A sample of data with n = 66 observations is used to run a multiple regression with 7 independent variables.
If this data set has SST = 2326.9523 and SSR = 1632.8843, what is the value of the F-statistic for the test of overall significance of this regression relationship?

Answer:

your answer is, A Population: soccer team, Sample: starting eleven player.

Step-by-step explanation:

I just took the test.

The population and the sample in the situation below is a Soccer team and starting eleven players respectively.

The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive.

Given, The coach wants to know which uniform the soccer team wants to wear, but he only asks the starting eleven players.

Since A population is an entire group that you want to draw conclusions about. A sample is a specific group that you will collect data from. The size of the sample is always less than the total size of the population.

and The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment.

Thus in our case,

Population: soccer team

Sample: starting eleven players

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Step-by-step explanation:

I hope i got it right...

Answer:

$3100 is invested at 9%

$4900 is invested at 11%

Step-by-step explanation:

Let's take "x" be the amount invested at 9%.

(x + 1800) is invested in another account at 11%.

The interest amount earned by the two accounts is $818.

Here we can use the simple interest formula and find the amount invested in each account.

Simple interest (I) = , where P- is the principal , N is the number of years and R is the interest rate.

Simple interest =

0.09x + 0.11(x+1800) = 818

Now we have to simplify and find the value of x .

Use the distributive property and simplify the second term.

0.09x + 0.11x + 198 = 818

0.2x + 198 = 818  

0.2x =818 - 198

0.2x = 620

x = 620/0.2

x = 3100.

So $3100 is invested at 9%

x + 1800 = 3100 + 1800

= $4900

$4900 is invested at 11%

Hope this helped.

Therefore, the value of q(α) is 0.

Let p(x) = x³ + ax² + bx + c be a polynomials with distinct roots α, β, and γ, where α, β, and γ are real numbers and α, β, and γ are also roots of another polynomial q(x)

.To find: the value of q(α).

Given:p(x) = x³ + ax² + bx + c

has three distinct roots α, β, and γ such that α, β, and γ are real numbers and α, β, and γ are also roots of q(x).

The root of p(x) are:

α, β, and γThe root of q(x)

are:α, β, and γ

Since α, β, and γ are the roots of q(x),

we have:q(x) = (x - α) (x - β) (x - γ) ... (1)

Let's evaluate q(α) using equation (1)

q(α) = (α - α) (α - β) (α - γ)q(α) = 0

(Since α, β, and γ are distinct)

Therefore, the value of q(α) is 0. Hence, the correct option is (D).

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There are 45 handshakes that can be made between 10 people.

According to the given question.

Number of people invited in a party = 10

As we know that

The formula for the number of handshake possible with n people is given by

Number of handshakes = n(n -1)/2

This is because each of the people can shake with n -1 (they would not shake their own hand), and the handshake between two people in not counted twice.

Therefore, the number of hands each person shook

= 10(10 -1)/2

= 10(9)/2

= 45

Hence, there are 45 handshakes that can be made between 10 people.

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Answer:

20 + r = 42

Step-by-step explanation:

Let r = the number of hats Rachel has made

Melissa's hats + Rachel's hats = total hats

20 + r = 42

To make an equation on how many Rachel made, we can just add.

20 + h = 42

Solve for h.

20 + h = 42

~Subtract 20 to both sides

h = 22

Best of Luck!

Given:

The expression is

\(\dfrac{\sqrt[3]{9}}{\sqrt[3]{4}}\)

To find:

The simplified form of given expression.

Solution:

We have,

\(\dfrac{\sqrt[3]{9}}{\sqrt[3]{4}}\)

It can be written as

\(\dfrac{\sqrt[3]{9}}{\sqrt[3]{4}}=\sqrt[3]{\dfrac{9}{4}}\)                    \(\left[\because \dfrac{\sqrt[a]{x}}{\sqrt[a]{y}}=\sqrt[a]{\dfrac{x}{y}}\right]\)

Therefore, the simplified form of given expression is \(\sqrt[3]{\dfrac{9}{4}}\).

