(10 points) Find the length of the curve on the given interval. *(t)=(t cos(t), tsin(t),t), s Vu’+ d’du= du= (u Vu? 1 + )C u Vu’+ a² + a?lnlu+ Vu’+ a)+C ) [0,1] (Hint:

The answer is: True. When matrix A is upper triangular, its eigenvalues are located on its main diagonal. If you find the eigenvectors corresponding to each eigenvalue, you can construct an eigenvector matrix S.

An upper triangular matrix is a square matrix in which all entries below the main diagonal are zero. An eigenvector of a matrix A is a nonzero vector x such that Ax is a scalar multiple of x. That is, there exists a scalar λ such that Ax = λx.
For a complete upper triangular matrix, all of its eigenvalues are on the diagonal. To see this, consider the characteristic polynomial of a complete upper triangular matrix:
p(λ) = det(A - λI)
where I is the identity matrix. Since A is upper triangular, its determinant is the product of its diagonal entries, and det(A - λI) is a polynomial of degree n (the size of the matrix) in λ. Therefore, there are n roots of p(λ), which correspond to the eigenvalues of A. Since A is completely upper triangular, all of its eigenvalues are on the diagonal.

Now, let's consider the eigenvector matrix S of A. This is a matrix whose columns are the eigenvectors of A. Since A is upper triangular, any eigenvector of A must also be upper triangular (or zero). Therefore, the eigenvector matrix S must also be upper triangular. In summary, if a is a complete upper triangular matrix, then all of its eigenvalues are on the diagonal, and its eigenvector matrix S is upper triangular. Therefore, the statement is true.
"If A is a complete upper triangular matrix, then it has an upper triangular eigenvector matrix S." When a matrix A is upper triangular, its eigenvalues are located on its main diagonal. If you find the eigenvectors corresponding to each eigenvalue, you can construct an eigenvector matrix S. Since A is upper triangular, the eigenvector matrix S will also be upper triangular.

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Answer:

3x³yz³

Step-by-step explanation:

18x⁶y²z⁵/6x³yz²​ = 18/6 x⁶⁻³ y²⁻¹ z⁵⁻² = 3x³yz³

Both vertex angles will be same as its an isosceles triangle

Let each be x

According to angle sum property

\(\\ \sf \longmapsto x+x+50=180\)

\(\\ \sf \longmapsto 2x+50=180\)

\(\\ \sf \longmapsto 2x=180-50\)

\(\\ \sf \longmapsto 2x=130\)

\(\\ \sf \longmapsto x=\dfrac{130}{2}\)

\(\\ \sf \longmapsto x=60°\)

Answer:

C. e = 8.1

Step-by-step explanation:

e-3.1= 5

e = 5+3.1

e = 8.1

Answer:

5)m=11/10

6)m=-17/2

7)m=18.13

8)m=-26/9

BTW The M is an EXAMPLE

Step-by-step explanation:

Answer:

50 meter ka 10 km

Step-by-step explanation:

50 meter ka 10 km

Answer:

Only plot B

Step-by-step explanation:

Answer:

Only Plot B

Step-by-step explanation:

The points in plot A are randomly scattered, and there is no recognizable pattern. So, this plot indicates no correlation between the points Tyler scored and the points Nolan scored.

In plot B, the total points Tyler’s team scored appear to increase as the points Tyler scored increase. This pattern indicates a positive correlation between the two variables.

So, only plot B indicates a positive correlation.

The standard deviation is usually presented in conjunction with the mean in the description of a continuous variable to provide information about both the central tendency and the variability of the dataset.

In statistical analysis, the standard deviation is a measure of the spread or dispersion of a dataset. It quantifies how much the values in a dataset deviate from the mean or average value. When describing a continuous variable, the standard deviation is typically presented alongside the mean to provide a comprehensive understanding of the distribution of the variable.

The mean represents the central tendency or average value of the dataset, while the standard deviation provides information about the variability or spread around the mean. By considering both the mean and the standard deviation together, you can gain insights into both the central value and the degree of dispersion of the variable.

