Simplify these rational expression. x^4+5x^3-2x^2+1/x^2+1

Sample size required is 333, 42, 97 and 33,285, respectively using  confidence level and different parameters of standard deviation.

To estimate a population mean to within 40 units with 99% confidence and a population standard deviation of 200, the sample size required can be calculated using the formula

n = (Zα/2)² * (σ²) / (E²)

where Zα/2 is the z-score corresponding to the desired level of confidence (99% in this case), σ is the population standard deviation, and E is the desired margin of error (40 units).

Plugging in the values, we get

n = (2.576)² * (200)²/ (40)²

n = 332.84

Therefore, a sample size of at least 333 should be used.

If the population standard deviation is changed to 50, the same formula can be used with the new value of σ:

n = (2.576)² * (50)²/ (40)²

n = 41.68

Therefore, a sample size of at least 42 should be used.

If using a 95% confidence level, the z-score changes to 1.96

n = (1.96)² * (200)²/ (40)²

n = 96.04

Therefore, a sample size of at least 97 should be used.

To estimate the population mean to within 10 units, the margin of error (E) is changed to 10 in the formula, and the sample size is recalculated

n = (2.576)² * (200)² / (10)²

n = 33,284

Therefore, a sample size of at least 33,285 should be used.

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The required sample size should be 166 to estimate the population mean within 40 units with 99% confidence, given a population standard deviation of 200.

To determine the required sample size for estimating a population mean with a given level of confidence and margin of error, we can use the formula:

n = (Z * σ / E)^2

Where:

n = Sample size

Z = Z-score corresponding to the desired confidence level (in this case, 99% confidence corresponds to a Z-score of 2.576)

σ = Population standard deviation

E = Margin of error (in this case, 40 units)

Substituting the given values into the formula, we have:

n = (2.576 * 200 / 40)^2

Simplifying further:

n = (12.88)^2

n ≈ 165.6544

Since the sample size must be a whole number, we round up the value to the nearest integer:

n = 166

Therefore, the required sample size should be 166 to estimate the population mean within 40 units with 99% confidence, given a population standard deviation of 200.

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The area of the rectangle is found to be 20 - 2·√(10) sq. units.

Let x be the length of the rectangle.

Let y be the width of rectangle.

Then, length is reduced by 4 and with is increased by 5.

x - 4 = y + 5 , (becomes square) ....eq 1

Area of square = 40 cm²

Then,

(x - 4) × (y + 5) = 40 cm²

From eq 1

(y + 5) × (y + 5) = 40 cm²

y² + 10y + 25 = 40

y² + 10y + 25 - 40 = 0

y² + 10y - 15 = 0

Solving equation by quadratic formula:

y = -5 + 2·√(10)

Then, for x:

x - 4 = 5 + -5 + 2·√(10) = 2·√(10)

x = 4 + 2·√(10)

Now,

Area of the rectangle, A = x × y

Put the values:

A = (-5 + 2·√(10)) × (4 + 2·√(10))

A = 20 - 2·√(10)

Thus, the area of the rectangle is found to be 20 - 2·√(10) sq. units.

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Answer: 360cm^2

Step-by-step explanation: the rectangle is 24 by 15

Answer:

A() it is located _25 and is the right of point A on the number line

Answer:

The Answer is C

Step-by-step explanation:

so if u draw out a number line, point A will be on the left side of the number line or in this case "0". So it is saying "point b is 5 less than point A" so since Point A is "-20" and it says "5 less than point A" so it would be adding up 5 more to -20 so it would be -25. But if it was 5 more than point A it would have been -15. If u take an example of money, like if u owe someone $20, it would be -$20 in your balance, and if he or she says u need to owe me 5 more $'s cuz there was damage now in your balance it would be -25.

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Answer:

 A is -4 B is 2.5 C is 4 D is -2.5

Step-by-step explanation:

Answer:

In the screenshot

Step-by-step explanation:

not sure about D, The square root of 6 is 2.449 and negative because of the line in front so -2.449? I'm not sure

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

An isotope with z > 83, which lies close to the band of stability, will generally decay through decay.

Therefore, an isotope with z > 83, which lies close to the band of stability, will generally decay through decay.

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Substitute the value of b in the equation to check which equation satisfy the value of b.