Note: We can further simplify this expression but be need use exponential properties.  

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

The equation of the line which passes through the point (11,13) and is perpendicular to the line 4x+6y=4y-6 is y = 3x - 20.

We have to find the slope of the line 4x+6y=4y-6. We can write the equation in slope-intercept form y = mx+b where m is the slope and b is the y-intercept.

4x+6y=4y-6

4x = -2y - 6

y = -2x/6 - 1

y = -1/3x - 1/2

Therefore, the slope of the line is -1/3.

Since the line is perpendicular to this line, its slope will be the negative reciprocal of -1/3.

The slope of the line is 3.

Using the point-slope form of a line, we can write the equation of the line passing through (11,13) with a slope of 3 as:

y - 13 = 3(x - 11)

Simplifying this equation in slope-intercept form;

y = 3x - 20

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Answer: $5

Step-by-step explanation:

938-3 = 935

935/ 15 = $62 on each person with a balance of $5

Answer:

y = 0.2x + 37

Step-by-step explanation:

A) Find an equation in the form y = mx + b, where x is the number of monthly minutes used and y is the total monthly of the Ringular plan.

(x, y) = (minutes, cost)

(110, 59)

(600, 157)

slope = m = dy/dx

dy/dx = change in y/change in x

m = dy/dx

m = (157 - 59)/(600-110)

m = 98/490

m = 0.2

a) the linear equation:

y - 59 = 0.2(x - 110)

y - 59 = 0.2x - 22

y = 0.2x - 22 + 59

y = 0.2x + 37

Initial velocity=0

Height=45m

G=10m/s^2

By the 2 nd equation of motion …(Under free fall)-

H = ut + 1/2 g t^2

45 = 0 + {1/2 * 10 * (t^2)} •: [0*t=0]

45 = 5 t^2

45/5 = t^2

9 = t^2

√9=t

3=t

Answer-: The time taken would be 1.3 seconds to reach the ground.

No, X or y-axis scale does not have to always start at zero. In a line chart, it's OK to start the axis at a number other than zero

A line that is used to take or mark measurements is known as an axis in mathematics. Two crucial axes of the coordinate plane are the x and y axes. A horizontal number line is the x-axis, while a vertical number line is the y-axis. The coordinate plane is created by the perpendicular intersection of these two axes.

Given,

No, X or y-axis scale does not have to always start at zero.

A line chart encodes data using location (x, y coordinates), whereas a bar chart represents data using length. In a line chart, it's OK to start the axis at a number other than zero despite many claims that they are always misleading since this minute difference influences how a reader utilizes the chart.

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Answer: 12 days

Step-by-step explanation:

if the price is declining by -3$ then you just divide -36$by the -3$ and you get the amount of days it declined

Explanation

the area of a hexagon is given by

let

s=12

replace,

I hope this helps you

If two fair dice are rolled, the conditional probability that at least one is a 6 given that the two rolls give different numbers is 1/6

Two fair dice are rolled

Total number of outcomes = 6 × 6

= 36

The probability is the ratio of  number of favorable outcomes to total number of outcomes

The probability = Number of favorable outcomes / Total number of outcomes

Consider the two events E and F

P(E/F) = P(E∩F) / P(F)

P(E∩F) = 5/36

P(F) = 30/36

Substitute the values in the equation

P(E/F) = (5/36) / (30/36)

= (5/36) × (30/36)

= 1/6

Therefore, the conditional probability is 1/6

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Evaluating the functions we will get the complete table:

x        f(x)       g(x)

0         2          1

1          5          7

2        25         16

3         125       29

4        625       46

5      3,125         67

To do so, we just need to evaluate the functions in the given values. The functions are:

g(x) = 5^x

f(x) = 2 + 3x + 2x^2

Evaluating them we will get.

