Show that x³ + y³ + z³ - 3xyz is a multiple of x+y+z

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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The c (PMF) of the random variable y can be determined by considering the conditional probabilities for each possible value of x.

Since x takes values from 1 to 4 with equal probability, we need to calculate the conditional probabilities of y given each value of x.

For x = 1, the possible values of y are {1}, and since y is uniformly distributed on {1}, the probability mass function P(y) = 1 for y = 1.

For x = 2, the possible values of y are {1, 2}, and y is uniformly distributed on {1, 2}. Thus, P(y) = 1/2 for y = 1 and y = 2.

For x = 3, the possible values of y are {1, 2, 3}, and y is uniformly distributed on {1, 2, 3}. Hence, P(y) = 1/3 for y = 1, y = 2, and y = 3.

For x = 4, the possible values of y are {1, 2, 3, 4}, and y is uniformly distributed on {1, 2, 3, 4}. Therefore, P(y) = 1/4 for y = 1, y = 2, y = 3, and y = 4.

The probability mass function (PMF) of y is as follows:

P(y = 1) = 1/4,

P(y = 2) = 1/4,

P(y = 3) = 1/4,

P(y = 4) = 1/4.

This indicates that for each value of y, namely 1, 2, 3, and 4, the corresponding probability is 1/4, reflecting a uniform distribution of y within the range determined by the value of x.

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Answer:

21

Step-by-step explanation:

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

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

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

Also, we have,

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

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

Then eq(2):

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

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

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

-28

Explanation

To evaluate this expression let's use the PEMDA acrostic

Parenthesis

Exponents

Multiplication

Division

Adition

Evaluating the correct problem:

\(\\ \sf\longmapsto \dfrac{BQ}{DQ}=\dfrac{RC}{CD}\)

\(\\ \sf\longmapsto \dfrac{26}{39}=\dfrac{18}{x}\)

\(\\ \sf\longmapsto \dfrac{2}{3}=\dfrac{18}{x}\)

\(\\ \sf\longmapsto 2x=54\)

\(\\ \sf\longmapsto x=27\)

In the grating equation nλ=d sin θ, the quantity θ will be determined in the lab by using meter sticks and geometry/trigonometry

The term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign

Here we have given that the grating equation nλ=d sin θ, the quantity θ will be determined in the lab.

The term grating equation in math states that d = 1/N where N is the grating constant, and it is the number of lines per unit length and n is the order of grating, which is a positive integer, representing the repetition of the spectrum.

And the term trigonometry is defined as a branch of mathematics concerned with relationships between angles and ratios of lengths.

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The nth term rule of the quadratic sequence is;

-5 + (n - 1)²

We are given the sequence as;

−5,−4,−1,4,11,20,31

Difference between the consecutive terms in order is seen to be; +1, +3, +5, +7, +9, +11

Thus, the pattern is;

-5 + 0 = -5

-5 + 1 = -4

-5 + 4 = -1

-5 + 9 = 4

From the pattern above, we can deduce that the nth term is gotten from the expression; -5 + (n - 1)²

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Answer:

$656.25

p=35000

t=5

r=2.5

interest=ptr/100

=35000x5x2.5/100

=4375

amount=p+i

=35000+4375

=39375

now,

5 yr= 5x12months = 60 months

$39375/60=$656.25

i think so...

Answer:

The answer of this question is False

Answer: y=6

Step-by-step explanation:

Data: y=3 and x=12

y=? and x=18

12/3=4 and 18/3=6

y=6

I hope this helps

The inflection points of the function f(x) = x⁴ - 2x²/3 are at

x = -0.77 and x = 0.77.

To find the inflection points of the function f(x) = x⁴ - 2x²/3, we need to locate the x-values where the concavity of the function changes.

This can be done by finding the second derivative of the function and determining where it equals zero.

First, let's find the second derivative of f(x):

f''(x) = 12x² - 4x/3

Setting f''(x) equal to zero and solving for x:

12x² - 4x/3 = 0

4x(3x - 1) = 0

This equation is satisfied when x = 0 and x = 1/3. However, we need to check the concavity around these points to confirm if they are inflection points.

By analyzing the sign of f''(x) in the intervals (-∞, 0), (0, 1/3), and (1/3, ∞), we observe that the concavity changes at x = -0.77 and x = 0.77.

These are the inflection points of the function f(x).

Therefore, the inflection points of f(x) = x⁴ - 2x²/3 are at x = -0.77 and x = 0.77.

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In the first month's payment for a $180,000 mortgage with a 5.5 percent, 30-year loan, a portion will go towards the principal. The exact amount can be determined using an amortization schedule.

