. If the scatterplot of x = hundreds of papers and y = total cost did not show a perfect linear relationship.

The conditions that must be satisfied in order to perform inference for regression of y on x are:

I. The population of values of the independent variable (x) must be normally distributed.

III. There is a linear relationship between x and the mean value of y for each value of x.

So, the correct answer is C. I and III.

In the given options, violating condition III would result in a violation of the conditions of inference for the above computer output. If the scatterplot of x = hundreds of papers and y = total cost does not show a perfect linear relationship, it means there is a deviation from the assumption of a linear relationship between x and the mean value of y for each value of x.

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The required confidence interval in the form of ˆp±E is (85.8% ± 3.3%).

The confidence interval has been given with percentage values, the value of E will also be in percentage.

Given confidence interval (79.2%, 92.4%) is to be expressed in the form of ˆp±E.

Let's recall the formula for the confidence interval. A confidence interval for a sample proportion can be given as:ˆ

                         p ± E

where E = Margin of Error

Let's try to find the value of ˆp and E from the given confidence interval.

Here, ˆp = (79.2% + 92.4%) / 2

              = 85.8%And

          E = (92.4% - 85.8%) / 2

             = 3.3%

Now we have calculated the values of ˆp and E.  Putting the values, we have:ˆ

            p ± E= 85.8% ± 3.3%

Therefore, the required confidence interval in the form of ˆp±E is (85.8% ± 3.3%).

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The degrees of freedom in a regression model is 2 if the model that has 10 observations and 7 independent variables.

The amount of rows of training data used to fit the model equals the degrees of freedom.

Total observation = 10

Number of independent variables = 7

Degree of freedom for regression = 10 – 7 - 1

= 2

Thus, the degrees of freedom in a regression model is 2 if the model that has 10 observations and 7 independent variables.

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The value of the F"(2) is √262.

What is the chain rule?

The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².

To find F"(2), we need to differentiate F(x) twice with respect to x.

First, we find F'(x):

F'(x) = f(x)

Next, we find F''(x):

F''(x) = f'(x)

To find f'(x), we need to apply the chain rule and the fundamental theorem of calculus. We have:

\(f(t) = \int\limits^{t^2}_1 \frac{\sqrt{6+u^4}}{u} , du\)

Let's define \(g(u) = \sqrt{6+u^4}/u\). Then, using the chain rule, we have:

\(f'(t) = g(t^2) \cdot 2t\)

Now, we can find F''(2) by evaluating f'(t) at t=2:

\(F''(2) = f'(2) = g(2^2) \cdot 2(2)\)

To find g(2²), we evaluate g(u) at u=2²=4:

\(g(4) = \sqrt{6+4^4}/4 = \sqrt{6+256}/4 = \sqrt{262}/4\)

Putting it all together, we have:

\(F''(2) = f'(2) = g(2^2) \cdot 2(2) = (\sqrt{262}/4) \cdot 4 = \sqrt{262}\)

Therefore, the value of the F"(2) is √262.

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Answer:

cos(11π/3) = 1/2

Explanation:

To find the value of cos(11π/3), we first need to find a coterminal angle. This is because 11π/3 is greater than 2π, which is the angle of the complete circle. Then, we can find the coterminal angle as

11π/3 - 2π = 5π/3

Now, we need to find cos(5π/3), so we will use the unit circle as follows

Therefore, the value of cosine is the first coordinate of the point in the unit circle. It means that

cos(5π/3) = 1/2

Then, cos(11π/3) = 1/2

So, the answer is

cos(11π/3) = 1/2

After simplification, the second option |−4| < |−5| is true.

In the given question,

There are four options. We have to check which option is true.

The given options are

1) |−5| < 4

2) |−4| < |−5|

3) |−5| = −5

4) |−4| > |5|

To find the true option we solve the given option one by one.

The first option is

|−5| < 4

Now solving

As we know that every value from the mod always give positive value.

So if we solve |−5| then the value is 5 and 5 is greater than 4. But in the given statement states that 4 is greater that 5. So the first statement is wrong.

Now solving the second statement.

|−4| < |−5|

After solving |−4|, the value is 4 and |−5| is 5.

So the simplified statement is 4 < 5 which is true.

Hence, the second statement is true.

Now we get the true statement so we haven't solve any further option.

If you want the solve next option the the way of solving the option is same.

Hence, the second option |−4| < |−5| is true.

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Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

The distance between home plate and second base is 90√2 feet

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

Shape of the field = square

Base edge = 90 ft

The distance between home plate and second base is the diagonal of the square field

This distance is calculated as

Distance = Base edge * √2 feet

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

Distance = 90 * √2 feet

Evaluate

Distance = 90√2 feet

Hence, the distance is 90√2 feet

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The given expression 5x+3x²-7x³+2 is a cubic expression.

