The length of a rectangle is 3 yd less then twice the width, and the area of the rectangle is 27 yd^2. Find the dimensions of the rectangle.

To determine the density of the random variable X + Y, where X and Y are independent random variables with specific densities, we need to find the convolution of the densities of X and Y.

The density function of X, fx(x), is given by fx(x) = e^(-x), for x > 0. Similarly, the density function of Y, fy(y), is given by fy(y) = e^(-y), for y < 0. Since X and Y are independent, we can find the density of X + Y by performing the convolution of their densities.

The convolution of the densities fx(x) and fy(y) can be calculated by integrating the product of the two densities over the entire range of values. In this case, since X and Y have specific ranges (x > 0 and y < 0), the convolution will only be performed within these ranges.

Once we determine the density of X + Y, we can find its expected value, E(X + Y), by calculating the integral of (x + y) multiplied by the density function of X + Y over the entire range of values.

It's important to note that the ranges of X and Y, i.e., x > 0 and y < 0, affect the calculation of the density of X + Y and the expected value. The specific calculations will require evaluating the integrals and applying the properties of exponential functions.

Therefore, the complete solution involves performing the convolution of the densities fx(x) and fy(y) to find the density of X + Y and then calculating the expected value E(X + Y) by integrating (x + y) multiplied by the density function of X + Y.

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Answer:Mathematics of Money:

Compound Interest Analysis With Applications

This site is a part of the JavaScript E-labs learning objects for decision making. Other JavaScript in this series are categorized under different areas of applications in the MENU section on this page.

Professor Hossein Arsham    

Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:

FV = PV(1 + r/m)mt

or

FV = PV(1 + i)n

where i = r/m is the interest per compounding period and n = mt is the number of compounding periods.

One may solve for the present value PV to obtain:

PV = FV/(1 + r/m)mt

Numerical Example: For 4-year investment of $20,000 earning 8.5% per year, with interest re-invested each month, the future value is

FV = PV(1 + r/m)mt   = 20,000(1 + 0.085/12)(12)(4)   = $28,065.30

Notice that the interest earned is $28,065.30 - $20,000 = $8,065.30 -- considerably more than the corresponding simple interest.

Effective Interest Rate: If money is invested at an annual rate r, compounded m times per year, the effective interest rate is:

reff = (1 + r/m)m - 1.

This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom.

Numerical Example: A CD paying 9.8% compounded monthly has a nominal rate of rnom = 0.098, and an effective rate of:

r eff =(1 + rnom /m)m   =   (1 + 0.098/12)12 - 1   =  0.1025.

Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year.

Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then

R = P × r / [1 - (1 + r)-n]

and

D = P × (1 + r)k - R × [(1 + r)k - 1)/r]

Step-by-step explanation:

The addition of the polynomial \(x^{3}+3xy-2xy^{2} +y^{3}\) with \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is  \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).

What is a polynomial?

⇒ A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

⇒ In the addition of polynomials, the like terms are added while in subtraction, the like terms are subtracted.

Calculation;

We have been given two polynomial which we have to add   \(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\)

The sign after addition or subtraction will always be of the variable having more value.

\((x^{3}+3xy-2xy^{2} +y^{3} )+(2x^{3}-5x^{2} y-3xy^{2}-2y^{3})\)

On adding like terms with each other

⇒ \((x^{3} +2x^{3})+ 3xy-5x^{2} y-(2xy^{2}+3xy^{2})+(y^{3}-2x^{3})\)

⇒ \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\)

Hence the addition of the polynomial\(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).

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Answer:

Angles 2 and 4 are vertical.

Answer:

Angles 2 and 4 are vertical

Answer:

-2.5, -8/4, -0.20, 0, 3/12

Step-by-step explanation:

Answer:if I’m not wrong I’m pretty sure the answer is 240.00

Step-by-step explanation:

29 students scored at least 70 but less than 90, which is evaluated by using the cumulative frequency.

To discover the number of understudies with scores more noteworthy than or rise to 70 but less than 90, we have to discover the cumulative frequency of scores between 70 and 90. 

From this table, ready to see that the total frequency of scores up to 70 is 63, and the total frequency of scores up to 90 is 92. So the number of understudies with scores over 70 and underneath 90 is:

Cumulative frequency of outcomes up to 90 - Cumulative frequency of outcomes up to 70

= 92 - 63

= 29

Therefore, 29 students scored at least 70 but less than 90.

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Let's assume the sum of the scores of the 28 students who took the test yesterday is 28 * 72 = 2016.

We know that the sum of the scores of all 30 students is (28 * 72) + x + y, where x and y are the scores of the two students who took the test this morning.

We also know that the mean of all 30 scores is 73. So we can write an equation:

[(28 * 72) + x + y]/30 = 73

Multiplying both sides by 30, we get:

2016 + x + y = 2190

So, x + y = 174.

We are given that the difference of the two scores is 22, so we can write another equation:

y - x = 22

Solving these two equations simultaneously, we get y = 98 and x = 76.

Therefore, the lower score from this morning is 76.

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Answer:

Look Below

Step-by-step explanation:

It reveals what type of slope it has. It reveals whether it is positive or negative. It tells when the line will cross the Y-Axis. This is just the groundwork of it but there is a whole list I think on what one equation can reveal about a line on a graph. Hope This Helps! If you find any fault in my answer please let me know! Have a good day!

I got a similar one too. It was 6(4.5x+1.5) ..

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

Percent value of the distance travelled:

Answer:

9a^4b^4c^2

Step-by-step explanation:

Area of a  square is expressed using the formula

A =L²

L is the side length of the square

Given that;

L = a²b²c

A = 3²(a²b²c)²

A = 9(a²)²(b²)²c²

A = 9a^4b^4c^2

Hence the area of the square is 9a^4b^4c^2

Answer:

Answer in Box:

BECAUSE

SEVEN

EIGHT

NINE

Answer per letter :

A- 60

B- -60

C- 13

E- 5

G- 24

H- 96

I- -2

S- 19

U- -18

V- -85

T- -46

N- -54

Solution:

Answer:

nth term = 18 - 3n

Step-by-step explanation:

nth term = a + (n - 1)d

a1 = 15

d = -3

nth term = a + (n - 1)d

= 15 + (n - 1)-3

= 15 + (-3n + 3)

= 15 - 3n + 3

= 18 - 3n

nth term = 18 - 3n

For instance, if you want to find the 10th term

nth term = 18 - 3n

10th term = 18 - 3(10)

= 18 - 30

= -12

10th term = -12

Answer:

A (one with 2 right next to each other horizontally)

Step-by-step explanation:

2 of them are dialated, and the other is vertical.

The two numbers are -80 and 80, with -80 being the smaller number and 80 being the larger number.

The product of these two numbers is (-80)(80) = -6400, which is the minimum possible value.

Let the two numbers be x and y, where x is the smaller number and y is the larger number.

Then we have:

y - x = 160 (since the difference between the two numbers is 160)

y = x + 160 (adding x to both sides)

We want to find the values of x and y that minimize their product, which is given by:

P = xy

Substituting y = x + 160, we get:

\(P = x(x + 160) = x^2 + 160x\)

To find the minimum value of P, we take the derivative with respect to x and set it equal to zero:

dP/dx = 2x + 160 = 0

Solving for x, we get:

x = -80

Substituting x = -80 into y = x + 160, we get:

y = 80.

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The total cost of Kayla's purchase of 0.1 pounds of medium binder clips and 0.2 pounds of jumbo binder clips is $1.20.

To calculate the total cost, we need to determine the cost of each type of binder clip separately and then sum them up.

The cost of medium binder clips is $5 per pound, and Kayla purchased 0.1 pounds. Therefore, the cost of medium binder clips is 0.1 pounds * $5 per pound = $0.50.

The cost of jumbo binder clips is $6 per pound, and Kayla purchased 0.2 pounds. Thus, the cost of jumbo binder clips is 0.2 pounds * $6 per pound = $1.20.

Finally, to find the total cost, we add the individual costs together: $0.50 + $1.20 = $1.70.

Therefore, the total cost of Kayla's purchase of 0.1 pounds of medium binder clips and 0.2 pounds of jumbo binder clips is $1.70.

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a) an = 3n-1 · 2

b) an = 2·n

c) an = 5·n + 8

d) an = 4n-1 · 1

Let's dive deeper into the details below.
(a) The sequence 2, 5, 10, 17, 26 is a geometric sequence with common ratio 3 and a1 = 2. Therefore, the closed formula is an = 3n-1 · 2.

(b) The sequence 0, 2, 5, 9, 14 is an arithmetic sequence with common difference 2 and a1 = 0. Therefore, the closed formula is an = 2·n.

(c) The sequence 8, 12, 17, 23 is an arithmetic sequence with common difference 5 and a1 = 8. Therefore, the closed formula is an = 5·n + 8.

(d) The sequence 1, 5, 23, 119 is a geometric sequence with common ratio 4 and a1 = 1. Therefore, the closed formula is an = 4n-1 · 1.

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Each of the tire has traveled 10000km / 5 tires = 2000km.

To determine how many km each tire has traveled, you can use the following formula:

Total distance traveled / Number of tires = KM per tire

For example, if the car has traveled 10000 km and there are 5 tires, you would divide 10000 by 5 to get 2000 km per tire.

Another way is to use a tire tread depth gauge to measure the depth of the tread on each tire, when the tread wear reaches a certain point, it means the tire has traveled a certain distance.

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The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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The population variance is closest to 67.43, hence option C: 67.00, by referring the formula for population variance where N plays the number of data points.

The following gives the formula for population variance:

σ2 = (1 /N) ∑ (xi – μ) 2

Where:

σ2 refers to the population variance.

N refers to the total number of data points

∑ (xi – μ) 2 is the sum of the squared differences between each data point and the mean of the population.

For example, consider a population with data values of 12, 8, 28, 22, 12, 30, 14. The mean of this population is:

12+8+28+22+12+30+14)/7 = 18.

The population variance is calculated as follows:

σ2 = (1/7) [(12-18)2 + (8-18)2 + (28-18)2 + (22-18)2 + (12-18)2 + (30-18)2 + (14-18)2]

= 67.43

Therefore, the population variance is closest to 67.43.

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Complete question is:

Consider a population with data values of 12 8 28 22 12 30 14. The population variance is the closest to:

A. 8.00

B. 8.64

C. 67.00

D. 74.67

Answer: A. On the Iberian Peninsula

Step-by-step explanation: It happened in Spain on the Iberian Peninsula.

Answer:

Iberian Peninsula

Step-by-step explanation:

Answer:

Ok its friday be happy

Step-by-step explanation:

Answer: uh 3.50 per a can I think

Step-by-step explanation:

Option D: a = 6

3/a -4/(a+2) = 0

3/a = 4/(a+2)

Multiply "a" on each side:

3 = 4a/(a+2)

Multiply "(a+2)" on each side:

3a+6 = 4a

Simplify by subtracting "3a" on both sides:

6 = 1a

6=a

Option D

Hope this helps!

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Answer:

height of the equilateral triangle is 5cm

by the use of Pythagoras

Step-by-step explanation: