if you divide 50 by half and add 20 what is the sum?​

The scale factor of Figure A to Figure B is; 5/9

The scale factor of the figure A to the Figure B, will be given by the ratio of the side of the figure A to the given corresponding side of the Figure B.

Now, we see that the corresponding longest sides of the Figures A and B are given as 36 and 20 respectively

The corresponding shortest sides of the Figures A and B are given as 25.2 and 14 respectively

Therefore, we can conclude that the scale factor of the Figure A to the Figure B = 20/36 = 14/25.2 = 5/9

Finally, in order to get the dimension of Figure 'B' we multiply the dimension of Figure 'A' by 5/9

The  scale factor of Figure A to Figure B = 5/9

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Answer: 12:50 am

Step-by-step explanation:

Let's say Amanda gets up at time t, in hours.

Given that Amanda spends one-seventh of her time showering, this means she spends (1/7)×t hours in the shower.

The remaining time she has is 6/7 of her original time, so the amount of time she spends getting dressed is (1/6)×(6/7)t = (1/7)t hours.

After getting dressed, Amanda has (6/7)t - (1/7)t = (5/7)t hours left. She then spends one-quarter of this time having breakfast, which means she spends (1/4)×(5/7)t = (5/28)t hours having breakfast.

We are also given that Amanda finishes breakfast at exactly 7:15 am, which is 15 minutes before her bus leaves at 8:00 am. This means she has (8:00 - 7:15) = 45 minutes left after finishing breakfast, or (3/4) hours.

So we can set up the equation:

(5/7)t + (5/28)t = (3/4)

Multiplying both sides by the least common denominator of 28:

20t + 5t = 21

Simplifying:

25t = 21

t = 0.84

Therefore, Amanda gets up at 12:50 am.

To find the estimated arrival time, we need to add the travel time of 4 hours and 44 minutes to the departure time of 9:33 a.m.

First, let's convert the departure time to minutes:

9:33 a.m. = 9 x 60 + 33 = 573 minutes

Now we can add the travel time:

573 + 4 x 60 + 44 = 819 minutes

Finally, we can convert the total minutes back to hours and minutes:

819 minutes = 13 hours and 39 minutes

Therefore, the estimated arrival time is 11:12 p.m.

Answer: x = 8

Step-by-step explanation: Let 'x' be the number we are looking for.

As per the question, equation will be : x^2 - 40 = 3x

                                                                x^2 - 3x - 40 = 0

Factor the equation. Or quadratic equation formula can also be used.

Factoring -

                    x^2 - 3x - 40 = 0

                    x^2 - 8x + 5x - 40 = 0

                     x(x-8) + 5( x-8) = 0

                       (x+5) ( x-8)  = 0

       x+5=0           ,        x-8 =0

        x = -5             ,       x = 8

As we need to find the positive solution, x = 8 is the answer.

VERIFICATION -

                 =   x^2 - 40

                 =   ( 8 )^2 - 40

                  = 64 - 40  

                  =  24  

And 3 times 8 is also 24.

Therefore, if we subtract 40 from the square of 8, the result will be 3 times the number (which is 8).

The nearest tenth, 44.5 minutes have gοne by.

Time is the οngοing prοgressiοn οf existence and events that take place in what appears tο be an irreversible οrder frοm the past thrοugh the present tο the future. It is οne οf the quantities that make up variοus measurements that are used tο cοmpare the lengths οf events οr the gaps between them, tο cοmpare hοw lοng they last, tο οrder events, and tο measure hοw quickly certain quantities in the physical wοrld οr in cοnsciοus experience change. The fοurth dimensiοn, in additiοn tο the three spatial dimensiοns, is frequently referred tο as time.

If Teresa has finished 57% οf her run, then she has 43% left tο cοmplete.

Let x be the number οf minutes that have gοne by.

Since 57% οf the run is cοmpleted in 78 minutes, we can set up the fοllοwing prοpοrtiοn:

57/100 = x/78

Sοlving fοr x, we get:

x = (57/100) * 78

x = 44.46

Therefοre, tο the nearest tenth, 44.5 minutes have gοne by.

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The Pearson correlation coefficient r for the given points is 0.529, rounded to three decimal places.

