The hyperbolic orbit of a comet is represented on a coordinate plane with center at (0, 4). One branch has a vertex at (0, 10) and its respective focus at (0, 14). Which equation represents the comet's orbit

The probability that a randomly selected family owns a dog or a cat is 0.61 and family owns a dog or doesn't own a cat is 0.39

AS we all know the rule of the probability is defined as the amalgamation of set theory and the probability theory yields some rules which form a part of the basic probability theory

Here we have listed down the rules as Multiplication Rule, Addition Rule and Complement Rule

Here we have given Information the following that is written as

=> Probability that a family can own a dog = 0.38.

=> Probability that a family can own a cat = 0.23.

Then the probability that a randomly selected family owns a dog or a cat is calculated as follows,

=> (0.38 + 0.23)

=> 0.61

And the the probability that a randomly selected family owns a dog or doesn't own a cat.

=> 1 - (0.38 + 0.23)

=> 1 - 0.61

=> 0.39

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The probability of drawing three green marble, with replacing them, is 61/100.

Given,

A bag contains four red marbles, six green marbles, eight yellow marbles, and two blue marbles.

We need to find the probability of drawing three green marble and replacing them.

A combination is used to select required items from a set where the order of selection does not matter.

It is given by:

n^Cr = n! / r! (n-r)!

Where n = the number of elements present in a set.

Find the number of each marble.

Red marbles - 4

Green marbles - 6

Yellow marbles - 8

Blue marbles - 2

Find the probability of drawing a green marble

P (G) = ^6C_1 / ^20C_1

         = (6!/1!)/(20!/19! 1!)

        = 720 / 20

P(G)= 36

Find the probability of drawing a yellow marble

P ( Y ) = ^8C_1 / ^20C_1

         = (8! /1! 7!) / (20! / 191 1!)

         = 8 / 20

        P ( Y ) = 2 / 5

Find the probability of drawing a blue marble

P ( B ) = ^2C_1 / ^20C_1

         = (2! / 1!) / (20! / 19! 1!)

         = 2 / 20

  P ( B )= 1/10

Find the probability of drawing a blue marble

P ( R ) = ^4C_1 / ^20C_1

         = (4! / 1!) / (20! / 19! 1!)

         = 24 / 20

P ( R ) =6/5

Find the probability of drawing a green marble, replacing it, then drawing a yellow marble

Both the probability is independent so,

P = P ( G ) X P ( Y )+P ( G ) X P ( R )+P ( G ) X P ( B )

 = 36 X 2 / 5+36 X 6/5+36 X1/10

P= 61/100

Thus the probability of drawing three green marble, and replacing them, is 61/100.

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An absolute value graph has one axis of symmetry that passes through the vertex.

From the preceding graph, it can be seen that when the coefficient of x increases, the v form moves closer to the line of symmetry and vice versa.

However, it is not always the case that the symmetry line and the y-axis coincide.

For instance:

A line of symmetry for the equation -y=|3x-6|-5 runs parallel to the y-axis and through the x-axis.

You must be aware of the location of the graph's vertex and the line of symmetry.

To obtain the value of x, which will be the x coordinate for the vertex of the graph, take the equation inside the absolute value and equal it with 0. Then, replace the value of x with the main equation to obtain the y coordinate for the vertex of the graph.

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The quadrilateral given is Parallelogram.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

(a) The quadrilateral is sketched as shown in the graph below.

(b) We have to write the equation of four lines AB, BC, CD and AD in the form y = mx + b. m is slope and b is intercept along Y axis.

Coordinates of vertices are A(-5, 2), B(-2, 6), C(3, 5) and D(0,1).

Equation of line AB :

Slope = (6 - 2) / (-2 - -5) = 4/3

Equation in point slope form is

(y - 2) = 4/3(x - -5)

y - 2 = 4/3 x + 20/3

y = 4/3 x + 26/3

Equation of line BC :

Slope = (5 - 6) / (3 - -2) = -1/5

Equation in point slope form is,

(y - 6) = -1/5 (x - -2)

y - 6 = -1/5 x - 2/5

y = -1/5 x + 28/5

Equation of line CD :

Slope = (1 - 5) / (0 - 3) = -4/-3 = 4/3

Equation in point slope form is,

y - 5 = 4/3 (x - 3)

y - 5 = 4/3 x - 4

y = 4/3x + 1

Equation of line AD :

Slope = (1 - 2) / (0 - -5) = -1/5

Equation in point slope form is,

y - 1 = -1/5 (x - 0)

y - 1 = -1/5 x

y = -1/5 x + 1

(c) Opposite sides are having the same slope.

From the sketch, opposite sides are equal.

So quadrilateral is either parallelogram or rectangle.

But if the figure is rectangle, adjacent sides are perpendicular and therefore the product of their slope is -1.

But it is not the case here.

So it is parallelogram.

Hence the given figure is a parallelogram.

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Question 9

[tex]\frac{\sin x}{23}=\frac{\sin 27^{\circ}}{11}\\\\\sin x=\frac{23\sin 27^{\circ}}{11}\\\\x \approx 71.7^{\circ}, 108.3^{\circ}[/tex]

Both of these cases satisfy the angle sum of a triangle.

Question 11

[tex]\frac{\sin x}{27}=\frac{\sin 74^{\circ}}{26}\\\\\sin x=\frac{27 \sin 74^{\circ}}{26}\\\\x \approx 86.6^{\circ}, 93.4^{\circ}[/tex]

Both of these cases satisfy the angle sum of a triangle.

The answer consists of 10 examples of mathematical solutions: the Pythagorean Theorem, the Quadratic Formula, the Binomial Theorem, the Divergence Theorem, the Fundamental Theorem of Calculus, the Law of Cosines, the Law of Sines, the Triangle Inequality, the Extreme Value Theorem, and the Mean Value Theorem.

1. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side.

2. The Quadratic Formula is used to calculate the roots of a quadratic equation.

3. The Binomial Theorem allows one to expand a binomial expression to any power.

4. The Divergence Theorem explains the relationship between a vector field and its associated flux.

5. The Fundamental Theorem of Calculus states the relationship between the derivative and integral of a function.

6. The Law of Cosines is used to calculate the length of a side of a triangle given the lengths of the other two sides and the angle between them.

7. The Law of Sines is used to calculate the length of a side of a triangle given the lengths of the other two sides and the angle between them.

8. The Triangle Inequality states that the sum of any two sides of a triangle must be greater than the third side.

9. The Extreme Value Theorem states that a continuous function on a closed interval has both a minimum and a maximum value.

10. The Mean Value Theorem states that for a given continuous function on a closed interval, there exists at least one point where the function's derivative equals the average rate of change over the interval.

The answer consists of 10 examples of mathematical solutions: the Pythagorean Theorem, the Quadratic Formula, the Binomial Theorem, the Divergence Theorem, the Fundamental Theorem of Calculus, the Law of Cosines, the Law of Sines, the Triangle Inequality, the Extreme Value Theorem, and the Mean Value Theorem. Each of these solutions explains a different mathematical concept or relationship.

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The function f(x) = 3x^4/4 - 32285040.75 and the line 81x + y = 0 is tangent to the graph of f at the point (-3,0)

To find a function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f, we can use the fact that the slope of the tangent line to a function f(x) at a point x = a is given by f'(a).

Since the line 81x + y = 0 has a slope of -81, we know that f'(a) = -81. So, we can set f'(a) = -81 and solve for a:

f'(a) = 3a^3 = -81
a^3 = -27
a = -3

Now we can use the point-slope form of a line to find the equation of the tangent line to the graph of f at x = -3:

y - f(-3) = f'(-3)(x + 3)

y - f(-3) = -81(x + 3)

We also know that the point (-3,0) lies on the graph of f and on the line 81x + y = 0. We can use this information to find the value of f(-3):

0 = -81(-3) + f(-3)
f(-3) = 243

So the equation of the tangent line is:
y - 243 = -81(x + 3)
y = -81x - 222

To find f(x) we can use the fact that f(x) = the antiderivative of f'(x)

∫f'(x)dx = f(x) + C

∫3x^3 dx = f(x) + C

3x^4/4 + C = f(x)

We can find the value of the constant C by using the point (x,y) = (-3,0) on the function f(x)

0 = 3(-3)^4/4 + C
C = -3^4*3/4 - 32285040.75

Therefore the function f(x) = 3x^4/4 - 32285040.75

And the line 81x + y = 0 is tangent to the graph of f at the point (-3,0)

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The equivalent expression of the perimeter of the regular hexagon is,

⇒ 42x + 24

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

A regular hexagon has six congruent sides.

And, The length of each side is represented by the expression (7x + 4).

Now, We know that;

The sum of all sides of a regular hexagon is called its perimeter.

Hence, We get;

Here, The length of each side is represented by the expression 7x + 4.

So, We get;

The perimeter of Hexagon = 6 × (7x + 4)

                                          = 42x + 24

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Answer:

Large numbers require a large number of zeros when writing in scientific notation.

To express such quantities in a simpler and more efficient manner, mathematicians and scientists use scientific notation.

Step-by-step explanation:

Answer:

45 minutes

Step-by-step explanation:

I attached a pic of my work.

Answer:

Step-by-step explanation:

12. all angles are the same size.

all ik sry

The total distance formula is the sum of the distances traveled during each leg of a journey. It is calculated by adding all the individual distances traveled together.

The total distance formula is used to calculate the total distance traveled during a journey.To calculate the total distance, start by determining the distances traveled during each leg of the journey. This could be the distance between two cities, the distance between two points in a city, or any other distance. Once you have determined the distances, add them all together. This will give you the total distance traveled during the journey. If the journey includes multiple modes of transportation, you can calculate the total distance for each mode and then add them together for the final total. Additionally, if the journey includes any stops, you can add the distance traveled between each stop to get the total distance for the entire journey. Once you have added all the distances together, you will have your total distance traveled.

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Vector w can be expressed as w=1u-2v as linear combination of vector u and v.

Vector equation would be w=Au + Bv

[1,1]=A[5,7] + B[2,3]

Here A and B are constants and we are trying to find their values.

We can split two equations as

1=5A+2B → equation a

1=7A+3B → equation b

Solving these equations by elimination method . Multiplying equation a with 3 and equation b with 2.

3=15A+6B

2=14A+6B

1=A → A=1

Putting value of A in equation b:

1=7+3B

1-7=3B

-6=3B

B=-6/3=-2

A = 1 and B = -2 . It means we can write w as 1u - 2v. We can recheck by plugging the values in any of the vector to confirm if the values are correct or not.

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Both f(x) and g(x) have the same y-intercept of (0,0). So the answer is c) f(x) and g(x) have the same y-intercept.

What is the y-intercept?

The point where a graph completely lies on the y-axis is known as the y-intercept. Any point which lies only on the y-axis has an x-coordinate equal to 0, as is known y-intercept.

The y-intercept of a function is the point at which the graph of the function crosses the y-axis. To find the y-intercept of a function, we can set x = 0 and find the corresponding value of y.

For function f(x) = 5x^2, when x = 0, y = 5(0)^2 = 0.

For function g(x) = 3(2)x, when x = 0, y = 3(2)(0) = 0.

Therefore, both f(x) and g(x) have the same y-intercept of (0,0). So the answer is c) f(x) and g(x) have the same y-intercept.

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On solving the provided question, we can say that  the slope of the line measured is 33m/s

A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

rise of line = 600m

run of line = 3mins

Slope = rise/run

Slope = 600/180

Slope = 3.33 m/sec

, the slope of the line measured is 3.33

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The standard deviation for this sample data set is 1.93.

What is deviation ?

Deviation refers to the difference between an individual value or observation and the average or mean value of a set of data. It can also refer to the extent to which a variable or set of data deviates from a standard or expected value.

To calculate the standard deviation for a sample data set, we first need to find the mean (average) of the data. In this case, the mean of the data set {5, 7, 6, 9, 6, 4, 4, 6, 5, 2, 5} is 5.45.

Once we have the mean, we can calculate the variance by taking the average of the squared differences between each data point and the mean. The variance is given by:

(1/n) * Σ(x_i - mean)^2

where n is the number of data points and x_i is the i-th data point.

The variance for this data set is 3.70.

Finally, we take the square root of the variance to get the standard deviation.

So, the standard deviation for this sample data set is 1.93.

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In Korea, tofu is typically offered during breakfast.

Describe breakfast.

The first meal of the day, known as breakfast, is often had in the morning. After an overnight fast, it is a crucial meal that gives the body and brain fuel. Protein and carbs are generally found in breakfast foods such eggs, bacon, oatmeal, toast, pancakes, yoghurt, cereal, and fruits. A nutritious breakfast may boost energy levels, jump-start the metabolism, and enhance focus and memory. A nutritious breakfast can also aid in lowering mid-day snacking and preventing overeating in the evening. Make sure to incorporate breakfast in your daily schedule since eating breakfast is crucial to living a healthy lifestyle.

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Answer: Chart A best represents this situation: Pairs (0,8) and (6,0).

Step-by-step explanation: If y represents the students score and x represents the number of questions that the student has answered incorrectly, then if the student has answered 0 questions incorrectly, they should have the highest possible score. This would mean that at no mistakes (x=0), the student would have the maximum score (y=8). This would create the ordered pair (0,8).

Following that logic, if the student has made a mistake on every single question (x=6), then they would have the lowest possible score (y=0). This would then make the ordered pair (6,0). Hope this helps!

Analyzing the figure given in the question,

a.

  1. The corresponding sides are ,

  2. The scale factor ratio is , 2.5.

b. The height of the backhoe is 180''.

Corresponding sides of a triangle are the sides of a triangle that are in the same position relative to the vertices of the triangle. In other words, they are the sides of the triangle that are opposite to the same angles.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

From the given figure,

length of base of the small triangle, let a = 52 inches

length of base of the bigger traingle, let b = 130 inches

height of the person , let c = 6ft = 6*12 inches = 72 inches

height of the backhoe, let d = ?

a.

Since the smaller and bigger traingles are similar triangles we can equate the proportion of corresponding sides ,

b/a = d/c = 130/52=2.5 -------- equation 1

Therefore the required scale factor is 2.5

b.

Using the 2nd ratio in equation 1,

d/c = 2.5

or, d/72 = 2.5

therefore, d = 180 inches

therefore the required height of the backhoe is 180 inches.

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If the mean of a population is 250 and the standard deviation is 20, we can say that approximately 68% of observations fall between 230 and 270, 95% of observations fall between 210 and 290, and 99.7% of observations fall between 190 and 310.

It's important to note that these percentages are approximate and based on the assumption that the population follows a normal distribution.

The normal distribution is a continuous probability distribution that is symmetric about the mean. The standard deviation (σ) is a measure of the spread of the data. Approximately 68% of the observations fall within one standard deviation of the mean, 95% of observations fall within two standard deviations of the mean, and 99.7% of observations fall within three standard deviations of the mean.

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The difference in the account balance after 30 years is $345.31.

What is compounded continuously?

Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.

Given:

A business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually.

After 30 years, the value of the bond will be $25,084.20.

The business owner's investment was compounded continuously instead of twice per year.

We have to find the difference in the account balance after 30 years?

Consider, the compounded continuously formula,

[tex]A = Pe^r^t[/tex]

Plug p = 7000

r = 4.3% = 0.043

t = 30

⇒ [tex]A = 7000e^(^0^.^0^4^3^*^3^0^) = 25429.51[/tex]

A = $25429.51

So, the difference is, $25429.51 - $25084.20 = $345.31

Hence, the difference in the account balance after 30 years is $345.31.

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The highlights listed above indicate that: 35 - 5D reflects the quantity of postcards sold.

The highlights listed above indicate that: 35 - 5D reflects the quantity of postcards sold.

The examples include:

D indicates the cost of each postcard.

35 - 5D is the number of postcards that were sold.

D(35 - 5D) denotes the revenue resulting from the sales.

Describe phrases.

Mathematical assertions called expressions include all of the followings.

Mathematical operator variables for numbers

The phrase is given as follows:

The query leads us to believe that:

D indicates the cost of each postcard

D(35 - 5D) denotes the revenue resulting from the sales.

The highlights listed above indicate that: 35 - 5D reflects the quantity of postcards sold.

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The given statement is untrue about Pat. Therefore, it is invalid.

If each of the premises must be true in order for the conclusion to be true, the argument can only be validated if it does so. The term "valid" refers to a statement that is true, whereas the term "invalid" refers to a statement that is untrue.

The given situation is an invalid one. Because it's still feasible for Pat to be a woman, even if the premise is accurate. She could be a single woman. Because of this, the premise cannot be used to prove that she is a woman.

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When we alter an expressions form but not its value, then these expression are called Equivalent expression.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

We alter an expressions form but not its value.

Now, Let an expression is,

⇒ (x + 2)²

And, We can change its form as;

⇒ x² + 4x + 4

Clearly, Both expression are equal but its form are change.

Hence, These expressions are equivalent.

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Answer:

yes

Step-by-step explanation:

The positive integers are the numbers 1, 2, 3, ...

The expression of the given conditions is 8x - 12.

A sentence that contains a minimum of two numbers or variables and at least one operation is called an expression. These operations can be subtraction, addition, multiplication, or division. The structure of an expression is:

Expression is (Number/variable, Math Operator, Number/variable)

On the other hand, An algebraic expression consists of unknown variables, numbers and arithmetic operators. The algebraic expression does not contain any equality or inequality symbols.

Let's call the number you are thinking of as "x".

Multiplying it by 2:

2x

Subtracting 3:

2x - 3

Multiplying the result by 4:

4(2x - 3) = 8x - 12

So the final expression is:

8x - 12

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Answer:

544

Step-by-step explanation:

34 * 2 = 68

68 *2 = 136

136 * 2 = 272

272 * 2 = 544 (month 12 = 1 year)

The range of time values describes the entire interval over which Georgiana would be interpolating is 0 to 30 minutes.

Now, According to the question:

We know that:

Linear model regression is used to predict the relationship between 2 variables by fitting the observed data in a linear equation.

What is the domain and range of a function?

The domain of a function is the set of x values for which it is defined, whereas the range is the set of y values for which it is defined.

As in the table, the minimum time for which the distance is defined is 0 minutes while the maximum time is 30 minutes. Therefore, the range of time values describes the entire interval over which Georgiana would be interpolating is 0 to 30 minutes.

                                     Distance over time

          Time(min)                                              Distance (miles)

              0                                                                   0

              5                                                                   4

             10                                                                   9

             15                                                                   13

            30                                                                   18

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Solving the provided question we can say that as exponents because one bacteria can expand to two bacteria, which can then multiply to four bacteria, which can then multiply to eight bacteria. hence, answer  A.

what are exponents?

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

because one bacteria can expand to two bacteria, which can then multiply to four bacteria, which can then multiply to eight bacteria. hence,

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