Compare and contrast the four different conic sections (orbits). Discuss their
eccentricities.

Answer:

the answer is 22

Step-by-step explanation:

-22 x -22=22

The probabilities, using the binomial distribution, are given as follows:

a. P(X = 2) = 0.2109.

b. P(X = 3) = 0.0469.

c. P(X ≥ 2) = 0.2617.

d. P(X < 3) = 0.9492.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

The mass probability formula is given by the equation presented as follows:

The parameters, and their meaning are listed as follows:

The parameter values for this problem are given as follows:

n = 4, p = 0.25.

Hence the relevant probabilities are given as follows:

Then:

P(x ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.2109 + 0.0469 + 0.0039 = 0.2617.

P(x < 3) = 1 - (P(X = 3) + P(X = 4)) = 1 - (0.0469 + 0.0039) = 0.9492.

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Answer:

The function y = 3(x - 2)^2 + 6 is in vertex form, which is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola.

In this case, the vertex is (2,6), and the coefficient "a" is 3, so we can write the equivalent function in standard form as follows:

y = 3(x - 2)^2 + 6

y = 3(x^2 - 4x + 4) + 6

y = 3x^2 - 12x + 18

Therefore, the equivalent function in standard form is y = 3x^2 - 12x + 18.

Answer: 5y²

Step-by-step explanation:

  Since 8y² and 3y² are similar terms, we can subtract the coefficients and keep the degree and variable the same.

8 - 3 = 5, so 8y² - 3y² = 5y²

Option C multiplies one and demonstrates that the result is one, proving that one has the attribute of multiplicative identity.

Any number multiplied by one is equal to itself, according to the multiplicative identity condition of 1. Hence, the following equation illustrates the multiplicative identity feature of 1.

C) 1/4 x 4 = 1

Adding 1/4 to 4 results in: 1/4 x 4 = (1 x 4) / 4 = 4/4 = 1

This demonstrates that when we multiple any number by 1, the result is always the same. Because they involve multiplying many numbers, not just 1, Options A, B, and D do not demonstrate the multiplicative identity characteristic of 1. Option C, on the other hand, multiplies one and demonstrates that the result is one, proving that one has the attribute of multiplicative identity.

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polynomial expression of degree 2 with 3 terms.

a. i. \( a^{3}\left(a^{2}+a+1\right) = a^{5}+a^{4}+a^{3} \)


ii. \( \left(3 x^{2}-4 x+3\right)-(4 x-10) = 3 x^{2}-7 x-7 \)


b. i. \( a^{5}+a^{4}+a^{3} \) is a polynomial expression of degree 5 with 3 terms.


ii. \( 3 x^{2}-7 x-7 \) is a polynomial expression of degree 2 with 3 terms.

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The true statement is all irrational and rational numbers have decimal expansions. (second option)

A rational number is a number that can be expressed as a fraction of two integers . Rational numbers have terminating decimals and they have decimal expansions. Examples of rational numbers are 1.5, 2 and 4.25

A irrational number is a number that cannot be expressed as a fraction of two integers . Irrational numbers have repeating decimals. Examples of irrational numbers are 22/7, 1/3.

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Answer:

I think it is 0.68. Try that. If not sorry.

The cost of one rose shrub costs $12 and one pot of ivy costs $24, respectively.

It takes two equations with two variables to solve a system of equations. The variables can then be solved for using algebraic techniques like substitution or elimination.

Let x be the cost of one rose bush and y be the cost of one pot of ivy.

From Mei's purchase, we have:

3x + y = 36

From Ming's purchase, we have:

9x + 8y = 168

Use the first equation to solve for y:

y = 36 - 3x

Substituting this into the second equation, we get:

9x + 8(36 - 3x) = 168

9x + 288 - 24x = 168

-15x = -120

x = 8

Substituting x = 8 into equation of y, we get:

y = 24

Hence, the cost of one rose bush is $8, and the cost of one pot of ivy is $24.

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The cord length is k* theta radian, where theta radian is the central angle and k is the proportionality constant. This means that the rope length is proportional to the central angle in radians.

The complete cord length for a full central angle of 2pai is 2pai * r if the cord arc is a segment of a circle of radius r, where k=2pai is the proportionality constant.

What is arc?

In mathematics, an arc is a portion of the boundary of a circle or curve. It is sometimes referred to as an open curve.

The measurement around a circle that determines its edge is called the circumference, often known as the perimeter. As a result, the distance between any two locations along an arc's circumference is how it is defined.

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To create a Pandas crosstab to compare the number of players in each position by foot, we first need to import the pandas library and then use the `pd.crosstab()` function with the appropriate parameters.

We can set `normalize='all'` to view the data as a percent of the total and `margins=True` to include row and column totals. Here's how we can do it:

```python
import pandas as pd

# Create a crosstab with the desired parameters
crosstab = pd.crosstab(df['Position'], df['Foot'], normalize='all', margins=True)

# Print the crosstab
print(crosstab)
```

To find the combination of footedness and position that is the rarest in our data, we can use the `idxmin()` function to find the index of the minimum value in the crosstab. Here's how we can do it:

```python
# Find the index of the minimum value in the crosstab
min_index = crosstab.idxmin()

# Print the combination of footedness and position that is rare
print('The most rare combination of footedness and position is', min_index)
```

The output of this code will show the combination of footedness and position that is the rarest in our data.

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On a roll of a number cube, the theoretical probability of the event of rolling a 8 is 0.

The Theoretical Probability is defined as the likelihood of an event occurring based on all possible outcomes in a given situation.

The theoretical probability is determined by dividing the number of ways the event can occur by the total number of possible outcomes.

The theoretical probability of rolling a specific number on a fair, six-sided number cube is 1/6, because there are 6 equally likely outcomes which are the numbers 1 to 6,

So, the theoretical probability of rolling an 8 on a number cube is 0 or 0%, because an 8 is not one of the possible outcomes when rolling a standard, six-sided number cube.

Therefore, the required probability is 0.

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A package that weighs 5 pounds will cost $15 for both options.

The equation can be used to symbolize the price, y: Y is equal to 5 plus 2 times the weight of the package, x.

Another choice is for the buyer to pay a one-time price of $15, which is represented by the equation y = 15, in order to send the package.

We'll compare the equation as a whole.

In this case,

5 + 2x = 15

Compile similar terms,

2x = 15 - 5

2x = 10

x = 10 / 2

x = 5

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The final answer of Using Descartes's Rule of Signs, we can determine that there are either 2 or 0 positive real zeros and 0 negative real zeros of [tex]f(x)=8x^4-7x^3-4x^2-2x+7[/tex]

To determine the possible numbers of positive and negative real zeros of f(x)=8x^(4)-7x^(3)-4x^(2)-2x+7 using Descartes's Rule of Signs, we must first count the number of sign changes in the polynomial.

For positive real zeros, we look at the original polynomial: f(x)=8x^(4)-7x^(3)-4x^(2)-2x+7.

There are two sign changes: from 8x^(4) to -7x^(3) and from -2x to +7.

Therefore, there are either 2 or 0 positive real zeros.

For negative real zeros, we look at the polynomial with x replaced by -x: f(-x)=8(-x)^(4)-7(-x)^(3)-4(-x)^(2)-2(-x)+7.

Simplifying, we get [tex]f(-x)=8x^4+7x^3-4x^2+2x+7[/tex]. There are no sign changes in this polynomial, so there are 0 negative real zeros.

In conclusion, Using Descartes's Rule of Signs, we can determine that there are either 2 or 0 positive real zeros and 0 negative real zeros of [tex]f(x)=8x^4-7x^3-4x^2-2x+7[/tex]

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I - The collapse of the housing market due to low interest rates, easy credit, insufficient regulation, and toxic subprime mortgages: C. Problems in financial markets.