What is statistics ?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of quantitative methods to gather, describe, and draw inferences from data, which can be used to make decisions, predictions, or conclusions about a population or a phenomenon.

We can use the following formula to calculate the Pearson correlation coefficient [tex]$r$[/tex] :

[tex]r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} $$[/tex]

where:

[tex]$n$[/tex] = the number of data points

[tex]$x$[/tex] and [tex]$y$[/tex] are the variables (in this case, the [tex]$x$[/tex] values are the first coordinate of each point and the [tex]$y$[/tex] values are the second coordinate of each point)

[tex]$\sum xy$[/tex]= the sum of the products of [tex]$x$[/tex] and [tex]$y$[/tex]

[tex]$\sum x$[/tex] and [tex]$\sum y$[/tex] = the sums of [tex]$x$[/tex] and [tex]$y$[/tex], respectively

[tex]$\sum x^2$[/tex] and [tex]$\sum y^2$[/tex] = the sums of the squares of [tex]$x$[/tex] and [tex]$y$[/tex] , respectively

Using this formula, we can calculate the necessary values:

[tex]n = 7$\\\\$\sum x = 28$\\\\$\sum y = 45$\\\\$\sum x^2 = 140$\\\\$\sum y^2 = 358$\\\\$\sum xy = 204$[/tex]

Plugging these values into the formula, we get:

[tex]r = \frac{7(204) - (28)(45)}{\sqrt{[7(140) - (28)^2][7(358) - (45)^2]}} $$[/tex]

[tex]$$ r = 0.529 $$[/tex]

Therefore, the Pearson correlation coefficient r for the given points is 0.529, rounded to three decimal places.

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The correct answer is D. They could file for Chapter 13 bankruptcy and discharge some of their debt.

Bankruptcy is a legal process in which a person or business unable to pay outstanding debts to creditors can get a fresh start. It is a form of debt relief in which a debtor is relieved of some or all of their financial obligations and is protected from creditors. Bankruptcy proceedings are conducted in federal courts under the bankruptcy laws of the United States.

In order for a couple with two children to file for Chapter 7 bankruptcy in Virginia, their monthly income must be less than $4,836 (based on the state’s median income for a 4-person household). With their reduced monthly income of $3,300, their total monthly income is $5,300 which is above the state requirement. Therefore, they would not qualify for bankruptcy. However, they may qualify for bankruptcy since it requires them to make payments based on their income. In Chapter 13 bankruptcy, they would be able to discharge some of their debt while still paying off some of the remaining debt.

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The approximate value of the given logarithmic expression as required to be determined is; 1.528.

As evident from the task content; it is required that the value of the logarithmic expression is to be determined.

Therefore, we have;

let the result of the expression be x; so that we have;

log₈ (24) = x

x log (8) = log (24)

x = log (24) - log (8)

x = 1.528

Ultimately, the approximate value of the logarithmic expression in discuss is; 1.528.

Complete question: The correct expression is; log₈ (24) .

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Answer:5

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

after doing the math RIGHT you should end up with 12

The correct answer to this question is "40|2" I just had the same question, so I know that my answer is correct.

I hope this helps you. :)

Step-by-step explanation:

4a.

as we can see in the table, if we have 1 processor and add a second one, we save 30 minutes (61 - 31 = 30).

4b.

if you solved 3. and filled the table correctly, you see that with 240 processors we need 1 minute + 60/240 = 1 1/4 = 1.25 minutes.

if we add additional 240 processors, we get 480 processors, and we need 1 minute + 60/480 = 1 1/8 = 1.125 minutes.

that means we save 1/8 minute (1 1/4 - 1 1/8 = 1/8) with doubling the amount of processors. that is 7.5 seconds.

4c.

the answer always depends on the circumstances.

in fast processes 7.5 seconds can be a long time, and it might be worth the effort to save that amount of time (like in real time processing as with industrial robotics, simulating and controlling trains or a space flight).

but for asynchronous calculations of certain numbers it might not matter, if the result is available 7.5 seconds earlier or later, and the extra effort is not worth it.

