A tin can has dimensions 2m ×1.5m×1m high. How many litres of kerosene oil can it hold?

Answer:

i cant see

Step-by-step explanation:

it, its to tiny

Answer:

Step-by-step explanation:

I can explain how the two graphs would look like.

If we are comparing two installment factors with respect to the total amount repaid (T) over time (N), we can plot two separate graphs on the same set of axes. The x-axis would represent the number of months (N) and the y-axis would represent the total amount repaid (T).

For each installment factor, we would plot a line that represents the total amount repaid over time. The shape and slope of each line would depend on the interest rate, the amount borrowed, and the number of payments per year.

The two lines would likely have a similar shape, but different slopes and intercepts. The slope of each line would depend on the interest rate and the amount borrowed, with steeper slopes indicating higher interest rates or larger amounts borrowed. The intercept of each line would depend on the amount borrowed and the number of payments per year.

To compare the two installment factors, we would look at the relative slopes and intercepts of the two lines. If one line has a steeper slope than the other, it would indicate that the total amount repaid increases more rapidly over time for that installment factor. If one line has a higher intercept than the other, it would indicate that the total amount repaid is higher at the beginning of the repayment period for that installment factor.

Overall, by plotting the two graphs on the same set of axes, we can visually compare how the total amount repaid (T) depends on the number of months (N) for both installment factors.

The solution of the inequality using the coordinate pair is 5.

Linear inequalities are those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given linear inequality is,

y ≤ -2x + 3

We have a coordinate pair (-1, 5).

So substitute x = -1 and y = 5 in the given inequality.

5 ≤ (-2 × -1) + 3

5 ≤ 2 + 3

5 ≤ 5

Hence the missing numbers are found.

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The boxplot for the provide data is present in above figure. Median or central tendency of data is equals to 8.08. The lower and upper limits of outliers are 7.928 and 8.248 respectively.

The first task is to compute the median and the quartiles. And, in order to compute the median and the quartiles, the data needs to be put into the ascending order, as shown in the above table. Since the sample size n = 14 is even, we have that (n+1)/2 = (14+1)/2 =7.5, is not an integer value, the median is computing by taking the average of the values at the positions 7ᵗʰ and 8ᵗʰ, as shown below Median = (8.08 + 8.08)/2 = 8.08

Quartiles : The quartiles are computed using the table with the data in the asencending order. For Q₁ we have to compute the following position:

pos(Q) = (n+1)× 25/100 = 15×25/100 = 3.75

Since 3.75 is not an integer number, Q₁ is computed by interpolating between the

values located in the 3ᵗʰ and 4ᵗʰ positions, as shown in the formula above

Q₁ = 8.04+ (3.75 - 3) (8.05 - 8.04) = 8.0475

pos(Q₃) = (n + 1)× 75/100

= (14+1)×75/100 = 11.25

Since 11.25 is not an integer number, Q₃ is computed by interpolating between

the values located in the 11ᵗʰ and 12ᵗʰ positions, as shown in the formula below

Q₃ = 8.12 + (11.25 - 11) × (8.15 8.12) = 8.1275

The interquartile range is therefore

IQR = Q₃ - Q₁ = 8.1275 - 8.0475 = 0.08

Now, we can compute the lower and upper limits for outliers:

Lower = Q₁ - 1.5 x IQR = 8.0475 - 1.5×0.08 =7.928

Upper = Q₃ + 1.5 x IQR = 8.1275 + 1.5× 0.08 =8.248

and then, an outcome X is an outlier if X < 7.928, or if X > 8.248.

In this case since all the outcomes X are within the values of Lower = 7.9275 and Upper = 8.2475, then there are no outliers. The above boxplot is obtained.

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a) The probability distribution for a player's winnings is shown in table.

b) The expected winnings for a player are $3.70.

What is probability distribution?

A probability distribution is a mathematical function that describes the likelihood of various variable values. Probability distributions are frequently represented using graphs or probability tables.

a) Since there are 10 possible digits for each of the four positions, there are a total of 10^4 = 10,000 possible sequences of numbers that could be drawn.

Only one of these sequences will be the winning sequence, corresponding to a probability of 1/10,000. If a player wins, the prize is $3,700. Therefore, the probability distribution for a player's winnings is shown in below table.

b) To find the expected winnings, we multiply each possible winning amount by its probability and add the products together:

E(Winnings) = (0) * (9999/10000) + (3700) * (1/10000)

= 37/10

= $3.70 (rounded to two decimal places)

Therefore, the expected winnings for a player are $3.70.

