what distribution is used with the global test of the regression model to reject the null hypothesis?

The values of x and y the triangles to the fight congruent are x = 3 and

y = 1.

What is congruent triangles?

Triangles with the same size and shape are said to be congruent. This implies that the corresponding sides and angles are both equal. Without comparing every angle and side of the two triangles, we can determine whether two triangles are congruent.

If given these triangles are congruent then all corresponding side must be equal

As we can see that both triangle are right triangle

Therefore hypotenuse of one triangle equal to another

x+1  = 4y   ..... (A)

And lenght ( height)  of one  must equal to another triangle

x = y +2          .... (B)

therefore

Plug the value of x = y + 2 in equation A

y + 2 + 1 = 4y

        3y = 3

          y = 1

and x = y+2

x = 1 + 2

x = 3

Hence, the values of x and y the triangles to the fight congruent are

x = 3 and y = 1.

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Complete question:

Complete question is attached below.

The Least-squares problem that has minimal norm can be given using factorization.

The least squares method is used to find the best fit for a set of data points by minimizing the sum of the offsets from the plotted curve. Singular value decomposition (SVD) is a factorization of a real or complex matrix.

It is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix. The singular value decomposition, guaranteed to exist, is A=UΣV.

When we have the equation system Ax=b, we calculate the SVD of A as A=UΣVT. The matrices U and VT have a very special property. They are unitary matrices. One of the main benefits of having unitary matrices like U and VT is that if we multiply one of these matrices by its transpose (or the other way around), the result equals the identity matrix.

The singular value decomposition (SVD) of matrix A is very useful in the context of least squares problems. It is also very helpful for analyzing the properties of a matrix.

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Answer:

The figure below shows the graph of rational function f; It has vertical asymptotes x 2 andx = 4, and horizontal asymptote y = 0. The graph does not have an x-intercept, and it passes through the point (~3,-1). The equation for f (x) has one of the five forms shown below. Choose the appropriate form for f (x), and then write the equation: You can assume that f (x) is in simplest form_ 0 f() f() f ()

Answer:

y = -3x + 1

Step-by-step explanation:

Answer:

The sample midrange for the data is 559

What is Sample midrange?

Although the sample midrange only uses a small fraction of the data, outliers can have a significant impact on it. It offers details on the distribution's skewness and heavy tails, which are identical to those of the random variable's distribution. Although the structure of this distribution is not obvious, with large sample sizes, the central limit will cause it to resemble a normal distribution.

According to question:

Minimum value: 34

Maximum values:  1084

The sample midrange can be computed as:

(Minimum value + Maximum value) / 2

⇒ (34+1084)/2

⇒ (1118)/2

⇒ 559

Hence, the sample midrange is 559

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The Complete Question is

To find the sum of 52 + 23 is the value is worked to be 75

Combining things and counting them as one big group is done through addition.

In math, addition is the process of adding two or more integers together.

Addends are the numbers that are added, and the outcome of the operation, or the final response, is referred to as the sum.

In this problem the addends include

The applying the addition operation

= 52 + 23

= 45

The sum is solved to be 75

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a) The mean of the sampling distribution of p is of 0.2.

b) The standard deviation of the sampling distribution of p is of: 0.0231, which is the amount that the sample proportions may differ from 0.2.

c) The shape of the sampling distribution of p is approximately normal.

The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has:

The parameters for this problem are given as follows:

p = 0.2, n = 300.

The 10% condition is given as follows:

Then the standard error of the sampling distribution of p is calculated as follows:

[tex]s = \sqrt{\frac{0.2(0.8)}{300}} = 0.0231[/tex]

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At some point, she will sell enough cards so that her sales cover her expenditures. So, the correct answer is ($40)

Lola is making greeting cards, which she will sell by the box at an arts fair. She paid $50 for a booth at the fair, and the materials for each box of cards cost $8. She will sell the cards for $10 per box of cards.

We are going to use 50, 8 and 10 to find are answer.

Therefore, we are going to divide the numbers:

[tex]\boxed{50/10}[/tex]

First, we need to figure out 50/10:

[tex]\boxed{50/10=5}[/tex]

[tex]\boxed{8x5=40}[/tex]

[tex]5=40\\(50/10=5=8x5=40)[/tex]

Therefore, at some point, she will sell enough cards so that her sales cover her expenditures. So, the correct answer is ($40)

Answer:

40

Step-by-step explanation:

For the study for investing the result of drugs in a particular diseases,

(1)This is an example of double blind experiment. So,correct option is option A

(2) The Correct option is option (C) i.e. the data can be treated as a random sample from the population of interest.

(3) The random variable X has approximately a normal distribution because of Central Limit Theorem i.e the Correct option is option (A).

Here , Spontaneous hydrostatic collapse is a disease in which teeth spontaneously turn into fluid. Jim Halpert decided to perform a study to find out if new drugs can prevent the development of this disease.

1. Since, neither researcher nor the employees were told who received which treatment, this is an example of a double-blind experiment.

2. In order to make thorough conclusions, the most important condition for statistical inference is usually that data can be treated as a random sample from the population of interest.

3. The sample mean age, X-bar of these residents has approximately a normal distribution because of the central limit theorem. Hence, we get all required answers for asking questions.

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Answer: A) 2 buses B) 7 vans C) 21 cars

Step-by-step explanation:

You divide 84 by the number of people the vehicle can take.

For a. 84/42=2, so you need 2 buses.

For b. 84/12=7, so you need 7 vans

For c. 84/4=21, so you need 21 cars

Answer: 6 pieces of candy

Step-by-step explanation:

The xx-value on the line when y=29 represents the length in inches of the catfish that would have a weight of 29.

Measuring is the act or process of determining the connection between two numbers. The act of measuring is the practice of putting a number on a characteristic of an object or event so that it can be compared to other things and phenomena. Calculating something's size or magnitude is what it is.

Comparing unknown amounts to known quantities is made easier by measurement. Measurement enables us to establish quantitative claims about the size, length, and speed of objects. Without measurement, the result will be inaccurate. Examples: Vehicle speed is measured using a speedometer.

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Given a line with the equation -3x+8y=-10, its slope can be calculated using the slope intercept form of the line that is 3/8.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies). The slope of a line in mathematics indicates how steep a line is. It is also referred to as the gradient. The "change in y" over the "change in x" of a line is referred to as the slope.

Here,

-3x+8y=-10

y=mx+c

where m=slope of line

8y=3x-10

y=3x/8-10/8

slope=3/8

The slope of given line whose equation is -3x+8y=-10 is 3/8 using slope intercept form of line.

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Answer:

Option D: 7/3x

Step-by-step explanation:

Because this line passes through the origin (0,0), we know that there is know b-value according to the equation y = mx + b. To figure out the equation, we must first calculate the slope of the linear function.

Slope = △y/△x

△y (change in y) = -7

△x (change in x) = -3

Therefore, the slope is 7/3 and the equation is y = 7/3x.

Using equation of motion to calculate the distance covered during acceleration is 540m

Distance is the total length between two points, while displacement is the length between two points, but it also takes into account the direction of the motion. Distance is a scalar quantity, while displacement is a vector quantity.

In this problem, we can either draw a velocity - time graph or proceed to solve using equations of motions.

We are required to calculate the distance covered during the period of acceleration.

Data;

a = v - u / t

a = acceleration

a = (60 - 30) / 12

a = 30 / 12

a = 2.5 m/s²

But we have another equation as

v² = u² + 2as

s = distance

60² = 30² + 2*2.5*s

x = 540

The distance covered is 540m

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Answer:10

Rewriting input as fractions if necessary:

3/5, 1/2

For the denominators (5, 2) the least common multiple (LCM) is 10.

LCM(5, 2)

Therefore, the least common denominator (LCD) is 10.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

3/5 = 3/5 × 2/2 = 6/10

1/2 = 1/2 × 5/5 = 5/10

Answer:

Step-by-step explanation:

1/2 + 3/5 = 5/10 + 6/10 = (5+6)/10 = 11/10 or 1 1/10 Your pair of fractions is 5/10 and 6/10

Answer:

[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]

Step-by-step explanation:

Apply natural logarithm chain rule:

[tex] \displaystyle{y = \ln(u) \to y' = \dfrac{u'}{u}}[/tex]

Where u is a function. The ' symbol indicates that the function to be derived. From this formula, we will have:

[tex] \displaystyle{y' = \dfrac{ \left (\dfrac{1 + x}{1 - x} \right)'}{ \dfrac{1 + x}{1 - x}}}[/tex]

Now we have to derive quotient functions, we can use quotient rule for this:

[tex] \displaystyle{y = \dfrac{u}{v} \to y' = \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]

Where u and v are functions. Therefore, from numerator:

[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{(1 + x)'(1 - x) - (1 + x)(1 - x)'}{ {(1 - x)}^{2} }}[/tex]

Derive using power rule and constant rule where:

[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: \: ( c \in \mathbb{R})}[/tex]

Thus:

[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1(1 - x) - (1 + x)( - 1)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x- ( - 1 - x)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x + 1 + x}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{2}{ {(1 - x)}^{2} }}[/tex]

Therefore, we will now have:

[tex] \displaystyle{y' = \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}}}[/tex]

Simplify expressions:

[tex] \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ {(1 - x)}^{2}} \times \dfrac{1 - x}{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ 1 - x} \times \dfrac{1 }{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ (1 - x)(1 + x)}}[/tex]

Therefore, the derived function is:

[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]

The value c guaranteed by the Intermediate Value Theorem over the interval [0, 2], where f(0) = 2, and f(2) = 10 is c = 1.5, f(1.5) = 5

The inequalities, 0 < 1.5 < 2, f(0) < f(1.5) < f2), verifies the Intermediate Value Theorem.

The Intermediate value theorem states that a value p that is between the f(a) and f(b), such that f(a) < p < f(b) or f(a) > p > f(b), then a number, c, exists between a and b such that f(c) = p

The derivative of the function f(x), f'(x) = 4·x² - 4·x + 2

The interval over which the Intermediate Value Theorem is to be verified = [0, 2]

The value of the function at the boundaries of the domain [0, 2], are;

f'(0) = 4 × 0² - 4 × 0 + 2 = 2

f'(2) = 4 × 2² - 4 × 2 + 2 = 10

Therefore, the value, f(c) = 5, indicates that we get;

f'(0) < f(c) < f'(2), and 0 < c < 2

We get; 4·x² - 4·x + 2 = 5

4·x² - 4·x + 2 - 5 = 0

4·x² - 4·x - 3 = 0

Completing the square

4·x² - 4·x = 3

x² - x = 3/4

x² - x + (-1/2)² = 3/4 + (-1/2)²

(x - 1/2)² = 3/4 + (-1/2)² = 1

x - 1/2 = ± √1 = ±1

x = 1 + (1/2) = 1.5, and x = -1 + 1/2 = -1/2

A value of x that satisfies the equation, f'(x) = 4·x² - 4·x + 2, is x = 1.5

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Answer: An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

The constant difference in all pairs of consecutive or successive numbers in a sequence is called the common difference, denoted by the letter d.

Step-by-step explanation: Hope this was helpful

An arithmetic sequence (arithmetic progression) is a number sequence with a common difference between successive terms. By using the arithmetic sequence formula, we can easily find the value of a term and the common difference in the sequence.

Example: 5, 7, 9, 11, 13, 15

An equation is quadratic if the greatest power of the coefficients is 2. Hence, for the given equations, only 6(2x + 4)2 = (2x + 4) + 2 is quadratic in nature.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation with one variable that goes like this: x ax2 + bx + c = 0. with a ≠ 0 .

                              The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. The answer could be simple or complicated.

Why it is called quadratic equation?

In mathematics, a quadratic issue is any problem that involves multiplying a variable by itself, often known as "squaring."

                         This vocabulary is based on the fact that a square's area is equal to the product of its side length and itself. The Latin word quadratum, which means square, is where the word "quadratic" derives.

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The complete question is -

Select all of the following equation(s) that are quadratic in form.

x4 – 6x2 – 27 = 0

3x4 = 2x

2(x + 5)4 + 2x2 + 5 = 0

6(2x + 4)2 = (2x + 4) + 2

6x4 = -x2 + 5

8x4 + 2x2 – 4x = 0

The distance between the 1st and the 3rd poles is 140 meters.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

ESB poles are placed along a road 70 meters apart.

So the distance between two poles is 70 meters.

So the distance between 1 and 3rd will be = 2*70 =140metets

Hence, the distance between the 1st and the 3rd poles is 140 meters.

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Complete Question:
Esb poles are placed along a road 70 metres apart. What is the distance between the 1st and the 3rd poles?

Answer:

The answer is C, 1.5

Step-by-step explanation:

In order to find the constant ratio for successive y-values, you must divide a term by the preceding term.