Answer:

5,400

Step-by-step explanation:

Answer:

Substitute the given value of r into the formula:

v = sqrt(2.5r)

v = sqrt(2.5(160))

v = sqrt(400)

v = 20

Therefore, the maximum safe speed is 20 miles per hou

Step-by-step explanation:

If the pedal starts at its highest point then its (A) h(t) = 5sin (12π\7 t)+11.

The pedal makes a full rοtatiοn every 5/6 secοnds, οr 1 rοtatiοn every 5/6 secοnds = 6/5 rοtatiοns per secοnd. Therefοre, the angular velοcity οf the pedal is w = 2π(6/5) = 12π/5 radians per secοnd. Let the time at which the pedal is at its highest pοint be t = 0. Then the functiοn that mοdels the height οf the pedal as a functiοn οf time is:

h(t) = A sin(wt) + h0

where A is the amplitude οf the οscillatiοn, which is half the distance between the highest and lοwest pοints, and h0 is the initial height οf the pedal.

The radius οf the circular mοtiοn οf the pedal is 7 inches, sο the amplitude οf the οscillatiοn is A = 7 - 4 = 3 inches. The initial height οf the pedal is the highest pοint, which is 7 inches abοve the grοund, sο h0 = 7 inches.

Therefοre, the functiοn that mοdels the height οf the pedal as a functiοn οf time is:

h(t) = 3 sin(12π/5 t) + 7

Simplifying the functiοn, we get:

h(t) = 5 sin(12π/7 t) + 7

Therefοre, the cοrrect answer is (A) h(t) = 5sin (12π\7 t)+11.

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The value of b is solved using square root is found to be b = 2√ac.

The section of a quadratic formula following the square root symbol, b²-4ac, is the discriminant. If we have two solutions, single solution, or none at all, the discriminant informs us.

The given equation is:

b²- 4ac = 0

Separating unknown value from the equation:

b² = 4ac

Taking square root both side.

√b² = √4ac

Simplifying

b = 2√ac

Thus, the value of b is solved using square root is found to be b = 2√ac.

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To calculate the monthly payment, we can use the formula for a fixed-payment loan:

P = (Pv * r) / (1 - (1 + r)^(-n))

Where:

Pv = present value of the loan

r = monthly interest rate

n = total number of payments

P = fixed monthly payment

a. To find the monthly payment, we need to first calculate the monthly interest rate and total number of payments:

Monthly interest rate = APR / 12 = 0.12 / 12 = 0.01

Total number of payments = 15 years * 12 months/year = 180

Plugging these values into the formula, we get:

P = (25000 * 0.01) / (1 - (1 + 0.01)^(-180)) = $285.41 per month

Therefore, the monthly payment is $285.41.

b. To determine the total amount paid over the term of the loan, we can simply multiply the monthly payment by the total number of payments:

Total amount paid = monthly payment * total number of payments

Total amount paid = $285.41 * 180 = $51,373.80

Therefore, the total amount paid over the term of the loan is $51,373.80.

c. To find the percentage of the total amount paid that is applied toward the principal and interest, we can use the amortization schedule. An amortization schedule breaks down each payment into its principal and interest components. Using a loan calculator or spreadsheet, we can generate the following schedule:   in file  attachment

From the table in file  attachment, we can see that the total principal paid over the term of the loan is $25,000 (the initial loan amount) plus $281.12, or $25,281.12. To find the percentage of the total amount paid that is applied toward the principal, we can divide the total principal by the total amount paid and multiply by 100:

Percentage of total amount paid applied toward principal = (Total principal / Total amount paid) * 100

Percentage of total amount paid applied toward principal = ($25,281.12 / $51,373.80) * 100 = 49.20%

Therefore, 49.20% of the total amount paid is applied toward the principal, while the remaining 50.80% is paid for interest.

Answer:

3 , 12,5

Step-by-step explanation:

The theoretical probability is greater than the experimental probability. So correct option is B.

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, science, finance, and engineering, to make predictions and inform decision-making. It is a fundamental concept in probability theory and plays a crucial role in many real-world applications.

Probability theory is an important branch of mathematics that is used to model and analyze random phenomena, such as games of chance, weather patterns, and stock prices. It has applications in many fields, including science, engineering, economics, and finance.