For example, let's say we have a continuous variable that represents the heights of a group of individuals. The mean height tells us the average height of the group, while the standard deviation indicates how much the heights of individuals vary around that average. A large standard deviation suggests that the heights are more spread out and less concentrated around the mean, while a small standard deviation indicates that the heights are more tightly clustered around the mean.

Therefore, when describing a continuous variable, presenting the standard deviation along with the mean provides a more complete picture of the dataset's central tendency and variability.

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Answer:

6

Step-by-step explanation:

\(\frac{2}{3}\) (18 - 9)

= \(\frac{2}{3}\) × 9 ( cancel 3 and 9 by 3 )

= 2 × 3 = 6

Answer:

6

Step-by-step explanation:

\(\frac{2}{3}\) (18 - 9)

Multiply \(\frac{2}{3}\) with 18 and 9. Which would look like this:

( \(\frac{2}{3}\) × 18 ) - ( \(\frac{2}{3}\) × 9 )

Calculate the values in the bracket and then subtract.

= \(\frac{36}{3}\) - \(\frac{18}{3}\)

= \(\frac{18}{3}\)

= 6

Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.

To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.

For Division A:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($230,000 / $2,120,000) * 100

Profit Margin ≈ 10.85%

For Division B:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($34,700 / $381,000) * 100

Profit Margin ≈ 9.11%

To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.

Net Income = Profit Margin * Sales

Net Income = 7% * $1,220,400

Net Income = $85,428

Return on Assets = Profit Margin * Asset Turnover

Return on Assets = 7% * 2.7

Return on Assets = 18.9%

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To find the critical numbers of the function f(x) = 12x^5 + 60x^4 - 100x^3 + 2, we need to find the values of x where the derivative of f(x) is equal to zero or undefined.

Let's start by finding the derivative of f(x):

f'(x) = 60x^4 + 240x^3 - 300x^2

Setting f'(x) equal to zero:

60x^4 + 240x^3 - 300x^2 = 0

Factoring out common terms:

60x^2(x^2 + 4x - 5) = 0

Setting each factor equal to zero:

60x^2 = 0   (gives x = 0)

x^2 + 4x - 5 = 0   (gives two solutions using quadratic formula)

Solving the quadratic equation, we have:

x = (-4 ± √(4^2 - 4(-5))) / 2

x = (-4 ± √(16 + 20)) / 2

x = (-4 ± √36) / 2

x = (-4 ± 6) / 2

The solutions for x are:

x = -5

x = 1

So, the critical numbers are A = -5, B = 0, and C = 1.

Now, to determine the behavior of f(x) at each critical number, we can examine the sign of the derivative f'(x) in the intervals surrounding these critical numbers.

Interval (-∞, A):

For x < -5, the derivative f'(x) = 60x^4 + 240x^3 - 300x^2 > 0. Therefore, f(x) is increasing in this interval.

Interval (A, B):

For -5 < x < 0, the derivative f'(x) = 60x^4 + 240x^3 - 300x^2 < 0. Therefore, f(x) is decreasing in this interval.

Interval (B, C):

For 0 < x < 1, the derivative f'(x) = 60x^4 + 240x^3 - 300x^2 > 0. Therefore, f(x) is increasing in this interval.

Interval (C, ∞):

For x > 1, the derivative f'(x) = 60x^4 + 240x^3 - 300x^2 > 0. Therefore, f(x) is increasing in this interval.

Now, let's determine whether f(x) has a local min, local max, or neither at each critical number.

At A = -5, since f(x) is increasing to the left of A and decreasing to the right of A, f(x) has a local maximum at x = -5.

At B = 0, since f(x) is decreasing to the left of B and increasing to the right of B, f(x) has a local minimum at x = 0.

At C = 1, since f(x) is increasing to the left of C and increasing to the right of C, f(x) does not have a local min or local max at x = 1.

Therefore, the answers are:

A = -5 corresponds to a local maximum (UMAX).

