Homework Set 5: Problem 4 Previous Problem Problem List Next Problem (2 points) Convert the integral below to polar coordinates and evaluate the integral. 23/ Louis Lexy dx dy Instructions: Please enter the integrand in the first answer box, typing thata for 8. Depending on the order of integration you choose, enter dr and otheta in either order into the second and third answer boxes with only one dr or otheta in each box. Then, enter the limits of integration and evaluate the integral to find the volume. SS. A В. CE D Volume = Note: You can earn partial credit on this problem.

Answer: The Third one is correct

Step-by-step explanation:

Answer:

33cm

Step-by-step explanation:

add all

numbers..........................

Step-by-step explanation:

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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a) To save enough funds to purchase the car in 2.5 years, monthly deposits of $373.69 are required, while weekly deposits of $86.21 are needed.

b) With annual deposits of $2,000, it will take approximately 5 years to accumulate sufficient funds to purchase the car. For borrowing options, under Option 1, the monthly installment amount is $349.56, which reduces to $291.55 with a $1,800 lump sum contribution from parents. Under Option 2, the monthly installment amount is $237.63 for the first 36 months, doubling thereafter.

a) To calculate the minimum required monthly savings, we use the future value formula with monthly compounding: \($10,000 = PMT * ((1 + 0.06/12)^(2.5*12) - 1) / (0.06/12)\). Solving for PMT, the monthly deposit required is approximately $373.69.

b) Similarly, for weekly deposits, we use the future value formula with weekly compounding: \($10,000 = PMT * ((1 + 0.06/52)^(2.5*52) - 1) / (0.06/52)\). Solving for PMT, the weekly deposit required is approximately $86.21.

c) Using the future value formula for annual deposits: \($10,000 = $2,000 * ((1 + 0.06)^t - 1) / 0.06\). Solving for t, the time required to accumulate $10,000, we find it will take approximately 5 years.

d) For Option 1, the monthly installment amount can be calculated using the present value formula: \($13,000 = X * (1 - (1 + 0.06/12)^-30) / (0.06/12).\) Solving for X, the monthly installment amount is approximately $349.56.

e) With a lump sum contribution of $1,800, the remaining loan amount becomes $13,000 - $1,800 = $11,200. Using the same formula as in (d), the new monthly installment amount is approximately $291.55.

f) For Option 2, the monthly installment amount during the first 36 months is $Y. After 36 months, the monthly installment amount doubles. Using the present value formula: \($13,000 = Y * (1 - (1 + 0.06/12)^-36) / (0.06/12) + 2Y * (1 - (1 + 0.06/12)^-30) / (0.06/12)\). Solving for Y, the monthly installment amount is approximately $237.63.

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Answer:9.51

38.04/4 = 9.51

Have a good day :)

Answer:

9.51

Step-by-step explanation:

Answer:

3 cm < x < 25 cm

Step-by-step explanation:

Given 2 sides of a triangle then the possible values for the third side are

let the third side be x

difference of sides < x < sum of sides , that is

14 - 11 < x < 14 + 11

3 < x < 25

In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

A normally distributed phenomenon using standard nomenclature can be described as follows:

A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is \(10^2 = 100\).

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The global extreme values of f(x, y) subject to the constraints:

f_min ≈ 0.426

f_max = 14/5 ≈ 2.8

Lagrange multipliers are a mathematical method used to find the extreme values (maximum or minimum) of a function subject to one or more constraints.