when x = 1

g(1) = 5^1 = 5

f(1) = 2 + 3*1 + 2*1^2 = 7

when x = 2

g(2) = 5^2 = 25

f(2) = 2 + 3*2 + 2*2^2 = 16

when x = 3

g(3) = 5^3 = 125

f(1) = 2 + 3*3 + 2*3^2 = 29

when x = 4

g(4) = 5^4 = 625

f(4) = 2 + 3*4 + 2*4^2 = 46

when x = 5

g(5) = 5^5 = 3,125

f(5) = 2 + 3*5 + 2*5^2 = 67

Then the complete table is:

x        f(x)       g(x)

0         2          1

1          5          7

2        25         16

3         125       29

4        625       46

5      3,125         67

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Answer:

Option C and D

Step-by-step explanation:

2π/3 refers 120°which falls in the second quadrant. In second quadrant sin  value is positive and tan & cos value is negative.

tan 120 = - tan 60 = -√3

The stress function satisfies the conditions of compatibility for a two-dimensional problem.

Given stress function is 50x² - 60xy - 70y²

To determine whether the stress function satisfies the conditions of compatibility for a two-dimensional problem, it is required to find the strains and then check for compatibility equations.

Strain components are given as,

εx = ∂υ/∂x + (du/dx)

εy = ∂υ/∂y + (du/dy)

γxy = ∂υ/∂y + (du/dx)

Here,

υ = 50x² - 60xy - 70y²

du/dx = 100x - 60

ydu/dy = -60x - 140y

∂υ/∂x = 100x - 60y

∂υ/∂y = -60x - 140y

∂²υ/∂y² = -140

∂²υ/∂x² = 100

Now,εx = 100x - 60

yεy = -140y - 60

xγxy = -60y - 60x

Taking derivative of εy w.r.t x,

∂(εy)/∂x = -60

Similarly, taking derivative of εx w.r.t y,

∂(εx)/∂y = -60

∴ The stress function satisfies the conditions of compatibility for a two-dimensional problem.

Stress components are given as,

σx = (C11εx + C12εy)

σy = (C21εx + C22εy)

τxy = (C44γxy)

Here,C11 = C22 = 100, C12 = C21 = -60 and C44 = 0

Therefore,

σx = 100(100x - 60y) - 60(-140y - 60x)

= 19600x - 8800

yσy = -60(100x - 60y) + 100(-140y - 60x)

= -19600y + 8800x

τxy = 0

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Answer:

21.8

Step-by-step explanation:

87.2 divided by 4

Answer:

261.60

Step-by-step explanation:

its 3 times 87.20

Answer:

c. 141 eighth-grade band students

Part B:

y = 3x

1/3y = x

A randomly selected subject has a 0.40 probability of completing more tasks than expected in 5 minutes while listening to relaxing music.

The Probability distribution is:

    X                     1                    2                3              4          

   P(x)             0.20          0.40      0.30             0.10

If listening to soothing music, the expected number of puzzles in 5 minutes can be calculated as follows:

            E(x) = ∑x p(x)

       ⇒ E(x) = 1 ×(0.20) + 2× 0.40 + 3 × 0.30 + 4× 0.1

       ⇒ E(x) = 0.20 + 0.8 + 0.9 + 0.4

       ⇒ E(x) = 2.3

Thus, a randomly selected subject could solve 5 puzzles while listening to soothing music. The probability of solving more tasks than expected in a minute is calculated as:

    P( X > 2.3) = P(X = 3) + P(X = 4)

                      = 0.30 + 0.10

                      = 0.40

Explanation for other  option:

(a) The probability that a randomly selected participant completes more tasks than expected in 5 minutes while listening to relaxing music does not equal 0.1.

(c) 5 randomly selected participants. The probability of completing more tasks than expected in a minute of listening to relaxation music does not equal 0.8.

(d) The probability that a randomly selected participant completes more tasks than expected in 5 minutes while listening to relaxing music is not equal to 1.

(e) The likelihood of randomly selected participants completing more tasks than expected in 5 minutes while listening to relaxing music cannot be determined.

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Answer:

2x^3 - 2x^2 - 9x + 3

Step-by-step explanation:

(2x^3 − 3x + 2) - (2x^2 + 6x − 1) =

2x^3 − 3x + 2 - 2x^2 + (-6x) − (-1) =  ==> distribute the negative sign to 2x^2,

                                                               6x, and -1 in (2x^2 + 6x − 1)

Adding a negative number is equivalent to subtracting by a positive number.

Subtracting a negative number is equivalent to adding by a positive number.

Hence:

2x^3 − 3x + 2 - 2x^2 - 6x + 1 =  

2x^3 - 2x^2 - 3x - 6x + 2 + 1 =  ==> rearrange the expression in which like

                                                      terms are matching

2x^3 - 2x^2 - 9x + 3 ==> simplify

1 - x - x² - x³ - x⁴ - x⁵ - x⁶ can be shown generating number of ways considering number of die rolls as infinite series and showing that expression is equivalent to the generating function.

To show that (1 - x - x² - x³ - x⁴ - x⁵ - x⁶)-¹ is the generating function for the number of ways a sum of r can occur if a die is rolled any number of times, we'll follow these steps:

1. Identify the generating function for a single die roll.
2. Consider the infinite series representing any number of die rolls.
3. Show that the given expression is equivalent to the generating function.

Step 1: For a single die roll, the possible outcomes are 1, 2, 3, 4, 5, and 6. The generating function representing this is:
F(x) = x + x²+ x³ + x⁴+ x⁵+ x⁶

Step 2: To consider any number of die rolls, we want to find the generating function that represents the sum of outcomes for an infinite number of rolls. This is the sum of the geometric series with a common ratio F(x), so the infinite series is:

G(x) = 1 + F(x) + F(x)² + F(x)³ + ...

Step 3: To show that the given expression is equivalent to the generating function, we want to show that G(x) = (1 - x - x² - x³- x⁴- x⁵ - x⁶)-¹.

We know that the sum of an infinite geometric series is:

Sum = 1 / (1 - r)

Here, r = F(x), so the sum of the series G(x) is:

G(x) = 1 / (1 - F(x))

Now, substitute F(x) from Step 1:

G(x) = 1 / (1 - (x + x²+ x³+ x⁴+ x⁵ + x⁶))

G(x) = 1 / (1 - x - x² - x³- x⁴- x⁵- x⁶)

Thus, we have shown that (1 - x - x²- x³ - x⁴ - x⁵ - x⁶)-¹ is the generating function for the number of ways a sum of r can occur if a die is rolled any number of times.

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When you multiply 4 with any number, you can use the doubling-up trick (that's the one you used for the two times table) twice. Here is an example: 2 x 4 is the same as 2 + 2 = 4 and then 4 + 4 = 8. So, 2 x 4 = 8.

Here is next double, double example are: 5 x 4 is the same as 5 + 5 = 10, so then 10 + 10 = 20. So, the answer is 5 x 4 = 20.

Here, is the table of four.

4×1=4

4×2=8

4×3=12

4×4=16

4×5=20

4×6=24

4×7=28

4×8=32

4×9=36

4×10=40

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Answer:

2x^2

Step-by-step explanation:

Q:

identify the quadratic term in the function f(x)=2x^2-3x+5

A:

The quadratic term is 2x^2.

Answer:

2x2-3x-5=0

Step-by-step explanation:

(2x2 -  3x) -  5  = 0

Answer:

The quadratic term in the function is  

Step-by-step explanation:

Given : Function  

To find : Identify the quadratic term in the function ?

Solution :

The quadratic  form of the function is  

Where,  is quadratic term.

On comparing with given function,  

is the quadratic term.

Therefore, the quadratic term in the function is

First, let's write on a table the information about the snow on the ground for the 11 hours it snowed:

period of time in hours amount of snow in inches

0 1

from 0 to 2 1 + t * 3 (initial amount plus 3 in/h * number of hours)

from 2 to 5 1 + 2*3 = 7 (the same amount as when it stopped raining)

from 5 to 11 7 + (t-5)/2 (amount at t = 5 plus 1 in/2h * number of

hours since hour 5)

Now, using this information on a graph, we obtain: