Use calculus to evaluate the following limits. Write DNE if the limit does not exist. Show all your work. 3x³+x²+1 x³+1 a. lim x →[infinity]0 x²-x x-3 x²-2x-3 b. lim C. lim x²-1 x-1 X-1 d. lim e. lim. f. 4 x-00-x²+8x-1 x+0x³+x²–2x x²+2 lim x+-1x²+1

Answer:

12

Step-by-step explanation:

of what means a division or a distribution

so this could mean percentage, a unit or just a number

to find a distributor we multiply and this should be the given equals number -6

Therefore we can find answer with applying multiply sign to get

-2 x - 6 = 12

As -12 / -2 means -2 of  12 = -6  

Answer:

A is correct

Step-by-step explanation:

Answer:

A and B

Step-by-step explanation:

The present worth (PW) of each project is calculated based on the given cash flows and the firm's minimum attractive rate of return (MARR) of 10% per year.

To calculate the PW of each project, we discount the cash flows at the MARR of 10% per year. The PW for each project is determined as follows:

Project 1: EOY 0: -\(10,000 + (5,125 / (1 + 0.10)^1) + (5,125 / (1 + 0.10)^2) + (5,125 / (1 + 0.10)^3) = $10,682.13\)

Project 2: EOY 0: -\(8,500 + (4,450 / (1 + 0.10)^1) + (4,450 / (1 + 0.10)^2) + (4,450 / (1 + 0.10)^3) = $9,202.79\)

Project 3: EOY 0: \(11,000 + (5,400 / (1 + 0.10)^1) + (5,400 / (1 + 0.10)^2) + (5,400 / (1 + 0.10)^3) = $9,834.71\)

The project with the highest PW is recommended. In this case, Project 1 has the highest PW of $10,682.13, so it would be the recommended project.

The IRR for each project can be determined by finding the discount rate that makes the PW equal to zero. Using the cash flows provided, the IRR for each project can be calculated using a trial-and-error approach or financial software. Let's assume the IRRs are as follows:

Project 1: IRR ≈ 17.5%

Project 2: IRR ≈ 15.3%

Project 3: IRR ≈ 13.8%

The project with the highest PW may differ from the project with the largest IRR due to the timing and magnitude of cash flows. The PW takes into account the timing of cash flows and discounts them to the present value. It represents the total value created by the project over its lifetime. On the other hand, the IRR considers the rate of return that equates the present value of cash inflows to the initial investment. It represents the project's internal rate of return.

Therefore, a project with a higher PW indicates higher overall value, while a project with a larger IRR implies a higher rate of return. These measures can lead to different rankings depending on the cash flow patterns and the MARR.

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The conditions for a sampling distribution of a sample mean, when you know the true involve random sampling, independence, and a large enough sample size.

The conditions for a sampling distribution of a sample mean, when you know the true mean, are as follows:

1. Random Sampling:

The samples should be selected randomly from the population to ensure that they are representative of the entire population.

2. Independence:

Each sample should be independent of the others.

This means that the outcome of one sample should not influence the outcome of another sample.

3. Sample Size:

The sample size should be large enough to ensure that the sampling distribution approximates a normal distribution.

In general, a sample size greater than 30 is considered sufficient.

Random sampling is important because it helps to minimize bias and ensure that the sample is representative of the population.

Independence is necessary to avoid any potential confounding factors that may influence the results.

Lastly, a sufficiently large sample size is needed to satisfy the central limit theorem, which states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution.

These conditions are important to ensure the validity and reliability of the statistical analysis.

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Answer:

Maksim's answer and explanation are not correct

The actual domain is 2 < x < Infinity

Step-by-step explanation:

The domain of a function is the set that is made up of the possible inputs of the function

The given function is f(x) = √(x - 2)

Maksim's response for the domain of f(x) is x ∈ R ('x' is a member of the set of all real numbers

The function is not defined when x < 2, at which the expression, x - 2, will become negative, and for which the square root of the negative number is imaginary

Therefore, the domain for which the function is defined is all real numbers larger than 2, which can be presented as follows;

The domain of f(x) = 2 < x < ∞

Therefore Maksim is wrong as the actual domain is limited to 2 < x < ∞.

The length on the blueprint is approximately 0.2667 units.

To find the length on the blueprint, we can set up a proportion using the given information.

Let's denote the length on the blueprint as "x".

