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Answer:

The right answer should be the second option: (16a^2)/(b^7)

The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression

Given data ,

Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.

So , on simplifying the equation , we get

= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²

= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²

= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²

Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.

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Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).

Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).

The interest accumulated in the account after the first and second year indicates;

The amount Miguel originally put into the bank is about $728

An interest is a reward or cost of borrowing or lending money.

Let P represent the amount Miguel deposited in the bank, and let r represent the interest rate in percentage, therefore, we get;

The amount in the account after the first year is; P + r·p = P·(1 + r)

P·(1 + r) = $757.12...(1)

The amount in the account after the second year can be obtained using the following formula;

Principal at the start of the second year = P·(1 + r)

Therefore; Amount = P·(1 + r)  + P·(1 + r) × r = P·(1 + r) × (1 + r) = P·(1 + r)²

P·(1 + r)² = $787.40...(2)

Equation (1) indicates that we get; (1 + r) = 757.12/P

Therefore; P·(1 + r)² = P·(757.12/P)² = 787.40

757.12²/P = 787.40

P = 757.12²/787.40 ≈ 728

The amount Miguel deposited in the bank is about $728

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Answer:

\(\frac{9344}{45}\)

Step-by-step explanation:

\(\frac{74752}{360}\)

Simplify by 8, and we get

\(\frac{9344}{45}\)

We can't simplify any more, so the answer is  \(\frac{9344}{45}\)

The required answer is the simplified fraction of the given problem 74752/360 is the whole fraction 9344/45, where 9344 represents the whole number part and 45 represents the fractional part.

To simplify the fraction 74752/360 as a whole fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both of them by it.

Step 1: Find the GCD of 74752 and 360. The GCD can be calculated using various methods, such as prime factorization or the Euclidean algorithm. In this case,  use the Euclidean algorithm.

Let's find the GCD using the Euclidean algorithm:

Divide 74752 by 360:

74752 ÷ 360 = 207 R 272

Divide 360 by 272:

360 ÷ 272 = 1 R 88

Divide 272 by 88:

272 ÷ 88 = 3 R 8

Divide 88 by 8:

88 ÷ 8 = 11 R 0

Since the remainder is 0, the GCD is the last non-zero remainder, which is 8.

Step 2: Divide both the numerator and denominator of the fraction by the GCD.

74752 ÷ 8 = 9344

360 ÷ 8 = 45

The simplified whole fraction is 9344/45.

A whole fraction refers to a fraction in which the numerator is equal to or greater than the denominator. It represents a whole number and a fraction together. For example, 3 1/4 is a whole fraction where the whole number part is 3 and the fractional part is 1/4.

Hence, the simplified fraction of the given problem 74752/360 is the whole fraction 9344/45, where 9344 represents the whole number part and 45 represents the fractional part.

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Answer:

1.4 centimeters.

Step-by-step explanation:

All you do is multiply the size of the bug (0.014) by how much the microscope will make it bigger (100). If you don't have a calculator just move the decimal two times to the right.

When we multiply our servings by a given amount, we're not multiplying our cost of cake by the same amount. This tells us that this is not proportional. One way to think about proportional relationships, we already said, that the ratio between the variables will be equivalent.

\( \frac{ab}{de} = \frac{bc}{ef} = \frac{ac}{df} \)=k

\( \frac{6}{18} = \frac{12}{ef} \)

\(ef = 36\)

\( \frac{12}{36} = \frac{ac}{15} \)

\(ac = 5\)

\( \frac{6}{18} = \frac{12}{36} = \frac{5}{15} = \frac{1}{3} \)

I hope it helps

Answer:-3x - 12 + 5x

Step-by-step explanation:

Answer:

\(1 < x < -1\)

Step-by-step explanation:

Given the inequality

\(|x| > 1\)

The modulus of x shows that x can be both positive and negative value.

If x is positive:

\(x > 1\)

\(1 < x\)

If x is negative:

\(-x > 1\)

Multiplying both sides of the inequality by minus will change the inequality sign

\(x < -1\)

Combining both inequalities:

\(1 < x < -1\)

Find the position on the number line in the attachment

Answer:

I believe the answer is 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Line A: y = 4

x can be anything greater than or equal to 0.

Line B: x = 8

y can by anything greater than or equal to 0.

The comments below the line answer do not have to be there. They are made so you can understand the question better.

The ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.

The idea of combinations can be used.

The number of ways to select k items from a set of n items is given by the formula for combinations:

C(n, k) = n! / (k! * (n - k)!)

In this case, n = 8 (the total number of routines they have learned) and k = 6 (the number of routines they will perform).

Using the formula, we can calculate:

C(8, 6) = 8! / (6! * (8 - 6)!)

= 8! / (6! * 2!)

The factorial function is represented in this case by the exclamation symbol (!).

The sum of all positive integers from 1 to n is the factorial of the number n.

Calculating the factorials involved:

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

2! = 2 * 1 = 2

Plugging in these values:

C(8, 6) = 40,320 / (720 * 2)

= 40,320 / 1,440

= 28

Therefore, the ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.

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The dimensions of the rectangle based on the information illustrated will be 4.5cm and 6cm.

Let the width = w

Let the length = 2w - 3

Area = 27

It should be noted that the area of a rectangle is illustrated as:

= Length × Width

(2w - 3)w = 27

2w² - 3w = 27

2w² - 3w - 27 = 0

2w² + 6w - 9w - 27 = 0

2w(w + 3) - 9(w + 3)

(2w - 9)(w + 3)

2w - 9 = 0

2w = 9

w = 9/2

w = 4.5m

Length = 2w - 3 = 2(4.5) - 3 = 9 - 3 = 6

Therefore, the dimensions of the rectangle based on the information illustrated will be 4.5cm and 6cm.

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The mean is 0.477514 (rounded to 6 decimal places).

The standard deviation is 0.288919 (rounded to 6 decimal places).

To calculate the mean and standard deviation, we will use the following formulas:

Mean = (sum of all values) / (number of values)

Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]

Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:

Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514

Therefore, the mean is 0.477514 (rounded to 6 decimal places).

Now we will calculate the standard deviation:

Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919

Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).

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The smallest positive debt that can be paid off using sticker trading is $7$ dollars.

To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.

Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.

The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.

In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.

Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.

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Answer: 411

Step-by-step explanation:

Answer:

Becky is 7 years old.

Step-by-step explanation: Let b - Becky's age ; Equation - 3b = 21. Divide both size by 3 to isolate the variable.

Answer:

Becky's 7 seven years old

Step-by-step explanation:

If 21 = 3x

x = 21/3

x = 7

Hope this helps :)

Pls brainliest...

Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.

To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:

Assumptions:

Tax depreciation is straight-line over five years.

Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.

Tax on salvage value is 30% of the difference between salvage value and book value of the investment.

The cost of capital is 12%.

Given:

Initial investment cost = $50,000

Useful life of the equipment = 5 years

To calculate the depreciation expense each year, we divide the initial investment by the useful life:

Depreciation expense per year = Initial investment / Useful life

Depreciation expense per year = $50,000 / 5 = $10,000

Now, let's calculate the book value at the end of each year:

Year 1:

Book value = Initial investment - Depreciation expense per year

Book value \(= $50,000 - $10,000 = $40,000\)

Year 2:

Book value = Initial investment - (2 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (2 \times$10,000) = $30,000\)

Year 3:

Book value = Initial investment - (3 \(\times\) Depreciation expense per year)

Book value = $50,000 - (3 \(\times\) $10,000) = $20,000

Year 4:

Book value = Initial investment - (4 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (4 \times $10,000) = $10,000\)

Year 5:

Book value = Initial investment - (5 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (5 \times $10,000) = $0\)

Based on the assumptions, the salvage value is $10,000 in Year 5.

If the asset is scrapped in Year 4, the salvage value is $15,000.

To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:

Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)

For Year 5:

Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)

For Year 4 (if scrapped):

Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)

Now, let's calculate the after-tax cash flows for each year:

Year 1:

After-tax cash flow = Depreciation expense per year - Tax on salvage value

After-tax cash flow = $10,000 - $0 = $10,000

Year 2:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 3:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 4 (if scrapped):

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $15,000 - $1,500 = $13,500

Year 5:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $10,000 - $3,000 = $7,000

Now, let's calculate the net present value (NPV) using the cost of capital of 12%.

