what would be the coefficient of determination if the total sum of squares (sst) is 86.24 and the sum of squares due to regression (ssr) is 46.9? (keep 3 decimal places)

In this case, an r value of 0.9 suggests a strong positive linear relationship between the number of hours studied and the grade point average(GPA).

The correlation coefficient, r, measures the strength and direction of the linear relationship between two variables.

In this case, an r value of 0.9 suggests a strong positive linear relationship between the number of hours studied and the grade point average.

A correlation coefficient can range from -1 to +1. A positive value indicates a positive relationship, meaning that as one variable increases, the other variable also tends to increase.

In this case, as the number of hours studied increases, the grade point average also tends to increase.

The magnitude of the correlation coefficient indicates the strength of the relationship. A correlation coefficient of 0.9 is considered very strong, suggesting that there is a close, linear relationship between the two variables.

It's important to note that correlation does not imply causation. In other words, while there may be a strong positive correlation between the number of hours studied and the grade point average,

it does not necessarily mean that studying more hours directly causes a higher GPA. There may be other factors involved that contribute to both studying more and having a higher GPA.

To better understand the relationship between the number of hours studied and the grade point average, let's consider an example.

Suppose we have a group of students who all studied different amounts of time.

If we calculate the correlation coefficient for this group and obtain an r value of 0.9, it suggests that students who studied more hours tend to have higher grade point averages.

However, it's important to keep in mind that correlation does not provide information about the direction of causality or other potential factors at play.

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The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

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The number of seconds where the football hit the ground is 2 seconds

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

The graph

The number of seconds where the football hit the ground is when the graph intersects with the x-axis at the second time

In this case, the point is (2, 0)

Also, the seconds is represented by x

So, we have

x = 2

Hence, the seconds the football hits the ground is 2

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Answer:

\(\frac{3}{10} , 0.48 , 0.73\)

Step-by-step explanation:

In order to put this number in order from least to greatest, we have to turn them into fractions with the same denominator, so firstly we write down all of the decimals as fractions, and we will get...

\(0.48 = \frac{48}{100} \\\\0.73 = \frac{73}{100}\)

Now, we need to find the smallest number that is divisible by 100 and by 10, and this number will be the least common denominator. The smallest number that is divisible by 100 and by 10 is 100, therefore 100 is the least common denominator. Now we have to make all of the fractions have the denominator of 100 and we do that in the following way...

\(\frac{48}{100}= \frac{48}{100}\\\\\frac{73}{100} = \frac{73}{100}\\\\\frac{3}{10} = \frac{(3)(10)}{(10)(10)} = \frac{30}{100}\)

By looking at this we need to understand that...

\(\frac{30}{100}<\frac{48}{100}<\frac{73}{100}\)

Therefore...

\(\frac{3}{10} < 0.48 < 0.73\)

Answer:  So our two integers are 17 and 45.

Step-by-step explanation:

The two integers are 17 and 45, See how we got it. X+Y=62. Substitute our first expression here for y, we have X+2X+11 =62.

Given that,

the two numbers are consecutive(also odd)

The two numbers are

x and x + 2

Sum of the numbers = 62

x + (x + 2) = 62

x + x + 2 = 62

2x = 62 - 2

2x = 60

x = 60/2

x = 30

Therefore, the two numbers are x = 30 and x + 1 = 32

Answer:

600

Step-by-step explanation:

12%=72

1%=6

100%=600

_________________________________

Range=20

Median=15

Step by step explanation:

Solution,

Given data=12,13,19,16,32,15,13

Highest score=32

lowest score=12

a. Range= highest score- lowest score

= 32-12

= 20

B. Arranging the data in ascending order

= 12,13,13,15,16,19,32

N( total number of items)= 7

Median= (N+1/2)th item

=(7+1/2) th item

= (8/2) th item

= 4 th item

Median = 15

Hope it helps

Good luck on your assignment

_________________________________

The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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Answer:

it is equallaterial.

Step-by-step explanation:

it id that because all of the side are the same

The variance of the sample mean x = 7 is 18(option c).

