determine whether the set s is linearly independent or linearly dependent. s = {(8, 2), (3, 5)}

The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

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The balance sheet that correctly represents the engineer's income, expenses and balance is illustrated below.

We should know that a balance sheet is a summary of assets and liabilities and income and expenses of a  legal person. We are told that the balance sheet shows a bi-weekly net pay.

This implies that a month has two bi-weeks, therefore every income and expense is multiplied by 2 to get the following figures.

Income                                             Amount

Bi-weekly income                          $2,175.25

Total Monthly Income                   $4,350.50

Expenses                 Percent                              Amount

Housing                        35%                                $1,522.68

Food/Household          10%                               $435.05

Savings                         10%                                $435.05

Transportation              15%                                $652.58

Debt                              5%                                   $217.53

Entertainment               6%                                   $261.03

Medical/Personal Care 5%                                  $217.53

Giving                             5%                                 $217.53

Clothing                         4%                                  $174.02

Miscellaneous               5%                                 $217.53

                                                                          $4,350.50

Balance

Income $4,350.50

Expenses $4,350.50

Balance $0

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The probability of rolling a number greater than 2 is 10/10 or 100%.

When rolling a 12-sided die with the set of equally likely outcomes {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, we want to find the probability of rolling a number greater than 2.

Since all the numbers in the given set are greater than 2, we can determine the probability by simply considering the ratio of the favorable outcomes to the total possible outcomes.

In this case, there are 10 favorable outcomes (3 to 12) and 10 total outcomes.

Thus, the probability of rolling a number greater than 2 is 10/10, which simplifies to 1, or 100%

. So, when rolling this specific 12-sided die, you have a 100% chance of rolling a number greater than 2.

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The R9,000 loan offer can be analyzed as follows;

A loan is a financial agreement that is made between a lender and a borrower, such that the borrower accepts a certain amount of money provided by the lender, which is to be paid back after a specified period of time, with an interest.

The total amount which has to be paid as repayment for the loan can be obtained by finding the product of the monthly installment and the total number of months to repay the loan:

Total amount Theo pays = R318.92 × 48 = R15308.16

The reasons banks and other financial institutions offer loans to people that did not apply for loans includes;

Theo's investment options can be analyzed as follows;

Option 1: Investment with simple interest calculation

Interest earned = R9,000 × 8% × 4 years = R2,880

The total value of the investment after 4 years = R9,000 + R2,880 = R11,880

Option 2: Investment with compound interest calculation

The total value of the investment after 4 years = R9,000 × (1 + 7%)⁴ = R11,797.16409

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Answer:

Step-by-step explanation:

the answer is 64 because 126-62 is 64

Answer:

His shifts were 1 hour each

Step-by-step explanation:

If Oliver worked a total of 14 hours in a span of 14 shifts, that would mean he worked 1 hour per shift because 1(14) = 14.

14/14 = 1 hour

Answer:

Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor .

Step-by-step explanation:

This question was not properly written

Complete Question

Select all the pairs of equivalent expressions.

a. (4³)³ and 4³ ⋅ 4³

b. (3⁴)⁴ and 3⁸ ⋅ 3⁸

c. 6⁴ ⋅ 3⁴ and 18⁸

d. 4³ ⋅ 5³and 20³

e. (4³)³ and 4³ ⋅ 4³ ⋅ 4³

2. Choose an equivalent expression for 12³ • 12⁹• 12⁴ • 12².

a. 12^4

b. 12^18

c. 12^35

d. 12^216

3. Choose an equivalent expression for 10⁶ ÷ 10⁴.

a. 10^2

b. 10^3

c. 10^10

d. 10^24

4. Select all the expressions that are equivalent to 7⁸ • 7.

a. 7³• 7³

b. 7^18/7^9

c. (7³)³

d. 7⁴ + 7⁵

e. 7⁴ • 7⁵

5. Is this equation correct?

6³⋅ 7³= 42³

A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³.

B. Yes; 6³ • 7³is equal to (6 • 7 • 3) or (42 • 3).

C. No; 6³ • 7³ is equal to (6 • 7 • 3) or (42 • 3).

D. No; 6³ • 7³ is equal to (6 • 7)³+ 3 or 42⁶.

Answer:

1 The correct answer is

d. 4³ ⋅ 5³ and 20³

e. (4³)³ and 4³ ⋅ 4³ ⋅ 4³

2b. 12^18

3 a = 10²

4a. 7³ • 7³

c. (7³)³

e. 7⁴ • 7⁵

5 A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³.

Step-by-step explanation:

1) Select all the pairs of equivalent expressions.

