Simplify -2/3+(-3/5)

Money Flow The rate of a continuous money flow starts at $1000 and increases exponentially at 5% per year for 4 years. Find the

77julia77 [94]

Answer:

Present value = $4,122.4

Accumulated amount = $4,742

Step-by-step explanation:

Data provided in the question:

Amount at the Start of money flow = $1,000

Increase in amount is exponentially at the rate of 5% per year

Time = 4 years

Interest rate = 3.5% compounded continuously

Now,

Accumulated Value of the money flow = $1000e^{0.05t}$

The present value of the money flow = $\int\limits^4_0 {1000e^{0.05t}(e^{-0.035t})} \, dt$

= $1000\int\limits^4_0 {e^{0.015t}} \, dt$

= $1000\left [\frac{e^{0.015t}}{0.015} \right ]_0^4$

= $1000\times\left [\frac{e^{0.015(4)}}{0.015} -\frac{e^{0.015(0)}}{0.015} \right]$

= 1000 × [70.7891 - 66.6667]

= $4,122.4

Accumulated interest = $e^{rt}\int\limits^4_0 {1000e^{0.05t}(e^{-0.035t}} \, dt$

= $e^{0.035\times4}\times4,122.4$

= $4,742

8 0

3 years ago

g In the sample of 134 South Korean tourists, 57 of them were satisfied with their Jeju experience. In the sample of 150 other c

nasty-shy [4]

Answer:

The test statistic = -0.93

Step-by-step explanation:

The test statistic is given by the formula

z = (X₁ - X₂) ÷ √(σₓ₁² + σₓ₂²)

where X₁ = proportion of data of South Korean tourists = (57/134) = 0.425

X₂ = proportion of other country tourists = (72/150) = 0.48

σₓ₁ = standard error in data 1 = √[p(1-p)/n]

= √(0.425 × 0.575/134) = 0.0427

σₓ₂ = standard error in data 2 = √[p(1-p)/n]

= √(0.48 × 0.52/150) = 0.0408

z = (X₁ - X₂) ÷ √(σₓ₁² + σₓ₂²)

z = (0.425 - 0.48) ÷ √(0.0427² + 0.0408²)

z = -0.055 ÷ 0.0590586996

z = -0.9313

Hope this Helps!!!

6 0

3 years ago

What is the absolute magnitude of a star that has a period of 62 days?

mylen [45]

your 62 days shirt

3 0

3 years ago

Read 2 more answers

(-2xy + 3 )(xy-1) e cần câu trả lời gấp ạ

Vikki [24]

(－2xy＋3)(xy－1)
－2x²y²＋2xy＋3xy－3
－2x²y²＋5xy－3

Hope my answer helped u :)

7 0

2 years ago

A farmer finds that if she plants 70 trees per acre, each tree will yield 30 bushels of fruit. She estimates that for each addit

Serjik [45]

The farmer should plant 40 trees per acre to maximize her yield to harvest.

<h3>What is a system of equations?</h3>

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let F be the number of fruit per acre

$F = (70 + x) \times (30 - 3x) \\F = 70 \times 30 - 70 \times 3x + 30 \times x - 3x^2 \\F = 2100 - 210 x + 30x - 3x^2 \\F = 2100 - 180x - 3x^2$

Factor out the 3 and complete the square

$F = -3x^2 - 180x + 2100\\F = -3 \times (x^2 + 60x - 700) \\F = -3 \times (x^2 + 2 * 30x + 30^2 - 30^2 - 700) \\F = -3 \times ((x + 30)^2 - 500 - 900) \\F = -3 \times ((x + 30)^2 - 400) \\F = -3 \times (x + 30)^2 + 1200\\$

So the vertex is at (-30, 1200)

70 - 30 = 40

The farmer should plant 40 trees per acre to maximize her yield to harvest.

Learn more about equations here;

brainly.com/question/10413253

#SPJ1

8 0

1 year ago