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ANSWER AND EXPLANATION:

Given:

Note that the acronym PEMDAS describes the order of operations and each letter stands for;

P - Parentheses

E - Exponents

M/D- Multiplication/Division (from left to right)

A/S - Addition/Subtraction (from left to right)

Following the above order of operations, we can go ahead and solve the expression as seen below;

Using the Distributive Property, we can go ahead and solve the expression as seen below;

We can see from the above that both methods give the same answer.

The relation between the events Y and W prevents us from completing the analysis.

The relation between the events Y and W prevents us from completing the analysis.

Case 1: W is more likely than Y then we have the following analysis:

Z, X, Y, and W are arranged in ascending order of more likeliness.

Case 2: Y is more likely than W then we have the following analysis:

Z, X, W, and Y are arranged in ascending order of more likeliness.

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Answer:

729 m^3

Step-by-step explanation:

Volume of cube = a^3

a= 9m

a^3= 9^3

hence volume = 729m^3

Student 1 made measurements with the least variability after performing the natural logarithm transformation on each measurement taken by the four students.

To determine which student made measurements with the least variability, we need to calculate the standard deviation for each student's set of measurements.

First, we calculate the natural logarithm of each measurement for all three students and compute their means

Student 1: ln(6.8), ln(6.3), ln(5.8), ln(5.8), ln(6.8)

Mean = 1.906

Student 2: ln(7.4), ln(3.6), ln(5.8), ln(5.3), ln(7.3)

Mean = 2.924

Student 3: ln(7.4), ln(3.6), ln(5.8), ln(5.3), ln(7.3)

Mean = 2.924

Then, we calculate the sample standard deviation for each student's set of measurements

Student 1: s = 0.367

Student 2: s = 1.592

Student 3: s = 1.592

Therefore, student 1 made measurements with the least variability, as their set of measurements has the smallest standard deviation.

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The slope of the line, m = -3

The equation passes through the point (-2, 5)

That is x₁ = -2, y₁ = 5

Substitute x₁ = -2, y₁ = 5, and m = -3

The point-slope form of the equatio of a line is:

y - y₁ = m(x - x₁)

y - 5 = -3(x - (-2))

y - 5 = -3(x + 2)

y - 5 = -3x - 6

y = -3x - 6 + 5

y = -3x - 1

The graph of the equation y = -3x - 1 is plotted below

Answer:

224

Step-by-step explanation:

200*0.12=24

200+24=224

The amount to be paid for the loan is $248.

'Simple interest is the interest amount for a particular principal amount of money at some rate of interest.

According to the given problem,

Principal amount (P) = $200

Rate of interest (r) = 12%

Time period (t) = 2 years

We know,

Final amount to be paid with interest (A) = P( 1 + rt )  

                                                                   = 200{ 1 + ( 0.12 × 2 )

                                                                   = 200( 1 + 0.24 )

                                                                   = 200 × 1.24

                                                                   = $248

Hence, we can conclude, we have to pay $248 for the loan.

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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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    2                                                                                                                                       -6x  -x+15 remove the parennthesies collect like tearms and reoreder like terms then you get your answer

Kate has 11 different types of flowers and wants to make a floral arrangement with 8 of them. There are 165 possible arrangements.So the correct option is option (b).

To calculate the number of possible floral arrangements, we can use the concept of combinations. Kate has 11 different types of flowers, and she wants to choose 8 of them for her arrangement.

The formula for combinations, denoted as C(n, r), is used to calculate the number of ways to select r items from a set of n items without considering their order. In this case, C(11, 8) is equal to 11! / (8! * (11-8)!), which simplifies to 165.

Hence, there are 165 possible floral arrangements that Kate can create using 8 out of her 11 different types of flowers.

Therefore, the correct answer is b. 165.

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One quarter is equal to the 0.25 dollars and one nickel equal to the 0.05 dollars. The total number of quarter in the Sang-Jin's piggy bank is 41.

Given information-

Sang-Jin has only quarters and nickels in her piggy bank.

She has 66 coins in the bank with a value of $11.50.

One quarter is equal to the 0.25 dollars.

One nickel equal to the 0.05 dollars.

Let x be the quarter and y be the nickels.

As there is total 66 coins. thus,

\(x+y=66\\ y=66-x\)

Suppose the above equation as the equation number 1.

As the total amount is $11.50. Thus,

\(0.25x+0.05y=11.50\)

Put the value of y from the equations 1 in the above equation. Thus,

\(0.25x+0.05(66-x)=11.50\\ 0.25x+3.3-0.05x=11.50\\ 0.2x=11.5-3.3\\ x=\dfrac{8.2}{0.2}\\ x=41\)

Thus the total number of quarter in the Sang-Jin's piggy bank is 41.

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Answer:

850

Step-by-step explanation:

you do $350(2.5)

Answer:

150

Step-by-step explanation:

Knowledge

The equation x² + 4x + 9 = 0 are complex numbers: x = -2 + i√5 and x = -2 - i√5.

To find the solutions for the equation x² + 4x + 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing this equation with the given equation x² + 4x + 9 = 0, we can see that a = 1, b = 4, and c = 9.

Plugging in these values into the quadratic formula, we have:

x = (-4 ± √(4² - 4(1)(9))) / (2(1))

x = (-4 ± √(16 - 36)) / 2

x = (-4 ± √(-20)) / 2

Since the value inside the square root is negative, we know that the solutions will involve complex numbers. Simplifying further, we have:

x = (-4 ± i√20) / 2

x = (-4 ± 2i√5) / 2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

x = -2 ± i√5

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Answer:

Yes

Step-by-step explanation:

Every input has only one output.

Answer:

A I assume

Step-by-step explanation:

I was between A and D ( The first one and the last) but I think a makes more sense

Answer:

87,500,306

Step-by-step explanation:

87 million 500 thousand 306

The number name for the numeral 87500306 is written as Eight crore seventy five lakh and three hundred six in  Indian system and Eighty seven million five hundred and three hundred six in International system.

To write the number name for the numeral 87500306.

A numeral is a figure, symbol, or group of figures or symbols denoting a number. Numerals are made up of digits; 1 is a digit, "123" is made up of 3 digits, and "123" is a numeral that represents the number one hundred twenty-three.

1. Indian system =8,75,00,306

Eight crore seventy five lakh and three hundred six.

2. International system 87,500,306

Eighty seven million five hundred and three hundred six.

So, the number name for the numeral 87500306 is written as Eight crore seventy five lakh and three hundred six in  Indian system and Eighty seven million five hundred and three hundred six in International system.

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Answer:

x > 12

Step-by-step explanation:

9x>108

x> 108/9

x > 12

Answer:

\( \boxed{ \tt{x > 12}}\)

Step-by-step explanation:

\(9x > 108 \\ x > \frac{108}{9} \\ x > 12\)

The equation of the line which passes through the coordinates (0,0) and (3.5,3.5) is y = x.

The slope intercept form of a line is given by:-

y = mx + c

Where,

m represents the slope of the line

c represents the y -intercept

(x,y) represents the coordinates of each point on the line.

We also know the slope of the line will be:-

(3.5-0)/(3.5-0) = 3.5/3.5 = 1

Hence, m = 1

Putting (0,0) in y = mx + c, we get,

0 = m*0 + c

0 = 0 + c

c = 0

Hence, the equation of the line is given by:-

y = x

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A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\sigma)= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) \(=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\)

So n \(=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

Te given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(\(\sigma\))= 2×1.55

Standard deviation of resistance(\(\sigma\))= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5\()^2\)

n=(15.996\()^2\)

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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Answer:

4

Step-by-step explanation:

Answer:2+2 = 4.............

Answer:

1. m<AOB = 50 degree

2. m<COD = 90 degree

3. m<BOD = 130 degree

4. m<AOD = 180 degree

Step-by-step explanation:

1. We see that <AOB has one leg at 0 and the other leg at 50 degrees, so the <AOB is 50 degrees.

2. We see that <COD has one leg at 0 and the other leg at 90 degrees, so the <COD is 90 degrees

3. We see that <BOD has one leg at 50 and the other leg at 180 leg, so the <BOD is 180 - 50 = 130 degree

4/ We see that <AOD has one leg at 0 and the other leg at 180 degrees, so the <AOD is 180 - 0 = 180 degrees

Answer:

5 inches = 12.7 cm

Step-by-step explanation:

Answer:

12.7

Step-by-step explanation:

if x = 2.54

then 5x = 12.7

5 x 2.54 = 12.7cm

The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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Answer:

8,024,832

Step-by-step explanation:

To solve the expression 27 × 18 × 3 × 43 × 128, you can follow these steps:

Start by solving the first two numbers:

Then, multiply the result by the next number:

Continue multiplying by the next number:

Finally, multiply by the last number:

Therefore, the final result of 27x18x3x43x128 is 8024832.

If one quarter of the Texas Guff coast is national seashore or state park  at the given figures, the length of the Texas shoreline is 0.8835km

The length is the measure of how long the shoreline is.

The given parameters sare

mileage of the seashore = 372 miles

Advancement of 0.0095 miles per year.

1/4 taken as gulf coast

Applying these parameters we have

372*0.0095*1/4*12

⇒ 96.102 miles

= 96.102/1000 = 0.96102 km

1000 miles = 1km

Therefore divide the value by 1000 to get

Therefore the length is 0.96102km

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Answer:

2 19/24 feet

Step-by-step explanation:

14 5/8 = 14 15/24

17 5/12 = 17 10/24 ==> 16 34/24

16 - 14 = 2

34/24 - 15/24 = 19/24

Answer = 2 19/24 feet

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-The Business Man

The term that suggests that the threat of loss has a greater impact on a decision than the possibility of an equivalent gain is prospect theory.

Prospect theory is a theory that describes how individuals make decisions under uncertainty. The theory suggests that people think about gains and losses differently and that the value they assign to a particular change in their situation depends on their current situation. The theory is based on the observation that people often violate the principle of expected utility. They make decisions that do not maximize their expected utility. The theory suggests that people evaluate outcomes based on changes from a reference point, rather than in absolute terms. This means that people are more sensitive to changes in their situation than to the situation itself.

For example, a loss of $100 is more painful than the pleasure of gaining $100, and the pleasure of gaining $100 is less than the pain of losing $100.

In summary, Prospect theory suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.

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The length of side LJ in triangle JKL is approximately 12.27 centimetre .

To determine the length of side LJ in triangle JKL, we can use the concept of similarity between triangles. When two triangles are similar, their corresponding sides are proportional.

Length of side XY in triangle XYZ: 8.7

Length of side XZ in triangle XYZ: 8.2

Length of side YZ in triangle XYZ: 7.8

Length of side JK in triangle JKL: 13.05

Let's set up the proportion using the corresponding sides:

XY / JK = XZ / LJ = YZ / KL

Substituting the given values:

8.7 / 13.05 = 8.2 / LJ = 7.8 / KL

Now, we can solve for LJ:

8.2 / LJ = 8.7 / 13.05

Cross-multiplying:

8.2 * 13.05 = 8.7 * LJ

106.71 = 8.7 * LJ

Dividing both sides by 8.7:

LJ = 106.71 / 8.7

LJ ≈ 12.27

Therefore, the length of side LJ in triangle JKL is approximately 12.27cemtimetre .

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