According to the blueprint, the width is 4 inches, and the actual length is 20 feet. We can set up the following proportion:

Width on Blueprint / Actual Width = Length on Blueprint / Actual Length

Plugging in the values:

4 inches / 20 feet = x / 16 feet

Now, we need to convert the units to be consistent. Since we have feet in the denominator on both sides, we can convert inches to feet by dividing by 12:

(4 inches / 12 feet) / 20 feet = x / 16 feet

Simplifying:

1/3 / 20 = x / 16

Now, we can cross multiply:

(1/3) × 16 = 20 ×x

Simplifying further:

16/3 = 20x

To solve for x, we can divide both sides by 20:

(16/3) / 20 = x

Simplifying:

16 / (3 × 20) = x

16 / 60 = x

Now, we can simplify the fraction:

4/15 = x

So, the length on the blueprint is 4/15 of a unit.

Alternatively, if you want to convert the fraction to decimal form, you can divide 4 by 15:

4 ÷ 15 ≈ 0.2667

Therefore, the length on the blueprint is approximately 0.2667 units.

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a. To find the joint pdf of Y1 and Y2, we can start by finding the transformation from (X1, X2) to (Y1, Y2):

Joint probability density function (joint PDF) is a concept used in probability theory and statistics to describe the probability distribution of multiple random variables simultaneously. It defines the likelihood of observing specific combinations of values for the variables.

Y1 = (X1/r1)/(X2/r2)

Y2 = X2

Solving for X1 and X2, we get:

X1 = r1Y1Y2

X2 = Y2

The Jacobian of this transformation is:

|J| = r1Y2

Using the transformation formula for joint pdfs, we have:

fY1,Y2(y1,y2) = \(fX1,X2(x1,x2) / |J|\)

                    = \(fX1(r1y1y2, y2) * fX2(y2) / r1y2\)

            =  \((1/2^(r1/2) * Gamma(r1/2)^(-1) * (r1y1y2)^(r1/2 - 1) * e^(-r1y1y2/2)) *(1/2^(r2/2) * Gamma(r2/2)^(-1) * y2^(r2/2 - 1) * e^(-y2/2)) / (r1y2)\)

Simplifying this expression, we get:

\(fY1,Y2(y1,y2) = (r1r2/2^(r1/2 + r2/2) * Gamma(r1/2)^(-1) * Gamma(r2/2)^(-1) * y1^(r1/2 - 1) * y2^(r2/2 - 1) * e^(-(r1y1+y2)/2)) / y2\)

b.  Y1 has an F distribution.

The marginal probability density function (marginal PDF) is a probability density function that describes the distribution of a single random variable from a joint probability distribution. It is obtained by integrating the joint PDF over all possible values of the other variables, effectively "marginalizing" or summing out the unwanted variables.

To find the marginal pdf of Y1, we integrate the joint pdf over Y2:

fY1(y1) = ∫fY1,Y2(y1,y2) dy2

       =\((r1r2/2^(r1/2 + r2/2) * Gamma(r1/2)^(-1) * Gamma(r2/2)^(-1) * y1^(r1/2 - 1) * e^(-r1y1/2) * ∫y2^(r2/2 - 1) * e^(-y2/2) / y2 dy2)\)

       =\((r1/(r1 + 2y1))^(r1/2) / (B(r1/2, r2/2) * 2^(r1/2))\)

where B is the beta function.

Recognizing the expression inside the integral as the pdf of a chi-square distribution with r2 degrees of freedom, we can evaluate the integral and simplify the result to get:

\(fY1(y1) = (r1/r2)^(r1/2) * y1^(r1/2 - 1) * (1 + r1/r2 * y1)^(-(r1+r2)/2) / (B(r1/2, r2/2) * 2^(r1/2))\)

This is the pdf of an F distribution with r1 and r2 degrees of freedom, where F = Y1/(r1/r2).

Therefore, we have shown that Y1 has an F distribution.

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Answer:

.75=x

Step-by-step explanation:

Usually, when finding x we must flip around the equation.

4x+5=3

8-5=3

4x=3

3/4=.75

So the answer is .75

Answer:

382 in ^3

Step-by-step explanation:

The 95% confidence interval for the mean amount (in milligrams) of nicotine in the sampled brand of cigarettes is C.39.2 to 40.8

We can use a t-table or a calculator to calculate the t-score. The t-score for a 95% confidence interval with 22 degrees of freedom (n-1) is around 2.074.

When we plug in the values, we get:

CI = 40 ± 2.074 * 1.8/√23 = 40 ± 0.763 = (39.237, 40.763)

As a result, the 95% confidence interval for the mean nicotine content of the studied cigarette brand is (39.237, 40.763) mg.

Because 39.2 to 40.8 is the closest response choice, the answer is 39.2 to 40.8.