7.5/5=1.5

The ratio of a : b : c in the linear equation is 2 : -1 : -1

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

ax + by + c = 0

The points on the line are given as

(2 ,3) and (8 , 15)

A linear equation is represented as

y = mx + c

Where

Slope = m

y-intercept = c

This means that

3 = 2m + c

15 = 8m + c

Subtract the equations

So, we have the following representation

6m = 12

Divide by 6

m = 2

Substitute m = 2 in 3 = 2m + c

3 = 2 * 2 + c

So, we have

c = -1

Substitute m = 2 and c = -1 in y = mx + c

y = 2x - 1

So, we have

2x - y - 1 = 0

Recall that

ax + by + c = 0

This means that

a : b : c = 2 : -1 : -1

Hence, the ratio is 2 : -1 : -1

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She needs 50 successful serves in the first 100 to attain her target. A 2% chance exists that this will occur.

She therefore has a 98% chance of requiring more than 100 serves to achieve her objective.

The study of probability, which is the potential of any event happening, is a field of mathematics that deals with the occurrence of random events. The probability value is given on a scale from 0 to 1.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.

Jo must not complete 50 successful serves in her first 100 attempts in order to need more than 100 serves.

With n=100 and p=0.4, our probability sample of potential outcomes has a binomial distribution.

We will use a normal distribution to approximate n because it is a big enough number. The normal distribution's characteristics are as follows:

To ensure that she receives more than 100 serves, we must determine the likelihood that there will be fewer than 50 successful services. Such is:

We determine X's z value as follows:

Next, we have

That indicates that there is a 98% chance she will require more than 100 serves to accomplish her objective.

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Answer:

1. Alternate exterior angles

2. Vertically opposite angles

3. Alternate interior angles

4. Corresponding angles

Answer:

The two numbers we are looking for are a rational number and an irrational number.

Step-by-step explanation:

To find the two numbers that, when multiplied by the square root of 360, give a rational number, we can consider the prime factorization of 360. 360 can be written as 2^3 * 3^2 * 5, so the square root of 360 is equal to √(2^3 * 3^2 * 5) = 2√(3 * 5) = 2√15.

Now, suppose we want to find a rational number that is equal to x * √15. We can rewrite this expression as x * √(3 * 5) = x * √3 * √5. For this expression to be rational, both x and √3 must be rational or both must be irrational.

If x is rational, then the expression x * √3 * √5 is rational. Therefore, one of the two numbers we are looking for is x, which is a rational number.

If x is irrational, then the expression x * √3 * √5 is irrational. Therefore, the other number we are looking for is √3, which is an irrational number.

Therefore, the two numbers we are looking for are a rational number and an irrational number.

The correct students about the function are;

B: The function represented by the table has a greater rate of change.

C: The function y = 7x + 8 has the greatest  y-intercept.

We are looking at the equation;

y = 7x + 8

The general equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, the slope of the given equation is 7 while the y-intercept is 8.

From the table, the rate of change which is also  is simply the slope from the formula;

m = (y₂ - y₁)/(x₂ - x₁)

m = (32 - 16)/(4 - 2)

m = 8

Looking at the given options, only options that are correct are Options B and C.

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The possible number of hours Henry could trim trees is t > 10.

The given information represents a scenario which demonstrates an inequality statement as Henry wants to earn at least $ 56, which means the amount earned should be greater than 56.

Let t be the possible number of hours Henry trim trees. As his per hour charge is $6 and he pays $4 in equipment fee, the inequality statement is:

6t – 4 > 56

Solving,

6t  > 56 + 4

6t  > 60

t > 10.

In order to earn at least $56, Henry must trim trees for at least 10 hours or more.

Note: The question is incomplete. The complete question probably is: Henry wants to earn more than $56 trimming trees. He charges $6 per hour and pays $4 in equipment rental fees. What are the possible number of hours Henry could trim trees?

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The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.

The variance of a random variable from its true population or sample mean is expected in probability theory and statistics. The term "variance" refers to a measurement of how widely apart a group of numbers are from one another.

Here,

Variance and standard deviation are both measures of spread. They calculate the deviation of each data point from the mean. The range of data increases with increasing variation. Using the original unit of measurement, the standard deviation measures the same thing as the variance (whereas variance is the original unit squared).

Therefore ,The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.

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Answer:

here u go

Step-by-step explanation:

The diagram below shows ΔOAG, where RN¯, NE¯, and ER¯ are mid-segments of the triangle.

If OA=(4x+3) units, NE=(2.5x) units, RN=4.5 units, and ER=(2x) units, determine the measures below.

The length of NE¯ is units.

The length of GO¯ is units.

The length of AG¯ is units.

The perimeter of ΔOAG is units.