B = 0 corresponds to a local minimum (LMIN).

C = 1 corresponds to neither a local min nor local max (NETHEA).

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Answer:

7816422510

Step-by-step explanation:

(((5602689*12)/-6) - 186734) + ((568531+2605285376)*30)

((67232268/-6) - 186734) + (2605853907*30)

( -11205378 - 186734) + 78175617210

−11392112 + (78175617210)

= 7816422510

(a)  Lease the vehicle is Categorical

(b) Price pay  Quantitative

(c)  The overall attractiveness of your vehicle's exterior is Categorical

(d)  Average miles-per-gallon is Quantitative

Now, According to the question:

a. Did you purchase or lease the vehicle?  CATEGORICAL DATA

b. What price did you pay?  QUANTITATIVE DATA

c. What is the overall attractiveness of your vehicle's exterior? (Unacceptable, Average,  Outstanding, or Truly Exceptional)  CATEGORICAL DATA

d. What is your average miles-per-gallon?  QUANTITATIVE DATA

Quantitative data can be measured in numbers, e.g. 20 miles per gallon. While categorical data refers to non-numerical responses, e.g. higher quality, better looks, and is generally obtained by choosing one response from a group of available answers.

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The true proportion of the side lengths of the quadrilaterals is A'B'/AB

From the question, we have the following parameters that can be used in our computation:

Quadrilaterals ABCD and A'B'C'D

These quadrilaterals are similar

So, it means that the corresponding side lengths are proportional

So. we have

Side length = AB

Corresponding side length = A'B'

The true proportion is then represented as

k = Corresponding side length/Side length

Substitute the known values in the above equation, so, we have the following representation

k = A'B'/AB

Hence, the proportion is A'B'/AB

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The length of the line segment XY which was bisected at point M is;

1) 32

2) 6

1) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;

XM = YM and XM + YM = XY

We are given that;

XM = 3x + 1

YM = 8x - 24

Thus;

3x + 1 = 8x - 24

8x - 3x = 1 + 24

5x = 25

x = 25/5

x = 5

Thus;

XM = 3(5) + 1 = 16

YM = 8(5) - 24 = 16

XY = 16 + 16 = 32

2) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;

XM = YM and XM + YM = XY

We are given that;

XM = 5x + 8

YM = 9x + 12

Thus;

5x + 8 = 9x + 12

9x - 5x = 8 - 12

4x = -4

x = -1

XM = 5(-1) + 8 = 3

YM = 9(-1) + 12 = 3

XY = 6

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Answer:

height of the peak AB is 40 feet.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:In the figure attached, A is the peak of mountain AB, ED is Tyler who is 6 feet high. Mirror placed at C, is 20 feet from the base of peak. Tyler is 3 feet away from the mirror.1). When Tyler sees the peak in the mirror, angle of incidence " i " and angle of reflection " r " made by incident ray AC and reflected ray EC will be equal.Now we can easily say ∠ r = ∠ E ( Alternate angles )∠ i = ∠ A ( alternate angles)Since ∠ i = ∠ r Therefore, ∠ A = ∠ E∠B = ∠D = 90°and ∠ACB = ∠ECDHence  ΔABC is similar to ΔCDE.2). Corresponding sides of these similar triangles are AB and ED, BC and CD, AC and CE.3). tanE = tanE = 0.5 ∠ E =  degreesNow ∠E = ∠A = 26.57°Therefore, tan(26.57) = 0.5 = AB = Therefore, height of the peak AB is 40 feet.

Answer:

2.5

Step-by-step explanation:

3x-5(-3x+14)=-25

3x+15x-70=-25

18x-70=-25

     +70  +70

__________

18x=45

______

18     18

x=2.5

Answer:

x = 2.5

Step-by-step explanation:

y = -3x + 14                Ec. 1

3x - 5y = -25              Ec. 2

Replacing Ec. 1 in Ec. 2:

3x - 5(-3x+14) = -25

3x -5*-3x -5*14 = -25

3x + 15x - 70 = -25

18x = -25 + 70

18x = 45

x = 45/18

x = 2.5

Answer:

4 dolars left

Step-by-step explanation:

im smart

To calculate depletion expense, you need to determine the depletion per unit. The depletion per unit can be calculated by taking (cost of the resource) / total units of capacity.