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Answer:

k = 12

Step-by-step explanation:

(x^2 + 16x + 64) - (x^2 + 4x - 32)

distributing - 1

x^2 +16r + 64 - x^2 - 4x + 32

12x +96

take a factor of 12

12(x + 8)

K = 12

There are 56 number of possible ways are there to select two items so that at least one jeans is chosen.

Combinations:

Combinations is the number of ways in which you can choose r elements out of a set containing n distinct objects.

The combination formula that will allow you to determine the number of combinations in no time:

C(n,r) = n! / (r! (n-r)!)

where:

C(n,r) is the number of combinations;

n is the total number of elements in the set; and

r is the number of elements you choose from this set.

Given,

A shop has 5 different shirts and 7 different jeans.

Here we need to find how many number of ways ways are there to select two items so that at least one jeans is chosen.

Let's say,

First, you picked up 1 jeans and 1 shirt …

Then the number of ways to do that is

=> ⁵C₁ x ⁷C₁

=> 5 x 7

=> 35

Similarly, in second case you picked up the only 2 jeans

number of ways to do that is

=> ⁷C₂

=> 21

So the final answer will be sum of both the cases that is

=>( ⁵C₁ x ⁷C₁ ) + (⁷C₂)

=> 35+21

=> 56 ways

Therefore, there are 56 possible ways to select two items so that at least one jeans is chosen.

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Answer:

64585128

Step-by-step explanation:

hope it may help you

Rose gets 12 refills by a coffee shop.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A coffee shop sells a mug for $8.95. Each refill costs $1.50.

And, Last month Rose spent $26.75 on a mug and refills.

Let number of refills she get = x

So, We can formulate;

⇒ $8.95 + $1.50x = $26.75

⇒ 8.95 + 1.50x = 26.75

⇒ 1.50x = 26.75 - 8.95

⇒ 1.50x = 17.80

⇒ x = 17.8 / 1.5

⇒ x = 12

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Answer:

I think 24 weeks that's my answer

The measure of angle ABC is given as follows:

m < ABC = 145º.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

In a parallelogram, we have that the opposite angles are supplementary.

The opposite angles for this problem are given as follows:

Hence the measure of angle ABC is given as follows:

m < ABC + 35º = 180º.

m < ABC = 145º.

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The correct answer is P(B) is equal to 0.22.

To find P(B), we can use the formula for total probability:

P(B) = P(B∣A) * P(A) + P(B∣A') * P(A')

Given that P(A∣B) = 0.3, P(A∣B') = 0.1, and P(A) = 0.6, we can substitute these values into the formula:

P(B) = 0.3 * 0.6 + 0.1 * (1 - 0.6)

Simplifying the equation:

P(B) = 0.18 + 0.1 * 0.4

P(B) = 0.18 + 0.04

P(B) = 0.22

Therefore, P(B) is equal to 0.22.

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The root mean square (RMS) of the function f(t) = 110 sin(50t) on the interval [0, 2π] is approximately 110 times the square root of 2π.

To find the root mean square (RMS) of the function f(t) = 110 sin(50t) on the interval [0, 2π], we follow these steps

Square the function f(t):

f²(t) = (110 sin(50t))² = 110² sin²(50t)

Integrate the squared function over the interval [0, 2π]:

∫[0, 2π] (110² sin²(50t)) dt

∫[0, 2π] (110²(1 - cos²(50t))) dt

Apply the trigonometric identity: sin²(x) = 1 - cos²(x):

\(\int\limits^0_{2\pi }\) (110² - 110² cos²(50t)) dt

Evaluate the integral:

= 110²t - (110²/2)\(\int\limits^0_{2\pi }\) cos(100t) dt

Apply the definite integral of cos(x) over the interval [0, 2π]:

= 110²t - (110²/2) * [sin(100t)/100] [0, 2π]

= 110²t - (55²/100) * (sin(200π) - sin(0))

Since sin(0) = 0 and sin(200π) = 0, the second term becomes zero:

= 110²t

Evaluate the integral over the interval [0, 2π]:

= 110² * (2π - 0) = 110² * 2π

Take the square root of the result to find the RMS:

RMS = √(110² * 2π) = 110 * √(2π)

Therefore, the RMS of the function f(t) = 110 sin(50t) on the interval [0, 2π] is 110 * √(2π).

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--The given question is incomplete, the complete question is given below " Question 2 i) The root mean square (RMS) of a function f(t) on domain [a,b] is defined to be fRMS Solf(t)]2 dx V b a Given f(t) = 110 sin(50t), find the rms on interval [0, 2π] "--

Step-by-step explanation:

you do 58.45 / 617.50 × 100 = 9.46%

hope this helps you

The statement "In the study of logic, p q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim pvq is, as a whole claim, true" is true.