B. The theoretical probability is greater than the experimental probability. If Sameer did fewer trials of the experiment, the two values likely would be closer. The reason for the difference is likely due to chance variation or random sampling error. With more trials, the experimental probability would likely approach the theoretical probability.

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In the Venn Diagram, it is verified that 11-bit word 10011011100 has the 15-bit Hamming code 100110111001010.

What is a Venn Diagram?

In order to solve problems based on the sets, we can use a Venn diagram to depict the logical relationship between sets and their components. Although other closed figures like squares may be used, a Venn diagram commonly uses intersecting and non-intersecting circles to indicate the relationship between sets.

To verify that the 11-bit word 10011011100 has the 15-bit Hamming code 100110111001010 for the Venn Diagram given, we need to check that the parity bits in the Hamming code are calculated correctly.

The Hamming code has three parity bits, calculated based on the positions of the 1's in the code word.

Using the rules for calculating the parity bits, we get -

Parity bit 1: covers all bit positions that have an odd index (i.e., 1, 3, 5, 7, 9, 11, 13, 15).

Calculated as the XOR of these bit positions: 1 XOR 0 XOR 0 XOR 1 XOR 1 XOR 0 XOR 0 XOR 1 = 0.

Parity bit 2: covers all bit positions that have a "2" bit in their binary representation (i.e., 2, 3, 6, 7, 10, 11, 14, 15).

Calculated as the XOR of these bit positions: 0 XOR 0 XOR 1 XOR 1 XOR 1 XOR 0 XOR 1 XOR 0 = 0.

Parity bit 3: covers all bit positions that have a "4" bit in their binary representation (i.e., 4, 5, 6, 7, 12, 13, 14, 15).

Calculated as the XOR of these bit positions: 1 XOR 1 XOR 1 XOR 1 XOR 0 XOR 1 XOR 0 XOR 0 = 1.

Therefore, the 15-bit Hamming code for the 11-bit word 10011011100 is:

100110111001010

which matches the given code.

Thus, we have verified that the 11-bit word 10011011100 has the 15-bit Hamming code 100110111001010.

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The probability of event B, P(B) is 0.7.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur.

The probability of an event can be calculated by dividing the number of outcomes in which the event occurs by the total number of possible outcomes.

We know that:

P(B^C) = 0.3

where;

We also know that the sum of the probabilities of an event and its complement is equal to 1, so:

P(B) + P(B^C) = 1

Substituting P(B^C) with 0.3, we get:

P(B) + 0.3 = 1

Subtracting 0.3 from both sides, we get:

P(B) = 1 - 0.3 = 0.7

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Answer:

$1081.36

Step-by-step explanation:

Lets use the compound interest formula to solve:

[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

Lets change 6.48% into a decimal first:

6.48% ->  -> 0.0648

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

[tex]A=500(1+\dfrac{0.0648}{4})^{4(12)}[/tex]

[tex]A=1081.36[/tex]

The investment is worth $1081.36 after 12 years.

The estimated number of unemployed workers in the 16 - 19 age group is 1. 54 million people .

The probability that a person selected at random is in the 25 - 44 age group is 38 %.

The probability that a person selected at random is in the 45 - 64 age group is 25 %.

The probability that a person selected at random is in the 45 or older is 31 %.

The number of unemployed workers in the 16 - 19 age group is :

= 16 % x 9. 63 million unemployed

= 1. 54 million people

The probability that should an unemployed person be selected at random, they fall into the 25 - 44 age group would be the same percentage as the percentage of people in that group which is 38 %. The same is true for the 45 - 64 age group percentage of 25 %.

The probability that a person would be 45 or older is:

= Percentage of those 45 - 64 + 65 +

= 25 % + 6 %

= 31 %

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Answer:

Step-by-step explanation:

y=-6

y=-10

y=-2

Answer:

m = 2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (5, 12) (7, 16)

We see the y increase by 4 and the x increase by 2, so the slope is

m = 4/2 = 2

So, the slope is 2

Answer:

  (c)  6.25

Step-by-step explanation:

You want the value of x = FG, given similar triangles DFG and RPQ.

Corresponding sides of similar polygons are proportional. This means ...