A cubic expression is a three-dimensional algebraic equation of the form ax³ + bx² + cx + d = 0, where the coefficients are a, b, and c, and the constant is d.

In order to classify the given expression as 5x+3x²-7x³+2, we need to rearrange the given expression,

\(5x+3x^2-7x^3+2\\\\=-7x^3+3x^2+5x+2\)

Since the highest power that is in the expression is 3, therefore, the given expression is a cubic expression.

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Using the Newton-Raphson method with an initial estimate xo = 3, the first improved estimate x₁ for the equation y = 10 sin(x) + x² - 8x + 15 is approximately x₁ = 2.958.

To find the first improved estimate x₁ using the Newton-Raphson method, we start with an initial estimate xo = 3 and iterate until convergence is reached. The method involves using the formula:

x₁ = xo - f(xo)/f'(xo),

where f(x) represents the given equation and f'(x) is its derivative.

1. First, we need to find the derivative of the equation f(x) = 10 sin(x) + x² - 8x + 15. The derivative is f'(x) = 10 cos(x) + 2x - 8.

2. Substitute xo = 3 into the formula for x₁:

x₁ = 3 - (10 sin(3) + 3² - 8(3) + 15)/(10 cos(3) + 2(3) - 8).

3. Evaluate the expression on the right side using a calculator to find x₁. Rounded to three significant figures, x₁ is approximately 2.958.

Therefore, the first improved estimate x₁ using the Newton-Raphson method with an initial estimate xo = 3 is approximately x₁ = 2.958.

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Answer:

600cm2

Step-by-step explanation:

Area of sheet = Length × Breadth

                        = (30 × 20) cm2

                        = 600 cm2

The equation for temperature change is T = -1.5t + 29 and the number line is plotted.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

Let T represent the temperature in degrees Celsius, and let t represent the time in hours after lunchtime.

Then write an expression for the situation as follows:

T = -1.5t + 29

Here, -1.5t represents the decrease in temperature per hour, since the temperature is dropping at a rate of 1.5 degrees Celsius per hour.

Adding 29 to -1.5t gives the initial temperature of 29 degrees Celsius at lunchtime.

To illustrate this situation on a number line diagram, we can plot the temperature T as a function of time t.

The diagram would have time t on the horizontal axis and temperature T on the vertical axis.

Label the point (0, 29) on the diagram to represent the temperature at lunchtime, and the point (x, 16) to represent the temperature at sunset, where x is the number of hours after lunchtime.

Then draw a straight line connecting these two points to represent the linear relationship between temperature and time.

The line slopes downward from left to right, indicating that the temperature is decreasing over time.

Therefore, the number line diagram is plotted.

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On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

Waymon's hourly rate for the first 40 hours of work was $10.77.

What is cost estimate ?

A cost estimate is a calculation of the probable cost of a project, program, or operation. It is an assessment of the resources required to complete a project or task, including the cost of labor, materials, equipment, and any other necessary expenses. Cost estimates are typically created during the planning phase of a project to help stakeholders determine the feasibility of the project and allocate resources appropriately. They may also be used during the execution and control phases of a project to monitor and manage costs, make adjustments to the budget, and ensure that the project remains within budget constraints. Cost estimates can vary in accuracy and detail depending on the stage of the project and the available information, but they are an essential component of effective project management.

Let's first find out how much Waymon earned for working 40 hours without overtime:

Total earnings = earnings for 40 hours + earnings for overtime

$479.27 = earnings for 40 hours + $48.47

Earnings for 40 hours = $479.27 - $48.47 = $430.80

Now, we can calculate his hourly rate for the first 40 hours of work:

Hourly rate = earnings for 40 hours / 40 hours

Hourly rate = $430.80 / 40

Hourly rate = $10.77

Therefore, Waymon's hourly rate for the first 40 hours of work was $10.77.

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The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

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(a) The differential equation that is satisfied by y is:

\(\frac{dy}{dt} = ky(1-y)\)

(b) To solve the differential equation, we separate the variables and integrate both sides:

\(\frac{dy}{y*(1-y)} = k*dt\)

Integrating both sides, we get:

\(\frac{lnly}{1-y} = k*t +c1\)

where C1 is an arbitrary constant of integration.

We can rewrite the equation in terms of y:

\(\frac{y}{1-y} = e^{(k*t+c1)}\)

Multiplying both sides by (1-y), we get:

\({y} = e^{(k*t+c1)} *(1-y)\)

\(y= \frac{C}{(1+(c-1)e^{-kt} }\)

where C = y(0) is the initial fraction of the population who have heard the rumor.

(c) In this case, the initial fraction of the population who have heard the rumor is y(0) = \(\frac{100}{1300}\) = 0.077. At noon, half the town has heard the rumor, so y(4) = 0.5.

Substituting these values into the equation from part (b), we get:

\(0.5= \frac{0.077}{1+(0.777-1) e^{-k4} }\)

Solving for k, we get:

\(k= ln(\frac{12.857}{4} )\)

Substituting this value of k into the equation from part (b), and setting y = 0.9 (since we want to find the time at which 90% of the population has heard the rumor), we get:

\(0.9= \frac{0.077}{1+(0.777-1) e^{-ln(12.857}*\frac{t}{4} }\))

Solving for t, we get:

t = 8.7 hours after the beginning (rounded to one decimal place)

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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Answer: a=5

Step-by-step explanation:

1/12a=10/24

24a=120

a= 5

We know that Gary's age is 11 years old. So, we just have to use an expression to indicate someone's age.

Let's consider the expression:

This expression represents Mr. Smith's age who is 27 years old. Let's prove it using Gary's age.

The inverse tangent of 0.9 is approximately 42.0 degrees.

Therefore, the correct answer is option C: 42.0⁰.

The inverse tangent, also known as arctangent, is a trigonometric function that gives the angle whose tangent is a given number. In this case, we want to find the inverse tangent of 0.9.

Using a calculator or reference table, we can find that the inverse tangent of 0.9 is approximately 42.0 degrees.

To understand why this is the case, we can consider the definition of the tangent function. The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle. The inverse tangent function reverses this relationship, giving us the angle when we know the tangent value.

In the case of 0.9, we can imagine a right triangle where the length of the side opposite the angle is 0.9 and the length of the side adjacent to the angle is 1. The inverse tangent of 0.9 tells us the angle that satisfies this relationship.

So, the inverse tangent of 0.9 is approximately 42.0 degrees.

Therefore, the correct answer is option C: 42.0⁰.

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Answer: 4

Step-by-step explanation:

the answer is x3

11x3=33

5x3=15

multiply by 3 on all of them    

mark brainliest plz

a) The probability of a very good poker player earning a profit (more than $0) after playing 40 hands in $100/$200 Texas Hold'em can be calculated using the normal distribution and the given mean ($1) and standard deviation ($31). b) The proportion of the time a very good poker player can expect to earn at least $500 after playing 100 hands in $100/$200 Texas Hold'em can be calculated using the normal distribution and the given mean ($1) and standard deviation ($31).

To compute these probabilities, we need to make some assumptions and use probability distribution calculations based on the given information.

a) To determine the probability of a profit after playing 40 hands, we can use the concept of the normal distribution. We need to calculate the z-score using the formula: z = (x - μ) / σ, where x is the desired profit, μ is the expected profit per hand, and σ is the standard deviation. In this case, x = $0, μ = $1, and σ = $31.

Once we have the z-score, we can use a standard normal distribution table or calculator to find the corresponding probability.

b) Similarly, to find the proportion of the time a player can expect to earn at least $500 after playing 100 hands, we need to calculate the z-score for x = $500, using the same formula as in part (a). Then, we can use the standard normal distribution table or calculator to find the corresponding proportion.

c) To determine the probability of earning a profit during a 14-hour session, we need to calculate the number of hands played, which is 20 hands per hour multiplied by 14 hours. Let's denote it as N. Then, we can calculate the mean profit for the 14-hour session by multiplying the expected profit per hand ($1) by N.

The standard deviation for the session can be calculated by multiplying the standard deviation per hand ($31) by the square root of N. Finally, we can use the normal distribution and the same z-score calculation as in part (a) to find the probability.

Please note that the above calculations assume that the profits from each hand are independent and follow a normal distribution. Real poker outcomes may deviate from these assumptions.

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Answer:

0. Amount of commission = $5,160

1. Linda's gross pay = $7,470

Explanation:

Part 1

Linda's sales for last month = $64,500

She is paid an 8% commission on merchandise she sells.

Therefore:

Amount of commission = 8% of $64,500

=8/100 x 64,500

=0.08 x 64,500

=$5,160

Part 2

Linda's Gross Pay = Monthly salary + Commision

=2,310 + 5,160

=$7,470

Linda's gross pay is $7,470

Answer:

7.9

Step-by-step explanation:

Using the half-life formula, there will be about \(30(0.5)^{11000/5730} \approx 7.9\) grams left.