Pamela and Debbie are shelving books at a public library. Pamela shelves 26 books at a time, whereas Debbie shelves 7 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?

Answer:

than it is any number between -2 and +5

Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
To learn more about : equity

https://brainly.com/question/27821130

#SPJ8

The general equation to the differential equation

(d) y' = -Vt + 17 + vt + 1 is y = ((v - V)/2)t² + 18t + C, where V and v are constants.

(e) y' - y = t, where y(0) = 1 is  \(y = -t - 1 + 2e^{t}\).

(d) To solve the differential equation y' = -Vt + 17 + vt + 1, we can separate the variables and integrate.

Separating variables:

dy = (-Vt + 17 + vt + 1) dt

Integrating both sides:

∫ dy = ∫ (-Vt + 17 + vt + 1) dt

Integrating each term:

y = (-V/2)t² + 17t + (v/2)t² + t + C

Combining like terms:

y = (-V/2 + v/2)t² + 17t + t + C

Simplifying:

y = ((v - V)/2)t² + 18t + C

So the general solution to the differential equation is y = ((v - V)/2)t² + 18t + C, where V and v are constants.

(e) To solve the differential equation y' - y = t, where y(0) = 1, we can use an integrating factor.

The differential equation can be written as:

y' - y = t

The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -1:

\(IF = e^{(-\int1 dt)} = e^{(-t)}\)

Multiplying the equation by the integrating factor:

\(e^{(-t)}(y' - y) = e^{(-t)}(t)\)

Applying the product rule on the left side:

\((e^{(-t)}y)' = e^{(-t)}(t)\)

Integrating both sides:

\(\int(e^{-t}y)' dt = \int e^{-t}(t) dt\)

Integrating each side:

\(e^{-t}y = -e^{-t}t - e^{-t} + C\)

Simplifying:

\(y = -t - 1 + Ce^{t}\)

Using the initial condition y(0) = 1:

1 = -0 - 1 + Ce⁰

1 = -1 + C

Solving for C:

C = 2

Therefore, the solution to the differential equation with the given initial condition is:

\(y = -t - 1 + 2e^{t}\)

To learn more about differential equation: https://brainly.com/question/1164377

#SPJ11

Step-by-step explanation:

Question 3 :

We have ,

Multiplying all three equations ,

=> a × b × c = bc * ac * ab

=> abc = a²b²c²

=> abc/a²b²c² = 1

=> 1/abc = 1

=> abc = 1

\(\rule{200}2\)

Answer:BrainlyIsGonnaDie

Step-by-step explanation:

The graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.

What is a misleading graph?

A misleading graph, sometimes referred to as a distorted graph, misrepresents data, amounts to statistical abuse, and may lead to the drawing of an inaccurate conclusion.

What is a data set?

A data set is a grouping of connected, discrete pieces of connected data that can be viewed separately, together, or handled as a single unit. A data structure of some kind is used to arrange a data set.

Here, we have

2 events with a cost of 1,000-1,499;

4 events with a cost of 1,500 to 1,999;

3 events with a cost of 2,000 to 2,499;

1 event with a cost of 3,000 to 3,499

We concluded from the given dataset that the cost of the event is plotted on the x-axis.

In a given dataset, the entry from 2500 to 2599 is missing.

The graph generates a point cluster that isn't actually displayed on the data components because of the missing item.

Hence, the graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.

To learn more about the dataset from the given link

https://brainly.com/question/26994360

#SPJ4

Correlation coefficient is a measure that assesses the linear correlation between two variables in a data set. Correlation coefficient is a dimensionless value that ranges from -1 to +1. A correlation coefficient of -1 shows a perfect negative correlation, while a correlation coefficient of +1 shows a perfect positive correlation.

A correlation coefficient of 0 shows no correlation between the variables. Here's how to compute the correlation coefficient for the given data set:a) x| 1 2 3 4 5 6 7 y| 2 1 4 3 7 5 6Let's first compute the means of x and y, and then we can compute the correlation coefficient:mean of x = (1+2+3+4+5+6+7)/7 = 4mean of y = (2+1+4+3+7+5+6)/7 = 4Now, we can use the formula for the correlation coefficient:

\(r = [(1-4)*(2-4) + (2-4)*(1-4) + (3-4)*(4-4) + (4-4)*(3-4) + (5-4)*(7-4) + (6-4)*(5-4) + (7-4)*(6-4)] / [(1-4)^2 + (2-4)^2 + (3-4)^2 + (4-4)^2 + (5-4)^2 + (6-4)^2 + (7-4)^2] = -0.02\)

So, the correlation coefficient for this data set is -0.02.b) x| 1 2 3 4 5 6 7 y| 5 4 7 6 10 8 9Again, let's compute the means of x and y:mean of x = (1+2+3+4+5+6+7)/7 = 4mean of y = (5+4+7+6+10+8+9)/7 = 7We can use the formula for the correlation coefficient:

\(r = [(1-4)*(5-7) + (2-4)*(4-7) + (3-4)*(7-7) + (4-4)*(6-7) + (5-4)*(10-7) + (6-4)*(8-7) + (7-4)*(9-7)] / [(1-4)^2 + (2-4)^2 + (3-4)^2 + (4-4)^2 + (5-4)^2 + (6-4)^2 + (7-4)^2] = 0.82\)

So, the correlation coefficient for this data set is 0.82.The result is different for both (a) and (b). The correlation coefficient for data set (a) is -0.02, which indicates almost no correlation, while the correlation coefficient for data set (b) is 0.82, which indicates a strong positive correlation.

To know more about correlation coefficient visit :

https://brainly.com/question/29704223

#SPJ11

Answer:

2

Step-by-step explanation:

10a² : 5a² = 10 : 5 = 2

Answer:

80

Step-by-step explanation:

thats the real answer

Answer:

11

Step-by-step explanation:

15-4 = x

15-4 = 11

x = 11

to isolate x, you move 4 to the other side and it becomes 15-4 = x

Answer:

2). 2

3). 5

4). 3

5). 6

Step-by-step explanation:

Answer:

x=10,-2 that should be the answer if it's not then oh well

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

24

To find the probability of getting 10 or more successes in a binomial experiment with p = 0.63 and n = 11 trials, we can use the cumulative probability function.

P(X ≥ 10) = 1 - P(X < 10)

Using a binomial probability formula, we can calculate the probability of getting exactly k successes:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where C(n, k) represents the binomial coefficient.

Let's calculate the probability for each value from 0 to 9 and subtract it from 1 to get the probability of 10 or more successes:

P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 9)

P(X < 10) = Σ[C(11, k) * p^k * (1 - p)^(11 - k)] for k = 0 to 9

Using this formula, we can calculate the probability:

P(X < 10) ≈ 0.121

Therefore, the probability of getting 10 or more successes in the binomial experiment is:

P(X ≥ 10) ≈ 1 - P(X < 10) ≈ 1 - 0.121 ≈ 0.879

Rounding to three decimal places, the probability is approximately 0.879.

Learn more about Probability here -:brainly.com/question/13604758

#SPJ11

In summary, the composition of two functions, f ∘ g, combines the outputs of the function g as inputs to the function f.

The composition of two functions, f ∘ g, is a new function that is formed by applying the output of the function g as the input of the function f.

To find the composition of f ∘ g, follow these steps:

1. Start with the function g(x) and evaluate it for a given input value, let's call it 'a'. This will give you g(a).
2. Take the output g(a) and use it as the input for the function f(x). Evaluate f(x) with this input value to get f(g(a)).
3. The final result f(g(a)) is the value of the composition of the two functions f ∘ g at the input 'a'.

In terms of composition notation, f ∘ g is read as "f composed with g" or "f of g". It represents the order in which the functions are applied: g is applied first, and then f is applied to the result of g.

In summary, the composition of two functions, f ∘ g, combines the outputs of the function g as inputs to the function f.

To know more about functions visit:

https://brainly.com/question/21145944

#SPJ11

Answer and Step-by-step explanation:

The area of a triangle is A = \(\frac{1}{2} bh\), where b equals the base, and h equals the height.

Plug the values into the equation and solve.