For b + 6 = 10,

b = 3 is not solution of equation.

For b + 8 = 11,

So b = 3 is solution of equation b + 8 = 11.

For equation 5 - b = 8,

So b = 3 is not solution of equation.

For equation b - 6 = 9,

So b = 3 is not a solution of equation.

Answer: b + 8 = 11

Dueck’s maximal error capacity regions are smaller than average error capacity regions for multi-user channels.

The average error capacity region for a multi-user channel is defined as the set of all probability distributions on the input space such that the probability of error for each user is less than a certain amount.

In contrast, the maximal error capacity region for a multi-user channel is defined as the set of all probability distributions on the input space such that there exists a probability distribution on the output space for which the probability of error for each user is less than a certain amount.

The maximal error capacity region is always smaller than the average error capacity region for a multi-user channel. This is because the maximal error capacity region is a subset of the average error capacity region.

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The standard form for the quadratic function is g(x) = x² + 2x - 1.

The standard form for a quadratic function is:

f(x) = ax² + bx + c

where a, b, and c are constants.

Out of the given options, the quadratic function that is already in standard form is:

g(x) = x² + 2x - 1

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Answer:

1. 20

2. 16

3. 50

4. 0

5. 12

6. -12

7. 45

8. 99

9. 54

10. 49

You're suppose to do the opposite of each problem. So since it's division, you would multiple. (Example: x/4=2  (4 x 2=8) (x=8) (8/4=2<---- answer proven)

A score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.

To compare the two scores, we can convert them to z-scores, which tell us how many standard deviations a particular value is from the mean. The formula for z-score is:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For the first score of x = 70 on an exam with μ = 82 and σ = 8, the z-score is:

z = (70 - 82) / 8 = -1.5

For the second score of x = 60 on an exam with μ = 72 and σ = 12, the z-score is:

z = (60 - 72) / 12 = -1.0

The z-score for the first score is lower than the z-score for the second score, which means that the first score is further below its mean than the second score is below its mean. Therefore, we can say that a score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.

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Biweekly salary last year algebraically will be S = (27)A.  Semimonthly salary this year algebraically will be S = ( A + R )6.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Last year, Andrea's annual salary was A dollar and she was paid biweekly. This year she received a raise of R dollars per year. She is now paid semimonthly.

Biweekly salary last year algebraically will be:-

S = (27)A.

Semimonthly salary this year algebraically will be:-

S = ( A + R )6.

Therefore, the biweekly salary last year algebraically will be S = (27)A.  Semimonthly salary this year algebraically will be S = ( A + R )6.

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Answer:

2x2 - 5x - 12 = 0.

(2x + 3)(x - 4) = 0.

2x + 3 = 0 or x - 4 = 0.

x = -3/2, or x = 4.

By using the concept of maxima of a function, it can be calculated that

For maximum area,

Length of the pen perpendicular to wall = 125 m

Length of the pen parallel to wall = 250 m

What is maxima of a function?

Maxima of a function gives the maximum value of the function within a given interval or within the entire domain.

Here, the concept of maxima of a function will be used

Let the side of the pen perpendicular to the wall be x meter and the side of the pen parallel to the wall be y meter

A shed is used as one side of the pen.

Length of fencing = x + y + x = (2x + y) meter.

By the problem,

2x + y = 500

y = 500 - 2x

Area of the pen (A) = xy

                                = x(500 - 2x)

\(\frac{dA}{dx} = \frac{d}{dx}(x(500 - 2x))\\\)

    = \(x(-2)+500-2x\\500 - 4x\)

For maximum area,

\(\frac{dA}{dx} = 0\\\)

\(500 - 4x = 0\\4x = 500\\x = \frac{500}{4}\\x = 125 \ m\)

y = 500 - 2 \(\times\) 125

y = 500 - 250

y = 250 m

\(\frac{d^2A}{dx^2} = \frac{d}{dx}(500 - 4x) = -4 < 0\)

Hence area is maximum

So, for maximum area,

Length of the pen perpendicular to wall = 125 m

Length of the pen parallel to wall = 250 m

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The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.

The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.

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a) To find the marginal cost, we need to find the derivative of the total cost function with respect to the rate of output (Q).