We will discount each year's after-tax cash flow to its present value using the formula:

\(PV = CF / (1 + r)^t\)

Where:

PV = Present value

CF = Cash flow

r = Discount rate (cost of capital)

t = Time period (year)

NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment

Let's calculate the NPV:

PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)

PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)

PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)

PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)

PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)

NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000

NPV = $22,954.24 - $50,000

NPV = -$27,045.76

The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.

Therefore, the investment may not be favorable.

Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.

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The complete question may be like :

Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.

You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.

Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.

Th straight line equation in general case is

y = mx + b

where m is the slope

and b is the y intercept ( the point where the line crosses the y axis)

In this case we see value of b is equal to 3

just looking at the picture

now to find m , its suficient to have the coordinates of 2 points

looking at the picture, two points are

(2,2) and (-2,4)

then m is found by m = ( y- y')/(x-x')

now replace the values (2,2) and (-2,4)

m= (2-4)/(2-(-2))

so then m ,the slope is -1/2

and b = 3

finally write in slope intercept form

y= -1/2x + 3

The data set  0, 2, 5, 8, and 10 have a higher standard deviation but the same mean.

The average distance between each data item and the mean is known as the mean absolute deviation.

The gap between each data value and the mean in absolute terms is represented by this average.

The given data set is 2, 2, 5, 8, 8.

Now, The standard deviation has other uses than serving as a measurement for the normal distribution. It is more commonly used as a measure of spread.

To have a greater standard deviation the data should have more differences from each other.

Therefore, 0, 2, 5, 8, 10 have the same mean but greater standard deviation.

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Answer:

ok simple. lets start with 15/30, 15/30 is basically 1/2 because 15 is half of 30

1/3 is not to the half point of 3 the half point of 3 is 1/5. 2/3 is more than halfway of 3 as it is more than  1.5/3. Do I make sense?

Step-by-step explanation:

hope this helps!!

Answer:

\((x+4)^2+(y-4)^2=16\)

Step-by-step explanation:

A tangent is a straight line that touches a circle at only one point.

Since the circle is tangent to both axes, and the center of the circle is in the second quadrant, the center of the circle lies on the line y = -x.

As the circle is tangent to the x-axis, the distance between the center of the circle and the x-axis is equal to the radius of the circle.

Similarly, as the circle is tangent to the y-axis, the distance between the center of the circle and the y-axis is also equal to the radius of the circle.

Therefore, the center of the circle will be 4 units to the left of the y-axis and 4 units up from the x-axis. Therefore, the coordinates of the center are (-4, 4).

\(\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Substitute the center (-4, 4) and the radius, r = 4, into the standard equation of a circle:

\(\implies (x - (-4))^2+(y-4)^2=4^2\)

\(\implies (x+4)^2+(y-4)^2=16\)

Therefore, the equation of the circle that satisfies the given conditions is:

\(\boxed{(x+4)^2+(y-4)^2=16}\)

Answer:

i do not know because i am a 4rth grader

The mean GPA is greater than 2.75.

A= 4.zero, A- = 3.7, B+ = 3.three, and many others). total the first-class factors, and overall the credit hours. Divide the overall satisfactory points by means of the overall credit score hours.

Grade point average (GPA) is the measure used to summarise your instructional fulfillment at Griffith. After the ebook of final grades every trimester, your software and career.

GPA is calculated and could be utilized by the college to tell choices, which include the subsequent: educational progression.

Divide the total range of grade factors earned with the aid of the total number of letter-graded units undertaken.

mean GPA = total/50

                     ⇒2.75.

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The given statement for b is a positive real number and m and n are positive integers, is true.

An integer is a number with no decimal or fractional part, and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 2, -8...

Given that, b is a real number and m and n are positive integers.

According to the above information, the calculation is as follows:

\(b^\frac{m}{n} = \sqrt[n]{b^m} = (\sqrt[n]{b} )^m\)

Hence, the statement is true.

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Answer:

Step-by-step explanation:

It will be 18

Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.