Find the slope of the line through each pair of points.
(-18, 7), (-10, -15)

Step 01: To write the relation, begin using the relation for seconds.

Step 02: To eliminate L, use the other relation, putting the liters in the numerator:

Step 03: Multiply everything by 154g.

Step 04: Multiply the numerators and the denominators.

Step 05: Multiply the numbers and simplify the units that are in the numerator and in the denominator.

Answer: It will take 143.3 seconds.

Okay, here we have this:

Considering the provided information we obtain that:

-The interval duration between 8 minutes and 13 minutes is 5 minutes. And the interval duration between 9 and 10 minutes is 1 minute. So, we have that the probability in this case is the ratio of the duration intervals: 1/5=0.20=20%.

Finally we obtain that the probability that washing dishes tonight will take him between 9 and 10 minutes is 20%.

Answer:

To graph y=5, you have to keep in mind that this means accross your line, y always equals 5. So it would look like the line you have in your picture except the line would move one space up; it would be on number five on the y-axis.

Step-by-step explanation:

Make sense? If you have a question feel free to comment (^-^)

Answer:

300 seconds

Step-by-step explanation:

The first dog run at v₁ = 15 m/sec     the second one run at  v₂ = 12 m/sec

we know that  d = v*t  then  t  =  d/v

Then the first dog will take  300/ 12  =  25 seconds to make a turn

The second will take   300 / 15   =   20 seconds to make a turn

Then the first dog in 12 turns 12*25 will be at the start point, and so will the second one at the turn 15.

To check  first dog    12 *  25 = 300

And the second dog 15 * 20 = 300

That means that time required for the two dogs to be at the start point together is

300 seconds, in that time the first dog finished the 12 turns, and the second had ended the 15.

Another procedure to solve this problem is as follows:

between  12  m/sec and  15 m/sec   the minimum common multiple  is 300 ( 300 is the smaller number that accept 12 and 15 as factors         12*15 = 300) Then when time arrives at 300 seconds the two dogs will be again in the starting point

Answer:

for answer 5 - 12 use the below

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

5)

we know the Hyp and the angle and want to find the Opp so use  Sin.. since it's got all of those.

Sin(35) = Opp / 10

10 * Sin(35) = Opp

5.7357 = Opp

x = 5.7 inches

6)

same as 5 but now we want to find the Adj side sooo... use Cos

Cos(54) = Adj / 36     ( from the picture I'm unsure if it's 36 or 35 )

36 * Cos(54) = Adj

21.160 =Adj

x = 21.2 meters

7)

now we know the angle and the Adj side and want to find the Opp , lets use Tan for that

Tan(20) = Opp / 47

47 * Tan(20) = Opp

17.1066 = Opp

x = 17.1 feet

8)

this is identical to 5) but the turned the shape so it looks different, but it's not

Sin(16) = Opp / 18

18 * Sin(16) = Opp

4.9614 = Opp

x = 5.0 cm

9)

this one is another   Opp and Adj  so use Tan again

Tan(65) = Opp / 7.5

7.5 Tan(65) = Opp

16.083 = Opp

x = 16.1 miles

10)

Hyp, angle , Adj, so use Cos

Cos(51) = Adj / 60

60 * Cos(51) = Adj

37.759 = Adj

x = 37.8 feet

11)

angle , Opp, find Hyp  sooo... use Sin

Sin( 36) = 28 / Hyp

Hyp = 28 / Sin(36)  

Hyp = 16.45798

x = 16.5 meters

12)

dealing with Adj, Opp and angle , use Tan again

Tan(60) = 90/ Adj

Adj = 90 / Tan(60)

Adj = 51.961

x = 52.0 inches

The prime factorization of the given numbers along with exponents are:

1. 90 = 2¹ × 3² × 5¹

a = 1, b = 2 , c = 1 , d= 0, e = 0, f= 0, g=0, h = 0

2. 980 = 2² ×  5¹ × 7²

a = 2, b = 0, c= 1, d= 2, e = 0, f= 0, g=0, h = 0

3. 12716 = 2² × 11¹ × 17²

a = 2, b = 0, c= 0, d= 0, e = 1, f= 0, g=2, h = 0

4. 31603 = 11¹ × 13² × 17¹

a = 2, b = 0, c= 0, d= 0, e = 1, f= 2, g=1, h = 0

Prime factorization of the numbers are as follow

1. 90 = 2^a3^b5^c7^d11^e13^f17^g19^h

prime factors of 90

= 2¹ × 3² × 5¹

= 2¹ × 3² × 5¹ × 7⁰ × 11⁰ × 13⁰ × 17⁰ × 19⁰

Here a = 1, b = 2 , c = 1 , d= 0, e = 0, f= 0, g=0, h = 0

2. 980 = 2^a3^b5^c7^d11^e13^f17^g19^h

prime factors of 980

= 2² ×  5¹ × 7²

= 2² × 3⁰ × 5¹ × 7² × 11⁰ × 13⁰ × 17⁰ × 19⁰

Here a = 2, b = 0, c= 1, d= 2, e = 0, f= 0, g=0, h = 0

3. 12716 = 2^a3^b5^c7^d11^e13^f17^g19^h

prime factors of 12716

= 2² × 11¹ × 17²

= 2² × 3⁰ × 5⁰ × 7⁰ × 11¹ × 13⁰ × 17² × 19⁰

Here a = 2, b = 0, c= 0, d= 0, e = 1, f= 0, g=2, h = 0

4. 31603 = 2^a3^b5^c7^d11^e13^f17^g19^h

prime factors of 31603

= 11¹ × 13² × 17¹

= 2⁰ × 3⁰ × 5⁰ × 7⁰ × 11¹ × 13² × 17¹ × 19⁰

Here a = 2, b = 0, c= 0, d= 0, e = 1, f= 2, g=1, h = 0

Therefore, the prime factorization of the numbers are:

1. 90 = 2¹ × 3² × 5¹

2. 980 = 2² ×  5¹ × 7²

3. 12716 = 2² × 11¹ × 17²

4. 31603 = 11¹ × 13² × 17¹

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Answer:

56/210---> 8/30---> 4/15

Step-by-step explanation:

we have to work money every day

Answer:

1/2

Step-by-step explanation:

Answer:

it is 1/2 or 9/18

Step-by-step explanation:

there was 18 shirts all together and half were white

good luck!

Point estimate from the sample is 0.985, margin error is 0.003.

Confidence interval is defined as the interval which is the estimate for the parameter of the sample or population to be contained.

(a) To calculate point estimate or sample mean :

Point estimate is the mid point of the confidence interval.

Given that true mean weight of candy bars is 0.982 ounces to 0.988 ounces.

Point estimate = (0.982 + 0.988) / 2 = 1.97 / 2 = 0.985

(b) Margin error is the one half of the total width of the interval.

Margin error = (0.988 - 0.982) / 2 = 0.003

(c) The confidence level of 90% in this problem can be interpreted as , if we do the interval construction for many times, about 90% of the total constructed intervals has the true population mean of weight of fun size candy bars.

Hence the point estimate and margin error are 0.985 and 0.003 respectively.

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The value of p(10) we get as  123.

What is Quadratic polynomial ?

A quadratic polynomial is a polynomial of degree 2, which means that it is a polynomial expression in one variable (usually written as x) that contains only terms of the form ax² + bx + c, where a, b, and c are constants. The highest exponent of the variable x in a quadratic polynomial is 2.

We are given a table of values for the quadratic polynomial p. Since p is a quadratic polynomial, it can be written in the form:

p(x) = ax² + bx + c

where a, b, and c are constants.

To find the value of p(10), we need to substitute x = 10 in the above equation and simplify:

p(10) = a(10)² + b(10) + c

p(10) = 100a + 10b + c

We don't know the values of a, b, and c, but we can use the values in the table to set up a system of equations.

From the table, we can see that:

p(0) = c = 3

p(1) = a + b + c = 6

p(2) = 4a + 2b + c = 11

Solving this system of equations, we get:

a = 1

b = 2

c = 3

Therefore, the quadratic polynomial p is:

p(x) = x² + 2x + 3

To find p(10), we substitute x = 10 in the above equation:

p(10) = (10)² + 2(10) + 3

p(10) = 100 + 20 + 3

p(10) = 123

Therefore, the value of p(10) is 123.

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The new image would be smaller in sample size than the original image.

For example, if the scale factor is 0.5, the new image will be half the size of the original image. To determine the exact size of the new image, the scale factor is multiplied with the width and height of the original image. For example, if the original image is 200 x 100 pixels, and the scale factor is 0.5, the new image will be

(200 x 0.5) = 100 x (100 x 0.5)

= 50 pixels.

The same concept applies when the scale factor is a decimal. For example, if the scale factor is 0.75, the new image will be three-quarters the size of the original image. In this case, the new image would be

(200 x 0.75) = 150 x (100 x 0.75)

= 75 pixels.

In summary, when the scale factor is less than 1, the new image will always be smaller than the original image, depending on the scale factor. The exact size of the new image can be determined by multiplying the width and height of the original image with the scale factor.

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There is a correlation that is likely for the number of car accidents and the weather as wet pavement and rainfall leads to more accidents.

The size and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is expressed as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

Weather-related issues will have an impact on our roads and reduce tire traction. Once more, it is advised to slow down while driving on slick roads, increase our following distance, and take more time to slow down when coming to a stop.

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Answer:

see explanation

Step-by-step explanation:

The perimeter is the sum of the 3 sides , then

2x - 6 + x + 4 + 10 > 50

3x + 8 > 50 ( subtract 8 from both sides )

3x > 42 ( divide both sides by 3 )

x > 14

(4)

The area is calculated by multiplying length and breadth , then

3(4x - 2) < 138 ( divide both sides by 3 )

4x - 2 < 46 ( add 2 to both sides )

4x < 48 ( divide both sides by 4 )

x < 12

Inferential statistics is one of the three basic ways of explaining the results of a research investigation. Group of answer choices Comparing variable quantities Graphing relationships between variables Comparing group percentages Making precise statements about data by correlating the scores of individuals on two variables.

Making precise statements about data by correlating the scores of individuals on two variables is one of the three basic ways of explaining the results of a research investigation.

This is also known as inferential statistics, which involves making predictions or generalizations about a larger population based on sample data.

The other two basic ways of explaining research results are descriptive statistics, which involves summarizing and describing the characteristics of a sample, and graphical representation, which involves using visual aids to display data and relationships between variables.

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The line HF that is perpendicular to GF and parallel to AE is presented in the image uploaded.

A perpendicular line is a line that intersects another line at 90 degrees or normal to the line.

A parallel line is a line that never intersect with another. In this type of line, the angle between the two parallel lines is zero.

Thus, the line HF that is perpendicular to GF and parallel to AE is presented in the image uploaded.

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The value of x after each step is performed is -3.5455.

To determine the value of x after each statement is performed, let's break down the given expression step by step:

Statement: x = 10 - 2 * 5 + (10/22 - 2) - 2

Multiplication and Division:

The expression starts with 2 * 5, which equals 10. The division 10/22 is approximately 0.4545 (rounded to 4 decimal places).

Addition and Subtraction:

Now we can substitute the results from the previous step into the expression:

x = 10 - 10 + (0.4545 - 2) - 2

Simplification:

We simplify the expression further:

x = 0 + (-1.5455) - 2

Addition and Subtraction:

Finally, we perform the remaining addition and subtraction:

x = -1.5455 - 2

x = -3.5455

Therefore, after performing the given statement, the value of x is approximately -3.5455.

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The statement "w1 ∪ w2 is a subspace of V if and only if w1 ⊆ w2 or w2 ⊆ w1" holds, meaning that the union of two subspaces is a subspace if and only if one subspace is contained within the other.

To show that the statement "w1 ∪ w2 is a subspace of V if and only if w1 ⊆ w2 or w2 ⊆ w1" holds, we need to prove both directions of the implication.

Direction 1: If w1 ∪ w2 is a subspace of V, then w1 ⊆ w2 or w2 ⊆ w1.

Assume that w1 ∪ w2 is a subspace of V. We will prove that either w1 ⊆ w2 or w2 ⊆ w1.