To calculate how much of the first month's payment goes towards the principal, we can follow these steps:

Step 1: Determine the monthly interest rate: Divide the annual interest rate by 12 to obtain the monthly interest rate. In this case, 5.5 percent divided by 12 equals 0.004583 (approx).

Step 2: Calculate the monthly payment: Use a loan payment formula or a mortgage calculator to determine the monthly payment amount. For a $180,000 mortgage with a 30-year loan term and a 5.5 percent interest rate, the monthly payment would be approximately $1,019.32 (approx).

Step 3: Create an amortization schedule: An amortization schedule shows the breakdown of each monthly payment, indicating the amount allocated to interest and principal. Using the loan details, create an amortization schedule or use an online tool to generate one.

Step 4: Locate the first month on the schedule: Find the first month's entry on the amortization schedule to determine the amount allocated to principal. This amount will vary depending on the specific terms of the loan. Locate the principal portion of the payment, which represents the reduction of the loan balance.

By following these steps and referencing the amortization schedule, you can determine the exact amount of the first month's payment that goes towards the principal of the $180,000 mortgage.

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Answer:

0.111111...

Step-by-step explanation:

Hi,

this function is stating that for any x the f is 9(3)^x.

SO if x was -4 it would be 9(3)^-4

Following order of operations we calculate the exponent first.

the answer is 0.1111111...

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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Answer:

Distance in 1 hr=8.5m

Therefore,

Distance in three hour=8.5×3

=25.5m

Answer:

4680

Step-by-step explanation:

65% of 7200 is 4680

Answer:

4680

Step-by-step explanation:

65% of 7200 is 4680

Answer:

138.86

Step-by-step explanation:

Multiply the radius by 2 to get the diameter.

Multiply the result by π, or 3.14 for an estimation.

That's it; you found the circumference of the circle.

The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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Answer:

Step-by-step explanation:

2 1/4 = 2

7 9/12 = 8

2 + 8 = 10

2 1/4 = 9/4 = 27/12

7 9/12 = 93/12

27/12 + 93/12

120/12

10

Best of Luck!

Answer:

The answer is CAD

Step-by-step explanation:

I got 100 on plato

Answer:

2.25

Step-by-step explanation:

5.20 * 1.06 = 5.512

11.70 - 5.512 = 6.188

6.188 / 2.75 = 2.25018

Round to the nearest hundredth which equals....

2.25

Answer:

4 airplanes

Step-by-step explanation:

1 = 2/3

6 = x

cross multiply

x = 6 × 2/3

therefore x = 4

Answer:

4 airplanes

Step-by-step explanation:

1 =2/3

6 =×

you have to cross multiply

× =6×2/3

Therefore x=4

Answer:

Since 30% of 100 ml = .3*100 = 30 ml

60 % of X ml = .6x which we are trying to solve

add

(X+100).36 = 30+.6x

.36x+36 = 30+.6x

so

6 = .24x

x = 25 ml

Step-by-step explanation:

I hope this helps you

The soccer team can have 1,716 different starting lineups. The number of ways to choose 1 player out of 13 for the goalkeeper position is given by the combination formula: C(13, 1) = 13.

To calculate the number of different starting lineups, we need to determine the combinations of players that can be chosen for the starting lineup. Since there are 13 players on the team and 11 positions in the starting lineup, we need to choose 1 player for the goalkeeper position and 10 players for the regular positions. Similarly, the number of ways to choose 10 players out of the remaining 12 players for the regular positions is given by the combination formula:

C(12, 10) = 66.

To find the total number of different starting lineups, we multiply the number of choices for the goalkeeper position by the number of choices for the regular positions: 13 * 66 = 858.

However, the order of the players in the lineup doesn't matter, so we need to divide the result by the number of permutations of the 10 regular players: 858 / 10! = 1716. The soccer team can have 1,716 different starting lineups.

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The correct option is (e): the dimensions of the one with the largest area 28 ft. x 28 ft.

let l be the length of rectangle and

   w be the width of rectangle

given perimeter 112

       i.e.  2 (l + w) = 112

       l + w = 56

         then l = 56 - w

area A = l w

           = w (56 - w)

         A' = 56 – 2 w

for critical point A' = 0, then

                56 – 2 w = 0

                 w = 28,

then l = 56 - w = 56 - 28 = 28

l × w = 28 × 28

a perimeter is a direction that surrounds a two-dimensional shape. The word comes frae the Greek peri (around) a meter (measure). The time period may be used both for the direction or its length - it can be thought o because the length o the outline o a form. the perimeter of a circle or ellipse is cried its circumference.