This principle is known as the exclusive disjunction, which means that the truth value of p v q is only true if either p or q is true, but not both.

In other words, if both p and q are true, then the statement p v q is still considered true because only one of them needs to be true for the whole statement to be true. This concept is essential in the study of logic as it helps to clarify the relationship between different statements and propositions.

Furthermore, this principle is often used in mathematics, computer science, and other fields that rely heavily on logical reasoning. It enables us to make accurate predictions and draw valid conclusions from a set of given premises or statements.

In conclusion, the exclusive disjunction is a crucial concept in the study of logic that helps us understand the truth value of compound claims. Therefore, the statement "In the study of logic, p q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim pvq is, as a whole claim, true" is true.

In the study of logic, the statement "p ∨ q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim p ∨ q is, as a whole claim, true" is actually false. This is because the given description refers to the "inclusive" sense of the disjunction (OR) operator, rather than the exclusive sense.

In logic, there are two types of disjunctions: inclusive and exclusive. The inclusive disjunction, represented by p ∨ q, is true when at least one of p or q is true. This means that if both p and q are true, the compound claim p ∨ q is also true, which matches the given description in the question.

On the other hand, the exclusive disjunction, represented by p ⊕ q or p XOR q, is true only when either p or q is true, but not when both are true. If p and q are both true, then the compound claim p ⊕ q is false.

So, the statement in the question actually describes the inclusive disjunction, not the exclusive disjunction, and is therefore false.

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Answers:

a)  2710 kg/m³

b)  5149 kg

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

Work shown for part a)

density = mass/volume

density = (6775 kg)/(2.5 m³)

density = (6775/2.5) kg/m³

density = 2710 kg/m³

-----------------------------------

Work shown for part b)

density = mass/volume

mass = density * volume

mass = (2710 kg/m³) * (1.9 m³)

mass = (2710*1.9) kg

mass = 5149 kg

Using similar phrases in combination, the abbreviated expression is: \(5x^2 + y^2 + 4y + 3x\)

Exponents, also referred to as powers, are a type of mathematical notation that illustrates the process of repeatedly multiplying a single integer. They are a shortened form of phrases that require repeatedly multiplying a base integer by itself.

A little increased number to the right of the base integer is an exponent. For example: aⁿ

Now, let us consider the given question:

First, we can simplify the expression by combining like terms. The terms with \(x^2\) are \(4x^2 + x^2 = 5x^2\). The terms with \(y^2\) are \(-y^2 + y^2 + y^2 = y^2.\) The terms with y and x are 4y + 3x.

So, the simplified expression is: \(5x^2 + y^2 + 4y + 3x\)

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Answer:

k=100

y the varies inversely as x

\(y \alpha {x}^{ - 1} \)

that is y is equal to inverse of x

introducing a constant k, you have

\( k = x \times y \\ 5 \times 20 \\ 100\)

a) probability of each event are 0.12, 0.25, 0.21, 0.42 b) events in this distribution are mutually exclusive. c) probability that an employee is male is 0.63 d) This experiment is collectively exhaustive

a. To determine the probability of each event, first calculate the total number of employees: 12,000 + 25,000 + 21,000 + 42,000 = 100,000. Next, divide the number of employees in each event by the total number of employees:
- Female and union: 12,000/100,000 = 0.12
- Female and nonunion: 25,000/100,000 = 0.25
- Male and union: 21,000/100,000 = 0.21
- Male and nonunion: 42,000/100,000 = 0.42

b. The events in this distribution are mutually exclusive, as each employee falls into one and only one category (e.g., an employee cannot be both male and female, or both union and nonunion).

c. To find the probability that an employee is male, add the probabilities of the male events:
Male and union (0.21) + Male and nonunion (0.42) = 0.63. So, the probability of an employee being male is 0.63.

d. This experiment is collectively exhaustive because the four events cover all possible employee categories in the textile industry (based on gender and union membership). The sum of the probabilities for all events equals 1 (0.12 + 0.25 + 0.21 + 0.42 = 1), indicating that all possibilities are accounted for.

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Answer: 8000

Step-by-step explanation:

From the question, we are informed that the expression 10³ × 2^w models the population of the bacteria after w weeks.

The number of bacteria that will be present in 3 weeks will then be:

= 10³ × 2^w

= 10³ × 2³

= 1000 × 8

= 8000 bacterias

Answer:

- red : x^2 + 2

- blue : x - 4

12 total

4+3=7

12-7=5

5km left

According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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