Suppose there exists an element v in w1 that is not in w2. Since w1 ∪ w2 is a subspace, it must be closed under scalar multiplication. Therefore, av is in w1 for any scalar a. But av is not in w2, which contradicts the assumption that w1 ∪ w2 is a subspace. Thus, we conclude that if w1 ∪ w2 is a subspace, then w1 ⊆ w2.

Similarly, we can prove that if w1 ∪ w2 is a subspace, then w2 ⊆ w1.

Direction 2: If w1 ⊆ w2 or w2 ⊆ w1, then w1 ∪ w2 is a subspace of V.

Assume that w1 ⊆ w2. To show that w1 ∪ w2 is a subspace, we need to demonstrate that it satisfies the three properties of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

Closure under addition: Take any two vectors u and v in w1 ∪ w2. Since w1 ⊆ w2, u and v are both in w2. Therefore, u + v is also in w2, and thus in w1 ∪ w2.

Closure under scalar multiplication: Take any vector u in w1 ∪ w2 and any scalar a. Since u is in w2, au is also in w2, and thus in w1 ∪ w2.

Contains the zero vector: The zero vector is in both w1 and w2, so it is in w1 ∪ w2.

Therefore, if w1 ⊆ w2, then w1 ∪ w2 is a subspace. Similarly, if w2 ⊆ w1, then w1 ∪ w2 is a subspace.

By proving both directions of the implication, we conclude that w1 ∪ w2 is a subspace of V if and only if w1 ⊆ w2 or w2 ⊆ w1.

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The equation of the line passing through M and perpendicular to PR would be y = -x + 6.

What is the equation of the line?

An equation of a line is a mathematical expression that describes the relationship between the variables x and y that defines the position of a point on the line. There are several ways to write the equation of a line, including slope-intercept form (y = mx + b), point-slope form (y - y1 = m(x - x1)), and standard form (ax + by = c).

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line. To find the midpoint of a line segment, you need to take the average of the x-coordinates and the y-coordinates of the two endpoints.

Given the line segment Q(-6, 2) and R(10, 6), the midpoint is:

((-6+10)/2 , (2+6)/2) = (2,4)

So the midpoint of the line segment Q(-6, 2) and R(10, 6) is (2,4).

Now find the slope of PR = 6-(-4)/10 = 10/10=1

Hence, the slope of the line passing through M and perpendicular to PR would be = -1.

Now we can form the equation of the line:

y - 4 = -1(x - 2)

y - 4 = -x + 2

y = -x + 6

Hence, the equation of the line passing through M and perpendicular to PR would be y = -x + 6.

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Answer:

F(t) = 10 + 5(t)

Step-by-step explanation:

The complete question is as follows;

Anumeha is mowing lawns for a summer job. for every mowing job, she charges an initial fee of \$10$10dollar sign, 10 plus a constant fee for each hour of work. her fee for a 555-hour job, for instance, is \$35$35dollar sign, 35. let f(t)f(t)f, left parenthesis, t, right parenthesis denote anumeha's fee for a single job fff (measured in dollars) as a function of the number of hours ttt it took her to complete it. write the function's formula.

Solution

We are interested in writing the function F(t) formula for the fee charged by Anumeha per job.

Now, the key to writing this function is knowing exactly the constant fee she charges on the job.

We were told that she got $35 for a 5 hour job.

Thus, the constant amount charged is as follows;

Since it’s $10 as initial fee and the constant fee is per hour;

35 = 10 + 5(x)

where x is the constant fee per hour

35 = 10 + 5x

5x = 35-10

5x = 25

x = 25/5

x = $5

This mess that she charges a constant fee of $5 per hour

So we can write the equation now.

F(t) = 10 + 5(t)

where t represents the number of hours she spent on the job

The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

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Using the slope we know that the distance Keira traveled is 32 miles.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise).

Find the difference between these two points' x-coordinates (run).

Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.

So, in the given situation:

c is calories burned and d is the distance.

Then,

x = kd

k is the slope = 200/10 = 20

Calories burned = 20 * distance cycled

When, c = 640:

640 = 20*distance

distance = 640/20

distance = 32 miles

Therefore, using the slope we know that the distance Keira traveled is 32 miles.

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Answer:

6 months

Step-by-step explanation:

if down payment is 2000 and he has 1100 now, thats a difference of 900

and since he saves 150 month...

900/150 = 6

6 months :)

The appropriate null and alternative hypotheses for this study would be: D. H0: μ = 34, HA: μ ≠ 34

The null hypothesis (H0) states that the average highway mpg (μ) of the new line of SUVs is equal to 34, which means the manufacturer's claim is accurate.

The alternative hypothesis (HA) states that the average highway mpg is not equal to 34, implying that the manufacturer's claim is inaccurate.

In hypothesis testing, the null hypothesis is the claim that is initially assumed to be true. The alternative hypothesis is the claim that contradicts the null hypothesis and is often the one the researcher wants to prove or find evidence for.

In this case, the researcher wants to test whether the manufacturer's claim of an average highway mpg of 34 is inaccurate, so the appropriate alternative hypothesis is that the average highway mpg is not equal to 34.

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Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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Given the polar equation r = 2 tan θ sec θ, we need to find its cartesian equation and identify the curve it represents.To convert a polar equation to a cartesian equation,

we use the following formula:x = r cos θ, y = r sin θTherefore, r = sqrt(x² + y²) and tan θ = y/x. Also, sec θ = 1/cos θ.Hence, we can substitute these values in the given polar equation:r = 2 tan θ sec θ => r = 2 (y/x) (1/cos θ)=> r = 2y / (x cos θ) => sqrt(x² + y²) = 2y / (x cos θ) => x² + y² = (2y / cos θ)²=> x² + y² = 4y² / cos² θ=> x² + y² = 4y² (1 + tan² θ)We know that 1 + tan² θ = sec² θTherefore, x² + y² = 4y² sec² θNow, sec θ = 1/cos θ, so the cartesian equation can be written as:x² + y² = 4y² (1/cos² θ) => x² + y² = 4y² / cos² θThis equation is a circle with center (0, 0) and radius 2/cosθ. It is centered on the y-axis. Therefore, the cartesian equation for the given polar equation is x² + y² = 4y² / cos² θ, and it represents a circle centered on the y-axis.

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The cartesian equation for the given polar equation is x² + y² = 4y² / cos² θ, and it represents a circle centered on the y-axis.

Given the polar equation r = 2 tan θ sec θ, we need to find its cartesian equation and identify the curve it represents. To convert a polar equation to a cartesian equation,

we use the following formula: x = r cos θ, y = r sin θ.

Therefore, r = √ (x² + y²) and tan θ = y/x.

Also, sec θ = 1/cos θ.

Hence, we can substitute these values in the given polar equation: r = 2 tan θ sec θ

=> r = 2 (y/x) (1/cos θ)

=> r = 2y / (x cos θ)

=> √(x² + y²) = 2y / (x cos θ)

=> x² + y² = (2y / cos θ)²

=> x² + y² = 4y² / cos² θ=>

x² + y² = 4y² (1 + tan² θ)

We know that 1 + tan² θ = sec² θ.

Therefore, x² + y² = 4y² sec² θ

Now, sec θ = 1/cos θ, so the cartesian equation can be written as:

x² + y² = 4y² (1/cos² θ) =>

x² + y² = 4y² / cos² θ

This equation is a circle with center (0, 0) and radius 2/cosθ. It is centered on the y-axis.

Therefore, the cartesian equation for the given polar equation is x² + y² = 4y² / cos² θ, and it represents a circle centered on the y-axis.

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Answer:

The REAL answer is -50

Step-by-step explanation:

The coefficient of determination will be 0.36.

the coefficient of correlation measures the strength and direction of the linear relationship between two variables, while the coefficient of determination measures the proportion of the total variation in one variable that is explained by the other variable.

The coefficient of determination is equal to the square of the coefficient of correlation, so if the coefficient of correlation is -0.6, we can square it to get 0.36. Therefore, the coefficient of determination will be 0.36.

knowing the coefficient of correlation between two variables can help us determine the coefficient of determination, which represents the proportion of the variation in one variable that is explained by the other variable.

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Answer:

let X be the number of ways they can be seated without condition,

let M the the number of ways they can be seated if the two people must sit together,

let N be the number of ways they can be seated if the two must not sit together.

X=7! =5040

M= 6!× 2!=1440

M+N=X

then N=X–M=5040–1440=3600ways