Given table:

X          7  5  11   1   11

(x₁ - x)² 0  4  16 36 16​

n = number of observations = 5

Variance σ² = 1/n-1 Σ\(\ \ n} \atop {i=1} \right.\) (\(X_{1}\) - X)²

= 1/5-1 (0 +4 + 16 + 36 + 16)

= 1/4(72)

= 18

Therefore variance σ² = 18

Hence the variance of the sample mean x = 7 is 18.

so option c is correct.

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​

Answer:

(-13/5,-12/5)

Step-by-step explanation:

To solve the system of two linear equations below algebraically using elimination:

x + 5y = -17

x - 3y = 7

We can use the elimination method by adding the two equations together to eliminate the x term. When we add the two equations, the x term cancels out:

(x + 5y) + (x - 3y) = -17 + 7

2x + 2y = -10

We can simplify the equation by dividing both sides by 2:

x + y = -5

Now we have one equation with one variable. We can substitute this equation into one of the original equations to solve for the other variable. Let's use the first equation:

x + 5y = -17

Substitute x + y for x:

(x + y) + 5y = -17

Simplify by combining like terms:

x + 6y = -17

Now we have two equations:

x + y = -5

x + 6y = -17

We can use the elimination method again by subtracting the first equation from the second equation:

(x + 6y) - (x + y) = -17 - (-5)

5y = -12

Divide both sides by 5:

y = -12/5

Now that we know the value of y, we can substitute it into one of the original equations to solve for x. Let's use the first equation:

x + y = -5

Substitute y = -12/5:

x - 12/5 = -5

Add 12/5 to both sides:

x = -13/5

So the solution to the system of equations is:

x = -13/5

y = -12/5

Therefore, the solution to the system of equations using elimination is (x,y) = (-13/5,-12/5).

Hello!

50 sheets => 50mm

1 sheet => 50mm/50 = 1mm

1mm = 0.1cm

the answer is 0.1cm

Answer: 0.1

Step-by-step explanation:

1mm=0.1cm

So each sheet is 0.1cm

The area of the Trapezium given in the question is 28ft²

The area of a trapezium is calculated using the relation :

Using the parameters given for our compuation:

height, h = 4

b1 = 9

b2 = 5

Inputting the parameters into our formula :

Area = 4/2(5 + 9)

Area = 2(14)

Area = 28ft²

Therefore, the area of the Trapezium is 28ft²

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The next four terms of the sequence are 9, 11, 13, and 15. The explicit formula for the sequence is an = 1 + (n - 1)2, which was verified by finding the 5th term of the sequence to be 9.

To find the next four terms of the given sequence 1, 3, 5, 7,..., we can observe that the sequence is an arithmetic sequence with a common difference of 2.

The next four terms would be:
9, 11, 13, 15

To write an explicit formula for the sequence, we can use the formula for arithmetic sequences:
an = a1 + (n - 1)d

Here, a1 is the first term of the sequence (which is 1), d is the common difference (which is 2), and n represents the position of the term in the sequence.

So, the explicit formula for the given sequence is:
an = 1 + (n - 1)2

To verify the formula, we can find the 5th term of the sequence using the formula:
a5 = 1 + (5 - 1)2
  = 1 + 4*2
  = 1 + 8
  = 9

Hence, the 5th term of the sequence is indeed 9.

The next four terms of the sequence are 9, 11, 13, and 15. The explicit formula for the sequence is an = 1 + (n - 1)2, which was verified by finding the 5th term of the sequence to be 9.

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We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Explanation:

1/5 of the beans are mung, so 4/5 of the beans are pinto. The two fractions add to 5/5 = 1.

Ignore the denominators and focus on the numerators for each fraction. We have 1 mung and 4 pinto. The values are read in this order to form the ratio 1:4 which is our answer. We cannot reduce this ratio any further.

The order is important because saying 4:1 would mean that we have 4 mung beans and 1 pinto, when it's the other way around.

Side note: The value 450 isn't needed. We could easily change it to any other multiple of 5 and get the same exact answer.

-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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it the second and last answers pi(d) and 2pi(r)

Answer:

The answers are 2πr, πr², and πd

Step-by-step explanation:

Circumference is area×π×2, and diameter is area×2, so it can also be d×π.

x-coordinate of the other point on the line that has a y value of -12 is 0

The slope of a line in mathematics serves as a gauge for how steep it is. It is described as the proportion of the y-coordinate change to the x-coordinate change between any two locations on a line. A line's slope can be either positive, negative, zero, or undefinable.

