(03.05 MC)
A moon's elliptical orbit around a planet is modeled by the equation 225x2 +576y2 = 176,400, where distance is measured in megameters
(Mm). If the planet is the center of the orbit's path, what is the maximum distance between the planet and its moon?

Answer:

36.3 units²

Step-by-step explanation:

Area of a trapezoid = A = ((a+b)/2)h = [tex]\frac{a+b}{2}[/tex]h

a = 4

b = 1.5+7=8.5

solve for h using pythagorean theorem:

1.5² + h² = 6²

h² = 36 - 2.25 = 33.75

h = [tex]\sqrt{33.75}[/tex] = 5.81

A = [tex]\frac{4+8.5}{2}[/tex](5.81) = 36.3125

Negative two and three tenths repeating is greater than negative eight thirds.

What are inequalities ?

Inequalities in mathematics is when comparing two non equal quantities.

if a is greater than b we write a>b (3>2) and -a<-b (-3<-2)

a=3 and b =2

In the given question

We have to compare   and

=   = -2.3

= -2.6

So, from this we can say than -2.3 is greater than -2.6

⇒ -2.3 > - 2.6

The scale factor of the dilation is the ratio of the lengths of the corresponding sides of the two triangles. Since triangle ABC and triangle A'B'C' both have side lengths of AB, BC, and CA, the scale factor is 1.

1. Calculate the length of the sides of triangle ABC:

AB = length of side AB of triangle ABC

BC = length of side BC of triangle ABC

CA = length of side CA of triangle ABC

2. Calculate the length of the sides of triangle A'B'C':

A'B' = length of side A'B' of triangle A'B'C'

B'C' = length of side B'C' of triangle A'B'C'

C'A' = length of side C'A' of triangle A'B'C'

3. Calculate the scale factor of the dilation:

Scale factor = (AB/A'B') x (BC/B'C') x (CA/C'A')

= (length of side AB of triangle ABC / length of side A'B' of triangle A'B'C')

x (length of side BC of triangle ABC / length of side B'C' of triangle A'B'C')

x (length of side CA of triangle ABC / length of side C'A' of triangle A'B'C')

= 1 x 1 x 1

= 1

Therefore, the scale factor of the dilation is 1.

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The standard form of the given expression is -4f²-6f + 3. The algebraic operation is addition.

What is an expression?

An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4a - 5 is an expression in which the terms 4m and 5 are separated by the arithmetic sign - and a is the variable of the given expression.

Like terms in mathematics are summands in a sum that differ only by a numerical factor. By adding their coefficients, similar terms can be regrouped. Like terms in a polynomial expression are those that have the same variables to the same powers, but with different coefficients.

Given expression is

(-2f² -3f -5) + (-2f² -3f + 8)

Open the parenthesis:

= -2f² -3f -5 -2f² -3f + 8

Combine like terms:

= (-2f²  -2f²) + (-3f -3f) +(-5+8)

= -4f² -6f -3

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The equation of the curve in the XY-plane that passes through (0,3) and whose tangent line at a point (x,y) has slope 2x/y^2 is y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant.

The equation of a curve in the xy-plane is given by F(x,y) = 0. To find such a curve that passes through the point (0,3) and whose tangent line at a point (x,y) has a slope of 2x/y^2, we can use the method of implicit differentiation.

First, we can find the equation of the tangent line at a point (x,y) on the curve by computing the derivative of F(x,y) with respect to x and setting it equal to 2x/y^2. This gives us:

F_x(x,y) = 2x/y^2

Next, we can use the fact that the curve passes through the point (0,3) to set up the following equation:

F(0,3) = 0

Solving for F(x,y) in terms of x and y and substituting in the equation for F_x(x,y) gives the implicit equation of the curve is

y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant

This is the equation of a curve in the XY-plane that passes through the point (0,3) and whose tangent line at a point (x,y) has a slope of 2x/y^2.

Therefore, The equation of the curve in the XY-plane that passes through (0,3) and whose tangent line at a point (x,y) has slope 2x/y^2 is y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant.

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The absolute value of a number is always positive, but the number itself can be positive or negative, and there are always two possible solutions for the absolute value equation, one positive and one negative, that are the same distance from 0.