TC = 100Q - Q² + 0.3Q³

Marginal cost (MC) = dTC/dQ

= d/dQ(100Q - Q² + 0.3Q³)

= 100 - 2Q + 0.9Q²

To find the average cost, we need to divide the total cost by the rate of output (Q).

Average cost (AC) = TC/Q

= (100Q - Q² + 0.3Q³)/Q

= 100 - Q + 0.3Q²

b) To find the rate of output that results in minimum average cost, we need to find the derivative of the average cost function with respect to Q. Then, we set it equal to zero and solve for Q.

AC = 100 - Q + 0.3Q²

dAC/dQ = -1 + 0.6Q

= 0-1 + 0.6Q

= 00.6Q

= 1Q

= 1/0.6Q

≈ 1.67

Therefore, the rate of output that results in minimum average cost is approximately 1.67.

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Answer:

the ordered pair (0, 1/6)

Step-by-step explanation:

To reflect a function across the y-axis, we replace every occurrence of x with -x. Therefore, the function g(x) is given by:

g(x) = f(-x) = 1/6(2/5)^(-x)

To find an ordered pair on g(x), we need to choose a value of x and evaluate g(x). For example, if we choose x = 0, then:

g(0) = 1/6(2/5)^(-0) = 1/6

Therefore, the ordered pair (0, 1/6) is on the graph of g(x).

Categorical charts are useful in displaying nominal data or numerical data that splits nicely into different categories so you can quickly see comparative results and trends.

The type of chart that is useful in displaying nominal data or numerical data that splits nicely into different categories is called a categorical chart. Categorical charts allow you to quickly see comparative results and trends by displaying data in separate categories or groups. This makes it easier to identify patterns and trends in the data and to draw conclusions about the relationships between different variables.

Examples of categorical charts include bar charts, column charts, and pie charts. Bar charts and column charts are commonly used to display numerical data, while pie charts are often used to display proportional data. Categorical charts can be used in a variety of contexts, such as business, education, and scientific research, to help communicate complex data in a clear and concise manner.

Overall, categorical charts are a powerful tool for organizing and displaying data in a way that makes it easy to identify patterns and trends. By using these charts, you can quickly and accurately visualize complex data sets and draw conclusions about the relationships between different variables.

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Answer:

82 is the median

Step-by-step explanation:

True. If the equation Ax = b is consistent, it means there exists at least one solution x that satisfies the equation.

This implies that the vector b can be expressed as a linear combination of the columns of matrix A.

Let's assume the matrix A has n columns. In order for the equation to be consistent, there must exist a combination of the columns of A that can produce the vector b. This means that any vector in the range of A (the span of the columns of A) can be reached by multiplying A with an appropriate vector x.

Since the equation Ax = b is consistent, the vector b is in the range of A, and therefore, the columns of A span R^m, where m is the number of rows in matrix A. This implies that any vector in R^m can be expressed as a linear combination of the columns of A, demonstrating that the columns of A span R^m.

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Answer:

a. Actual size: 20 m x 15m

b. 1,000,000 : 1

Step-by-step explanation:

(a) Since scale is 1:1000, multiply both length and width on the floor pan to get actual length and width of house

a. Actual size

= 2 x 1000 cm x 1.5 x 1000 cm

= 2000 cm x 1500 cm

= 20m x 15m (since 1 m = 100 cm

(b) Area on plan = 2 x 1.5 = 3 cm²

Actual area = 2000 x 1500 = 3,000,000 cm²

Ratio of actual area to floor plan area
= 3,000,000 / 3 = 1,000,000 : 1

When we divide 27 by 7, we have 3; 3 * 7 = 21

27 - 21 = 6; we have a remainder of 6

Divide the remainder by 7, we have 6/7

Therefore, we have:

Answer:

105

Step-by-step explanation:

1,000 divided by 3.5% is 35

35 x 3 is 105

Since you are just asking for just the interest and not the total the answer is 105

The interest that Amy should pay is $105.

Given that,

Based on the above information, the calculation is as follows:

\(= 1000 \times 3.5\% \times 3\)

= 105

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The expression for the aggregate demand curve is AD: Y = 11.5 - 75π.The aggregate demand curve represents the relationship between the aggregate output (Y) and the inflation rate (π).

To calculate the expression for the aggregate demand curve, we need to combine the IS curve and the monetary policy curve. The aggregate demand curve represents the relationship between the aggregate output (Y) and the inflation rate (π).

Given:

Monetary policy curve: r = 1.5% + 0.75π

IS curve: Y = 13 - 100r

Substituting the monetary policy curve into the IS curve, we get:

Y = 13 - 100(1.5% + 0.75π)

Simplifying the equation:

Y = 13 - 150% - 75π

Y = 13 - 1.5 - 75π

Y = 11.5 - 75π

Therefore, the expression for the aggregate demand curve is:

AD: Y = 11.5 - 75π

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Answer:

-1 1/3

Step-by-step explanation:

4-8=-4

-4/3

-1 1/3

Hope this has helped. have a good day.

Answer:

-4/3

Step-by-step explanation:

First solve the numerator

4-8 = -4

Then divide by the denominator

-4/3

The result is -4/3

Answer:

2x(4x-8)=o

0Step-by-step explanation:

but i know this  3x^2-4x-8=-6

Answer:

x=0,2

Step-by-step explanation:

Here,

or, 3x=0                               or,    4x-8=0

or, x=0/3                              or,    4x=8

∴x=0                                 or,    x=8/4

                                       ∴ x=2

∴x=0,2

The graph that represents a function that has a positive leading coefficient is the one where the line is moving up and to the right.

A function is a set of mathematical operations that produces a unique output for each input value. A function is a mathematical tool that is used to model various phenomena and operations. Functions are used in many branches of mathematics and science to describe different relationships between variables and quantities.

A coefficient is a term that refers to a numerical factor that is multiplied to a variable or an algebraic term in an equation or function.

A graph is a visual representation of data that is displayed in a chart or diagram. Graphs are used to represent the relationship between different variables and to illustrate data in a clear and easy-to-understand format.

To find the graph that represents a function with a positive leading coefficient, we need to look at the slope of the line in each graph. The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate as you move along the line from left to right.If the slope of a line is positive, the line is moving up and to the right. If the slope of a line is negative, the line is moving down and to the right. If the slope of a line is zero, the line is horizontal.The graph that represents a function with a positive leading coefficient is the one where the line is moving up and to the right. This is because the coefficient of the x-term in a linear function determines the slope of the line, and a positive coefficient produces a line that is moving up and to the right.

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The following graph represents a function that has a positive leading coefficient:

The answer is letter B.

A leading coefficient is the coefficient of the first term of a polynomial in standard form.

The leading coefficient indicates the degree and direction of the polynomial function.

If the leading coefficient is positive, then the polynomial increases to the right and decreases to the left.

If the leading coefficient is negative, then the polynomial decreases to the right and increases to the left.

We can determine the leading coefficient of a polynomial function by examining the term with the highest degree of the function and the sign in front of it.

If the sign is positive, then the leading coefficient is positive.

If the sign is negative, then the leading coefficient is negative.

If the sign is not given, then the leading coefficient can be either positive or negative.

For example, the leading coefficient of the polynomial function y = 4x3 - 3x2 + 2x - 1 is 4, which is positive.

Therefore, the polynomial function increases to the right and decreases to the left.

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The total develop a product  amount capitalized for the patent through March 31, 2020, is $557,000.

To the total amount capitalized for the patent through March 31, 2020,  the research and development costs, the costs associated with obtaining the patent, and the legal fees for defending the patent.

The research and development costs incurred by Chan Resources to develop the product amount to $280,000. These costs are eligible for capitalization.

The costs associated with obtaining the patent total $97,000. These costs are also eligible for capitalization.

The legal fees paid for the successful Defense of the patent amount to $180,000. These fees are considered direct costs of maintaining and defending the patent and are also eligible for capitalization.

To calculate the total amount capitalized for the patent through March 31, 2020,

Research and development costs: $280,000

Costs associated with obtaining the patent: $97,000

Legal fees for defense: $180,000

Total amount capitalized for the patent through March 31, 2020:

$280,000 + $97,000 + $180,000 = $557,000

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Answer:

28

Step-by-step explanation:

Answer:

Miles: 250

Cost: $87.5

Step-by-step explanation:

Plan 1: 250x0.13=32.5

32.5+55=87.5

Plan 2: 250x0.15= 37.5

37.5+50=87.5