Calculating the perimeter has widespread realistic packages. the fringe may be used tea calculate the length o fence required tea surround a yard or garden. the perimeter of a wheel (its circumference) describes Hou far it's going to roll in a revolution. similarly, the amount o string wound around a spoil is related tea the spoil’s perimeter.

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P(M ≤ $7) = Φ(-1/3√n) where Φ is the standard normal cumulative distribution function (cdf).

Suppose that the amount of margin that a pipe, valve and fitting distributor can make on a specific type of fitting is a random variable with mean $8 and standard deviation of $3.

The distributor sells those fitting to a large number of customers on a regular basis. The probability that the average margin for the distributor is normally distributed is: Normal Distribution

This is because of the following reasons: The pipe, valve and fitting distributor makes sales to a large number of customers on a regular basis.

The Central Limit Theorem (CLT) is the basis of the normal distribution assumption. It's possible to use it since it's a random variable. It is also possible to verify the assumption since the sample size is large. Furthermore, a normally distributed variable has well-known properties, making it easier to calculate probabilities.

Let X be the amount of margin that the pipe, valve and fitting distributor makes on a specific type of fitting.Suppose X ~ N(8, 3²). Let M be the average margin of the distributor.

Then: M ~ N(8, 3/√n)

Where n is the number of fittings sold.

The probability that the average margin is less than or equal to $7 is given by:

P(M ≤ $7)

= P(Z ≤ (7-8)/(3/√n))

= P(Z ≤ -1/3√n) where Z is the standard normal distribution

Therefore, P(M ≤ $7) = Φ(-1/3√n) where Φ is the standard normal cumulative distribution function (cdf).

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The product pick list generated by an order processing system is used by warehouse personnel or fulfillment staff to gather and prepare items for shipment.

The product pick list is a crucial tool in the order fulfillment process. It contains detailed information about the products ordered by customers, such as their names, quantities, and locations within the warehouse. Warehouse personnel or fulfillment staff rely on this pick list to efficiently gather the required items from the shelves or storage areas.

When an order is received, the order processing system automatically generates a pick list based on the products included in the order. This pick list serves as a guide for the warehouse staff, enabling them to quickly locate and pick the items needed to fulfill each order accurately. The pick list typically organizes the items in a logical order, such as by aisle or location, to optimize the picking process and minimize the time spent searching for items.

By using the product pick list, the warehouse personnel can ensure that the correct items are picked and prepared for shipment, reducing the likelihood of errors or mix-ups. This helps streamline the order fulfillment process, improve efficiency, and ultimately deliver a positive customer experience.

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Answer:

Vowels: E,O,E

Constants: G,M,T,R,Y

Step-by-step explanation:

Vowels: A,E,I,O,U

Constants: Any thing else

GEOMETRY

Vowel: E,O,E

Constants: G,M,T,R,Y

Hope this helps!

Answer:

Step-by-step explanation:

Vowels, in general, are {a, e, i, o, u}, and all 21 of the remaining letters are consonants, with y treated as either a vowel or a consonant.

In the word GEOMETRY, the vowels are {e, o} but also {y|, and

the consonants are {g, m, t, r}

Please note:  the word "constants" does not apply here.  It's "consonants."

The total amount of money she deposited is $45 + $45 = 2x$45

The number in the log as a power of the base y = -6.

What is  logarithmic identity ?

Logarithmic identities are mathematical formulas or rules that are used to manipulate logarithmic expressions. These identities are derived from the properties of logarithms and can be used to simplify or solve logarithmic equations.

The following are some commonly used logarithmic identities:

Product rule: log_a (x * y) = log_a (x) + log_a (y)

This identity states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the individual numbers.

Quotient rule: log_a (x / y) = log_a (x) - log_a (y)

This identity states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the individual numbers.

According to the question:
To write the number in the log as a power of the base, we can use the following logarithmic identity:

log_a (x) = y is equivalent to\(a^y = x\)

Using this identity, we can rewrite the logarithmic expressions as follows:

y = log3 243 can be written as \(3^y = 243\)

y = log2 1/64 can be written as \(2^y = 1/64\)

Now, we can solve for y by taking the appropriate power of both sides of each equation:

For the first equation, we can write:

\(3^y = 243\)

\(3^y = 3^5 (since 243 = 3^5)\)

Therefore, y = 5.

For the second equation, we can write:

\(a^y = 1\)

Since any non-zero number raised to the power of 0 is equal to 1, we have:

\(a^y = a^0\)

Therefore, y = 0.

For the third equation, we can write:

\(2^y = 1/64\)

\(2^y = 2^-6 (since 1/64 = 2^-6)\)

Therefore, y = -6.

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