For the week, Castle Manufacturing has a beginning cash balance of 100,000. They spend 99,000 on direct materials, 19,000 on direct labor, and 29,000 on manufacturing overhead. They also have cash sales of 10,000, accounts receivable collections of 220,000 and asset sales of 30,000. They also purchased assets in the amount of 20,000 and had sales commissions and other administrative expenses in the amount of 40,000. What was Castle Manufacturing cash balance at the end of the week?

Answer:

The slope is -3

Step-by-step explanation:

This is so because the line in pointing down, leading to the fact that the slope is negative, and rise over run is 3/1......

Therefore, the slope of the line is -3

To find the slope of the line, first start with a point on the graph.

Let's use the point (0,3) which we call point A.

The other point we will call point B.

Now remember that slope can be found using the ratio rise/run

between any two points that are on that line.

To get from point A to point B along this line, we must

first go down 3 units so we say that our rise is -3.

From there we move 1 unit to the right so our run is 1.

So our slope or rise/run is -3/1 which reduces to -3.

Answer:

The system y=-3x + 4 and 3y = -9x+ 12 would contain infinitely many solutions.

Step-by-step explanation:

Any system of equations that have the same equations would have infinitely many solutions.

In other words, if the two linear equations have the same slope and y-intercept, then the system of solutions would contain infinitely many solutions. So, their graphs would have exactly the same line

Also If the equation ends with a true statement, for instance, 3 = 3, then the system has infinitely many solutions or all real numbers.

Given the system of equations

\(y=-3x + 4\)

\(3y = -9x+ 12\)

Writing both equations in the slope-intercept form

\(y=mx+b\)

where m is the slope and b is the y-intercept

y=-3x + 4

Here,

m = -3

b = 4

3y = -9x+ 12

dividing both sides by 3

y = -3x + 4

Here,

m = -3

b = 4

As both equations have the same slope and y-intercept 'b'. Thus, the system of equations has infinitely many solutions.

Now checking:

\(\begin{bmatrix}y=-3x+4\\ 3y=-9x+12\end{bmatrix}\)

substitute y = -3x+4

\(\begin{bmatrix}3\left(-3x+4\right)=-9x+12\end{bmatrix}\)

for y = -3x+4

Expressing y in terms of x

\(y=-3x+4\)

Thus, the solution would contain

\(y=-3x+4,\:x=x\)

We know that If the equation ends with a true statement, for instance, x = x, then the system has infinitely many solutions or all real numbers.

Thus, the system y=-3x + 4 and 3y = -9x+ 12 would contain infinitely many solutions.

The domain of a function is the set of all inputs for which the function remains valid. Since the graph shows the number of coffee stores after 1992. The domain will only makes sense for positive numbers, since a negative year doesn't make any sense. Therefore, the domain is:

Answer:

10/4

15/6

20/8

Step-by-step explanation:

Answer:

190

Step-by-step explanation:

The distance between the tree and the rock formation is approximately 304.14 meters.

To find the distance between the tree (point T) and the rock formation (point R), we can use the law of cosines. The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the unknown distance between the tree and the rock formation as 'd.'

We have a triangle with sides of lengths 200 meters (side ST), 150 meters (side SR), and d meters (side TR). The angle opposite side ST is 120 degrees.

According to the law of cosines:

d² = 200² + 150² - 2 * 200 * 150 * cos(120°)

Now, we can calculate this expression to find the value of d:

d² = 40000 + 22500 - 60000 * cos(120°)

Using the value of cos(120°) ≈ -0.5, we have:

d² = 40000 + 22500 - 60000 * (-0.5)

d² = 40000 + 22500 + 30000

d² = 92500

Taking the square root of both sides to solve for d:

d = √92500

d ≈ 304.14

Therefore, the distance between the tree and the rock formation is approximately 304.14 meters.

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The answer can be checked by multiplying the divisor, quotient, and remainder, and then adding the quotient to the result.

After performing polynomial long division, the answer may be checked by following these steps:

1. Multiply the divisor by the quotient obtained from the division.

2. Add the obtained product to the remainder.

3. The result should be equal to the dividend.

In other words, you can check the answer by multiplying the divisor, quotient, and remainder, and then adding the quotient to the result.

This should give you the dividend.

To explain this step-by-step:

1. Perform the polynomial long division to obtain the quotient and remainder.

2. Multiply the divisor by the quotient obtained in the division.

3. Add the obtained product to the remainder.

4. The result should be equal to the dividend.

Remember to follow the correct order: multiply the divisor by the quotient first, and then add the remainder.

This method allows you to verify the correctness of the division.

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-6 = 3x - 6y

4x = 4 + 5y

ok

x = (4 + 5y)/4

Substitution

-6 = 3[(4 + 5y)/4] - 6y

-6 = [12 + 15y]/4 - 6y

-6 + 6y = [12 + 15y]/4

-24 + 24y = 12 + 15y

24y - 15y = 12 + 24

9y = 36

y = 36/9

y = 4

x = (4 + 5(4))/4

x = [4 + 20)/4

x = 24/4

x = 6

Solution x = 6, y = 4

No, a horizontal line is not a function

A horizontal line is a straight line that runs along the x-axis and has a constant y-value. The equation of a horizontal line is of the form y = b where b is a constant.

A function is a set of ordered pairs where every input is associated with exactly one output. In terms of graphs, a function is a graph where for each x-value, there is only one y-value.

A horizontal line is not a function, because for any x-value on the line, there is only one y-value. It violates the vertical line test which states that if a vertical line intersects a graph in more than one point, then it is not a function.

A horizontal line intersects the x-axis at every point, so it is not a function.

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Answer:

11

Step-by-step explanation:

55/5 equals 11

Answer:

11

Step-by-step explanation:

55 divided by 5 equals 11

Answer:

Step-by-step explanation:

oaxy8g7qd c7heuhwciwycowbobwxicx

donvc

A. a. The object is moving forward for a total of 18 seconds.

b. The object's velocity at t=14s is 3 m/s.

c. The object's maximum speed is 8 m/s.

d. The object's average speed is 4 m/s.

e. The object's average velocity is 2 m/s.

B. To answer these questions, we need to analyze the graph of the object's motion.

a. To determine the total seconds the object is moving forward, we count the number of seconds where the velocity is positive.

From the graph, we can see that the object is moving forward for a total of 18 seconds.

b. To find the object's velocity at t=14s, we look at the slope of the graph at that point. The slope represents the object's instantaneous velocity. From the graph, we can see that the slope at t=14s is 3 m/s.

c. The object's maximum speed is represented by the highest point on the graph. From the graph, we can see that the object reaches a maximum speed of 8 m/s.

d. The object's average speed is calculated by dividing the total distance traveled by the total time taken.

From the graph, we can see that the object travels a distance of 72 meters in a total time of 18 seconds. Therefore, the average speed is 72 meters / 18 seconds = 4 m/s.

e. The object's average velocity is determined by dividing the total displacement by the total time taken.

Since the graph does not provide information about the object's displacement, we cannot calculate the average velocity based on the given graph alone.

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Answer:

A,

23/6v+28

Step-by-step explanation:

Answer:

D. 23/6v+28

Step-by-step explanation:

Answer:

its answer is A

Step-by-step explanation:

as perimeter is tge edition of all sides

Answer:

12, i think

Step-by-step explanation:

I cant really see the umbers, so I guessed

Answer: The board is 54 inches wide

The width of a whiteboard, in inches, is 54.

Multiplication is a type of mathematical operation. The repetition of the same expression types is another aspect of the practice.

For instance, the expression 2 x 3 indicates that 3 has been multiplied by two.

We know that the width of the whiteboard is 4.5 feet.

However, if we need to express this width in inches, we have to convert feet to inches, as the two units are not directly comparable.

There are 12 inches in a foot.

Therefore, to convert a value in feet to inches, we can simply multiply the value by 12. In other words, 1 foot is equal to 12 inches.

So, to convert the width of the whiteboard from feet to inches, we can simply multiply the width (4.5 feet) by the conversion factor of 12 inches/foot as follows:

4.5 feet × 12 inches/foot = 54 inches

Therefore, the whiteboard is 54 inches wide.

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Answer:

  see attached

Step-by-step explanation:

The attachment is my effort to complete the proof. It appears to me the idea is to show that B=3+1 and that 1=3+C. Then you substitute (3+C) for 1 and you've got the proof you want.

_____

The given statements and reasons are intended to give you enough clues that you can figure out the logic that is being used. Once you have done that, you fill in the missing details.

The remote interior angles are (180 - 5) / 2 = 87.5 degrees each.

so option D and E are correct.