II - Consumers are very worried about the economy: B. Negative demand shift.

1 - The collapse of the housing market due to low interest rates, easy credit, insufficient regulation, and toxic subprime mortgages falls into the category of "Problems in financial markets" (C). This event can lead to a recession because it can cause a decrease in the wealth of households, leading to a decrease in consumer spending and a decrease in aggregate demand.

II - Consumers being very worried about the economy falls into the category of "Negative demand shift" (B). This event can lead to a recession because when consumers are worried about the economy, they tend to save more and spend less, leading to a decrease in aggregate demand. This decrease in demand can cause businesses to decrease production and lay off workers, leading to a decrease in income and further decrease in demand.

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The pair of functions that are not inverses of each other is (A).

To determine if two functions, g(x) and h(x), are inverses of each other, we need to check if the composition of the two functions, g(h(x)) and h(g(x)), both result in x.

A. g(x) = 2 + 9 = 11, h(x) = 1/2x - 9

g(h(x)) = g(1/2x - 9) = 2 + 9 = 11

h(g(x)) = h(11) = 1/2(11) - 9 = -3/2

Since g(h(x)) ≠ x and h(g(x)) ≠ x, the functions g(x) and h(x) are not inverses of each other.

B. g(x) = x - 1, h(x) = x + 1

g(h(x)) = g(x + 1) = (x + 1) - 1 = x

h(g(x)) = h(x - 1) = (x - 1) + 1 = x

Since g(h(x)) = x and h(g(x)) = x, the functions g(x) and h(x) are inverses of each other.

C. g(x) = 3x - 6, h(x) = 1/3x + 2

g(h(x)) = g(1/3x + 2) = 3(1/3x + 2) - 6 = x

h(g(x)) = h(3x - 6) = 1/3(3x - 6) + 2 = x

Since g(h(x)) = x and h(g(x)) = x, the functions g(x) and h(x) are inverses of each other.

D. g(x) = 3x + 4, h(x) = x - 4/3

g(h(x)) = g(x - 4/3) = 3(x - 4/3) + 4 = 3x - 4

h(g(x)) = h(3x + 4) = (3x + 4) - 4/3 = 3x + 8/3

Since g(h(x)) ≠ x and h(g(x)) ≠ x, the functions g(x) and h(x) are not inverses of each other.

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The annual payment for the loan is $48,867.89.

To find how much is the annual payment for the loan, we must first find the total cost of the land and the loan amount.

The total cost of the land is $4,100 × 215 = $881,500.

The down payment is 25% of the total cost, so the down payment is $881,500 × 0.25 = $220,375.

The loan amount is the total cost minus the down payment, so the loan amount is $881,500 - $220,375 = $661,125.

To find the annual payment, we can use the formula A = P(1 + r)^n / [(1 + r)^n - 1], where A is the annual payment, P is the loan amount, r is the annual interest rate (APR), and n is the number of years.

Plugging in the values, we get:

A = $661,125(1 + 0.0675)^20 / [(1 + 0.0675)^20 - 1]

A = $661,125(1.0675)^20 / [(1.0675)^20 - 1]

A = $661,125(3.0878) / (3.0878 - 1)

A = $2,040,756.55 / 2.0878

A = $977,357.72

So the annual payment is $977,357.72 / 20 = $48,867.89.

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To divide two polynomials, P(x) and D(x), we can use either synthetic or long division. In this example, we'll use long division to divide P(x) by D(x) and express P in the form P(x)=D(x)⋅Q(x)+R(x).

First, we must make sure the degree of P(x) is greater than or equal to the degree of D(x). In this case, P(x)=-x^3-2x+6 and D(x)=x+1, so P(x) has a greater degree than D(x).

Next, we must write down P(x) and D(x) with the same degree. In this example, we can multiply D(x) by -x^2 to get -x^3+1. Then, P(x)=-x^3-2x+6 and D(x)=-x^3+1.

We can now start the long division process. First, we divide the leading coefficients, -1 and -1, so our quotient is 1. We then multiply the quotient by D(x), which gives us -x^3+1. We subtract this result from P(x), and the result is -2x+6.

Next, we divide the leading coefficients, -2 and -1, so our quotient is 2. We then multiply the quotient by D(x), which gives us -2x^2+2. We subtract this result from our previous result, -2x+6, and the result is 6.

Finally, we have reached the end of the long division process. Our quotient is Q(x)=2x+1 and our remainder is R(x)=6. Therefore, P(x)=D(x)⋅Q(x)+R(x), or -x^3-2x+6=(-x^3+1)⋅(2x+1)+6.

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Answer:

n = 15

Step-by-step explanation:

A

the area (A) of a rectangle is calculated as

A = length × width

here length = n - 3 and width = 2 , then

A = 2(n - 3)

given A = 24 , then

2(n - 3) = 24

B

solving the equation for n

2(n - 3) = 24 ← divide both sides by 2

n - 3 = 12 ( add 3 to both sides )

n = 15

Answer: a = 20°

Step-by-step explanation:

     We know that a straight line is equal to 180 degrees and that the little box represents 90 degrees. We will write an equation to solve.

               a = 180° - 90° - 70°

               a = 20°

Answer:

20 degrees

Step-by-step explanation:

Straight Angle: 180 degrees

You know that there is a right angle which is 90 degrees. You can subtract 180 by 90 to get 90. Then you are given an angle measurement of 70 degrees. Subtract 70 from 90 to get 20.

20 is the measure of the missing angle

The ratio of strawberries to bananas in the basket is 12:18 or 2:3. To find this ratio, you simply take the number of strawberries and place it over the number of bananas. In this case, there are 12 strawberries and 18 bananas, so the ratio is 12:18.

However, this ratio can be simplified by dividing both numbers by their greatest common factor, which is 6. So, the simplified ratio of strawberries to bananas is 2:3. This means that for every 2 strawberries, there are 3 bananas in the basket.

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The perimeter of the inside of the track is approximately 354.36 meters.

What is the circumference?

In geometry, the circumference is the perimeter of a circle or ellipse.

To find the perimeter of the inside of the track, we need to find the length of the inside edge of the track and add it to twice the length of the semicircles at each end.

The inside edge of the track is formed by two parallel lines, each offset by a distance of 56 m from the outer edge. The length of this edge is equal to the length of the long straight edge minus twice the offset distance:

length of inside edge = 130 m - 2(56 m)

length of inside edge = 18 m

The length of each semicircle at each end is equal to half the circumference of a full circle with a radius equal to the width of the track (56 m). Therefore, the length of both semicircles is:

2 x (1/2 x 2π x 56 m) = 2π x 56 m

Adding the length of the inside edge to twice the length of the semicircles, we get:

perimeter of inside track = 18 m + 2π x 56 m

perimeter of inside track = 18 m + 112π m

the perimeter of the inside track ≈ 354.36 m (rounded to two decimal places)

Hence, the perimeter of the inside of the track is approximately 354.36 meters.

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Using some rules for interior angles, we will see that:

x = 22.5

y = 22.5

Remember that the sum of the interior angles of any triangle is 180°.

Now, we can see that :

3x + k = 180°

Where k is the missing angle in the left triangle.

k = 180° - 3x

if we add the 3 interior angles, we will get:

2x + y + 180° - 3x = 180°

y - x = 0°

So x and y have the same value.

If now use the top triangle, we can write:

(90 - y) + 3x + 2x = 180

And we know that y = x

90 -x  + 3x + 2x = 180

90 + 4x = 180

4x = 180 - 90  =90

x = 90/4 = 22.5

Then:

x = 22.5

y = 22.5

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Therefore, the height (in feet) of the lighthouse is 88 feet.

A person's or something's height can be described as their vertical position or their vertical extension (how "tall" they are) (how "high" a point is). For example, "The height of the structure is 50 m" or "The height of an airplane in-flight is roughly 10,000 m".

Let's use proportions to solve the problem. We can set up a ratio of the height of the lighthouse to the length of its shadow, and another ratio of the height of the lamppost to the length of its shadow, and then equate the two ratios:

height of lighthouse / length of shadow of lighthouse = height of lamppost / length of shadow of lamppost

Let's plug in the given values:

h / 144 = 5.5 / 9

To solve for the height of the lighthouse, we can cross-multiply and simplify:

9h = 144 × 5.5

9h = 792

h = 88

Therefore, the height of the lighthouse is 88 feet.

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By taking the longer route, the amount of money Kelsey will save is $7.38.

To find out how much money Kelsey saves by taking the longer route, we need to calculate the total cost of each route and compare them.

For the shorter route, the total cost is the cost of gas plus the cost of tolls.
- The cost of gas is the distance traveled divided by the miles per gallon of the car, multiplied by the price of gas: (214 mi / 34.0 mpg)($3.29/gal) = $20.48
- The cost of tolls is $9.75
- So the total cost of the shorter route is $20.48 + $9.75 = $30.23

For the longer route, the total cost is just the cost of gas, since there are no tolls:
- The cost of gas is (236 mi / 34.0 mpg)($3.29/gal) = $22.85
- So the total cost of the longer route is $22.85

Now we can compare the two costs to find out how much money Kelsey saves by taking the longer route:
$30.23 (shorter route) - $22.85 (longer route) = $7.38

Therefore, Kelsey saves $7.38 by taking the longer route.

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The equation of the area of the square is x² + 6x = 1, it is in the form x² + 6x = a where a is 1 and a constant to be found.

A regular quadrilateral is square. A square has equal lengths on each of its four sides and angles. Each of the four angles is 90 degrees, or a right angle. The two adjacent sides of a square are equal in length, making it a particular instance of a rectangle.

Its attributes are: Each of its four sides is the same length.

Each of its four angles has the same dimensions.

At right angles, or 90°, the two diagonals split in half.

A square has two opposed sides that are equally long and parallel.

A square's diagonal lengths are equal.

The length of the side of the given square is 3 + x.

The area of the square is given as:

A = (s)(s)

Substituting the value of the side and area we have:

10 = (3 + x)(3 + x)

10 = 9 + 3x + 3x + x²

x² + 6x = 10 - 9

x² + 6x = 1

Hence, the equation of the area of the square is x² + 6x = 1, it is in the form x² + 6x = a where a is 1 and a constant to be found.

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The value οf x and y in the shape will be 18/5 mm and 15/2 mm respectively.

An integer is any number including 0, pοsitive numbers, and negative numbers. It shοuld be nοted that an integer can never be a fractiοn, a decimal οr a per cent. Sοme examples οf integers include 1, 3, 4, 8, 99, 108, -43, -556, etc.

Integers are a set οf cοunting numbers (pοsitive and negative), alοng with zerο, that can be written withοut a fractiοnal cοmpοnent. As mentiοned abοve, an integer can be either pοsitive, negative οr zerο.

All natural numbers are alsο integers that start frοm 1 and end at infinity.

All whοle numbers are alsο integers, starting frοm 0 and ending at infinity.

An integer is a whοle number withοut any fractiοn οr decimal part.

Using alternate angles and vertically οppοsite angles we can find their ratiο and prοpοrtiοn in οrder tο get the value οf x and y.

[tex]\frac{x}{9} =\frac{3}{y} =\frac{2}{5}[/tex]

x = 2(9)/5 = 18/5 mm

y = 3(5)/2 = 15/2 mm

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