  FG/PQ = DF/RP

  x/5 = 10/8

  x = 5(10/8) = 50/8 . . . . multiply by 5

  x = 6.25

__

Additional comment

It can be a bit confusing that x is the middle-length value. That is ...

  4 : 5 : 8 = 5 : x : 10

The numbers in the second ratio of shortest-to-longest sides are 5/4 = 1.25 times those in the first ratio. Then x=1.25·5 = 6.25.

Answer:

The reduced echelon form of the given matrix B is [ 1 0 0 -5 | 0 ], [ 0 1 0 3 | 0 ], and [ 0 0 1 0 | 0 ]. The parametric description of the set of solutions for the given system of linear equations is { [5x4, -3x4, 0, x4] | x4 ∈ R }.

Step-by-step explanation:

Using row operations to reduce the matrix B to reduced row echelon form, we have:

[ 1 3 -5 4 | 0 ]

[ 1 4 -8 7 | 0 ]

[-3 -7 9 -6 | 0 ]

R2 - R1 -> R2

R3 + 3R1 -> R3

[ 1 3 -5 4 | 0 ]

[ 0 1 -3 3 | 0 ]

[ 0 2 4 6 | 0 ]

R1 - 3R2 -> R1

R3 - 2R2 -> R3

[ 1 0 4 -5 | 0 ]

[ 0 1 -3 3 | 0 ]

[ 0 0 10 0 | 0 ]

R3/10 -> R3

[ 1 0 4 -5 | 0 ]

[ 0 1 -3 3 | 0 ]

[ 0 0 1 0 | 0 ]

R2 + 3R3 -> R2

R1 - 4R3 -> R1

R2 + 3R3 -> R3

[ 1 0 0 -5 | 0 ]

[ 0 1 0 3 | 0 ]

[ 0 0 1 0 | 0 ]

Therefore, the reduced echelon form of the matrix B is:

[ 1 0 0 -5 | 0 ]

[ 0 1 0 3 | 0 ]

[ 0 0 1 0 | 0 ]

asterisk

can you make it step by step easy to understand

Certainly! Here are the steps to find the reduced row echelon form of the matrix B = [1, 3, -5, 4, 1, 4, -8, 7, -3, -7, 9, -6]:

Write the matrix in augmented form, with a vertical line separating the coefficients from the constant terms.

[ 1 3 -5 4 | 0 ]

[ 1 4 -8 7 | 0 ]

[-3 -7 9 -6 | 0 ]

Use row operations to transform the matrix into row echelon form. The goal is to create zeros below the leading entries (the first nonzero element) in each row. Here are the steps:

a. Subtract the first row from the second row, and subtract 3 times the first row from the third row:

[ 1 3 -5 4 | 0 ]

[ 0 1 -3 3 | 0 ]

[ 0 2 4 6 | 0 ]

b. Subtract 3 times the second row from the first row, and subtract 2 times the second row from the third row:

[ 1 0 4 -5 | 0 ]

[ 0 1 -3 3 | 0 ]

[ 0 0 10 0 | 0 ]

c. Divide the third row by 10 to create a leading 1 in the third row:

[ 1 0 4 -5 | 0 ]

[ 0 1 -3 3 | 0 ]

[ 0 0 1 0 | 0 ]

Use row operations to transform the matrix into reduced row echelon form. The goal is to create leading 1's in each row, and zeros above and below the leading 1's. Here are the steps:

a. Subtract 4 times the third row from the first row, and subtract 3 times the third row from the second row:

[ 1 0 0 -5 | 0 ]

[ 0 1 0 3 | 0 ]

[ 0 0 1 0 | 0 ]

The matrix is now in reduced row echelon form. The leftmost nonzero entry in each nonzero row is 1, and each leading 1 is the only nonzero entry in its column. The rows are arranged so that all rows with all zeros are at the bottom of the matrix.