\(A = \frac{1}{2} (6)(9)\\\\\\A = 3(9)\\\\\\A = 27\)

The area is 27.

#teamtrees #PAW (Plant And Water)

Answer: If an organization wants to test whether a minority of its employees are dissatisfied with their bonus, the alternative hypothesis would be that the true population proportion is greater than the null hypothesis proportion.

Specifically, the null hypothesis would be that the proportion of employees who are dissatisfied with their bonus is equal to or less than a certain value (usually 0.5 or 0.1, depending on the context). The alternative hypothesis would be that the proportion of employees who are dissatisfied with their bonus is greater than this value.

For example, if the null hypothesis is that 20% of employees are dissatisfied with their bonus, the alternative hypothesis would be that more than 20% of employees are dissatisfied with their bonus.

The alternative hypothesis is typically the hypothesis of interest, as it represents the hypothesis that the organization wants to investigate and potentially take action on.

Step-by-step explanation:

The alternative hypothesis would be that the true population proportion of dissatisfied employees regarding their bonus is greater than the assumed proportion.

The null hypothesis assumes that the proportion of dissatisfied employees regarding their bonus is equal to the assumed proportion. The alternative hypothesis, in contrast, assumes that the proportion of dissatisfied employees is greater than the assumed proportion. In this case, the organization wants to test whether a minority of its employees are dissatisfied with their bonus, which implies that the assumed proportion is less than 50%. Therefore, the alternative hypothesis states that the true population proportion of dissatisfied employees regarding their bonus is greater than the assumed proportion. By conducting hypothesis testing, the organization can determine whether the evidence supports the null hypothesis or the alternative hypothesis and make decisions accordingly.

For more questions like Hypothesis visit the link below:

https://brainly.com/question/28840598

#SPJ11

The diameter of the circle is approximately 60 inches.

To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.

In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).

To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.

The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.

In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.

for such more questions on  diameter

https://brainly.com/question/30460318

#SPJ8

Answer:

8 Square meters

Step-by-step explanation:

plus the 6m and 2m this meters is both side , so add that then it'll become 8 Square meters

or multiply the 6m and 2m it'll become 12m

Increasing the given sample size will decreases the probability because σx will decreases as n value increases.

In Statistitics whenever we test a hypothesis for testing a statistic, we use confidence interval. Confidence interval is on either side of an assumed value a margin of error. Margin of error is calculated as critical value * sigma/sqrt of n. Thus we find that whenever n increases, margin of error decreases.

Thus making confidence interval narrower and thus making probability for accepting null hypothesis a less value. As the pattern sizes increase, the range of every sampling distribution decreases so they emerge as more and more leptokurtic. The variety of the sampling distribution is smaller than the variety of the authentic populace. Therefore, as a pattern length increases, the pattern imply and general deviation might be nearer in fee to the populace imply μ and general deviation σ.

To learn more about probability, refer: brainly.com/question/13604758

#SPJ4

Answer:

Step-by-step explanation:

A: x = 12-4 = 8

B: x =  12/4 = 3

No wonder you asked for help. Some of the questions don't make sense!

x+3 = 9 ⇒ x=6, which doesn't match either A or B.

3·x = 9 ⇒ x=3, which matches B

9 = 3·x is the same as the previous equation, i.e., B.

3+x = 9, doesn't match either A or B.

x = 9-3, doesn't match either A or B

x = 9÷3 ⇒ x=3, which matches B

x+x+x = 9 ⇒ x=3, which matches B

I'm guessing that there is an error in tape A, and x should be 6, not 8.

All the equations to one of the two tape diagrams are matched with each other in the answer given below.

Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the given information in the question,

A: 

x = 12-4

x = 8

B: 

x = 12/4

x = 3

x+3 = 9

x=6, it doesn't match either A or B.

3·x = 9

x=3, it matches with B

9 = 3·x it is similar to the previous equation that is B.

3+x = 9, it doesn't match either A or B.

x = 9-3, it doesn't match either A or B

x = 9÷3

x=3, this matches with B

x+x+x = 9

x=3, this matches with B

I'm guessing that there is an error in tape A, and x should be 6, not 8.

