Determine The Pythagorean Triple Generated With X= 6, Y = 2. (2024)

The bird is 55 ft above the ground

How to find her horizontal distance from the turtle?

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Check the attached image for the drawing.

From the drawing:

sin 30° = x/100 (opposite/hypotenuse)

x = 100 * sin 30°

x = 50 ft

height of the bird above the ground = x + 5

height of the bird above the ground = 50 + 5 = 55 ft

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The mean weight of the three reserve players is 221 pounds.

We can begin by finding the total weight of the nine players:

9 players x 177 pounds per player = 1593 pounds

Next, we can find the total weight of all twelve players (nine players and three reserves):

12 players x 188 pounds per player = 2256 pounds

To find the total weight of the three reserve players, we can subtract the weight of the nine players from the weight of all twelve players:

2256 pounds - 1593 pounds = 663 pounds

Finally, to find the mean weight of the three reserve players, we divide their total weight by their number:

663 pounds / 3 players = 221 pounds

Therefore, the mean weight of the three reserve players is 221 pounds.

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The highway has had a negative effect on the genetic diversity of the Florida panther population by reducing gene flow and increasing genetic differentiation between the northern and southern subpopulations.

This can lead to a decrease in genetic variation within each subpopulation and a loss of adaptive potential, which may increase the risk of inbreeding depression and reduced fitness.

Assuming Hardy-Weinberg equilibrium, the expected value of Fst under random mating is:

Fst = (Ht - Hs) / Ht,

where Ht is the expected heterozygosity of the total population and Hs is the expected heterozygosity of the subpopulations.

If we assume that the two subpopulations have equal effective population sizes of 75 individuals, then the expected heterozygosity of the total population is:

Ht = (2 * 75 * (1 - (1/2N))) / (2 * 75 - 1),

where N is the total population size (150 in this case) and 1/2N is the frequency of alleles that are identical by descent due to common ancestry.

Since the subpopulations are assumed to be in Hardy-Weinberg equilibrium, the expected heterozygosity of each subpopulation is:

Hs = 2pq,

where p and q are the frequencies of the two alleles in each subpopulation.

With an Fst of 0.1, we can use the above equations to solve for p and q in each subpopulation. We find that p = 0.73 and q = 0.27 in the northern subpopulation, and p = 0.66 and q = 0.34 in the southern subpopulation.

Comparing these frequencies, we can see that there is a significant genetic differentiation between the two subpopulations, indicating limited gene flow between them. The highway likely acts as a barrier to dispersal, preventing or reducing the movement of individuals between the northern and southern subpopulations.

Therefore, we can conclude that the highway has had a negative effect on the genetic diversity of the Florida panther population by reducing gene flow and increasing genetic differentiation between the northern and southern subpopulations. This can lead to a decrease in genetic variation within each subpopulation and a loss of adaptive potential, which may increase the risk of inbreeding depression and reduced fitness.

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Answer:

[tex]x^{2}[/tex]-[tex]\frac{2}{3}x[/tex]+[tex]\frac{1}{9}[/tex]-[tex]\frac{1}{3(3x-4)}[/tex]

Step-by-step explanation:

Answer:

Cylinder, pyramid, cube, cuboid, prism

Step-by-step explanation:

If Henry has 878 pegs in each box if there are 7 boxes then he has 6146 total pegs.

Number of pegs in one box = 878

Thus, number of pegs in 7 boxes = 878 × 7

= 6146 pegs

Hence Henry has 6146 pegs in 7 boxes.

This is a concept of multiplication. Multiplication in mathematics is a technique for determining the sum of two or more numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main application that is obvious.

In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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The percentage that Tom will be charged is 2 % per month or 24 % per annum.

The expression for the amount owed to the grandfather is 250 + 8 (5.00).

The expression for the amount owed to the bank is 250 (1.02 ) ^ 8.

How to find the percentage ?

The percentage can be found by dividing the interest payment by the total amount borrowed :

= 5 / 250

= 2 %

In a year, this is :

= 2 % 12 months

= 24 %

The expression for the amount owed to the bank is 250 (1.02)^8 because this is the way compound interest is represented. The other expression is therefore owed to the grandfather.

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eigenvalues.

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Between 100 and 1000 perfect cubes are 10-5+1=boxed6.

As per the question given,

To find the number of perfect cubes between 100 and 1000, we can find the largest perfect cube less than or equal to 1000 and the smallest perfect cube greater than or equal to 100, and then count the number of perfect cubes between them.

The largest perfect cube less than or equal to 1000 is 10^3=1000. The smallest perfect cube greater than or equal to 100 is 5^3=125. Therefore, the perfect cubes between 100 and 1000 are the cubes of the integers from 5 to 10, inclusive. There are 10-5+1=\boxed{6} perfect cubes between 100 and 1000.

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If the sum of two numbers is 4 and one number is -6, then the second number is 10

The sum of two numbers = 4

The first number = -6

Consider the second number as x

Then the equation will become

The first number + second number = The sum of two numbers

The second number = The sum of two numbers - The first number

Substitute the values of each term in the equation

-6 + x = 4

Move -6 to the right-hand side of the equation

x = 4 + 6

Addition of the numbers in the equation

x = 4 + 6

x = 10

Therefore, the second number will be 10

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The expression when the fractions are equivalent is 3/4 = 6/8

How to make the fraction equivalent

From the question, we have the following parameters that can be used in our computation:

3/4 = []/8

Represent the blank with a variable x

So, we have the following representation

3/4 = x/8

Make the variable x the subject of the formula

So, we have the following representation

x = 8 * 3/4

Evaluate

x = 6

Hence, the missing numerator is 6

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Complete question

Fill in the missing numerators to make equivalent fractions ​

3/4 = []/8

The dimensions of the garden are 24 ft by 29 ft.

Let's say the width of the rectangular garden is x feet.

Then the length is 5 feet longer than the width, so the length is (x+5) feet.

The area of a rectangle is given by the formula: A = length x width.

We are given that the area is 696 square feet, so we can set up the equation:

696 = (x+5) * x

Simplifying this equation, we get:

696 = x^2 + 5x

Rearranging terms, we get:

x^2 + 5x - 696 = 0

This is a quadratic equation that can be factored as:

(x + 29)(x - 24) = 0

So the solutions are x = -29 or x = 24.

Since the width can't be negative, we can discard x = -29 and conclude that the width of the garden is 24 feet.

The length is 5 feet longer than the width, so the length is:

x + 5 = 24 + 5 = 29

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Answer:

I have questions about how to make the sentence easier

The car rises by approximately 16.43 meters along the vertical direction.

How to determine the vertical distance through which the car rises​

The vertical distance through which the car rises is equal to the component of the distance traveled that is perpendicular to the ground.

If the road is inclined at an angle of 8° to the horizontal, then the angle between the direction of motion and the horizontal is also 8°.

Therefore, the component of the distance traveled that is perpendicular to the ground is:

d = 120 sin 8°

Using a calculator, we get:

d ≈ 16.43 meters

Therefore, the car rises by approximately 16.43 meters along the vertical direction.

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The amount payable to the boys out of GHC144 is GHC 86.4.

What is Ratio?

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Total amount = GHC 144

Ratio = 3 :2

Total of ratio= 3+ 2 = 5

So, amount that boys will get

= 3/5 x 144

= GHC 86.4

and, amount that girls will get

= 2/5 x 144

= GHC 57.6

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The values of the function increase as the x-values approach negative infinity.

Limit of function:

The theory of limits of functions serves as the basis for calculus because it underpins the concept of a derivative. How do limits work?Let's explain what "limit" means using an illustration. Consider the function f. (x). X should have values that are close to the provided constant "a." Then, the relevant set of values are taken by f(x).

It is determined that the following choice of the function's end behavior is correct using limit concepts:

The values of the function increase as the x-values approach negative infinity.

------------------------------

The end behavior of a function f(x) is given by [tex]\lim_{x \to \infty} f(x)[/tex]

We can see from the graph that the function grows when x approaches both negative and positive infinity since y is heading upward. Thus,

[tex]\lim_{x \to \infty}f(x)= \infty[/tex] , and thus, the correct option is the second one, that is:

The values of the function increase as the x-values approach negative infinity.

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The complete sentence is, There are 12 quarters in 3 units.

What is a quarter?

A quarter represents one-fourth of the whole part.

A quadrant of a circle is the quarter of the complete circle.

From the given information 3 lines are given and each line is divided into 4 parts so we can call each part a quarter.

Therefore, The statement is, There are 12 quarters in 3 units.

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If a system of two linear equations has one solution, the two lines will intersect at exactly one point on the graph.

What is a Linear Equation?

A linear equation is the one in which the variables are raised to power 1 or -1.

The solution of an equation refers to all the possible values of the variable that can satisfy the equation.

Linear equations can be solved graphically by plotting the lines of the given equations and the point of intersection of lines gives the solution.

The lines will intersect as many times as there are solutions to the given system of linear equations.

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The values of the expected number and probability are;

Option C. E(sales) = 6.45

Option A. P(10 sales) = 5.4%

How to determine the value

The formula for calculating the expected number of sales is expressed as;

E = N × P

Given that the parameters are;

E is the expected numberN is the number of trialsP is the probability of successes

Then, we have;

E(sales) = 129 × 0. 05

multiply the values

E(sales) = 6.45

The probability of teleworker making 10 sales;

P(10 sales) = 6.45/129-10 × 100/1

P(10 sales) = 5.4%

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a) The probability that at least 879 actually did vote is given as follows:

P(X≥879​) = 0.0244.

b) The result suggests that there is enough evidence to consider that the proportion is greater than 69%, as the probability is less than 0.05.

How to obtain probabilities using the normal distribution?

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].

The parameters of the binomial distribution for this problem are given as follows:

n = 1227, p = 0.69.

Hence the mean and the standard deviation are given as follows:

[tex]\mu = 1227 \times 0.69 = 846.63[/tex][tex]\sigma = \sqrt{1227 \times 0.69 \times 0.31} = 16.2[/tex]

The probability that at least 879 people voted, using continuity correction, is one subtracted by the p-value of Z when X = 878.5, hence:

Z = (878.5 - 846.63)/16.2

Z = 1.97

Z = 1.97 has a p-value of 0.9756.

1 - 9756 = 0.0244 = 2.44%.

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Answer:

qualitative and ordinal.

Step-by-step explanation:

They are both two types of qualitative data under Categorical data.

Nominal and ordinal are the levels of measurement for which data can be qualitative. Therefore, the correct option is option A, D.

What is level of measurement?

A categorization that describes the type of information contained inside the importance attributed to variables is called level of measurement and scale of measure. The most well-known classification was created by psychiatrist Stanley Smith Stevens and included four levels or measurement scales: nominal, ordinal, interval, or ratio.

This system of defining several measurement levels originated within psychology and has drawn heavy criticism from academics in other fields. Additional classifications include those made by Chrisman, Mosteller, and Tukey. Nominal and ordinal are the levels of measurement for which data can be qualitative.

Therefore, the correct option is option A, D.

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Answer:

x = 0 and x = 1

Step-by-step explanation:

Look in the second and third columns where the number is the same.

On the row where x = 0, both f(x) and g(x) turn out to be 1.

On the row where x = 1, both f(x) and g(x) turn out to be 1/2.

They are asking you to point out where f(x) and g(x) are the same. This is happening at x = 0 and x = 1

In case you didn't know, on some of the online platforms, when the answers have circles beside them, there is one right answer. When the answers have squares beside them, you are able to mark more than one right answer (which there may or may not be more than one right answer.)

The probability of exactly three of the hearts are white is 0.3061

Total number of candy heart = 52

Number of white candy heart = 20

Number of yellow candy heart = 10

Number of pink candy heart = 2

Number of green candy heart = 12

You select 7 pieces of candy randomly from the box, without replacement.

The number of ways to select 3 white hearts out of 20

= C(20, 3) = 1140

The number of ways to select 4 non-white hearts out of 32

C(32, 4) = 35960

Total number of ways to select exactly three white hearts

= 1140 * 35960

= 41006400

The total number of ways to select 7 hearts out of 52

C(52, 7) = 133784560

Probability of selecting exactly three white hearts

41006400 / 133784560

= 0.3061

Therefore, the probability is 0.3061

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The index form is simplified to -12x4y²4z

What are index forms?

Index forms are described as mathematical forms of writing numbers or variables that are large or small in a more convenient way.

Other names for index forms are;

Scientific notationStandard forms

They are are numbers with power or exponents of variables or numbers.

From the information given, we have that;

( -3x³y²z)4​

To simply, expand the bracket, we have;

-12x4y²4z

Hence, the expression is -12x4y²4z

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The mean can be calculated by adding the numbers together and dividing the result by the number of observations. The mean of scores is 81.

What is Mean?

In mathematics and statistics, the concept "mean" refers to the mean of a set of variables. There are several ways to determine the mean, including geometric means, harmonic means, and simple arithmetic means (putting the numbers together and dividing the result by the amount of observations).

How to Find the Mean

Finding the mean is very simple. Add up all the numbers, then divide it by the quantity of observations. The mean formula is below:

[tex]\frac{x_1+x_2+,,,,,,,,,,x_n}{n}[/tex]

We know that mean of a given set of data,

[tex]Me an=\frac{Total Sum of given data }{total number of values given}\\\\\\ Mean=\frac{90+87+58+79+91}{5} \\\\Mean=\frac{405}{5} \\\\Mean=81[/tex]

Hence, mean of the given scores is 81.

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An expression for the percent error in Theresa estimate is (5.4-5)/5 ×100.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Theresa estimated that a caterpillar was 5 centimeters long. Later, she found its actual length to be 5.4 centimeters.

Now, percent error = (Actual length-Expected length)/Expected length ×100

= (5.4-5)/5 ×100

= 0.4/5 ×100

= 0.08×100

= 8%

Therefore, the percent error in Theresa estimate is 8%.

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The fraction with the required denominator is (-2p -p²)/(4-p²).

What is a fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

A fraction, p/p-2.

To change the denominator to 4-p²:

Multiply and divide the fraction by (-2-p),

we get,

p/(p - 2) x (-2-p)/ (-2-p)

= (-2p -p²)/(4-p²)

Therefore, the fraction is (-2p -p²)/(4-p²).

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Arun's mistake is that for the multiplication of 24 by 1, he should have added only one zero, instead of two zeros.

The correct result of the product is of 288.

How to multiply the numbers?

The multiplication operation for this problem is given as follows:

24 x 12.

Then the two separate products are given as follows:

24 x 2 = 48.24 x 1 = 24.

To the (n - 1)th product, we add a zero, and then add each product, hence the result is given as follows:

48 + 240 = 288.

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