Given function is;

f(x, y) = 4x³ + 4x²y + 5y²;    where, x, y ≥ 0, x + y ≤ 1

First, we need to set up the Lagrangian function:

L(x, y, λ) = 4x³ + 4x²y + 5y² - λ(x + y - 1)

Taking partial derivatives with respect to x, y, and λ and setting them equal to zero, we get:

∂L/∂x = 12x² + 8xy - λ = 0

∂L/∂y = 4x² + 10y - λ = 0

∂L/∂λ = x + y - 1 = 0

Solving these equations simultaneously,

x = 2/5, y = 3/5, λ = 26/25

We also need to check the boundary of the feasible region, which is the line x + y = 1. We can set y = 1 - x and substitute into the function f(x, y):

g(x) = f(x, 1-x) = 4x³ + 4x²(1-x) + 5(1-x)² = 4x³ - x² + 6x - 5

Taking the derivative of g(x) with respect to x and setting it equal to zero,

g'(x) = 12x² - 2x + 6 = 0

Solving for x,

x = (1 ± √7)/6

Therefore, the global maximum of f(x, y) subject to the constraints is:

f_max = f(2/5, 3/5) = 4(2/5)³ + 4(2/5)²(3/5) + 5(3/5)² = 14/5

f_min = f((1 - √7)/6, (5 + √7)/6) = 4((1 - √7)/6)³ + 4((1 - √7)/6)²((5 + √7)/6) + 5((5 + √7)/6)² ≈ 0.426

Therefore, the global extreme values of f(x, y) subject to the constraints:

f_min ≈ 0.426

f_max = 14/5 ≈ 2.8

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Answer:

(0, -5/2).

Step-by-step explanation:

The coordinates of the mid point of (x1, y1) and (x2, y2) are

(x 1 + x2)/2 , (y1 + y2)/ 2

So here we have:

(-3 + 3)/ 2, (-4 + -1)/2

= 0/2, -5/2

= (0, -5/2).

Answer:

-3<x<-2

And

3.5<x<4.5

Step-by-step explanation:

Answer:

y= 1/2x+3.5

Step-by-step explanation:

Answer:

y= 1/2x+3.5

I took the test this is right

Step-by-step explanation:

Work Shown:

y = 15.6 - 3.8x

y = 15.6 - 3.8*3

y = 4.2

The value of t in the upper tail, for 33 degrees of freedom and an area of 0.01, is ____________. (The exact value is missing and needs to be calculated.)

To find the value of t in the upper tail for 33 degrees of freedom and an area of 0.01, we can follow these steps:

Identify the degrees of freedom (df): In this case, the degrees of freedom are given as 33.

Determine the significance level (α): The area in the upper tail is given as 0.01, which corresponds to a significance level of 0.01 or 1% (since it's a one-tailed test).

Find the critical value (t-critical): We need to find the t-critical value associated with the significance level of 0.01 and 33 degrees of freedom.

Look up the t-critical value: Using statistical tables or software, we can find the t-critical value. By searching for the area of 0.01 in the upper tail and the corresponding degrees of freedom (33), we can find the critical t-value.

Once the t-critical value is obtained, it will represent the value of t in the upper tail for 33 degrees of freedom and an area of 0.01.

Please note that without the specific value of t-critical for the given conditions, we cannot provide the exact answer in this case. The calculation of t-critical can be performed using statistical software or by referring to t-distribution tables.

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In the equation y = $7.20x + $790, "y" represents the total cost. An equation is a mathematical statement that shows the relationship between two or more variables. In this equation, there are two variables - "x" and "y". The variable "x" represents the number of units produced or sold, while "y" represents the total cost.

The coefficient of "x" in the equation, which is 7.20, represents the variable cost per unit. This means that for each unit produced or sold, there is an additional cost of $7.20. The constant term, which is $790, represents the total fixed costs. Fixed costs are those costs that do not vary with the number of units produced or sold.To find the total cost of producing or selling a certain number of units, we can plug in the value of "x" into the equation and solve for "y". For example, if we want to find the total cost of producing 100 units, we can substitute x=100 into the equation:
y = $7.20(100) + $790
y = $720 + $790
y = $1510
Therefore, the total cost of producing 100 units is $1510. In summary, "y" represents the total cost in the given equation, which is determined by both fixed and variable costs.
In the equation y = $7.20x + $790, "y" represents option C: total costs. This equation has two components: "$7.20x" represents the variable costs per unit, where x is the number of units, and "$790" represents the total fixed costs. By adding these two components together, you get the total costs (y) for producing x units.

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The value of expression is 18.

A modulus function is a function that determines a number or variable's absolute value.  A function with absolute values is another name for it. This function's result is always positive. let's suppose if you want to find modulus of -2 then you will get 2 as the answer.

now according to question

4|a|+8-a at a=-2

here a is negative that means modulus will give us positive value.

put a =-2 in the expression and get the answer. modulus of -2 will give us +2

so

=4(2)+8-(-2)

=8+8-(-2)

=8+8+2

=18

hence the answer is 18.

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Answer:

Step-by-step explanation:

tru i took the test

By using the empirical rule, the approximate percentage of lightbulb replacement requests numbering between 19 and 40 is 99.3%.

The empirical rule is a statistical guideline which relates to bell-shaped distributions.

According to the rule, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.

We know that mean is 40 and a standard deviation is  7.

To find the approximate percentage of lightbulb replacement requests numbering between 19 and 40

z₁ = (19 - 40) / 7 ≈ -3.00

z₂ = (40 - 40) / 7 = 0.00

Here, z₁ is the number of standard deviations that 19 is below the mean, and z₂ is the number of standard deviations that 40 is above the mean.

According to the empirical rule, approximately 99.7% of the data falls within three standard deviations of the mean.

Therefore, the approximate percentage of lightbulb replacement requests numbering between 19 and 40 is

percentage ≈ 99.7% * (1 - 0.00135) ≈ 99.3%

Note that, we subtracted the area under the normal curve beyond three standard deviations, which is approximately 0.15%, from 100% to get the percentage of data within three standard deviations.

Therefore, approximately 99.3% of the daily requests to replace fluorescent lightbulbs fall between 19 and 40.

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-2.7 x 10^-2 in scientific notation is -0.027.

Answer:-0.027

Step-by-step explanation:

We keep all of the numbers that's why there's still the 2 and 7 and it's negative, then we move the decimal point left 2 times because that is the power of 10.

When the number next to the 10 is positive, we would move the decimal point to the right, when it is negative like it is here (-2), it is moved to the left. I hope that helps!

Answer:

6%.

Step-by-step explanation:

For arguments sake lets assume each fruit cost $1.

He spent $50 for the fruit.

His income from the 30 kg he sold was $35.

His income from  the remaining 20Kg  was $18.

Total income = $35 + $18 = $53

So his profit was  53 - 50 = $3.

= (3/50) * 100

= 6%

Answer:

-p - 8

Step-by-step explanation:

1 - 3p + 2p - 9 = -p - 8

To estimate the sum of a convergent alternating series with an absolute error of less than 0.001, we can use the Alternating Series Estimation Theorem.

This theorem states that the error made by approximating the sum of an alternating series with the nth partial sum is less than or equal to the absolute value of the (n+1)th term.

In other words, if we want the absolute error to be less than 0.001, we need to find the smallest value of n such that |a(n+1)| < 0.001, where a(n) is the nth term of the alternating series.

Then, using the Alternating Series Test, we know that the terms of the series must approach zero as n goes to infinity. So, if we want the absolute error to be less than 0.001, we need to find the smallest value of n such that:

|a(n+1)| < 0.001

Now, we can rearrange this inequality to solve for n:

|a(n+1)| < 0.001

a(n+1) < 0.001 (since the series is alternating)

(-1)(n+1) * a(n+1) < 0.001 (-1 to account for the alternating signs)

a(n+1) > -0.001

Since the terms of the series are decreasing in magnitude, we can assume that the smallest value of |a(n+1)|. Therefore, we can set n = 1 to get:

|a(2)| < 0.001

|(-1)2 * a(2)| < 0.001

|a(2)| < 0.001

So the absolute error will be less than 0.001 if we use the first two terms of the series to estimate the sum.

The total of the convergent alternating series can be estimated with a minimum of two terms and an absolute error of less than 0.001.

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Answer:

C

Step-by-step explanation:

EASY IVE DONE IT

Using conversion of units and the relationship between velocity, distance and time, it is found that the distance between the two stations is of:

c. 454 kilometers

Velocity is distance divided by time, that is:

\(v = \frac{d}{t}\)

In this problem:

Then, solving for the distance:

\(v = \frac{d}{t}\)

\(75.6 = \frac{d}{6}\)

\(d = 6(75.6)\)

\(d = 453.6[/tex

Rounding up, 454 km, option c.

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Answer:

x = 55

Step-by-step explanation:

Step 1: Write out equation

x - 15 = 40

Step 2: Add 15 to both sides

x - 15 + 15 = 40 + 15

x = 55

Answer:

\( \huge{ \fbox{ \sf{x = 55}}}\)

Step-by-step explanation:

\( \star{ \sf{ \: x - 15 = 40}}\)

\( \text{Step \: 1 \: : Move \: 15 \: to \: right \: hand \: side \: and \: change \: its \: sign}\)

\( \mapsto{ \sf{x = 40 + 15}}\)

\( \text{Step \: 2 \: : Add \: the \: numbers : 40 \: and \: 15}\)

\( \mapsto{ \boxed {\sf{ {x = 55}}}}\)

Hope I helped!

Best regards! :D

~\( \sf{TheAnimeGirl}\)

The answer is D) 5/4.

To find the limit of the given function as x approaches 2, we can plug the value of 2 directly into the function. However, since the denominator of the function becomes 0 when x=2, we need to simplify the function first.

(x^2 + x - 6)/(x^2 - 4) can be factored as [(x+3)(x-2)]/[(x+2)(x-2)].

We can then cancel out the common factor of (x-2) in the numerator and denominator, leaving us with (x+3)/(x+2) as the simplified function.

Now, we can plug in the value of 2 into this simplified function:

limx→2 (x+3)/(x+2)

= (2+3)/(2+2)

= 5/4

Therefore, the answer is D) 5/4.

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Answer:

1022

Step-by-step explanation:

360+600+12+45+9=1022

The given statement is true all else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant.  

The T Statistic is used in a T test when you are deciding if you should support or reject the null hypothesis. It’s very similar to a Z-score and you use it in the same way: find a cut off point, find your t score, and compare the two. You use the t statistic when you have a small sample size, or if you don’t know the population standard deviation.

Here we have the statement All else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant.

And we need to identify whether the statement is true or not.

As per the definition of t statistics, we have identified that the t statistic falls from 0. which states that is goes on the negative direction.

Hence, the more likely it is that the difference between two population averages is statistically significant.

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Step-by-step explanation:

Factoring using the quadratic form involves using the quadratic formula to find the two values that, when multiplied together, give the original quadratic equation. The quadratic formula is as follows:

x = (-b ± √(b^2 - 4ac)) / 2a

To use the quadratic formula to factor a quadratic equation, first rewrite the equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. Then, plug the values of a, b, and c into the quadratic formula to solve for x. The two values of x that you find are the factors of the original quadratic equation.

Here's an example:

Suppose you want to factor the quadratic equation 2x^2 + 7x + 3 = 0. In this case, a is 2, b is 7, and c is 3. Plugging these values into the quadratic formula, we get:

x = (-7 ± √(7^2 - 4 * 2 * 3)) / 2 * 2

Solving this equation, we get x = (-7 ± √(49 - 24)) / 4, which simplifies to x = (-7 ± √(25)) / 4. Since the square root of 25 is 5, we can further simplify this to x = (-7 ± 5) / 4, which gives us the solutions x = -1 and x = -3/2.

Therefore, the two factors of the original equation 2x^2 + 7x + 3 = 0 are x + 1 and x + 3/2.