Given

vertex=(8,6)

intercept=-12

To find:  x-coordinate of the other point that has a y value of -12

Equation of line

y=mx+c

Putting the values, we get

6=8m-12

m=18/8

m=9/4

Now, finding the x coordinate

y=mx+c

-12=9/4x-12

x=0

Hence,  x-coordinate of the other point that has a y value of -12 is 0.

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Answer:

(c)- 4/13

Step-by-step explanation:

There are 4 types of cards in a ordinary deck clovers, diamands, hearts, and spades

each set has 1 seven each, so 4 sevens total.

Also, each type of card has 13 different cards in it

so, your answer is 4/13

Here, given

sides of polygon= a(3,7)b(3,3)c(7,3)d(7,7)

Let, 3 = x1 & 7= y1   , 3= x2  & 7= y2   , 7= x3  & 3= y3   ,  7=  x4  & 7= y4

\(\frac{1}{2}\) [det.(9-21)+det.(9-21)+det.(49-21)+det.(49-21)] {we took determinants of all the given sides}

\(\frac{1}{2}\) (32)

16cm^2

Hence, the area of the polygon is 16cm2.

The formula for calculating the area of ​​a regular polygon is: area = (number of sides x 1 side length x apothem distance) / 2, where the value of the apothem is the formula apothem = [(1) Length side). / {2 × (tan (180 / number of sides))}].

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(a) The outcomes are 8

(b) Values of X are : 0, 1, 2, 3

(a) To determine the number of outcomes in the sample space, we need to consider all the possible combinations of the switches.

Since each switch can either fail (F) or not fail (NF), there are two possible outcomes for each switch. Therefore, the total number of outcomes in the sample space can be calculated as 2 × 2 × 2 = 8.

(b) Let X represent the number of switches that fail. We can define the values of X as 0, 1, 2, or 3, depending on the number of switches that fail. The probability of each outcome can be calculated using the binomial distribution formula.

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Answer:

Its the first one . A

Step-by-step explanation:

The solution set for the given inequality is {-1, 0, 1, 2, 3}. Therefore, option A is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -10<3x-4<8.

Now, -10<3x-4

Add 4 on both the sides of an inequality, we get

-6<3x

-2<x

Now, 3x-4<8

Add 4 on both the sides of an inequality, we get

3x<12

x<4

-2<x<4

Solution set is {-1, 0, 1, 2, 3}

Therefore, option A is the correct answer.

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Answer:

1:9

Step-by-step explanation:

a=4 and b=36

4:36

Simplify it by dividing by 9

1:9

(it could also be 9 depending on what is a and b)

a. The truck rental cost when you drive 85 miles is  $85.7.

b. The number of miles driven when the cost is $65.96 is 0.42x.

a. To find the truck rental cost when driving 85 miles, we can substitute the value of x into the given function.

f(x) = 0.42x + 50

Substituting x = 85:

f(85) = 0.42(85) + 50

= 35.7 + 50

= 85.7

Therefore, the truck rental cost when driving 85 miles is $85.70.

b. To determine the number of miles driven when the cost is $65.96, we can set up an equation using the given function.

f(x) = 0.42x + 50

Substituting f(x) = 65.96:

65.96 = 0.42x + 50

Subtracting 50 from both sides:

65.96 - 50 = 0.42x

15.96 = 0.42x

To isolate x, we divide both sides by 0.42:

15.96 / 0.42 = x

38 = x

Therefore, the number of miles driven when the cost is $65.96 is 38 miles.

In summary, when driving 85 miles, the truck rental cost is $85.70, and when the cost is $65.96, the number of miles driven is 38 miles.

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There are 70 ways to choose 4 shoes from the pile of 8.

We can apply the combination formula, which is: to select 4 shoes from the pile of 8:

The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

where n is the total number of shoes (8) and k is the number of shoes we want to choose (4).

Substituting the values, we get:

\({ }^8 C_4=\frac{8!}{4!*(8-4)!}=\frac{8*7*6*5}{4*3*2*1} =70\)

Therefore, there are 70 ways to choose 4 shoes from the pile of 8.

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