Therefore, the reduced row echelon form of the matrix B is:

[ 1 0 0 -5 | 0 ]

[ 0 1 0 3 | 0 ]

[ 0 0 1 0 | 0 ]

For (b):

From the reduced echelon form obtained in part (a), we can write the system of equations as:

x1 + 0x2 + 4x3 = -5

0x1 + x2 - 3x3 = 3

0x1 + 0x2 + x3 = 0

We can solve for the basic variables (x1, x2, x3) in terms of the free variable(s):

x1 = -5 - 4x3

x2 = 3 + 3x3

x3 = free

Therefore, the general solution to the system of equations is:

x = [-5 - 4x3, 3 + 3x3, x3]

where x3 is any real number, since it is the free variable. This is the parametric description of the set of solutions. We can also write this solution set in set-builder notation as:

{ [-5 - 4x3, 3 + 3x3, x3] | x3 ∈ R }

This means that any vector in the solution set can be obtained by choosing a value for the free variable x3 and plugging it into the expressions for x1, x2, and x3. For example, if we choose x3 = 0, we get the solution (x1, x2, x3) = (-5, 3, 0). If we choose x3 = 1, we get the solution (x1, x2, x3) = (-9, 6, 1), and so on.

Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]

Therefore, the amount saved by paying off the loan early at payments 19, 25, and 31 are $170.90, $264.73, and $568.94, respectively.

Percent is a way of expressing a number as a fraction of 100. It is often used to represent parts of a whole or to describe the relative size of quantities. The symbol for percent is %, and it means "per hundred". For example, 50% means 50 per hundred, or 50/100, which is equivalent to the fraction 1/2. Percentages are commonly used in finance, economics, science, and everyday life to express changes, comparisons, and proportions.

Here,

To find the amount saved by paying off the loan early, we need to calculate the remaining balance at the end of each month if the loan is paid off early and subtract it from the remaining balance if the loan is paid off on schedule.

After payment 18, the remaining balance is $3,493.39. To pay off the loan early, the Schrodt's would need to make an extra payment of $168.85 at this point. Using the formula for the remaining balance of a loan, we can find the new remaining balance after payment 19:

New balance after payment 19 = 3493.39 - 168.85 + (0.15/12)*3493.39

= $3,322.49

Amount saved by paying off at payment 19 = 3493.39 - 3322.49

= $170.90

Similarly, the new remaining balances and amounts saved at payments 25 and 31 can be calculated:

New balance after payment 25 = 2718.43 - 168.85 + (0.15/12)*2718.43

= $2,453.70

Amount saved by paying off at payment 25 = 2718.43 - 2453.70

= $264.73

New balance after payment 31 = 1883.50 - 168.85 + (0.15/12)*1883.50

= $1,314.56

Amount saved by paying off at payment 31 = 1883.50 - 1314.56

= $568.94

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Answer:

Step-by-step explanation:

I can provide you with the steps to solve the simultaneous equations y=5-x and y=x+1 using the given graphs.

a) To draw the graph of y=x+1 on the same grid, we can plot the points where x=0 and x=5, and connect them with a straight line. When x=0, y=1 and when x=5, y=6, so the line passes through (0,1) and (5,6).

b) To solve the simultaneous equations y=5-x and y=x+1, we can look for the point where the two graphs intersect on the same grid. This point represents the values of x and y that satisfy both equations simultaneously.

From the first equation, we know that when x=0, y=5, and when x=5, y=0. From the second equation, we know that when x=0, y=1, and when x=5, y=6.

By looking at the graphs, we can see that the two lines intersect at the point where x=4 and y=1. Therefore, the simultaneous solution of the equations is x=4 and y=1.

Answer:

Using the LIFO method, the last units purchased are assumed to be sold first. Therefore, the cost of goods sold (COGS) is calculated as follows:

COGS = 15 × $65 + 55 × $59 + 7 × $51 = $3,675

To calculate the ending inventory balance, we need to add up the cost of the remaining units using the LIFO method. Since there are 20 units on hand at the end of the year, we can use the following steps:

Assume that the first 15 units purchased (at $51 each) and 5 units from the second purchase (at $59 each) make up the 20 units on hand.

Calculate the cost of these units: 15 × $51 + 5 × $59 = $1,120

Subtract this amount from the cost of the second purchase (55 units at $59): 55 × $59 - $1,120 = $2,905

Therefore, the ending inventory balance at the end of the year using the LIFO method is $2,905.

Step-by-step explanation: