Your goal here is to find the least squares line y(x) = mx + b for the following data: (-2, 1), (2, 1), (-1,-1), (0, -2), (2,-2), and (-2, 1) Feel free to use a calculator! The normal equation for determining the approximating parameters ħ and în are: Then the least squares line is: y(x) = = number + number

To find the slope of a line perpendicular to line j with a slope of -6/7, the slope of the perpendicular line, line k, is 7/6.

To find the slope of a perpendicular line, we need to use the formula that says that the slope of a line perpendicular to a given line is the negative reciprocal of that line.

This can be written as follows: If a given line has slope m, then the slope of a line perpendicular to it is -1/m.

Now, in this case, we need to find the slope of a line perpendicular to line j.

To do this, we first need to find the slope of line j. We can use the formula for slope that says: Slope = \((y_2 - y_1)/(x_2 - x_1)\), where \((x_1, y_1)\) and \((x_2, y_2)\) are any two points on the line.

So, let's plug in the coordinates of the two given points (9, 5) and (2, 11) into this formula to find the slope of line j:

Slope of line j = (11 - 5)/(2 - 9) = -6/7

Now that we have the slope of line j, we can use the formula for the slope of a perpendicular line to find the slope of line k:

Slope of line k = -1/(-6/7) = 7/6

Therefore, the slope of line k is 7/6.

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The recursive relation of the data distribution a(n) = a ( n - 1 ) x n - ( n - 1 ).

A sequence of values is defined by a mathematical equation termed as a recursive relation, also known as recursive relation. It derives current value(s) through specified initial value(s) and previous value dependent rule(s). In essence, it generates numeric sequences.

Note that every individual unit can be derived by multiplying the preceding one with a rising integer, and subsequently subtracting a descending integer:

1 x 1 - 0 = 1

1 x 2 - 1 = 1

1 x 3 - 2 = 5

5 x 4 - 3 = 17

17 x  5 - 4 = 71

71 x 6 - 5 = 247

We can deduce the relation of a(n) = a ( n - 1 ) x n - ( n - 1 ).

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The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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The missing part in the first triangle is 14

The missing part in the second triangle is 13.

The Pythagorean theorem is a fundamental theorem in geometry that applies specifically to right triangles.

According to Pythagorean theory, the square of the length of a right triangle's hypotenuse is equal to the sum of the squares of its legs.

For the first triangle as shown;

16^2 = 8^2 + t^2

t = √16^2 - 8^2

t = √192

t = 14

For the second triangle;

w= √8^2 + 10^2

w = 13

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Answer:

16

Step-by-step explanation:

47% is 0.47

34 x 0.47 = 15.98

So a trick question, its either 15 students or 16 students.... I would say 16 students, although the percentage would be 47.05%

16 students either have glasses or contacts.

Answer:

$60.90

Step-by-step explanation:

Roy makes $10.15 each time he mows his neighbor's lawn. In April he mowed he lawn 2 times. In May he mowed the lawn 3 times. In June he mowed the lawn 1 time. How much money did Roy make in all?

April: 2 times

May: 3 times

June: 1 time

2 + 3 + 1 = 6 times

6 time * 10.15 each time

= $60.90

Answer:

$60.90

Step-by-step explanation:

Add the number of times Roy mowed in total

April: 2

May: 3

June: 1

2 + 3 + 1 = 6

Multiply that amount by the $10.15 he makes each time he mows

10.15(6) = 60.9

If m/n is the probability that you do not eat green candy after you eat a red candy, then m + n is 6.

A bag contains 8 green candies and 4 red candies. If you eat five candies, there are relatively prime positive integers m and n so that m/n is the probability that you do not eat green candy after you eat a red candy. Below list the ways to accomplish this ordering along with their respective probabilities:

GRRRR : \(\frac{8}{12}\times\frac{4}{11} \times\frac{3}{10} \times\frac{2}{9} \times\frac{1}{8}\)

GGRRR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{4}{10} \times\frac{3}{9} \times\frac{2}{8}\)

GGGRR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{4}{9} \times\frac{3}{8}\)

GGGGR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}\)

GGGGG : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}\)

The sum is \(\frac{8\times3\times4(2+14+42+70+70)}{12.11.10.9.8}\)

Probability that you do not eat green candy after you eat a red candy =\(\frac{1}{5}\)

so m = 1 and n = 5

m + n =6

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Answer:

answer is c

Step-by-step explanation:

C is the only one with the correct slope

The correct image include the following: B. Green: image A.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By applying a rotation of 270° clockwise about the point (1, 2) to the coordinate of the vertices of blue block D, the coordinate the vertices of of its image would be located at the position of the Green: image A.

In this context, we can reasonably infer and logically deduce that Green: image A is the correct transformed shape.

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Answer:

0.2637

Step-by-step explanation:

Population size is top 15 ranking restaurants.

Number of draws = 3

Number of observed successes = 5

Probability formula :  [r . x } { n -r] [n - x]

solving the equation we get 24 / 91 which is approximately 0.2637

Answer:

45

Step-by-step explanation:

my brain told me

Chris can lift 54 kilograms above his head.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here, 4 rocks with 12 kg each and a box weighing 6 kilograms

therefore the total weight = 4 ×12 + 6

                                           = 54 kg

Hence Chris can carry 54 kg above his head

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According to the properties of the standard normal distribution, approximately 99.7% of the values lie within three standard deviations of the mean. Therefore, the answer is 99.7%.

To determine the percentage of videos on the streaming site that are between 264 and 489 seconds, we need to calculate the area under the normal curve within that range. Since the distribution is approximately normal with a mean of 264 seconds and a standard deviation of 75 seconds, we can use the properties of the standard normal distribution to find the desired percentage.

First, we need to convert the values 264 and 489 to z-scores, which represent the number of standard deviations a particular value is away from the mean. The z-score formula is given by:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:

z1 = (264 - 264) / 75 = 0

z2 = (489 - 264) / 75 = 3

Next, we can use a standard normal distribution table or a calculator to find the area under the curve between z = 0 and z = 3. The area represents the percentage of videos falling within that range. The answer is 99.7% .

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Answer :

⠀

Explanation :

⠀

Solution :

where,

⠀

We know that,

\( {\longrightarrow \bf \qquad (AC) {}^{2} = (AB) {}^{2} +( BC) {}^{2} }

\)

⠀

Now, we will substitute the given values in the formula :

\( {\longrightarrow \sf \qquad (AC) {}^{2} = (8) {}^{2} +( 6) {}^{2} }\)

⠀

We know that, (8)² = 64 and (6)² = 36. So,

\( {\longrightarrow \sf \qquad (AC) {}^{2} = 64 + 36 }\)

⠀

Now, adding 64 and 36 we get :

\( {\longrightarrow \sf \qquad (AC) {}^{2} = 100 }\)

⠀

Now, we'll take the square root of both sides to remove the square from AC :

\( {\longrightarrow \sf \qquad \sqrt{(AC) {}^{2}} = \sqrt{100} }\)

⠀

\( {\longrightarrow \sf \qquad AC = \sqrt{100} }\)

⠀

We know that, square root of 100 is 10 .

\( {\longrightarrow \bf \qquad AC = 10 }\)

⠀

So,

Answer:

y

a= ——

(r + 1 )t

Step-by-step explanation:

divide both sides

Answer:

The digit that fit into the blank space is 6

Step-by-step explanation:

Here, we want to enter digits into the blank space that can make the expression valid.

Let’s try 6;

6583 < 6612 < 6687

This is actually correct.

Can we have any other digit here?

No, i don’t think so.

Putting in a 5 will make the first number greater than the middle

Putting in a 7 will make the middle number greater than the last and thus render the expression invalid

Answer:

$48

Step-by-step explanation:

24/3 = 8

8 x 6 = $48

Answer:

48

Step-by-step explanation:

because butterfly method 6 time 24 =144 and didved 144 by 3 which gives you 48

We are required to evaluate using Synthetic division:

To do this, we follow these steps:

Step 1: Set the denominator equal to zero to find the number to put in the division box. Next, make sure the numerator is written in descending order.

p+6=0

Therefore: p =-6

Step 2: Bring the leading coefficient down as follows.

Step 3: Multiply the number in the division box (-6) with the number you brought down (1) and put the result in the next column. Add the two numbers together and write the result in the bottom of the row.

Step 4: Multiply the number in the division box(-6) with the number you brought down (-1) and put the result in the next column.

Step 5: We repeat the same process until the last digit.

Step 6: The last digit is the remainder. Therefore we write our result taking note that the power of p will start from 3 which is one less the original function.

:

Answer:

\((a)\ L = 18.84\) --- arc length

\((b)\ A = 113.04\) --- sector area

Step-by-step explanation:

Given

\(r = 12\)

\(\theta = 90\)

Solving (a): The arc length

This is calculated using:

\(L = \frac{\theta}{360} * 2\pi r\)

So, we have:

\(L = \frac{90}{360} * 2* 3.14 * 12\)

\(L = 0.25* 2* 3.14 * 12\)

\(L = 18.84\)

Solving (b): The sector area

This is calculated using:

\(A = \frac{\theta}{360} * \pi r^2\)

So, we have:

\(A = \frac{90}{360} * 3.14 * 12^2\)

\(A = 0.25 * 3.14 * 12^2\)

\(A = 113.04\)

Answer:

In the United States, most competitive swimming pools are 25 yards long. This is the most standard length competition pool, and the one most commonly mistaken for an Olympic sized pool (by those who were not competitive swimmers).Most US high schools, public recreation centers, universities and YMCA's have 25-yard pools. Swimmers refer to this type of pool as "short course", or "short course yards". On paper, the acronym is SCY.

Step-by-step explanation:

PLWS MARK ME BRAINLIEST

Its a weird problem but I think u should use formula:

(a+b)^2=a^2+2ab+b^2

5(q+p+3)=5q+15+5p=(√5q+√5p)^2

it is only thing u can do.

Answer:

C. no association?

Step-by-step explanation:

Looks like there's no association to me. Association usually are in a linear line or curves. The data points given do not form such shapes. Hope that's right.

Here's some clarification: https://open.lib.umn.edu/macroeconomics/chapter/nonlinear-relationships-and-graphs-without-numbers/

Answer:

,mnl.khvmfjdrykytdd7ir rvrtuy

Step-by-step explanation:

Answer:

$50.00

Step-by-step explanation:

By using a system of equations, we will see that the solution is:

x = 25, y = -50, z = -15

We can write this as a system of equations:

4x + 2y - z = 15

x + y - z = -10

-3x - y + z = 60

Notice that if we add the second and third equations, we get:

(x + y - z) + (-3x - y + z ) = -10 + 60

-2x = 50

x = 50/-2 = -25

So we already got the value of x. Replacing that in the second equation we et:

25 + y - z = -10

Isolating y we get:

y = -10 - 25 + z = z - 35

Now we can replace that in the first equation:

4x + 2y - z = 15

4*25 + 2*(z - 35) - z = 15

100 + z - 70 = 15

z = 15 - 100 + 70 = -15

And using:

y =  z - 35 = -15 - 35 = -50

Then the soution to the matrix equation is:

x = 25, y = -50, z = -15

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Option (D) She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1 is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Patti is using mental math to evaluate the expression (70 + 12.8 + 30) + 6.1.

The number expression is:

= (70 + 12.8 + 30) + 6.1

As we know from the commutative property

a +  b = b + a

Applying commutative property in the number expression:

= (70 + 30+ 12.8) + 6.1

She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1.

Thus, option (D) She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1 is correct.

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Answer:

If we put x=17/4

f(4×17/4-15)=8×17/4-27

f(2x=34-27

f(x)=7.

Hope i helped you.

Answer:324.24??? Not sure just a guess.

Step-by-step explanation:

Answer:

Just plug in where n is= 150 then solve the answer is 100

Step-by-step explanation:

2(150)-200