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3 years ago

Please Answer ASAP

Mathematics

1 answer:

Yuki888 [10]3 years ago

5 0

Michelle's balance after 8 years is $10,790.48.

Kristen's balance after 8 years is $3,770.55.

Gabriella's balance after 8 years is $24,780.42.

Judy's balance after 8 years is $3618.62.

The person with the most money at the end of the 8 years is Gabriella. If I were to choose one of the options, I would choose Gabriella's option

<h3>What is Michelle's balance after 8 years?</h3>

The formula that can be used to determine the future value of an amount with compounding is:

FV = P (1 + r)^nm

Where:

FV = Future value
P = Present value
R = interest rate / number of compounding
m = number of compounding
N = number of years

Future value with monthly compounding = $2000 x ( 1 + 0.035/12)^(12 x 8) = $2645.18

Future value with continuous compounding = : A x e^r x N

A= amount
e = 2.7182818
N = number of years
r = interest rate

1000 x e^0.018 x 8 = $8,145.30

Total = $8,145.30 + $2645.18 = $10,790.48

<h3>What is Kristen's balance after 8 years?</h3>

Future value with quarterly compounding = 2500 x (1 + 0.012 / 4)^(4 x 8) = $2,751.50

Future value with quarterly compounding = 500 (1 .0225)^(8x4) = $1019.05

Total = $3,770.55

<h3>What is Gabriella's balance after 8 years?</h3>

$3000 x e^0.032 x 8 = $24,780.42

<h3>What is Judy's balance after 8 years?</h3>

Future value with exponential increase = 1050 x (1.015)^8 = $1,182.82

Future value with biannual compounding = 1950 x (1 + 0.028/2)^(8 x 2) = $2435.80

Total = $3618.62

To learn more about future value, please check: brainly.com/question/18760477

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Zanzabum

Answer:

x = 2

Step-by-step explanation:

The product of distances from the intersection of secants to the near and far intersections with the circle are the same. For a tangent, the near and far points of intersection with the circle are the same. This relation tells us ...

(2√3)(2√3) = x(x +4)

12 = x² +4x

16 = x² +4x +4 . . . . . add the square of half the x-coefficient to complete the square

4² = (x +2)² . . . . . . . . write as squares

4 = x +2 . . . . . . . . . . positive square root

2 = x . . . . . . . . . . . . . subtract 2

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<em>Alternate solution</em>

If you believe x to be an integer, you can look for factors of 12 that differ by 4.

12 = 1×12 = 2×6 = 3×4

The factors 2 and 6 differ by 4, so x=2 and x+4=6.

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3 years ago

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dalvyx [7]

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Step-by-step explanation:

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3 years ago

If 72 is 120% of a number, what is 80%<br> of this number?

cupoosta [38]

Answer:

Step-by-step explanation:

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 172 = 120% × Y

STEP 272 =

120

100

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Multiplying both sides by 100 and dividing both sides of the equation by 120 we will arrive at:

STEP 3Y = 72 ×

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120

STEP 4Y = 72 × 100 ÷ 120

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Finally, we have found the value of Y which is 60 and that is our answer.

You can easily calculate 72 is 120 percent of what number by using any regular calculator, simply enter 72 × 100 ÷ 120 and you will get your answer which is 60

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3 years ago

The planets in our solar system do not travel in circular paths. Rather, their orbits are elliptical. The Sun is located at a fo

qwelly [4]

1. The distance between the perihelion and the aphelion is 116 million miles

2. The distance from the center of Mercury’s elliptical orbit and the Sun is 12 million miles

3. The equation of the elliptical orbit of Mercury is $\frac{x^{2}}{3364}}+\frac{y^{2}}{3220}=1$

4. The eccentricity of the ellipse is 0.207 to the nearest thousandth

5. The value of the eccentricity tell you that the shape of the ellipse is near to the shape of the circle

Step-by-step explanation:

Let us revise the equation of the ellipse is

$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ , where the major axis is parallel to the x-axis

The length of the major axis is 2a
The coordinates of the vertices are (± a , 0)
The coordinates of the foci are (± c , 0) , where c² = a² - b²

∵ The Sun is located at a focus of the ellipse

∴ The sun located ate c

∵ The perihelion is the point in a planet’s orbit that is closest to the

Sun ( it is the endpoint of the major axis that is closest to the Sun )

∴ The perihelion is located at the vertex (a , 0)

∵ The closest Mercury comes to the Sun is about 46 million miles

∴ The distance between a and c is 46 million miles

∵ The aphelion is the point in the planet’s orbit that is furthest from

the Sun ( it is the endpoint of the major axis that is furthest from

the Sun )

∴ The aphelion is located at the vertex (-a , 0)

∵ The farthest Mercury travels from the Sun is about 70 million miles

∴ The distance from -a to c is 70 million miles

∴ The distance between the perihelion and the aphelion =

70 + 46 = 116 million miles

1. The distance between the perihelion and the aphelion is 116 million miles

∵ The distance between the perihelion and the aphelion is the

length of the major axis of the ellipse

∵ The length of the major axis is 2 a

∴ 2 a = 116

- Divide both sides by 2

∴ a = 58

∴ The distance from the center of Mercury’s elliptical orbit to the

closest end point to the sun is 58 million miles

∵ The distance between the sun and the closest endpoint is

46 million miles

∴ The distance from the center of Mercury’s elliptical orbit and

the Sun = 58 - 46 = 12 million miles

2. The distance from the center of Mercury’s elliptical orbit and the Sun is 12 million miles

∵ The major axis runs horizontally

∴ The equation is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

∵ a = 58

∵ c is the distance from the center to the focus of the ellipse

∴ c = 12

∵ c² = a² - b²

∴ (12)² = (58)² - b²

- Add b² to both sides

∴ (12)² + b² = (58)²

- Subtract (12)² from both sides

∴ b² = (58)² - (12)² = 3220

- Substitute these values in the equation

∴ $\frac{x^{2}}{3364}}+\frac{y^{2}}{3220}=1$

3. The equation of the elliptical orbit of Mercury is $\frac{x^{2}}{3364}}+\frac{y^{2}}{3220}=1$

The eccentricity (e) of an ellipse is the ratio of the distance from the

center to the foci (c) and the distance from the center to the

vertices (a) ⇒ $e=\frac{c}{a}$

∵ c = 12

∵ a = 58

∴ $e=\frac{12}{58}$ = 0.207

4. The eccentricity of the ellipse is 0.207 to the nearest thousandth

If the eccentricity is zero, it is not squashed at all and so remains a circle.

If it is 1, it is completely squashed and looks like a line

∵ The eccentricity of the ellipse is 0.207

∵ This number is closed to zero than 1

∴ The shape of the ellipse is near to the shape of the circle

5. The value of the eccentricity tell you that the shape of the ellipse is near to the shape of the circle

Learn more:

You can learn more about conics section in brainly.com/question/4054269

#LearnwithBrainly

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3 years ago

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Leviafan [203]

Well, it depends, there may be multiple common factors, if it's the greatest common factor, then there is only one. The way to do this is to list all the factors of each number.

So Factors of

18: 1,2,3,6,9,18

27: 1,3,9,27

Common Factors : 1, 3, 9

Greatest Common Factor: 9

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3 years ago