These are the correct options

d. 4³ ⋅ 5³and 20³

4³ × 5³ = 8000

20³ = 8000

e. (43)3 and 43 ⋅ 43 ⋅ 43

2. Choose an equivalent expression for 12³ • 12⁹• 12⁴• 12².

For an Algebraic Expressions,

We have the rule

x^a × x^b = x ^a+ b

Hence: 12³ • 12⁹• 12⁴ • 12².

= 12^3+9+4+2 = 12^18

Hence, b. 12^18

3. Choose an equivalent expression for

10⁶ ÷ 10⁴.

For an Algebraic expressions

x^a ÷ x^b = x ^a - b

Therefore

10⁶÷ 10⁴ = 10²

a. 10^2 Is the correct option

4. Select all the expressions that are equivalent to 7⁸ • 7.

7⁸ . 7= 7^8+1

= 7^9 or 7⁹

The equivalent expressions are:

a. 7³ • 7³ = 7⁹

b. 7^18/7^9 = 7⁹

c. (7³)³ = 7⁹

e. 7⁴ • 7⁵ = 7⁹

5. Is this equation correct?

6³ ⋅ 7³ = 42³

A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³

Answer:

the length of inch is 20

Step-by-step explanation:

because 21 inch -20=1

Answer:

x = 70

Step-by-step explanation:

Answer:

Step-by-step explanation:

b/c we know that the inside angles of a triangle add to 180

180 = 38 + x + x + 2

180 = 40 + 2x

140 = 2x

70 = x

The probability that a student passed the course depends on various factors, such as the grading criteria, the weightage of homework in the overall assessment, and the performance of the students.

To determine the probability that a student passed the course given that they did not complete their homework, we need to consider the grading criteria and the weightage of homework in the overall assessment. If the completion of homework carries a significant weight in the final grade, students who did not complete their homework would have a lower chance of passing the course. However, if homework is not a major factor in the grading scheme, other factors such as class participation, performance on exams, and projects might have a greater impact on the final grade.

Additionally, the overall performance of the students in the class would affect the probability. If the majority of students perform well in the course, irrespective of completing their homework, the probability of passing the course without completing homework could be higher. On the other hand, if the majority of students who pass the course have consistently completed their homework, the probability would be lower.

Without specific information about the grading criteria, weightage of homework, and the performance distribution of the students, it is challenging to provide an exact probability. Therefore, the probability that a student passed the course given that they did not complete their homework can vary based on these factors and would need more specific information to be determined accurately.

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Answer:

1,2,5

Step-by-step explanation:

That is just the definition of an element :) the other two answers contradict these.

Step-by-step explanation:

option A (2)

thank you !

hope it helps

The order would be DE < FD < EF. To order the sides of triangle ΔDEF from shortest to longest, you need to compare the lengths of the sides.

1. Determine the lengths of sides DE, EF, and FD.
2. Compare the lengths to find the shortest side.
3. Identify the next shortest side.
4. The remaining side will be the longest.

Once you have the side lengths, simply arrange them in ascending order (from shortest to longest) to answer your question. For example, if DE is 3 units, EF is 5 units, and FD is 4 units, the order would be DE < FD < EF.
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The airline should sell at most 78 tickets to ensure that the probability of having at least one empty seat is less than 10%.

a. We can use the sample proportion of 0.90 to construct a confidence interval for the population proportion of people who will show up. Assuming the normality of the sample proportion, the 95% confidence interval is given by:

sample proportion ± margin of error

where the margin of error is given by:

margin of error = z* * sqrt(p * (1-p) / n)

Here, z* is the critical value of the standard normal distribution for a 95% confidence level, which is 1.96. Using the given information, we have:

n = 400

p = 0.90

Plugging in these values, we get:

margin of error = 1.96 * sqrt(0.90 * 0.10 / 400) ≈ 0.045

So the 95% confidence interval is:

0.90 ± 0.045

Therefore, we can be 95% confident that between 85.5% and 94.5% of the people who buy a ticket will actually show up.

b. Let x be the number of tickets the airline sells. Assuming that the probability of a person showing up is independent across different flights, the number of people who show up on any given flight follows a binomial distribution with parameters n = x and p = 0.90. We want to find x such that the probability of having at least one empty seat is less than 10%.

In other words, we want to find x such that:

P(X < n) ≤ 0.10

where X is a binomial random variable with parameters n and p. Using the complement rule and the binomial probability formula, we can rewrite this as:

P(X ≥ n) ≥ 0.90

1 - P(X < n) ≥ 0.90

1 - ∑(k=0 to n-1) [ n choose k * p^k * (1-p)^(n-k) ] ≥ 0.90

We can solve for n numerically using a calculator or software. One way to do this is to start with a small value of n and increase it until we find the smallest value of n that satisfies the inequality. Using the software, we can find that n ≈ 78.

The airline should sell at most 78 tickets to ensure that there is less than a 10% chance of running out of seats.

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Overall, the perception of the inhabitants of Caldas, Colombia regarding the effects of climate change on water quality reflects their concerns about the potential impacts on their local water resources.

The inhabitants of the department of Caldas, Colombia have a perception that climate change is affecting the quality of water in their region. They believe that the changing climate patterns, such as altered rainfall patterns and increased temperatures, are leading to negative impacts on water quality. This perception highlights the concerns and awareness among the local population regarding the potential consequences of climate change on the water resources of Caldas.

The perception of the inhabitants of Caldas, Colombia regarding the effects of climate change on water quality is likely influenced by various factors. Firstly, the region has experienced changes in rainfall patterns, including alterations in the timing, intensity, and duration of rainfall events. These changes can have significant implications for water quality as they can affect the runoff patterns, erosion rates, and the dilution of pollutants in water bodies.

Secondly, rising temperatures associated with climate change can contribute to increased evaporation rates, leading to reduced water availability and higher concentrations of pollutants in water bodies. Higher temperatures can also affect the ecological balance of aquatic ecosystems, potentially causing the proliferation of harmful algal blooms or disrupting the natural habitats of aquatic species.

Furthermore, the perception of the inhabitants may be influenced by local observations and experiences. They might have noticed changes in water color, odor, or taste, or they may have witnessed the decline in aquatic biodiversity or the occurrence of water-related health issues.

Overall, the perception of the inhabitants of Caldas, Colombia regarding the effects of climate change on water quality reflects their concerns about the potential impacts on their local water resources. It highlights the need for scientific research, sustainable water management practices, and public awareness campaigns to address the challenges posed by climate change and ensure the availability of clean and safe water for the region.

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Answer: 70

Step-by-step explanation: 90-18/3=84

84 - 14 =  70

70 + 14 = 84

Answer:

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Step-by-step explanation:

The initial-value problem is given by the differential equation dy/dt = y²e^(-t), with the initial condition y(0) = a, where t ≥ 0. To solve this initial-value problem, we can use the method of separation of variables.

First, we separate the variables by writing the equation as dy/y² = e^(-t) dt. Then we integrate both sides of the equation. Integrating the left side gives us ∫(1/y²) dy, which simplifies to -1/y. Integrating the right side gives us ∫e^(-t) dt, which simplifies to -e^(-t).

Now, we have -1/y = -e^(-t) + C, where C is the constant of integration. We can solve for y by taking the reciprocal of both sides, which gives y = -1/(-e^(-t) + C). Simplifying further, y = 1/(e^(-t) - C).

To find the particular solution that satisfies the initial condition y(0) = a, we substitute t = 0 and y = a into the equation. This gives a = 1/(e^0 - C), which simplifies to a = 1/(1 - C). Solving for C, we find C = 1 - 1/a.

Finally, substituting this value of C back into the general solution, we have y = 1/(e^(-t) - (1 - 1/a)), which simplifies to y = 1/(e^(-t) + 1/a - 1).

In summary, the solution to the initial-value problem dy/dt = y²e^(-t), y(0) = a, where t ≥ 0, is y = 1/(e^(-t) + 1/a - 1)

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The ship is approximately 27.97 km from its starting point.

Among the options provided, the closest answer is 28 km (option b).

To find the distance of the ship from its starting point, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ship has traveled a distance of 25 km at 35° N of E, and then a distance of 15 km at 50° N of W. Let's break down the distances into their north and east components.

For the first leg:

North component = 25 km * sin(35°)

East component = 25 km * cos(35°)

For the second leg:

North component = 15 km * sin(50°)

East component = -15 km * cos(50°)  [Note the negative sign since it's N of W]

Now, let's calculate the north and east components:

For the first leg:

North component = 25 km * sin(35°) ≈ 14.3 km

East component = 25 km * cos(35°) ≈ 20.4 km

For the second leg:

North component = 15 km * sin(50°) ≈ 11.5 km

East component = -15 km * cos(50°) ≈ -9.63 km

To find the total north and east components, we add the corresponding components together:

Total North component = 14.3 km + 11.5 km ≈ 25.8 km

Total East component = 20.4 km + (-9.63 km) ≈ 10.8 km

Now, we can use the Pythagorean theorem to find the distance from the starting point:

Distance = √((Total North component)² + (Total East component)²)

        ≈ √((25.8 km)² + (10.8 km)²)

        ≈ √(665.64 km² + 116.64 km²)

        ≈ √(782.28 km²)

        ≈ 27.97 km

Therefore, the ship is approximately 27.97 km from its starting point.

Among the options provided, the closest answer is 28 km (option b).

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Answer:

2/4

Step-by-step explanation:

Answer:

B and C

Step-by-step explanation:

vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent = they are equally large.

the angles listed in B and C are mirrored across either an imaginary or a directly visible line. and that makes them vertical angles.

Answer:

Our problem is \(x^2-2x+6=0\), but as we can see, we are unable to factor. We have to use the quadratic equation to solve.

\(x^2-2x+6=0\)

\(\frac{-b+-\sqrt{b^2-4ac}}{2a}\)

Positive Quadratic Formula:

\(\frac{-(-2)+\sqrt{(-2)^2-4(1)(6)}}{2(1)}\)

\(=\frac{2+\sqrt{4-24}}{2}\\=1+\frac{\sqrt{-20}}{2}\)

Negative Quadratic Formula:

\(\frac{-(-2)-\sqrt{(-2)^2-4(1)(6)}}{2(1)}\)

\(=\frac{2-\sqrt{4-24}}{2}\\=1-\frac{\sqrt{-20}}{2}\)

Since both of our answers are the square root of a negative number, we know that the quadratic equation has no real solution.

*We could have also used the Discriminant Test to determine whether the quadratic equation has real roots or not. However, for our means, the quadratic equation seems enough.

Answer:

D. No real Solution

Step-by-step explanation:

Hello!

Let's use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

In our equation:

This comes from the standard form of a quadratic: \(ax^2 + bx + c\)

Now, solve:

Since the radicand (-5) is negative, there are no real solutions. The correct answer is Option D.

The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²

Surface area is the total area that the surface of an object occupies. It is a measure of how much area is covered by the exterior of an object. The formula for the surface area of a cylinder is:

Where r = radius of the base and h = height of the cylinder.

Here we have

Diameter of the cylinder = 2.8 cm

Radius of the cylinder = 2.8/2 = 1.4 cm

Height of the cylinder = 3.7 cm  

Using the formula,

The surface area of a cylinder SA= 2πr² + 2πrh

The surface area of the cylinder

= 2π(1.4)² + 2π(1.4)(3.7)

= 2π(1.4)² + 2.8π(3.7)

Here, the total surface area of the cylinder will equal the amount of wrapping paper needed to completely cover the cylinder

Therefore,

The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²

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hi i think its A. SA = 2π(1.4)2 + 2.8π(3.7) hope this helped have a nice day! :)

Answer:

Step-by-step explanation:

The probability of occurring event A is 23% or 0.23.

To find the probability of event A:

Divide the number of events in A to the total number of events.

Number of events in A = 12

Total number of events = 12+20+20

=52

P(A)=Number of events in A/Total number of events

\(=\frac{12}{52}\)

Divide both sides by 12:

\(=\frac{3}{13}\)

\(=0.23\)

\(=23\) %

Hence, the probability of occurring event A is 23% or 0.23.

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FMECA is a bottom-up hardware approach to risk assessment. It is an inductive, or data-driven, linking elements of a failure chain as follows: Effect of Failure, Failure Mode, and Causes/Mechanisms. To estimate the reliability of software, most software prediction models use the probability density function to predict "Mean Time To Failure."

FMECA is a systematic and structured analytical methodology used to identify potential failures in a system, equipment, process, or product, and to assess the effect and probability of those failures. FMECA stands for Failure Modes, Effects, and Criticality Analysis. FMECA is similar to FMEA (Failure Modes and Effects Analysis) in that it is used to identify failure modes and assess their risk.

However, FMECA goes beyond FMEA by analyzing the criticality of each failure mode. This makes it an effective tool for identifying the most significant failure modes and prioritizing them for corrective action. A Probability Density Function (PDF) is a function that describes the likelihood of a random variable taking on a particular value.

PDF is used in software prediction models to estimate the reliability of software by predicting "Mean Time To Failure" (MTTF). MTTF is the average time between failures of a system, equipment, process, or product.

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Answer:

y = 30

z = 115

Step-by-step explanation:

z° + 65° = 180°

(Exterior Angles on the same side of transversal)

z° = 180° - 65°

z° = 115°

z = 115

(5y - 85)° + z° = 180°

(Linear pair angles)

(5y - 85)° + 115° = 180°

(5y - 85)° = 180° - 115°

(5y - 85)° = 65°

5y - 85 = 65

5y = 65 + 85

5y = 150

y = 150/5

y = 30

The probability that a randomly selected student is taking a math class or an English class is 0.79.

Using the formula for the union of two events, P(A or B) = P(A) + P(B) - P(A and B), where A is the event "taking a math class" and B is the event "taking an English class", we can find the desired probability:

P(A or B) = 0.76 + 0.75 - 0.72 = 0.79

So,  "0.79" (which is given in upto two decimal places) is the probability that a randomly selected student is taking a math class or an English class.

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By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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Answer:

XXL and XXL

Step-by-step explanation:

Answer:

XXL AND XXL

Step-by-step explanation:

:) hope its right