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To measure the magnitude of the orbital angular momentum L and the projection of the angular momentum along a particular axis (say, the z-axis), we need to use the mathematical formalism of quantum mechanics.

In quantum mechanics, the orbital angular momentum L of a particle is an operator that acts on the wave function describing the particle's motion. Similarly, the z-component of the angular momentum Lz is also an operator.

The magnitude of the orbital angular momentum L can be calculated from the components of the angular momentum operator using the expression:

L^2 = L₁^2 + L₂^2 + L₃^2

where L₁, L₂, and L₃ are the x, y, and z components of the angular momentum operator, respectively. To measure the magnitude of the orbital angular momentum, we would need to measure the values of L₁ L₂, and L₃ and use them to calculate L^2.

The projection of the angular momentum along a particular axis (say, the z-axis) is given by the operator L₃. To measure the z-component of the angular momentum, we would need to measure the value of L₃ for a particular state of the system.

In practice, these measurements are often carried out using experiments involving the interaction of particles with magnetic fields. The behavior of the particles in the magnetic field allows us to infer information about the angular momentum of the particles.

The measurement of the magnitude and projection of angular momentum is an important part of many areas of physics, including quantum mechanics and solid-state physics.

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The distance traveled in the time interval 0 ≤ t ≤ 6, given the velocity function v(t) = t^2 - 6t - 16, can be determined by calculating the definite integral of the absolute value of the velocity function over the given time interval. The result is 128 units of distance.

To find the distance traveled in the given time interval, we need to integrate the absolute value of the velocity function v(t) = t^2 - 6t - 16 over the interval 0 ≤ t ≤ 6. The reason for taking the absolute value is that distance is a scalar quantity and does not depend on the direction of motion.

Taking the integral of the absolute value of the velocity function, we have:

∫|v(t)| dt = ∫|t^2 - 6t - 16| dt

To evaluate this integral, we need to split it into intervals where the velocity function is positive and negative. The absolute value function essentially removes the negative sign from the expression inside the absolute value brackets.

Next, we find the points where the velocity function changes sign by setting v(t) = 0:

t^2 - 6t - 16 = 0

Solving this quadratic equation, we find t = -2 and t = 8 as the points where the velocity changes sign.

Now, we evaluate the integral over the intervals [0, 2] and [2, 6] separately, considering the absolute value of the velocity function within each interval.

∫|v(t)| dt = ∫(t^2 - 6t - 16) dt over [0, 2] + ∫(-(t^2 - 6t - 16)) dt over [2, 6]

Evaluating the definite integrals, we obtain:

(128/3) + (128/3) = 256/3

Therefore, the distance traveled in the time interval 0 ≤ t ≤ 6 is 256/3 units of distance, which is approximately 85.33 units of distance.

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a) f1(t) = 1 is a even function, the even part is simply 1/2, and the odd part is 0.

b) f2(t) = t^3 - 2t is odd function, the even part is t^3 - t, and the odd part is   -t.

Part (a) asks us to classify the function f1(t) = I as even, odd, or neither. Here, I represents a constant, so f1(t) is a constant function.

A function f(t) is even if f(-t) = f(t) for all t in the domain of f. In other words, the function has symmetry about the y-axis.

A function f(t) is odd if f(-t) = -f(t) for all t in the domain of f. In other words, the function has rotational symmetry about the origin.

For a constant function, we have f(-t) = I = f(t) for all values of t. Therefore, f1(t) is even.

Part (b) asks us to classify the function f2(t) = t^3 - 2t as even, odd, or neither.

To determine whether f2(t) is even, odd, or neither, we need to apply the definitions of even and odd functions.

If f2(t) is even, then we have f2(-t) = f2(t) for all t.

If f2(t) is odd, then we have f2(-t) = -f2(t) for all t.

We can check these conditions as follows:

f2(-t) = (-t)^3 - 2(-t) = -t^3 + 2t

Since f2(-t) is not equal to f2(t) for all t, we know that f2(t) is not even.

We can also check if f2(t) is odd:

f2(-t) = (-t)^3 - 2(-t) = -t^3 + 2t = -f2(t)

Since f2(-t) = -f2(t) for all t, we know that f2(t) is odd.

To find the even and odd parts of a function, we use the following formulas:

even part of f(t) = (f(t) + f(-t))/2

odd part of f(t) = (f(t) - f(-t))/2

For f1(t) = I, the even part is (I + I)/2 = I/2, and the odd part is (I - I)/2 = 0.

For f2(t) = t^3 - 2t, the even part is (t^3 - 2t + (-t)^3 - 2(-t))/2 = t^3 - t, and the odd part is (t^3 - 2t - (-t)^3 + 2(-t))/2 = -t.

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Answer: 11g

Step-by-step explanation:

This is so because 6g and 5g are both like terms

They both have the variable g which makes them like terms

U can just add like terms straight away

To simplify an expression with like terms, you add their coefficients. In this case, we have [tex]6g+5g[/tex].

Combine Like Terms:
[tex]6g+5g[/tex]

[tex]=\fbox{11g}[/tex]

Answer:

3. [tex]y=(x-3)(x-2)[/tex]

4. [tex]y = (x + 2)^2[/tex]

Step-by-step explanation:

In this problem, we are asked to find the equations in their factored form of the graphed parabolas.

3. We can see that the parabola's vertex is at (3, -4). We can plug the coordinates of that point into the vertex form equation:

[tex]y=(x-a)^2 + b[/tex]

where [tex](a,b)[/tex] is the vertex of the parabola.

[tex]y=(x-3)^2 -4[/tex]

Then, we can expand the right side of the equation to an unfactored form.

[tex]y=x^2-6x+9 -4[/tex]

[tex]y=x^2-6x-5[/tex]

Finally, we can factor the right side of the equation.

[tex]\boxed{y=(x-3)(x-2)}[/tex]

4. First, input the vertex's coordinates into the vertex form equation.

[tex]y=(x - (-2))^2 + 0[/tex]

Then, simplify.

(Remember that subtracting a negative is the same as adding the positive)

[tex]\boxed{y=(x+2)^2}[/tex]

Answer: We can calculate the size of the lot in acres and then compare it to the minimum size of 3/4 of an acre that the family is looking for.

1 acre = 43,560 square feet

So, a 30,000 sq-ft lot is equivalent to:

30,000 sq-ft / 43,560 sq-ft/acre = 0.6864 acres

Since 0.6864 acres is less than 3/4 of an acre, the family's agent will be wasting her time by showing them the house with a 30,000 sq-ft lot. The lot is not big enough for the family's needs.

Step-by-step explanation:

The conditions on a, b, and c for which the Linear equations has solutions are det(A) ≠ 0,  Rank[A|B] = Rank(A).

(a) 3x + 2y - z = a

x + y + 2z = b

5x + 4y + 32 = c

For this system to have solutions, the augmented matrix [A|B]  must have a unique solution. This is equivalent to determinant of the coefficient matrix A is non-zero, and the system is consistent (the row rank of the augmented matrix is equal to the row rank of the coefficient matrix). Therefore, the conditions on a, b, and c for this system to have solutions are:

det(A) ≠ 0

Rank[A|B] = Rank(A)

(b) -3x + 2y + 4z = a

-x - 2y + 3z = b

-x - 6y + 232 = 0

For this system to have solutions, the conditions are the same as in (a):

det(A) ≠ 0

Rank[A|B] = Rank(A)

(c) 4x - 2y + 3z = a

2x - 3y – 2z = b

4x - 2y + 32 = c

For this system to have solutions, the conditions are the same as in (a) and (b):

det(A) ≠ 0

Rank[A|B] = Rank(A)

For each system of linear equations to have solutions, the number of equations must be equal to the number of variables, and the determinant of the coefficient matrix must be non-zero.

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Answer:chicken nuggets

Step-by-step explanation:

chickemn nuggets

In a 100-meter race, the runner travels the 1st and 2nd 50-meters in time t1 and t2. Then t1>t2. So, the correct option is D.

During the first half , the runner has to start from the rest and will gain some velocity as he move further from start point, where as for the second half , as he already has the velocity required to run, he will complete the second half faster than first half.

Let us assume that V1 is the velocity , that the runner is having during the first half. V1 doesn't start as soon as he starts running, at first the body is in rest and velocity V1 starts increasing after he travels few distance.

And Let V2 be the velocity for the runner in second half , as he already have the velocity V1, there will be no delay to start the second half. So, second half takes less time than first half. This can be expressed as:

t2>t1

where t2 is second half time and t1 is first half time.

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Complete question is:

In a 100-meter race, the runner travels the 1st and 2nd 50-meters in time t1 and t2. usually: group of answer choices

a) do not know t1 or t2 is longer.

b) t1 = t2

c) t1<t2

d) t1>t2

The engineer's balance sheet would show a monthly income of $9,002.60 ($4,501.30 x 2), total expenses of $4,001.36, and a balance of $499.94.

Balance sheet is a financial statement that contains details of a company's assets or liabilities at a specific point in time.

First we can use the given information to create the following balance sheet for the civil engineer:

INCOME:

Bi-weekly net pay: $2,250.65 x 2 = $4,501.30 (this assumes two pay periods per month)

EXPENSES:

     TOTAL EXPENSES: $4,001.36

BALANCE: $4,501.30 - $4,001.36 = $499.94

Therefore, the engineer's balance sheet would show a monthly income of $9,002.60 ($4,501.30 x 2), total expenses of $4,001.36, and a balance of $499.94.

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The correct statement is -

company {R} charges less money for 1 hour of service compared to company {P}.

Division is used to split a number into equal parts. It is one of the four arithmetic operations.

Given is that Limousine Company {P} charges a rental fee plus an additional charge per hour. The equation {y} = 50 + 30x shows the total cost. The cost to rent a limousine from Company {R} is shown below in the table as -

Time :   1       2        3         4       5

Cost : $100  $125  $150  $175  $200

We can write the unit charge for company {P} as -

{r₁} = $30

We can write the unit charge for company {R} can be calculated as -

{r₂} = (125 - 100) ÷ (2 - 1)

{r₂} = $25

We can conclude -

company {R} charges less money for 1 hour of service compared to company {P}.

Therefore, the correct statement is -

company {R} charges less money for 1 hour of service compared to company {P}.

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Answer: To find the minimum point of the curve y = x^2 + 4x - 7, we need to find the vertex of the parabolic function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

where a = 1 (coefficient of x^2), b = 4 (coefficient of x), and c = -7 (constant term). So, we have:

x = -4 / (2 * 1) = -2

The y-coordinate of the vertex can be found by substituting the x-coordinate into the original equation:

y = -2^2 + 4 * -2 - 7 = 4 - 8 - 7 = -11

So, the minimum point of the curve y = x^2 + 4x - 7 is located at the point (-2, -11).

Step-by-step explanation:

The vector operations defined for a position vector a and a velocity vector b are vector addition and scalar multiplication.

Simplified Vector expression is (3u - 29) x u + (3u - 29) x v.

False, as the process that follows, solving for θ by dividing by the magnitude of v and taking the inverse sine, is only valid if v x a = 0.

1.28: The vector operations defined for a position vector a and a velocity vector b are vector addition and scalar multiplication.

1.29: Using the properties of the cross-product, the simplified expression is:

3u x u + 3u x v - 29 x u - 29 x v

Using the fact that the cross-product is distributive over vector addition, we can write this as:

3u x u + 3u x v - 29 x u - 29 x v = (3u - 29) x u + (3u - 29) x v

So the simplified vector expression is (3u - 29) x u + (3u - 29) x v.

1.30: False.

The given equation,

v x (a x R) = 0,

can be simplified to a scalar triple product,

(v x a) · R = 0.

Since the scalar triple product is equal to the determinant of a matrix formed by the three vectors,

this equation implies that either v x a = 0 or R = 0.

Therefore, the process that follows, solving for θ by dividing by the magnitude of v and taking the inverse sine, is only valid if v x a = 0.

The vector operations defined for a position vector a and a velocity vector b are vector addition and scalar multiplication.

Simplified Vector expression is (3u - 29) x u + (3u - 29) x v.

False as the process that follows, solving for θ by dividing by the magnitude of v and taking the inverse sine, is only valid if v x a = 0.

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Expanding the polynomial, (7x + 5)(2x³ − 4x² + 9x − 3), we have: A. 14x^4 - 18x³ + 43x² + 24x - 15.

By applying the distribution property, we can expand a given polynomial expression like the one given above.

Given, (7x + 5)(2x³ − 4x² + 9x − 3), distribute to eliminate the parentheses:

7x(2x³ − 4x² + 9x − 3) + 5(2x³ − 4x² + 9x − 3)

14x^4 - 28x³ + 63x² - 21x + 10x³ - 20x² + 45x - 15

Combine like terms:

14x^4 - 18x³ + 43x² + 24x - 15

The correct solution is option A.

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Step-by-step explanation:

A = 1/2 bh

divide by 1/2

2A = bh

divide by h

2A/h = b

Hope this helps.

Answer:

[tex] b = \dfrac{2A}{h} [/tex]

Step-by-step explanation:

[tex] A = \dfrac{1}{2}bh [/tex]

[tex] 2A = 2 \times \dfrac{1}{2}bh [/tex]

[tex] 2A = bh [/tex]

[tex] \dfrac{2A}{h} = \dfrac{bh}{h} [/tex]

[tex] \dfrac{2A}{h} = b [/tex]

[tex] b = \dfrac{2A}{h} [/tex]

Andrew's monthly net income is $65280.

Lisa's monthly net income is $60960.

The total monthly net income is $126240.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Andrew's monthly gross income.

= $81, 600

Lisa's monthly gross income.

= $76,200

Now,

Tax = 20%

So,

Andrew's monthly net income.

= 80/100 x 81, 600

= $65280

Lisa's monthly net income.

= 80/100 x 76,200

= $60960

Now,

Total monthly net income.

= 65280 + 60960

= $126240

Thus,

Andrew's monthly net income = $65280

Lisa's monthly net income = $60960

Total monthly net income = $126240

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The final answers are:

a) P(A) = 7/12

b) P(B) = 11/36

To compute the probabilities of Events A and B, we can use a table to list all possible outcomes and their corresponding sums:

Die 1 Die 2 Sum

1         1         2

1         2         3

1         3         4

1         4        5

1         5        6

1         6        7

2         1        3

2         2        4

2         3        5

2         4        6

2         5        7

2         6        8

3         1        4

3         2        5

3         3        6

3         4        7

3         5        8

3         6        9

4         1        5

4         2        6

4         3        7

4         4        8

4         5        9

4         6        10

5         1         6

5         2         7

5         3         8

5         4         9

5         5         10

5         6         11

6         1          7

6         2          8

6         3               9

6           4          10

6         5          11

6         6          12

a) Event A: The sum is greater than 6. From the table, we can see that there are 21 outcomes where the sum is greater than 6 (highlighted in bold). Thus, the probability of Event A is:

P(A) = 21/36 = 7/12

b) Event B: The sum is divisible by 3 or 5 (or both). From the table, we can see that the sums that are divisible by 3 or 5 (or both) are:

3, 5, 6, 9, 10, 12

There are 11 outcomes with these sums (highlighted in bold). Thus, the probability of Event B is:

P(B) = 11/36

Therefore, the final answers are:

a) P(A) = 7/12

b) P(B) = 11/36

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The fraction of the total of paper clips Cecily put in the jar and drawer is [tex]\frac{97}{100}[/tex] (see the attachment below).

Paper clips in the jar: 37/100, which means Cecily put 37 clips in the jar.

Paper clips in the drawer: 6/10, now let's find out the number of clips this fraction is equivalent to:

100 (total clips) / 10 x 6 = 60

Total clips: 60 +37= 97. This number of clips can be expressed as [tex]\frac{97}{100}[/tex] .

To represent this in a grid color a total of 97 squares in a grid with 100 squares as it is shown below.

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The value of C is 108°

Given [tex]a=33,\ \ b=26, \ \ \angle B=31^0 .[/tex]

We have to find [tex]\angle C, \ \angle A \ and\ c[/tex]

We can use the cosine formula to find these:

[tex]cosB=\frac{a^2+c^2-b^2}{2ac}\\cos31^o=\frac{33^2+c^2-26^2}{2(33)(c)}\\0.8572=\frac{413+c^2}{66c}\\56.5752c=413+c^2\\i.e. c^2-56.5752c+413=0\\\Rightarrow c=47.9647, \ 8.6104\\So, \mathbf{c=48 \ or \ c=9}\\Now if c=48:\\cosA=\frac{b^2+c^2-a^2}{2bc}\\=\frac{26^2+48^2-33^2}{2(26)(48)}\\[/tex]

[tex]=\frac{1891}{2496}\\=0.75761\\\therefore A=cos^{-1}(0.75761)=40.746^0\approx 41^0\\i.e. \mathbf{\angle A= 41^0}\\cosC=\frac{a^2+b^2-c^2}{2ab}\\=\frac{33^2+26^2-48^2}{2(33)(26)}\\=\frac{-539}{1716}\\=-0.3141\\\therefore C=cos^{-1}(-0.3141)=108.306^0\approx 108^0[/tex]

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The missing term y in the given data having mean is 33.

The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.

Given that, the mean = 13,

we need to find the value of y.

4+6+9+y+16+19 / 6 = 13

y = 33

Hence, the missing term y in the given data having mean is 33.

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The Total Stockholder's Equity is $1,266,290.00

Income Statement Amount $ Amount $

Sales Revenue 1,585,000.00

Interest Revenue 2,940.00

Total Revenue  1,587,940.00

Less: Expenses  

Cost of merchandise sold 793,000.00

Selling and admin expense 158,000.00

Credit card expense 7,650.00

Bad debt reinstated (5,500.00)

Total Operating expense  953,150.00

Net Income  634,790.00

Statement of changes in Stockholder's Equity Amount $ Amount $

Beginning Common Stock 515,000.00

Add: Common Stock issued -

Ending Common Stock  515,000.00

Beginning Retained Earnings 116,500.00

Add: Net Income 634,790.00

Ending Retained Earnings  751,290.00

Total Stockholder's Equity  1,266,290.00

Balance Sheet Amount $ Amount $

Assets  

Cash  586,350.00

Inventory  303,000.00

Accounts Receivable 399,200.00

Allowance for uncollectible accounts (10,200.00) 389,000.00

Notes Receivable  63,000.00

Interest Receivable  2,940.00

Total Assets  1,344,290.00

Liabilities & Stockholder's Equity  

Liabilities  

Current Liabilities  

Accounts Payable 78,000.00

Current Liabilities  78,000.00

Stockholder's Equity  

Common Stock 515,000.00

Retained Earnings 751,290.00

Total Stockholder's Equity  1,266,290.00

Total Liabilities & Stockholder's Equity  1,344,290.00

Statement of cash flows Amount $ Amount $

Cash flow from operating activities  

Cash sales 310,000.00

Inflow from customers 997,350.00

Payment for inventory (675,000.00)

Payment for expenses (158,000.00)

Net Cash flow from operating activities  474,350.00

Cash flow from investing activities  

Notes receivable provided  (63,000.00)

Cash flow from financing activities  

Cash flow from financing activities  -

Net Change in cash  411,350.00

Add: Beginning cash balance  175,000.00

Ending cash balance 586,350.00

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The change in Kareem's total pay for each copy of Math is fun he sells is $90. Kareem's total pay if he doesn't sell any copies of Math is fun is  $2500.

Total Pay means regular straight-time earnings or base salary, plus payments for overtime, shift differentials, incentive compensation, bonuses, and other special payments, fees, allowances or extraordinary compensation.

Given that, the equation 90x+2500 = y, represents the relation between number of copies (x) Kareem sells and total pay (y) he receives,

We are asked to find, Kareem's total pay if he doesn't sell any copies of History is Fun and the change in Kareem's total pay for each copy of History is Fun he sells,

So, from the equation, 90x+2500 = y,

If we compare this equation with the general equation of the line, i.e. y = mx+c, where m is the slope, which shows 'change', we will get m = 90.

Therefore, the change in Kareem's total pay is $90.

Now, the number of copies he is selling is shown by x, if he sells no copy, then x = 0,

Therefore, Kareem's total pay, for x = 0,

y = 2500+90(0)

y = 2500

Hence, the change in Kareem's total pay for each copy of Math is fun he sells is $90. Kareem's total pay if he doesn't sell any copies of Math is fun is  $2500.

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The solution is [tex]x_1[/tex] = 3 and [tex]x_2[/tex]= 0.

Simplex method is an approach to solving linear programming models by hand using slack variables, tableaus, and pivot variables as a means to finding the optimal solution of an optimization problem.

Given:

We transfer the row with the resolving element from the previous table into the current table, elementwise dividing its values ​​into the resolving element:

[tex]P_2[/tex] = [tex]P_2[/tex] / [tex]x_{2,1[/tex] = 12 / 4 = 3;

[tex]x_{2,1[/tex] = [tex]x_{2,1[/tex] / [tex]x_{2,1[/tex] = 4 / 4 = 1;

[tex]x_{2,2[/tex] = [tex]x_{2,2[/tex] / [tex]x_{2,1[/tex] = 3 / 4 = 0.75;

[tex]x_{2,3[/tex] = [tex]x_{2,3[/tex] / [tex]x_{2,1[/tex] = 0 / 4 = 0;

[tex]x_{2,4[/tex] = [tex]x_{2,4[/tex] / [tex]x_{2,1[/tex] = 1 / 4 = 0.25;

The remaining empty cells, except for the row of estimates and the column Q, are calculated using the rectangle method, relative to the resolving element:

[tex]P_1[/tex] = ([tex]P_1[/tex] . [tex]x_{2,1[/tex]) - ([tex]x_{1,1[/tex] . [tex]P_2[/tex]) / [tex]x_{2,1[/tex]= ((6 x 4) - (1 x 12)) / 4 = 3

[tex]x_{1,1[/tex]= (([tex]x_{1,1[/tex]. [tex]x_{2,1[/tex]) - ([tex]x_{1,1[/tex] . [tex]x_{2,1[/tex])) / [tex]x_{2,1[/tex]= ((1 x 4) - (1 x 4)) / 4 = 0

[tex]x_{1,3[/tex]= (([tex]x_{1, 3[/tex]. [tex]x_{2,1[/tex]) - ([tex]x_{1,1[/tex] . [tex]x_{2,3[/tex])) / [tex]x_{2,1[/tex]= ((1 x 4) - (1 x 0)) / 4 = 1

[tex]x_{1,4[/tex] = (([tex]x_{1, 4[/tex]. [tex]x_{2,1[/tex]) - ([tex]x_{1,1[/tex]. [tex]x_{2,4[/tex])) / [tex]x_{2,1[/tex]= ((0 x 4) - (1 x 1)) / 4 = -0.25

Objective function value

We calculate the value of the objective function by elementwise multiplying the column [tex]C_b[/tex] by the column P, adding the results of the products.

Max P = (C[tex]b_1[/tex] x [tex]P_{01[/tex]) + (C[tex]b_{11[/tex] x [tex]P_2[/tex])= (0 x 3) + (7 x 3) = 21;

Evaluated Control Variables

We calculate the estimates for each controlled variable, by element-wise multiplying the value from the variable column, by the value from the Cb column, summing up the results of the products, and subtracting the coefficient of the objective function from their sum, with this variable.

Max [tex]x_1[/tex]= ((C[tex]b_1[/tex] . [tex]x_{1,1[/tex]) + (C[tex]b_2[/tex] . [tex]x_{2,1[/tex]) ) - k[tex]x_1[/tex] = ((0 x 0) + (7 x 1) ) - 7 = 0

Max [tex]x_2[/tex]= ((C[tex]b_1[/tex] . [tex]x_{1,2[/tex]) + (C[tex]b_2[/tex] . [tex]x_{2,2[/tex]) ) - k[tex]x_2[/tex] = ((0 x 1.25) + (7 x 0.75) ) - 5 = 0.25

Max [tex]x_3[/tex]= ((C[tex]b_1[/tex] . [tex]x_{1,3[/tex]) + (C[tex]b_2[/tex] . [tex]x_{2,3[/tex]) ) - k[tex]x_3[/tex] = ((0 x 1) + (7 x 0) ) - 0 = 0

Max [tex]x_4[/tex]= ((C[tex]b_1[/tex] . [tex]x_{1,4[/tex]) + (C[tex]b_2[/tex] . [tex]x_{2,4[/tex]) ) - k[tex]x_4[/tex] = ((0 x -0.25) + (7 x 0.25) ) - 0 = 1.75

Since there are no negative values ​​among the estimates of the controlled variables, the current table has an optimal solution.

The value of the objective function:

F = 21

The variables that are present in the basis are equal to the corresponding cells of the column P, all other variables are equal to zero:

[tex]x_1[/tex] = 3;

[tex]x_2[/tex]= 0;

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