To know more about equation:

https://brainly.com/question/29657983

#SPJ2

The given statement "The median of a quantitative data set is always one of the individual data values" is false.

When a given data set is arranged in ascending order the observation which at the between of the data is the median of that data set. It is a value in the set whose left and right both have the same number of observations.

The given statement is not true, this is because the median is the mid-value of any data set.

Hence, the given statement "The median of a quantitative data set is always one of the individual data values" is false.

Learn more about Median here:

https://brainly.com/question/21396105

#SPJ4

Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

Carla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.

Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.

Learn more about Compensation: https://brainly.com/question/13978016

#SPJ4

56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

Learn more about the ratio here:

brainly.com/question/1504221

#SPJ4

Answer:

Sorry there is no table or picture to show the subjects ;-;

Step-by-step explanation:

Answer:

Step-by-step explanation:

35

Answer:

7

Step-by-step explanation:

add all then divide by amnt of numbers

To prove that X(=0), we need to show that when X is a scalar function, its derivative with respect to time is zero.

Let's consider a scalar function X(t). The derivative of X(t) with respect to time is denoted as dX/dt. To prove that X(=0), we need to show that dX/dt = 0.

The derivative of a scalar function X(t) is computed as dX/dt = AX(t), where A is a constant matrix and X(t) is a vector function.

Since X(=0), the derivative becomes dX/dt = A(0) = 0. Thus, the derivative of X(t) is zero, which proves that X(=0).

Now, let's consider the second part of the question. We are given that X1, X2, and X3 are linearly independent solutions of the differential equation X'=AX. We need to prove that 2X1-X2+3X3 is also a solution of the same differential equation.

We can verify this by substituting 2X1-X2+3X3 into the differential equation and checking if it satisfies the equation.

Taking the derivative of 2X1-X2+3X3 with respect to time, we get:

d/dt (2X1-X2+3X3) = 2(dX1/dt) - (dX2/dt) + 3(dX3/dt)

Since X1, X2, and X3 are linearly independent solutions, we know that dX1/dt = AX1, dX2/dt = AX2, and dX3/dt = AX3.

Substituting these expressions, we get:

2(dX1/dt) - (dX2/dt) + 3(dX3/dt) = 2(AX1) - (AX2) + 3(AX3)

Using the properties of matrix multiplication, this simplifies to:

A(2X1-X2+3X3)

Thus, we can conclude that 2X1-X2+3X3 is also a solution of the differential equation X'=AX.

The proof shows that for a scalar function X(=0), the derivative is zero. Additionally, for the given linearly independent solutions X1, X2, and X3, the expression 2X1-X2+3X3 is also a solution of the differential equation X'=AX.

To know more about function visit:

https://brainly.com/question/11624077

#SPJ11

Answer:

55

Step-by-step explanation:

The test statistic (6.01) is lesser than the critical value (2.167), we reject the null  thesis. Therefore, there's sufficient  substantiation to support the claim that the recent  friction for the number of mountain rambler deaths is  lower than 136.2.

To find a 90 confidence interval for the population  friction, we can use the  ki-square distribution with 7 degrees of freedom. thus, we can say with 90 confidence that the population  friction lies within the interval(3.325,14.067).    

To test the claim that the recent  friction for the number of mountain rambler deaths is  lower than136.2, we can conduct a one-  tagged  thesis test using the  ki-square distribution. The null and indispensable  suppositions are as follows  Null  thesis( H ₀) The recent  friction is equal to or lesser than136.2( σ ² ≥136.2).

Indispensable  thesis( H ₁) The recent  friction is  lower than136.2( σ ²<136.2).  

Using the given information, we can calculate the test statistic as  Test Statistic =

(( n- 1) * s ²) σ ²  

where n is the sample size( 8) and s ² is the recent  friction(115.1).  Calculating the test statistic yields  Test Statistic

= (( 8- 1) *115.1)/136.2 ≈6.01  

With a significance  position of 1 and 7 degrees of freedom( n- 1), the critical  ki-square value is  roughly2.167.

For such more questions on critical value :

https://brainly.com/question/15970126

#SPJ11