An interior angles is described as the inner of the two angles formed where two sides of a polygon come together.

In a triangle, the sum of the interior angles is 180 degrees.

so if angle 5 is an interior angle, then the two remote interior angles must add up to 180 degrees minus the measure of angle 5.

Then angle 5 is equal to x degrees, then the remote interior angles are (180 - x) / 2 degrees each.

Because  we are  looking for the remote interior angles of angle 5, we can set x = 5, so the remote interior angles are (180 - 5) / 2 = 87.5 degrees each.

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We are given a trapezoid and we are asked to determine one of its angles. To do that we need to have into account that the following angles are equal:

Also, the sum of two different angles must be equal to 180, therefore, we have the following relationship:

Replacing the value of angle W:

Subtracting 112 to both sides:

Therefore, the measure of angle Z is 68.

Answer:

area=368

perimeter=49

Step-by-step explanation:

17 x 24 = 368

17 + 24 = 41

41 + 8 = 49

Answer:

-35

Step-by-step explanation:

\(-5 = \frac{1}{7}a\\-35 = a\)

I got this by multiplying the numerator by 7. This allows the denominator to be the same as the numerator, thus equalling 1.

1 * a = a

Answer: a = -35

Step-by-step explanation:

1. -5 = 1/7(a) || GIVEN

2. -5 * (7) = (7) * 1/7(a) || Isolate "a" on one side of the equation by multiplying 7 to the other side.

3. -35 = a

Answer:

first step. 10+20+30+40+50+60=210

second step. 10+20+30+40+50+60 and 6=200.1

third step. 5+10+15+20+25+30+3+105+3=216

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.

Let A be the event that it is raining, and B be the event that it is the Wet season.

P(A) = P(A|B)P(B) + P(A|B')P(B')

Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.

The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.

Now we can calculate the probability that it is raining when you arrive:

P(A) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.

(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.

Let C be the event that your visit is during the Wet season.

P(C|A) = (P(A|C)P(C)) / P(A)

We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.

Now we can calculate the probability that your visit is during the Wet season:

P(C|A) = (3/4)(1/3) / (13/36)

= 1/4 / (13/36)

= 9/52

Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.

(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.

Let D be the event that it is raining when you return.

If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.

If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.

Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.

Let C' be the event that your visit is during the Dry season.

P(D) = P(D|C)P(C) + P(D|C')P(C')

Since P(C) = 1/3 and P(C') = 2/3, we can calculate:

P(D) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.

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The vertex of the parabola y = f(x + 1) is (1, -1).

To find the vertex of the parabola given by the equation y = f(x + 1), we need to determine the effect of the transformation on the vertex coordinates.

The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.

In the given equation, y = f(x + 1), we can see that the transformation is a horizontal shift of 1 unit to the left. This means that the new vertex will be located 1 unit to the left of the original vertex.

Given that the original vertex is (2, -1), shifting 1 unit to the left would result in a new x-coordinate of 2 - 1 = 1. The y-coordinate remains the same.

Therefore, the vertex of the parabola y = f(x + 1) is (1, -1).

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Answer:

D or an F depends on the grading system

Step-by-step explanation:

Answer:

55ft

Step-by-step explanation:

Answer:

breadth = 3.5 m

Step-by-step explanation:

length = 15.6 m

Area of rectangle = 54.6 sqm

breadth = \(\frac{Area}{length}\)

             \(= \frac{54.6}{15.6}\\\\= \frac{54.6*10}{15.6*10}\\\\=\frac{546}{156}\\\\= 3.5\)

(a)the Jordan canonical form of A is:

\(\left[\begin{array}{ccc}-1&1&0\\0&3&0\\0&0&3\end{array}\right]\)

(b)the Jordan canonical form of A is:

\(\left[\begin{array}{ccc}4&0\\0&1\end{array}\right]\)

(a) Matrix A = (-1 3)

To find the Jordan canonical form of A, we first need to find the eigenvalues of A. The characteristic polynomial of A is given by:

p(λ) = det(A - λI) = det([-1-λ, 3; 0, 3-λ]) = (λ+1)(λ-3)

So the eigenvalues of A are  λ1= -1 and λ2 = 3.

Next, we need to find a basis for each generalized eigenspace of A. For λ1 = -1, we have:

(A - λ1I) = \(\left[\begin{array}{ccc}0&3\\0&4\end{array}\right]\)with rank 1

So the dimension of the generalized eigenspace for λ1 is 2 - 1 = 1. We need to find a vector x such that (A - λ1I)x = 0, but (A - λ1I)^2x ≠ 0. In this case, we can take x = (3,0). Then we have:

(A - λ1I)x = \(\left[\begin{array}{ccc}1&3\\0&4\end{array}\right]\) \(\left[\begin{array}{ccc}3\\0\end{array}\right]\) = \(\left[\begin{array}{ccc}0\\0\end{array}\right]\)

(A - λ1I)^2x = \(\left[\begin{array}{ccc}1&3\\0&4\end{array}\right]\)\(\left[\begin{array}{ccc}1&3\\0&4\end{array}\right]\) \(\left[\begin{array}{ccc}3\\0\end{array}\right]\)= \(\left[\begin{array}{ccc}0\\0\end{array}\right]\)

So the generalized eigenspace for λ1 is spanned by the vector x = (3,0).

For λ2 = 3, we have:

(A - λ2I) = \(\left[\begin{array}{ccc}-4&3\\0&0\end{array}\right]\) with rank 1

So the dimension of the generalized eigenspace for λ2 is 2 - 1 = 1. We need to find a vector x such that (A - λ2I)x = 0, but (A - λ2I)^2x ≠ 0. In this case, we can take x = (3,4). Then we have:

(A - λ2I)x = \(\left[\begin{array}{ccc}-4&3\\0&0\end{array}\right]\) \(\left[\begin{array}{ccc}3\\4\end{array}\right]\) = \(\left[\begin{array}{ccc}0\\0\end{array}\right]\)

(A - λ2I)^2x =\(\left[\begin{array}{ccc}-4&3\\0&0\end{array}\right]\)  \(\left[\begin{array}{ccc}-4&3\\0&0\end{array}\right]\) \(\left[\begin{array}{ccc}3\\4\end{array}\right]\) = \(\left[\begin{array}{ccc}0\\0\end{array}\right]\)

So the generalized eigenspace for λ2 is spanned by the vector x = (3,4).

Now we can form the Jordan canonical form of A using the basis vectors we found for the generalized eigenspaces:

J = [(c1, 1, 0), (0, λ2, 0), (0, 0, λ2)] = \(\left[\begin{array}{ccc}-1&1&0\\0&3&0\\0&0&3\end{array}\right]\)

(b) Matrix A = \(\left[\begin{array}{ccc}1&2\\3&2\end{array}\right]\)

To find the Jordan canonical form of A, we first need to find the eigenvalues of A. The characteristic polynomial of A is given by:

p(λ) = det(A - λI) = det([(1-λ), 2; 3, (2-λ)]) = λ^2 - 3λ - 8 = (λ-4)(λ+1)

So the eigenvalues of A are λ1 = 4 and λ2 = 1.

Next, we need to find a basis for each generalized eigenspace of A. For λ1 = 4, we have:

(A - λ1I) = \(\left[\begin{array}{ccc}-3&2\\3&-2\end{array}\right]\) with rank 1

For λ2 = 1, we have A - λ2I =

\(\left[\begin{array}{ccc}0&2\\3&1\end{array}\right]\)

and the corresponding generalized eigenspace is the span of the vectors {(2,-3), (1,0)}. To find a basis for the cycle, we need to find a generalized eigenvector v such that (A - λI)v = (A - I)v = u, where u is the original eigenvector. Solving this equation gives v = (-1,3), so a basis for the cycle is {(2,-3), (1,0), (-1,3)}.

Therefore, the Jordan canonical form of A is:

\(\left[\begin{array}{ccc}4&0\\0&1\end{array}\right]\)

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Answer:

Hamster 1: 12 minutes. hamster 2: 20 minutes

Step-by-step explanation:

The first hamster took 8 minutes while the second hamster tool 20 minutes.

Equation

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the time required for the first hamster and y the time for the second hamster.

x = y + 8    (1)

(1/x + 1/y)7.5 = 1

[1/(y + 8) + 1/y ]7.5 = 1

y = 12 minutes

x = 12 + 8 = 20 minutes

The first hamster took 8 minutes while the second hamster tool 20 minutes.

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Answer:

4:22 6:33

Step-by-step explanation:

These two ratios simplify down to 2:11

Answer:

Step-by-step explanation: uhm maybe 4/3 idrk-