A teacher collected data from her students on the amount of homework that each student completed over the week. She used a scale of integers from 0 to 10 where 0 meant none of the
homework was completed and 10 meant that all of the homework was completed.
a) Would the data be discrete or continuous? Explain.(3)
b) Would the data be ordinal data or nominal data? Explain.(3)

you have too draw a scatter

The median of the solutions to the equation 3x³ + 5x² − 6x − 10 = 0 is -√2. The correct answer is A.

To find the median of the solutions to the equation 3x³ + 5x² − 6x − 10 = 0, first find the solutions of the equation and then find the middle value of those solutions.

Group the terms and factor out (3x + 5).

(3x³ + 5x²) + (-6x − 10) = 0

(3x + 5)(x²) + (3x + 5)(-2) = 0

(3x + 5)(x² - 2) = 0

Factor (x² - 2).

(3x + 5)(x + √2)(x - √2) = 0

So the solutions of the equation are x = -5/3, x = -√2, and x = √2.

To find the median of these solutions, we need to order them from least to greatest:

-5/3 < -√2 < √2

The median of these solutions is -√2.

Therefore, the correct answer is (A) -√2.

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Answer:

Step-by-step explanation:

[tex]-\frac{1}{2}[/tex] x ≤ 17

( [tex]-\frac{2}{1}[/tex] )( [tex]-\frac{1}{2}[/tex] ) x ≤ 17( [tex]-\frac{2}{1}[/tex] )

x ≥ - 34

The fraction amount of pizza eaten is given by A = ( 5/6 ) of the pizza

The amount of pizza left over B = ( 1/6 ) of the pizza

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction of pizza eaten be represented as A

Now , the value of A is

Let the amount of pizza eaten by Tyler be p = ( 1/2 ) of the pizza

Let the amount of pizza eaten by Dean be q = ( 1/3 ) of the pizza

Now , the fraction of pizza eaten A = p + q

On simplifying , we get

The fraction of pizza eaten A = ( 1/2 ) + ( 13 )

The fraction of pizza eaten A = ( 3 + 2 ) / 6

The fraction of pizza eaten A = ( 5/6 ) of the pizza

And , the amount of pizza left B = 1 - A

On simplifying , we get

The amount of pizza left = 1/6 of the total pizza

Hence , the fractions are solved

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Hannah will have $681.98 in her savings account after 3 years at 2.75% simple annual interest.

To calculate the amount of money Hannah will have in the account after 3 years, we can use the formula for simple interest:

Simple interest = principal x rate x time

where:

principal is the amount of money initially deposited

rate is the annual interest rate (expressed as a decimal)

time is the number of years

In this case, the principal is $630, the rate is 2.75% (or 0.0275 as a decimal), and the time is 3 years. Plugging these values into the formula, we get:

Simple interest = $630 x 0.0275 x 3 = $51.98

This means that after 3 years, Hannah will have earned $51.98 in simple interest. To find the total amount of money in her account, we need to add this interest to the original principal:

Total amount = principal + simple interest

Total amount = $630 + $51.98 = $681.98

Therefore, after 3 years Hannah will be having $681.98 in her account after 3 years at 2.75% simple annual interest.

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The complete question is :

Hannah deposits $630 in a savings account at 2. 75% simple annual interest. How much money will she have in the account after 3 years?

Answer:

Direct proportion and inverse proportion are two types of relationships between two variables.

Direct proportion is a relationship in which two variables increase or decrease together at the same rate. In other words, if one variable increases, the other variable also increases, and if one variable decreases, the other variable also decreases. The mathematical expression for direct proportion is:

y = kx

where y is the dependent variable, x is the independent variable, and k is a constant of proportionality.

On the other hand, inverse proportion is a relationship in which two variables change in opposite directions. In other words, if one variable increases, the other variable decreases, and if one variable decreases, the other variable increases. The mathematical expression for inverse proportion is:

y = k/x

where y is the dependent variable, x is the independent variable, and k is a constant of proportionality.

So, the main difference between inverse proportion and direct proportion is the direction of change between the two variables. In direct proportion, the two variables change in the same direction, while in inverse proportion, the two variables change in opposite directions.

Therefore , the solution of the given problem of unitary method comes out to be 29 1/3 yards of fabric.

To finish the job using the unitary method, multiply the measures taken from this microsecond section by two variable. In a nutshell, when a wanted thing is present, the characterized by a group but also colour groups are both eliminated from the unit technique. For expression instance, 40 changeable-price pencils would cost Inr ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

If 1 2/9 yards of cloth are required for each choir robe, then 24 choir robes will require:

=> 1 2/9 * 24 = (1*9+2)/9 * 24 = 11/9 * 24

We add the numerators and denominators together to multiply fractions:

=> 11/9 * 24/1 = (1124)/(91) = 264/9

264/9 yards of cloth will be required to make 24 choir robes. This can be stated simply as:

(Rounded to the closest 1/3 yard) 264/9 = 29 1/3 yards of fabric.

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Answer:

Equation of parabola in vertex form:
y = -5( x + 1)² + 3

Equation of parabola in standard form:
y = -5x² -10x - 2

Step-by-step explanation:

The vertex form equation for a parabola is

y = a(x - h)² + k

where (h, k) is the vertex and a is a constant

Given (h, k) = (- 1, 3)
h = -1 , k = 3

y = a( x - (-1) )² + 3
y = a(x + 1)² + 3

To find a, we know the parabola passes through point(- 2, - 2). Plug in x = -2, y = -2 and solve for a

- 2 = a( -2 + 1)² + 3

-2 = a(-1)² + 3

-2 = a · 1 + 3

-2 = a + 3

Subtract 3 from both sides:

-2 - 3 = a + 3 -3

-5 = a

or

a = -5

Equation of parabola in vertex form:
y = -5( x + 1)² + 3

The standard form of this parabola is y = ax² + bx + c

Expand (x + 1)² = x² + 2 · 1 · x + 1² = x² + 2x + 1

Therefore

y = -5( x + 1)² + 3 becomes
y = -5( x² + 2x + 1) + 3

y = -5x² -10x - 5 + 3

y = -5x² -10x - 2

(a) We can use the identity cos(180° - θ) = -cos(θ) to rewrite cos(165°) as cos(180° - 15°) cos(165°) = cos(180° - 15°) = -cos(15°) To find cos(15°),

we can use the half-angle formula for cosine: cos(15°) = cos(30°/2) = sqrt((1 + cos(30°))/2) = sqrt((1 + sqrt(3)/2)/2) = (sqrt(2) + sqrt(6))/4

Therefore, cos(165°) = -cos(15°) = -(sqrt(2) + sqrt(6))/4 (b) Using the product-to-sum identity, we have cos(80°)cos(20°) + sin(80°)sin(20°) = cos(80° - 20°) = cos(60°) = 1/2 Therefore, cos(80°)cos(20°) + sin(80°)sin(20°) = 1/2.

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This statement is false. A right exact functor preserves exactness of short exact sequences at the right-hand side, but it does not necessarily preserve exactness at the left-hand side. An example of a right exact functor that is not left exact is the tensor product functor.

The following statements can be proved or disproved as follows:
(a) Every ring is an IBN ring.
This statement is false. A ring is said to be an IBN (Invariant Basis Number) ring if all of its finitely generated free modules have unique rank. However, not all rings have this property. For example, the ring of polynomials over a field F, F[x], is not an IBN ring.
(b) In a ring R, if for any a,b∈R,ab=0, then ba=0.
This statement is true. If ab=0, then b is a zero divisor in the ring R. Since zero divisors are symmetric, this implies that ba=0 as well.
(c) The characteristic of a finite field is a prime number.
This statement is true. The characteristic of a finite field is the smallest positive integer n such that n*1=0 in the field. Since a finite field is also an integral domain, it cannot have zero divisors, and therefore the characteristic must be a prime number.
(d) Every right exact functor is also left exact.
This statement is false. A right exact functor preserves exactness of short exact sequences at the right-hand side, but it does not necessarily preserve exactness at the left-hand side. An example of a right exact functor that is not left exact is the tensor product functor.

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The toy has a volume of 200 cm³. The correct answer is Option d.

This is because when an object is submerged in water, it displaces an amount of water equal to its volume. In this case, the pool toy displaces 200 mL of water, which means it has a volume of 200 cm³ (since 1 mL is equal to 1 cm³). The correct answer is Option d.

It is not correct to say that the toy weighs 200 grams (option a), as the weight of the toy is not related to the amount of water it displaces. Similarly, it is not correct to say that the toy absorbed 200 mL of water (option b), as the toy is simply displacing the water, not absorbing it.

Finally, it is  correct to say that the toy has a surface area of 200 cm² (option c), as the amount of water displaced is related to the toy's volume, not its surface area.

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Answer: 43.96 inches^2

Step-by-step explanation:

The Gauss-Jordan elimination method can be used to solve this system of linear equations. First, we need to create an augmented matrix containing all the coefficients of the system:

\begin{bmatrix}
   7 & 7 & 7 & 0 \\
   2 & 2 & -4 & 6 \\
   1 & 1 & -2 & -1 \\
   0 & 0 & 1 & 0 \\
\end{bmatrix}

We then use a series of row operations to reduce the matrix to row echelon form:

\begin{bmatrix}
   7 & 7 & 7 & 0 \\
   0 & -4 & -5 & 6 \\
   0 & 1 & -3 & -1 \\
   0 & 0 & 1 & 0 \\
\end{bmatrix}

Finally, we solve the system of equations by performing back substitution and we get the following solution:

x1 = 0, x2 = 6, x3 = 1, x4 = -2, x5 = 1

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To decode the words 0011, 0101, 0110 and 1111, we can find the corresponding codeword in the standard array. The codewords for 0011, 0101, 0110 and 1111 are 0011, 0101, 0110 and 1111, respectively.

To construct a standard array for this code, we can start by finding the generator polynomial of the code. This can be done by multiplying the generator matrix with its transpose and finding the resultant matrix. This results in the generator polynomial: 110101001.

To construct the standard array, we first construct a parity check matrix, which is the transpose of the generator matrix: 0101 1001 1100 1000.

From the parity check matrix, we can then construct the standard array. The standard array consists of all the possible codewords given the generator polynomial and the parity check matrix. It can be constructed by multiplying the generator matrix with all possible vectors of length 3.

The standard array of the code is:
0011  0101  0110  1001  1010  1100  1101  1111

To decode the words 0011, 0101, 0110 and 1111, we can find the corresponding codeword in the standard array. The codewords for 0011, 0101, 0110 and 1111 are 0011, 0101, 0110 and 1111, respectively.

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Answer:

Step-by-step explanation:

i don’t know

Answer:i really don´t know hopefully you get thw\e answer correct.

Step-by-step explanation:

The lengths of RS and ST are 20 and 1 respectively

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units system the base unit for length is the metre.

here, we have,

to solve for RS and ST;

The given parameters are:

RS= 2x+10, ST= x−4, RT= 21

This means that

RT = RS + ST

So, we have:

2x + 10 + x - 4 = 21

Evaluate the like terms

3x = 15

Divide by 3

x = 5

Substitute x = 5 in RS= 2x+10 and  ST= x−4

RS= 2*5+10 = 20

ST= 5−4 = 1

Hence, the lengths of RS and ST are 20 and 1 respectively

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Answer:

25/99

Step-by-step explanation:

If the tickets are numbered 1-100, half of the tickets will be even and half of the tickets will be odd

Number of even tickets = 50

Number of odd tickets = 50

Let A be the event =>  even ticket on first draw

Let B be the event => odd ticket on second draw

P(even on first draw) = P(A)
= Number of even tickets/total number of tickets

= 50/100

= 1/2

Once a ticket has been drawn and the second draw is without replacement,

Total number of tickets remaining = 100 - 1 = 99

Total number of odd tickets remaining given first ticket drawn is even
= 50

P(odd ticket second draw | first draw is even) = P(B | A)
= 50/99

P(A and B) = P(A) · P(B | A)

= 1/2 x 50/99

= 50 / (2 x 99)

= 50/198

= 25/99

Probability that it is an even number:

[tex] \tt \: P(E) = \frac{F.O.}{T.O.} [/tex]

[tex] \tt \: P(E) = \frac{50}{100} = \frac{1}{2} [/tex]

Pribability that it is an odd number:

[tex] \tt \: P(E) = \frac{F.O.}{T.O.} [/tex]

[tex] \tt \: P(E) = \frac{50}{99} = 0.505051[/tex]

(2π)^(-1)E[∫▒〖e^(-√(-1) xy)]dy〗

The characteristic function of a random variable X is defined as ∅(t) = E[e^(√(-1)tx)]. To show that (2π)^(-1) ∫▒〖e^(-√(-1) xt)∅(t)dt〗 is the Lebesgue density of X, we need to demonstrate that it is a probability density function.

We first calculate the integral to obtain (2π)^(-1) ∫▒〖e^(-√(-1) xt)∅(t)dt〗 = (2π)^(-1) ∫▒〖E[e^(-√(-1) xt +√(-1) tx)]dt〗.

Since the expectation is a constant, we can pull it out of the integral to get (2π)^(-1)E[∫▒〖e^(-√(-1) xt +√(-1) tx)]dt〗.

Now, if we substitute t = y-x and rewrite the integral, we obtain (2π)^(-1)E[∫▒〖e^(-√(-1) x(y-x))e^(√(-1) xy)]dy〗.

This simplifies to (2π)^(-1)E[∫▒〖e^(-√(-1) xy)]dy〗.

Because the integrand is 1, the integral is simply y. Then, the expectation becomes E[y] which is the mean of the random variable X. Thus, the Lebesgue density of X is (2π)^(-1)E[y], which is the probability density function of X.

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70 hours will Audrey spend on her English assignments.

2.9 days will it take Audrey to complete her assignments.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Mr. Dalton has told her she will have 28 assignments this semester.

She needs to spend 2.5 hours on each assignment.

So, she will spend on Assignments

= 28 x 2.5

= 70 hours

Now, In one day = 24 hours

So, to complete the assignments it will take

= 70/ 24

= 2.9 days

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The composite functions f ∘ g and g ∘ f are:
domain of f = (-∞, ∞)
domain of g = (-∞, ∞)
domain of f ∘ g = (-∞, ∞)
domain of g ∘ f = (-∞, ∞)

The composite functions f ∘ g and g ∘ f are formed by plugging one function into the other. To find f ∘ g, we plug the function g into the function f:

f ∘ g = f(g(x)) = f(x2/3) = (x2/3)3 = x2

To find g ∘ f, we plug the function f into the function g:

g ∘ f = g(f(x)) = g(x3) = (x3)2/3 = x2

The domain of a function is the set of all possible values of x that make the function defined. The domain of f is all real numbers, since the function f(x) = x3 is defined for all values of x:

domain of f = (-∞, ∞)

The domain of g is also all real numbers, since the function g(x) = x2/3 is defined for all values of x:

domain of g = (-∞, ∞)

The domain of f ∘ g is the intersection of the domain of f and the domain of g, which is all real numbers:

domain of f ∘ g = (-∞, ∞)

The domain of g ∘ f is also the intersection of the domain of g and the domain of f, which is all real numbers:

domain of g ∘ f = (-∞, ∞)

Therefore, the answers are:

domain of f = (-∞, ∞)
domain of g = (-∞, ∞)
domain of f ∘ g = (-∞, ∞)
domain of g ∘ f = (-∞, ∞)

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Answer:

79° , 65° , 144°

Step-by-step explanation:

65° , x° and 36° lie on a straight line and sum to 180° , that is

65° + x° + 36° = 180°

101° + x° = 180 ( subtract 101° from both sides )

x= 79°

y + 10 and 65° are alternate angles and are congruent , then

y + 10 = 65°

z and 36° are same- side interior angles and sum to 180° , that is

z + 36° = 180° ( subtract 36° from both sides )

z = 144°

The probability of selling exactly 4 houses in one day is 0.0548, or about 5.48%.

To find the probability of selling exactly 4 houses in one day, use the Poisson distribution formula:

P(X = x) = (λ^x)(e^-λ) / x!

Where:

λ = the average number of events (in this case, the average number of houses sold)

x = the number of events we want to find the probability of (in this case, 4 houses)

e = the base of the natural logarithm (approximately 2.71828)

So, plugging in the values: P(X = 4) = (1.6^4)(e^-1.6) / 4! = (6.5536)(0.2019) / 24 = 0.0548

Therefore, since the data is Poisson distributed, selling exactly 4 houses in one day has a probability of 0.0548, or about 5.48%.

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Answer:

The quotient of (2x³ + x² - x - 4) ÷ (x + 4) is 2x^2 - 7x + 17, and the remainder is 27x - 4.

Step-by-step explanation:

     2x^2 - 7x + 17

x + 4 | 2x^3 + x^2 - x - 4

- (2x^3 + 8x^2)

---------------

-7x^2 - x

+ (-7x^2 - 28x)

-------------

27x - 4

Therefore, the quotient of (2x³ + x² - x - 4) ÷ (x + 4) is 2x^2 - 7x + 17, and the remainder is 27x - 4.

We round up to the nearest whole number because we are unable to have half a player. As a result, the softball team is allowed to send 7 players to the competition.

The equal sign joins two expressions to create a mathematical formula called an equation. An illustration formula could be 3x - 5 = 16. By resolving this equation, we find that the value of the variable x is 7.

To begin, let's define a few variables:

x: The softball team's total roster size

y: the sum of the players' meal expenses

We can construct the equation shown below:

$1353 - $943.50 - $31.50x = y

Simplifying this equation, we get:

$409.50 - $31.50x = y

we can set up another equation:

y = $31.50x

Now we can substitute the second equation into the first equation to eliminate y:

$409.50 - $31.50x = $31.50x

Simplifying this equation, we get:

$409.50 = $63x

Dividing both sides by 63, we get:

x = 6.5

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So, by resolving the given, we obtain the result: Alexandria thus shells expressions out a total of $12.86 for the 14 tracks.

Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

Alexandria downloads 13 tracks at $0.99 each, for a grand total of $12.87 (13 x $0.99).

She also spends $1.49 downloading one song.

The price before the coupon is thus $12.87 + $1.49 = $14.36.

The final price is $14.36 - $1.50 = $12.86 after the coupon for $1.50 discount is applied.

Alexandria thus shells out a total of $12.86 for the 14 tracks.

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The value of angle XYZ is 0.020 degrees using the cosine function.

Simply put, inverse trigonometric functions are the opposites of the fundamental trigonometric functions sine, cosine, tangent, cotangent, secant, and cosecant. The terms arcus functions, antitrigonometric functions, and cyclometric functions are also used to describe them. To find the angle for any trigonometric ratio, apply these inverse trigonometric functions. The fields of engineering, physics, geometry, and navigation all heavily utilise the inverse trigonometry functions.

From the given right triangle we observe that:

cos y = 6 / 15 = adjacent side /hypotenuse

y = arccos(6/15)

y = 0.020 degrees

Hence, the value of angle XYZ is 0.020 degrees using the cosine function.

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We can state this by responding to the provided question B, D, and E are expressions the expressions that have values of 1/6.

Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression.

We need to simplify each expression to see which ones are equivalent to 1/6:

6. 1/6 is not equivalent to 6/1.

B. 3÷18 = 1/6

C. 2/3 of 2 equals 6 (not equivalent to 1/6)

D. 1÷6 = 1/6

E. 1/3 ÷ 2 = 1/6

B, D, and E are the expressions that have values of 1/6.

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(a) The F statistic for testing that all effects equal 0 is given by:
F = [(R2 / k) / ((1 - R2) / (n - k - 1))]
where R2 is the coefficient of determination, k is the number of predictor variables, and n is the total number of observations.
To derive this expression, we start with the definition of the F statistic:
F = [(SSR / k) / (SSE / (n - k - 1))]
where SSR is the sum of squares for regression and SSE is the sum of squares for error.
We know that R2 = SSR / SST, where SST is the total sum of squares. Therefore, we can rewrite SSR as:
SSR = R2 * SST
Substituting this back into the F statistic, we get:
F = [(R2 * SST / k) / (SSE / (n - k - 1))]
We also know that SST = SSR + SSE, so we can substitute this back into the F statistic:
F = [(R2 * (SSR + SSE) / k) / (SSE / (n - k - 1))]
Simplifying the expression, we get:
F = [(R2 / k) / ((1 - R2) / (n - k - 1))]
This is the expression for the F statistic in terms of the R2 value.

(b) The F statistic for comparing nested models is given by:
F = [(R2_2 - R2_1) / (k_2 - k_1)] / [(1 - R2_2) / (n - k_2 - 1)]
where R2_1 and R2_2 are the R2 values for the smaller and larger models, respectively, and k_1 and k_2 are the number of predictor variables in the smaller and larger models, respectively.
To derive this expression, we start with the definition of the F statistic:
F = [(SSR_2 - SSR_1) / (k_2 - k_1)] / [(SSE_2 / (n - k_2 - 1))]
where SSR_1 and SSR_2 are the sum of squares for regression for the smaller and larger models, respectively, and SSE_2 is the sum of squares for error for the larger model.
We know that R2 = SSR / SST, so we can rewrite SSR_1 and SSR_2 as:
SSR_1 = R2_1 * SST
SSR_2 = R2_2 * SST
Substituting these back into the F statistic, we get:
F = [((R2_2 * SST) - (R2_1 * SST)) / (k_2 - k_1)] / [(SSE_2 / (n - k_2 - 1))]
Simplifying the expression, we get:
F = [(R2_2 - R2_1) / (k_2 - k_1)] / [(1 - R2_2) / (n - k_2 - 1)]

This is the expression for the F statistic for comparing nested models in terms of the R2 values.

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Answer:

30

Step-by-step explanation:

40/4=10

25%=10

40-10=30