An absolute value equation of the form |x| = k (where k is a constant) will have two solutions, one positive and one negative, that are the same distance from 0 on the number line.

For example, if the equation is |x| = 5, the two solutions of the equation are x = 5 and x = -5.

This is because the absolute value of a number represents the distance of that number from 0 on the number line, and this distance is the same regardless of whether the number is positive or negative. Therefore, for any non-negative value k, there are two numbers that are that distance away from 0, one positive and one negative.

For example, the distance of 5 from 0 is 5 units, and the distance of -5 from 0 is also 5 units. Therefore, |5| = |-5| = 5.

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keeping in mind that a centroid cuts all medians at a 2 : 1 ratio, meaning that the median AE gets cut on a 2 : 1 ratio, meaning AG : GE = 2 : 1, Check the picture below.

The radius of the circle is 48 feet.

Circle:

The round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)

The arc length of a circle is given by the formula arc length = (angle/360) * 2 * pi * radius.

In this case, the angle is 75 degrees, and the arc length is 10* pi feet.

So, we can set up the equation: (75/360) * 2 * pi * r = 10 * pi

Solving this equation for the radius, we get: r = (10pi) / ( (75/360) * 2 * pi) = (10360) / 75 = 48 feet. So, the radius of the circle is 48 feet.

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Answer:

C.  37.5

Step-by-step explanation:

From inspection of the given triangle, we can see that the straight line that divides the triangle into two smaller triangles is an angle bisector since it divides the angle into two congruent angles.

Angle Bisector Theorem

An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

[tex]\implies x:15=40:16[/tex]

Solve for x:

[tex]\implies \dfrac{x}{15}=\dfrac{40}{16}[/tex]

[tex]\implies \dfrac{x}{15}=2.5[/tex]

[tex]\implies x=2.5\times 15[/tex]

[tex]\implies x=37.5[/tex]

Answer: ur mom

Step-by-step explanation: is so pretty

There are 48 different possible outcomes.

The total number of possible outcomes in a scenario like this is determined by finding the product of the number of possible outcomes for each individual event.

Independent events are events that are not affected by each other and have no influence on each other's outcome. The probability of two independent events occurring together is the product of their individual probabilities.

When flipping a coin, there are 2 possible outcomes (heads or tails).

When rolling a fair die with 4 sides, there are 4 possible outcomes (1, 2, 3, or 4).

When rolling a fair die with 6 sides, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6).

To find the total number of possible outcomes, we multiply the number of outcomes for each event:

2 * 4 * 6 = 48

Therefore, there are 48 different possible outcomes.

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On solving the provided question, we can say that The probability of a person purchasing both a beverage and gasoline is 0.060, or 6%.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

At a gas station, 84% of customers buy gasoline

[tex]P (A) = 0.84[/tex]

5% of customers buy gasoline and a beverage

[tex]P (B) = = 0.05[/tex]

conditional probability = P (A and B) = P(A) × P(B/A)

[tex]P(B/A) = P (A and B) / P(A)\\P ( B/A ) = 0.0595 = 0.060 or 6%\\[/tex]

The likelihood of a person purchasing both a beverage and gasoline is 0.060, or 6%.

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The balanced chemical equations, of the combustion reactions found by plugging in the right coefficients in front of the molecules according to the rules of conservation of atoms are;

1) 2C + 2O₂ ⇒ 2CO₂

2) CH₄ + 2O₂ ⇒ CO₂ + 2H₂O

3) 2C₄H₁₀ + 13O₂ ⇒ 8CO₂ + 10H₂O

A combustion reaction is one in which a combustible substance reacts with an oxidizer such as oxygen, to become oxidized.

1) 2C + ...O₂ ⇒ CO₂

The number of carbon atoms in the reaction side of the equation is 2, and the number of oxygen atoms in the reaction side are 2

In the product side of the equation, we get;

The number of carbon atoms = 1

The number of oxygen atoms = 2

The ratio of the number of oxygen atoms in the reaction side to the number of oxygen atoms in the product side = 1 : 1

The ratio of the number of carbon atoms in the reaction side to the number of oxygen carbon in the product side = 2 : 1

Multiplying the O₂ by 2 and the CO₂ by 2, we get;

2) CH₄ +... O₂ ⇒ CO₂ + ....H₂O

Reaction side;

Number of carbon atoms = 1

Number of hydrogen atoms = 4

Number of oxygen atoms = 2

Product side;

Number of carbon atoms = 1

Number of hydrogen atoms = 2

Number of oxygen atoms = 3

Set the coefficient of O₂ as 2, and the coefficient of H₂O as 2, we get;

The above equation is balanced

3) 2C₄H₁₀ + ...O₂ ⇒ ...CO₂ + ....H₂O

Reaction side;

Number of carbon atoms = 8

Number of hydrogen atoms = 20

Number of oxygen atoms = 2

Product side;

Number of carbon atoms = 1

Number of hydrogen atoms = 2

Number of oxygen atoms = 3

Multiply the O₂ by 13, the CO₂ by 8, and the H₂O by 10, we get the balanced equation as follows;

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As per the box plot diagram, the values of the three quartiles is 1254 and the interquartile range is 560.75

The term box plot in math is defined a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

Here we have given that following data give the total food expenditures for the past one month for a sample of 20 families.

And by using the given data, we have to plot the box plot then we get the following diagram,

By using the diagram, we have identified the following values,

Population size: 20

Median: 1055.5

Minimum: 427

Maximum: 2199

First quartile: 703.25

Third quartile: 1254

Interquartile Range: 560.75

Outlier: 2199

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The number of years after which the population is less than 6000 is 5 years.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation

We have,

The rate at which the population is decreasing per year = 7%.

The equation for the number of population after t years.

P = C [tex](1 - 0.07)^t[/tex]

Now,

After 5 years,

P = 8500 [tex](1 - 0.07)^5[/tex]

P = 8500 x [tex]0.93^5[/tex]

P = 8500 x 0.69

P = 5865

The population after 5 years is 5865 which is less than 6000.

Thus,

After 5 years the population will be less than 6000.

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The graph of the proportional relation is the one in the second option.

"a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1"

A general linear equation can be written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Particularly, if the y-intercept is 0, then we have:

y = a*x

We have a proportional relationship.

Notice that when x = 0 we have:

y = a*0

y = 0

So the proportional relationships always pass through the point (0, 0).

Then the correct option is the second one:

"a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1"

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The product of two rational numbers is a rational number.

In any field containing integers, rational numbers, along with addition and multiplication, produce a field that also contains the integers. In other words, a field only has characteristic zero if and only if it contains the field of rational numbers as a subfield. The field of rational numbers is a prime field.

"A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator 'p' and a non-zero denominator 'q'."

Therefore, when we are multiplying two rational numbers, their product must be a rational number.

This is because, numerators of both rational numbers are integers and denominators of both the numbers are non-zero integers.

Hence, the product is a rational number.

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The number of candy bars that Beth has sold, given the total they have sold and the amount sold by Carly, is 125 candy bars

To find the number of candy bars that Beth has sold, you can assume that the amount of candy sold by Carly is denoted as x.

This means that the amount of candy bars sold by Beth is:

= 2x - 1

The total sold by both Beth and Carly is therefore:

= 2x - 1 + x

The number of candy bars sold by Carly is:

188 = 2x - 1 + x

188 = 3x - 1

3x = 188 + 1

x = 189 / 3

x = 63

This means that the candy bars sold by Beth is:

= 2 ( 63 ) - 1

= 126 - 1

= 125 candy bars

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Answer:

Step-by-step explanation:

To prove that the diagonals of an isosceles trapezoid are congruent, we will first define the terms and draw a diagram of the isosceles trapezoid.An isosceles trapezoid is a quadrilateral with two congruent legs, a pair of parallel bases, and congruent base angles.Let's call the isosceles trapezoid ABCD and let the parallel sides be AB and CD, and the congruent legs be AD and BC. Let the diagonals be AC and BD.Since, AD and BC are congruent legs, therefore ∠BAD = ∠CAD by the definition of congruent legs.And since ABCD is a trapezoid, therefore, AB || CD and therefore, ∠BAD = ∠CBD, due to alternate angles are congruent.Therefore, ∠CAD = ∠CBD, by CPCTC (corresponding parts of congruent triangles are congruent)AC = BD , since both are congruent by ASA (angle-side-angle) congruence.Thus, the diagonals of an isosceles trapezoid are congruent.

Correct option is A, the cost of the meal plan is non-linear.

The simplest approach to tell if a function is linear is to look at its graph. A linear function produces a straight line on a graph. A nonlinear function is not straight and is curved in some way. A linear function results in a straight line on a graph. As a result, non-linear functions can be of any kind. Although determining a function's linearity from its input/output table or equation is the simplest method, it is also possible to do so.

Based on the given conditions, formulate:

The definition of linear function

8-10 meals = (135-123) = (10-8) =10/2=5

10-12 meals: (155-135) = (12-10)

=20/2

= 10

12-21 meals: (220-155) = (21-12)

= 65/9

=7 2/9

5 < 7 2/9 < 10

So the cost of the meal plan is non-linear.

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Complete question -

A. 73.91% of respondents were under the age of 30 and did not snore.

B. Data show that snoring is not age-independent as most snorers are over 30 years of age.

A. The first step is to convert all percentage population groups into numbers. This helps make things clearer.

Total number of adults surveyed = 995 adults

Number of adults over the age of 30 = 81.5% of 995

                                                              = 81.5/100 × 995

                                                              = 810.925

                                    ≈ 811(part of the population can be counted).

Number of adults under 30 = 995 - 811 = 184 adults.

Number of all adults who snore = 36.8% of 995

= 36.8/100 × 995 ≈ 366 adults who snore

Of the total 995, 32% of the snorers were over 30 was.

Number of snorers over 30 × 995 ≈ 318 adults

Snorers under 30 = 366 - 318 = 48 adults

Number of under 30s recorded 30 - under 30 snorers

= 184 - 48 = 136

Converting this to percentage: 136/184× 100 = 73.91%

so 73

B. From the data, snoring is not independent of age as most of the people that snored were above 30 years. Snoring is related to the age. This is because that the most of the younger adults did not snore, while more of the older adults snored.

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So, on solving the provided question we can say that Percent = 140/250 x100 = 56%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

A percentage is a ratio of one unit of an event's result to the entire sample multiplied by 100%. It denotes parts per 100. We divide the percentage of the sample that liked the options by the total sample to arrive at the calculation. As a result, we compute:

Percent = 140/250 x100 = 56%

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It can be concluded that -

Given are the questions as shown in the image.

[1] -

Greater is the value of amount of tablespoon of sugar per oz of tea, sweetest it will be.

For table {1}, we can write -

m₁ = (12/18) = 2/3

For table {2}, we can write -

m₂ = 6/16 = 3/8

m₁ = 2/3 = (2 x 8)/(3 x 8) = 16/24

m₂ = 3/8 = (3 x 3)/(8 x 3) = 9/24

m₁ > m₂

Version A of iced tea will be sweetest.

[2] -

Greater is the value of amount of strawberry puree per unit of the total amount of liquid, stronger will be the strawberry flavor.

For Nick -

m₁ = 8/12 = 80/120

For Sam -

m₂ = 12/20 = 72/120

m₁ > m₂

Hence, Nick's claim is true.

Therefore, it can be concluded that -

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Answer:

Step-by-step explanation:

To make a boxplot, we need to know the minimum, Q1, median, Q3, and maximum.

The minimum is the smallest value: 15

The maximum is the largest value: 34

The median is found by arranging the numbers from smallest to largest and finding the middle point:

15, 20, 25, 25, 27, 28, 30, 34; there is not an exact middle here so we take the two middlemost points and divide by 2: 25+27/2 = 52/2 = 26

Q1 takes the numbers to the left of the median and finds the middle of those points. 15, 20, 25, 25. Again, there is no exact middle, so we use the same method as above. 20+25/2 = 22.5

Q1 takes the numbers to the right of the median and finds the middle of those points. 27, 28, 30, 34. Again, there is no exact middle, so we use the same method as above. 28+30/2 =  29

Now, use these points to construct!

Answer:

BOX 2

Step-by-step explanation:

look at the photo

Answer:

x=17

Step-by-step explanation:

the sumof angles of triangle is 180

so 6x+10+x+17+4x-34=180

11x-7=180

11x=187

x=17

Answer:

x = 17

Step-by-step explanation:

Since we know the angles of a triangle add up to 180, we can make the equation:

6x + 10 + x + 17 + 4x - 34 = 180

Then, we add 34 to both sides and put like terms near each other:

6x + x + 4x + 10 + 17 = 214

Then, combining like terms and subtracting 27 from both sides gives us:

11x = 187

Divide both sides by 11 gives us:

x = 17

So, the value of x = 17.

Hope this helped!

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You need to deposit $55,555 each year until your retirement to achieve your retirement goal.

To find the amount you need to deposit each year, you need to calculate the present value of your future withdrawals, considering the time value of money and taking into account the interest rate.

One way to do this is to use the formula for present value:

PV = FV/(1 + r)^t

where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years until the future value.

In this case, FV is $50000 per year for 30 years, so the total future value is $50000 × 30 = $1,500,000. And t is 15 years, so the present value is:

PV = $1,500,000/(1 + 0.04)^15 = $1,500,000/1.8 = $833,333

So, you need to deposit $833,333/15 = $55,555 each year until you retire to achieve your goal.

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The required expected value of the score is 4.92.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

A long hit with success has a 0.4 chance of happening. The following formula can be used to determine which strategy—the short hit or the long hit—will improve the expected value of the score:

Expected value of long hit = P(successful hit)4.2 + P(unsuccessful hit)5.4

= 0.4×4.2 + (1 - .04)×5.4

= 4.92

Thus, required score is 4.92.

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The domain and range for the function W = 15T + 400 is domain = set of all real numbers from 0 to 90 and range = set of all real numbers from 400 to 1750.

What is the range and domain of a function?

A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range. It is only a function in a relation if each x value has exactly one y value.

The collection of all potential inputs for a function is its domain.

The function for Total amount of water in the tank is given as -

W = 15T + 400

Where, T is the total number of minutes when the water is added.

So, according to the definition of range and domain -

T = domain = Number of minutes when the water is added

W = range = Total amount of water in the tank

W was a function of T for the next 90 minutes.

So, the domain will be the set of all real numbers from 0 to 90.

At, T = 0 -

W = 15(0) + 400

W = 400

At, T = 90 -

W = 15(90) + 400

W = 1350 + 400

W = 1750

So, the range will be set of all real numbers from 400 to 1750.

Therefore, the domain and range is (0,90) and (400,1750) respectively.

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According to the given measurement, the total amount of intake is 621.0435 ml

Here we have given the following measurements they are listed as follows:

=> 1/2 cup of orange juice,

=> 2/3 glass of milk, full cup of lemonade,

=> full glass of water,

=> 1 popsicle (3 ounces) and

=> 4 ounces ice chips.

Here we also know that

1 cup = 8 oz

1 glass = 6 oz

And as per the Si measurements,

1 oz = 29.5735 ml.

To order to calculate the total amount of intake we have to sum all the given measurements, then we get,

=> 1/2(8) + 2/3(6) + 6 + 3 + 4

When we simplify this one then we get,

=> 4 + 4 + 6 + 3 + 4 = 21

Now, we have to convert ounce into milliliter, for that we have multiply 29.5735 with the total measurement, then we get,

=> 21 x 29.5735 = 621.0435 ml

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Answer:

[tex]\boxed{a_5 = 40.5}[/tex]  

Step-by-step explanation:

Common ratio r of a geometric sequence is the ratio of each term to the previous term and is a constant

Thus if you have a sequence a₁, a₂, a₃, a,...
[tex]r = \dfrac{a_2}{a_1} = \dfrac{a_3}{a_2} = \dfrac{a_4}{a_3} \cdots[/tex]

For a geometric sequence with common ratio [tex]r[/tex] and a starting value of [tex]a_1[/tex]the nth term is given by the formula:
[tex]a_n = a_1r^{n-1}[/tex]

Here [tex]a_1 = 8, r = 1.5[/tex]

and we are asked to find the 5th term

[tex]a_5 = 8 \times 1.5^{(5-1)}\\\\= 8 \times 1.5^4\\\\=40.5\\\\[/tex]ANSWER

The terms of the sequence are
8, 12, 18, 27, 40.5 with 8 being the first term and 40.5 the 5th term