Depletion is an accounting method used to allocate the cost of natural resources over their useful life. It is commonly used in industries such as mining, oil and gas extraction, and timber harvesting, where companies extract and deplete natural resources as part of their operations.

The first step in calculating depletion expense is to determine the cost of the resource. This includes all costs incurred to acquire and develop the resource, such as exploration costs, development costs, and acquisition costs. These costs are typically capitalized and then allocated over the estimated recoverable units of the resource.

Once you have determined the cost of the resource, you need to calculate the total units of capacity. This refers to the estimated amount of resource that can be extracted or harvested from the reserve. For example, in mining, it could be measured in tons of ore, while in oil and gas extraction, it could be measured in barrels or cubic feet.

To calculate the depletion per unit, divide the cost of the resource by the total units of capacity. This will give you the amount of depletion expense that should be recognized for each unit extracted or harvested.

It's important to note that there are different methods for calculating depletion expense, such as units-of-production method and percentage depletion method. The units-of-production method calculates depletion based on actual production or extraction during a given period. On the other hand, the percentage depletion method allows for a fixed percentage deduction from gross income based on statutory rates.

In conclusion, to calculate depletion expense, you need to determine the depletion per unit by dividing the cost of the resource by the total units of capacity. This allows for an appropriate allocation of costs over the useful life of natural resources.

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We need to round up to the next full number because we are unable to equation have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

We may divide the total number of persons by the capacity of each boat to determine the number of boats required to hold a party of 1,254 individuals:

8 individuals per boat times 1,254 passengers is 156.75 boats.

We need to round up to the next full number because we are unable to have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.

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Answer:

c = 7

d = 4

Step-by-step explanation:

To determine the values of c and d in the given equation, expand the brackets and rearrange the terms:

\(\begin{aligned}2(c-6x)+d(5x-1)&=2(4x+5)\\2c-12x+5dx-d&=8x+10\\5dx-12x+2c-d&=8x+10\\(5d-12)x+(2c-d)&=8x+10\end{aligned}\)

To solve for d, equate the terms in x:

\(\begin{aligned}(5d-12)x&=8x\\5d-12&=8\\5d&=20\\d&=4\end{aligned}\)

To solve for c, equate the constants and substitute the found value of d:

\(\begin{aligned}2c-d&=10\\2c-4&=10\\2c&=14\\c&=7\end{aligned}\)

Therefore, the values of c and d are:

Check by substituting the found values of c and d into the original equation:

\(\begin{aligned}2(c-6x)+d(5x-1)&=2(4x+5)\\\\c=7,\;d=4\implies 2(7-6x)+4(5x-1)&=2(4x+5)\\14-12x+20x-4&=8x+10\\20x-12x+14-4&=8x+10\\8x+10&=8x+10\end{aligned}\)

Answer:

Step-by-step explanation:

we know that the interior angles are supplementary,

(2x-10)+(4x+16)=180

2x-10+4x+16=180

6x=180+6

6x=186

x=31

Answer:x^2-16x+63

Step-by-step explanation: We just add up (x^2-17x+70)+(x-7). So, we have x^2 (-17x+x)+(70-7)= x^2 - 16x + 63.

The angle measures of the triangle are 90 degrees, 113.5 degrees, and 157.5 degrees.

The interior angles of a triangle can be calculated using the ratio 4 : 5 : 7. To find the angle measures, we must first find the sum of all three angles. This is done by adding 4 + 5 + 7, which gives us a total of 16.

Now, let's divide each angle's ratio by 16, which gives us the following results:

4/16 = 0.25, 5/16 = 0.3125, and 7/16 = 0.4375.

