Prove x²+y² = (x+y) (x-y)​

Answer:

16.24 Units

Step-by-step explanation:

The perimeter of the triangle is the sum of the length of the sides of the triangle. Given the points on the vertices, the length of each side may be found using the formula

Length = √(x2 - x1)^2 + (y2 - y1)^2

Considering the pair (-1, 2), (3, 1), the length of that side

= √(3 -- 1)^2 + (1-2)^2)

= √(16 + 1)

= √17 units

Considering the pair (-1, 2), (7, 2), the length of that side

= √(7 -- 1)^2 + (2-2)^2)

= √(64)

= 8

Considering the pair  (3, 1),  and (7, 2), the length of that side

= √(7 - 3)^2 + (2  - 1)^2

= √(16 + 1)

= √17

Hence the perimeter of the triangle

= √17 + 8 + √17

= 4.12 + 8 + 4.12

= 16.24 Units

Sample size n= 601 (rounded up) needed for 90% confidence, 4% margin of error, assuming p=0.5.

To conclude the model size expected to measure a general population degree with a security cradle at 90% conviction, we can use the condition:

n = \((z^2 * p * q)/E^2\)

Where:

n is the model size

z is the z-score

p is the surveyed people degree

q is 1-p

E is the ideal wellbeing cradle

we can expect a protected estimate for p of 0.5, which grows the model size.

Expecting a security cushion of 4%, we have:

n = \((1.645^2 * 0.5 * 0.5)/0.04^2\)

n ≈ 600.25

We need a model size of something like 601 to get a space for compromise of 4% at 90% sureness, assembling to the accompanying whole number.

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Answer:

To get the Greates Common Factor (GCF) of 39375 and 779625 we need to factor each value first and then we choose all the copies of factors and multiply them:

39375:    3 3     5 5 5 5 7  

779625:    3 3 3 3 5 5 5   7 11

GCF:    3 3     5 5 5   7  

The Greates Common Factor (GCF) is:   3 x 3 x 5 x 5 x 5 x 7 = 7875

Step-by-step explanation:

Answer:

192\(feet^3\)

Step-by-step explanation:

The formula for the area of a rectangle is : \(length*width\)

In order to work out the volume you would first need to work out the area. You can do this by multiplying the length of 6 by the height of 4, this gives you 24.

To workout the volume you would need to multiply the area of 24 by the width of 8, this gives you 192.

1) Multiply 6 by 4.

\(6*4=24\)

2) Multiply 24 by 8.

\(24*8=192 feet^3\)

The following specific topics are covered in 8th grade math:

-Mathematical operations

-Resolving equations with a single unknown

- One-variable linear equations

-Expressions in algebra

- square roots and squares

- Geometry

- Cube and cube root

-Data management

These are the headings that were previously mentioned. These subjects need to be investigated in depth going forward.

Algebraic expressions: What are they?

Using letters or alphabets to represent numbers without giving their exact quantities is the idea behind algebraic expressions. The fundamentals of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables.

What components make up one-variable linear equations?

One-variable linear equation is represented by the following equation:

A and B are two integers, and X is a variable, hence ax+b = 0. There is just one answer to this equation.

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Answer:

$5026

Step-by-step explanation:

if you divide 70 by 15 you get 4.66666667

then multiply 4.6666667 by 1077 and you get 5026

Answer:

Step-by-step explanation: If the square is 30 ft on one side the other side must be too. So 30x30 = 900. Now, we know the rectangle must also be 900 in area. So, the width must be 10feet and the length must be 90ft because 10x90 is also 900. How I got the length? I did 10x2+70.

The population of the town will be 64000 in 2024.

In this problem we have the case of an exponential model representing the population of a town. Exponential models are represented by the following formula:

y = a · rⁿ

Where:

According to the statement, the town has an initial population of 250, represented by the initial population (a), and increases its population by a factor of 2, represented by the common rate (r).

If we know that a = 250, r = 2 and n = 8, then the estimated population of the town in 2.024, that is, 8 years after 2.016 is:

y = 250 · 2⁸

y = 250 · 256

y = 64000

The population will be 64000 in 2024.

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Answer:

Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. We may determine the scale factor by dividing these distances by 2.

Step-by-step explanation:

Answer:

Distributive property

Step-by-step explanation:

In order to solve this equation we first need to distribute 3 into 2y+5, we use the distributive property to do this.

To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

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Answer:

b. x > -6

Step-by-step explanation:

> [greater than], and < [less than] inequalities are not filled in because the value is not included, but is only greater or less than.

≥ [greater than or equal to], and ≤ [less than or equal to] inequalities are filled in because the value is included, and it is greater than or less than.

Given that there is an empty circle with an arrow moving in the positive direction from -6, the inequality must be a greater than, and since the value is -6, x > -6.

Probability of rolling a 6 on a single die is 1/6

There are two vowels out of 5 ( A and E)

The probability of getting a vowel would be 2/5

The probability of getting both a 6 and a  vowel would be 1/6 x 2/5 = 2/30 = 1/15

Answer: 1/15

Answer:

For people who have answers options 1/30, 1/6, 4/15, 1/3 The answer is 4/15!

Step-by-step explanation:

I took the k12 6.11 Quiz: Compound Probability question 5
Good luck on the other questions!

\( \frac{x}{4} = - 12 \: \: multiply \: \: both \: \: sides \: \\ \\ 4 \times \frac{x}{4} = 4 \times ( - 12) \: \: reduce \: \: and \: \: multiply \: \\ \\ = x = - 48 \\ \\ hope \: \: it \: \: helps\)

A linear-quadratic state estimator and a particle filter are both estimation techniques used in control systems, but they differ in their underlying principles and application domains.

A linear-quadratic state estimator, often referred to as a Kalman filter, is a widely used optimal estimation algorithm for linear systems with Gaussian noise. It assumes linearity in the system dynamics and measurements. The Kalman filter combines the predictions from a mathematical model (state equation) and the available measurements to estimate the current state of the system. It provides a closed-form solution and is computationally efficient. However, it relies on linear assumptions and Gaussian noise, which may limit its effectiveness in nonlinear or non-Gaussian scenarios.

On the other hand, a particle filter, also known as a sequential Monte Carlo method, is a non-linear and non-Gaussian state estimation technique. It employs a set of particles (samples) to represent the posterior distribution of the system state. The particles are propagated through the system dynamics and updated using measurement information. The particle filter provides an approximation of the posterior distribution, allowing it to handle non-linearities and non-Gaussian noise. However, it is computationally more demanding than the Kalman filter due to the need for particle resampling and propagation.

The choice between a linear-quadratic state estimator and a particle filter depends on the characteristics of the system and the nature of the noise. The Kalman filter is suitable for linear and Gaussian systems, while the particle filter is more versatile and can handle non-linearities and non-Gaussian noise. However, the particle filter's computational complexity may be a limiting factor in real-time applications.

In summary, a linear-quadratic state estimator (Kalman filter) is a computationally efficient estimation technique suitable for linear and Gaussian systems. A particle filter, on the other hand, provides more flexibility by accommodating non-linearities and non-Gaussian noise but requires more computational resources. The choice between these methods depends on the specific system characteristics and the desired accuracy-performance trade-off.

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Using the z-distribution, the 95% confidence interval to describe the total percentage of students who do not like ice cream is:

(8.34%, 17.66%).

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

In this problem, we have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

For this problem, the estimate and the sample size are given, respectively, by:

\(\pi = 0.13, n = 200\)

Hence the bounds of the interval are:

As a percentage, the interval is:

(8.34%, 17.66%).