Multiply each of these numbers by 360 degrees, the total number of degrees in a triangle, and you will get the angle measures:

0.25 x 360 = 90 degrees,

0.3125 x 360 = 113.5 degrees, and

0.4375 x 360 = 157.5 degrees.

Therefore, the angle measures of the triangle are 90 degrees, 113.5 degrees, and 157.5 degrees.

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The probability that the alleged father was not the father is: 0.024, or 2.4% and The probability that the alleged father could be the father is: 0.953, or 95.3%.

To calculate the probability that the alleged father was not the father, we first need to calculate the z-score for a pregnancy length of 240 days and for a pregnancy length of 306 days. The z-score formula is:

where x is the pregnancy length, mu is the mean pregnancy length, and sigma is the standard deviation of pregnancy length.

For a pregnancy length of 240 days, the z-score is:

For a pregnancy length of 306 days, the z-score is:

To calculate the probability that the alleged father was not the father, we need to find the area under the normal distribution curve to the left of the z-score for a pregnancy length of 240 days and to the right of the z-score for a pregnancy length of 306 days, and then add these probabilities together. Using a standard normal distribution table or calculator, we find that the probability to the left of z = -3.08 is approximately 0.001, and the probability to the right of z = 2.00 is approximately 0.023. Therefore, the probability that the alleged father was not the father is:

To calculate the probability that the alleged father could be the father, we need to find the area under the normal distribution curve between the z-scores for a pregnancy length of 240 days and a pregnancy length of 306 days. Using a standard normal distribution table or calculator, we find that the probability between z = -3.08 and z = 2.00 is approximately 0.953. Therefore, the probability that the alleged father could be the father is:

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1. A simplified expression for the volume of the above prism is 15x³ cubic units.

2. Destiny made her mistake in step 1, and the correct solution with steps is shown below.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 3x × 5x ×  x

Volume of rectangular prism = 15x³ cubic units.

Question 2.

Given the following expression, \(\frac{5(x+2)-(8-x)}{2}\)

Step 1: we would open the bracket;

\(\frac{5x\;+\;10\;-\;8\;+\;x}{2}\)

Step 2: we would collect like-terms and evaluate;

\(\frac{5x\;+\;x\;+\;10\;-\;8}{2}\\\\\frac{6x\;+\;2}{2}\)

Step 3: we would split;

\(\frac{6x}{2}+ \frac{2}{2}\)

Step 4: we would divide;

3x + 1

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The equation that the graph of the systems of equations solve is:

x^2 - 2x + 3 = 2x^2 - 4x + 3

This is the second equation listed.

Answer as a fraction: x = 7/2

Answer as a decimal: x = 3.5

=====================================================

Work Shown:

n = sample size = number of values

n = 7

S = sum of the values

S = 5 + 7 + 2 + 6 + (x+1) + (x) + 7

S = 2x+28

Dividing S over n will get us the average, which in this case is 5

S/n = average

(2x+28)/7 = 5

2x+28 = 7*5

2x+28 = 35

2x = 35-28

2x = 7

x = 7/2 which is the answer in fraction form

x = 3.5 which is the answer in decimal form

The decimal value is exact without any rounding.

Answer:

3.5

Step-by-step explanation:

So the average of numbers can be defined as: \(average=\frac{sum}{amount}\)

In other words, (the sum of numbers) / (the amount of numbers)

In our case, there is 7 numbers. The sum can be written as: \(5+7+2+6+x+(x+1)+7\)

Adding like terms we get: \(28+2x\)

Now combing the sum and amount we get the fraction: \(\frac{28+2x}{7}\)

Since we're given the average, we can set that equal to our expression to solve for x:

\(5=\frac{28+2x}{7}\)

No all we do is use some basic algebraic properties

Original Equation:

\(5=\frac{28+2x}{7}\)

Multiply both sides by 28

\(35 = 28+2x\)

Subtract 28 from both sides

\(7=2x\)

Divide both sides by 2x

\(3.5=x\)