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Answer:

34.8%

Step-by-step explanation:

$600+15%

=600+15/100*600

=600+90

=$690

You have $450 and you want to purchase a product of $690(regular price+sales tax)

$690-$450

=$240

Percentage of $240 discount

=240/690*100

=34.78%

Approximately 34.8%

Answer:

18.2

Step-by-step explanation:

divide 91 by 5

x x x x x. x x x x x x x x x x xx. x

a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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The slope of the line will be 1/2 in the given graph.

The slope of the line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The graph is given in the question.

According to the given graph, we can take two points (2, 2) and (6, 4).

The line passes through points (2, 2) and (6, 4).

Let

x₁ = 2, y₁ = 2

x₂ = 6, y₂ = 4

∵ Slope m = (y₂ - y₁)/(x₂ -x₁  )

Substitute values in the formula

The slope of line = (4 - 2)/(6-2)

The slope of line = (2)/(4)

The slope of line = 1/2

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The distance between your house and school is 4.1 miles.

According to the given question.

Point c represents your house.

Point d represents post office which is directly west to the point c i.e from house.

And point e represents school which is west of the post office.

Also, it is given that the distance between house and post office, cd is 1.7 miles.

And the distance between the post office and school,de is 2.4 miles.

Now, if we see the attached figure we can say that

cd + de = ce

⇒ 1.7miles  + 2.4miles  = 4.1 miles

Hence, the distance between your house and school is 4.1 miles.

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Answer:

I’m joining rn does it still work?

Step-by-step explanation:

Answer:

It's not very high

Step-by-step explanation:

The angle that the string and the ground maje, is acute, because it's smaller than a right angle. So, since it is an acute angle, it's not very high. It is about 30cm high.

Suppose that b is a positive integer greater than or equal to 2. When 197 is converted to base b, the resulting representation has 4 digits. What is the number of possible values for b?

The possible values of b are 4 and 5

The conditions are given as:

So, we start by converting 197 to base 2 and above.

This is done as follows:

197 to base 2

2 | 197

    98 R 1

    49 R 0

    24 R 1

    12 R 0

    6 R 0

    3 R 0

    1 R 1

    0 R 1

So, we have:

197 = 11000101 in base 2

11000101 has more than 4 digits.

This means that b cannot be 2

Using the above method of conversion, we have:

See that as the base increases, the number of digits decreases.

The numbers in base 4 and 5 have 4 digits.

Hence, the possible values of b are 4 and 5

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The given expression is equivalent to 28.

We have the following expression -

c - 3y

We have the given expression as -

c - 3y

For c = 7 and y = - 7, we can write -

7 - 3(- 7)

7 + 21

28

Therefore, the given expression is equivalent to 28.

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Answer:

Step-by-step explanation:

To express the confidence interval 0.039 < p < 0.479 in the form p ± E, we need to find the midpoint of the interval and half of the width.

The midpoint of the interval is the average of the lower and upper bounds:

Midpoint = (0.039 + 0.479) / 2 = 0.259

The width of the interval is the difference between the upper and lower bounds:

Width = 0.479 - 0.039 = 0.44

Half of the width is obtained by dividing the width by 2:

Half Width = 0.44 / 2 = 0.22

Therefore, the confidence interval 0.039 < p < 0.479 can be expressed as:

p ± E = 0.259 ± 0.22

So, the correct option is:

D. 0.259 ± 0.22

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Answer:

It's 38.

Step-by-step explanation:

the sum of three consecutive even integers is 108, the largest number in the sequence would be 38.

I hope this helps you!

Answer:

We can use algebra to solve this problem. Let's call the smallest of the three consecutive even integers x. Since the integers are consecutive and even, the next two integers will be x+2 and x+4.

The problem states that the sum of three consecutive even integers is 108, so we can write an equation:

x + (x+2) + (x+4) = 108

We can simplify this equation by combining like terms:

3x + 6 = 108

3x = 102

x = 34

So, the smallest of the three consecutive even integers is 34.

The next two integers will be x+2 = 34+2 = 36 and x+4 = 34+4 = 38

The largest number of the three consecutive even integers is x+4 = 38.