Hence, we may conclude that function(x) behaves as though it will eventually approach infinity as x approaches infinity and will eventually approach negative infinity as x approaches negative infinity.
what is function?Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
F(x) also approaches positive infinity as x gets closer to infinity.
F(x) also approaches negative infinity as x gets closer to its opposite.
This is due to the fact that as x increases or decreases in value, the term with the largest x power determines how the function behaves.
Hence, we may conclude that f(x) behaves as though it will eventually approach infinity as x approaches infinity and will eventually approach negative infinity as x approaches negative infinity.
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Consider the code over F4 with generator matrix 11 10 01 10 00
11 Construct a standard array for the code, and use it to decode
the words 00 11 01 and 11 11 10.
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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Find out how long it takes a $2500 investment to earn $400 interest if it is invested at 8% compounded quarterly. Round to the nearest tenth of a year
It will take approximately 2.9 years (or 2 years and 11 months) for the $2500 investment to earn $400 interest at a rate of 8% compounded quarterly.
A = [tex]P(1 + r/n)^{nt}[/tex]
Where:
A = the total amount that includes principal and interest, P = the principal that is the initial amount invested, r = the annual interest rate, n = the number of times is the interest is compounded per year, and t = the time
$2900 = [tex]$2500(1 + 0.08/4)^{4t}[/tex]
Simplifying this equation, we get:
1.16 = (1 + 0.02
By calculating the natural logarithm of both sides, we arrive at:
ln(1.16) = 4t ln(1.02)
t ≈ 2.9 years
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Write the gradient and y-intercept of each line
a. Y=10x+20
b. Y=10-20x
c. Y=-2. 5+0. 5x
The required gradient and y-intercept for the given lines is given by ,
1. gradient = 10 and y-intercept = 20
2. gradient = -20 and y-intercept = 10
3. gradient = 0.5 and y-intercept = 2.5
Equation of a line in slope-intercept form = y = mx + c.
where 'm' is the slope of the line
And 'c' is the y-intercept.
For the line Y = 10x + 20
Compare with standard form we get,
Slope of the line is 10 .
And the y-intercept is 20.
This implies,
gradient is 10 and the y-intercept is (0, 20).
For the line Y=10-20x
Compare with standard form we get,
Slope of the line is -20
And the y-intercept is 10.
This implies,
the gradient = -20
And the y-intercept = (0, 10).
For the line Y=-2. 5+0. 5x
Compare with standard form we get,
Slope of the line is 0.5
And the y-intercept is -2.5
This implies,
the gradient = 0.5
And the y-intercept = (0, -2.5)
Therefore, the gradient and the y-intercept for each line is equal to,
Y=10x+20 , gradient = 10 and y-intercept = 20
Y=10 -20x , gradient = -20 and y-intercept = 10
Y=-2. 5+0. 5x , gradient = 0.5 and y-intercept = 2.5
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There are 100 prize tickets in a bowl, numbered 1-100. What is the probability that an even numbered prize will be chosen at random, not replaced, then an odd numbered prize ticket will be chosen?
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:
Total outcome = 100Favourable outcome = 50 (because there are 50 even numvers and 50 odd numbers)[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:
Total outcome = 99 (because one ticket was taken out and was not replaced)Favourable outcome = 50[tex] \tt \: P(E) = \frac{F.O.}{T.O.} [/tex]
[tex] \tt \: P(E) = \frac{50}{99} = 0.505051[/tex]
A university law school accepts 4 out of every 11 applicants. If the school accepted 360 students, find how many applications they received.
Answer:
990 applicants
Step-by-step explanation:
We know
A university law school accepts 4 out of every 11 applicants.
If the school accepted 360 students, find how many applications they received.
To get from 4 to 360, we time 90
We take 11 times 90 = 990 applicants
So, they received 990 applicants.
write the equation for the sequence below
Answer: x = p/2
Step-by-step explanation:
x = next one
p = previous
in order to solve the next one, you would do :
x (the one you are trying to solve) = p (the previous one : 1/8) divided by 2
x = p/2
help me do this pls it is to hard
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
What is a Fraction?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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Audrey’s university English teacher Mr. Dalton has told her she will have 28 assignments this semester. Audrey has discovered that she needs to spend 2.5 hours on each assignment.
How many hours will Audrey spend on her English assignments?
AND
How many days will it take Audrey to complete her assignments?
I need explanation please!
70 hours will Audrey spend on her English assignments.
2.9 days will it take Audrey to complete her assignments.
What is Unitary Method?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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darr Question Details 9. Divide using synthetic division. (x^(3)-2x^(2)+10)-:(x-2)
The answer is: x^(2) + 20/(x-2)
Synthetic division is a method of dividing a polynomial by a linear factor. It is a shorthand version of long division that is quicker and easier to do.
Here are the steps to solve this problem using synthetic division:
1. Write the coefficients of the dividend in a row: 1 -2 0 10
2. Write the constant term of the divisor to the left of the row: 2 | 1 -2 0 10
3. Bring down the first coefficient: 2 | 1 -2 0 10
|_______
1
4. Multiply the first coefficient by the divisor and write the result under the second coefficient: 2 | 1 -2 0 10
|___2___
1 0
5. Add the second coefficient and the result: 2 | 1 -2 0 10
|___2___
1 0
6. Repeat the process with the remaining coefficients: 2 | 1 -2 0 10
|___2__0_20
1 0 0 20
7. The final row of numbers represents the coefficients of the quotient and the remainder: (x^(2) + 0x + 0) + 20/(x-2)
So, the answer is: x^(2) + 20/(x-2)
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help me please, I been trying to get help for hours now.
We can conclude that -
General exponential growth equation is : [tex]$f(x)=a(1+r)^{x}[/tex]General exponential decay equation is : [tex]$\frac {dN}{dt}= -\lambda N[/tex]Option {A} and option {E} represent the exponential decay.Option {B}, {E} and {D} represent exponential growth.What is exponential function?The exponential function is of the form -
f(x) = eˣ
Given is to write the exponential growth and exponential decay equation.
{ 1 } -
The general exponential growth equation is -
[tex]$f(x)=a(1+r)^{x}[/tex]
{ 2 } -
The general exponential decay equation is -
[tex]$\frac {dN}{dt}= -\lambda N[/tex]
Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.
Therefore, we can conclude that -
General exponential growth equation is : [tex]$f(x)=a(1+r)^{x}[/tex]General exponential decay equation is : [tex]$\frac {dN}{dt}= -\lambda N[/tex]Option {A} and option {E} represent the exponential decay.Option {B}, {E} and {D} represent exponential growth.To solve more questions on functions, visit the link-
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if
a real estate office sells 1.6 houses on an average weekday and
sales of houses on weekdays are poison distributed. What is the
probability of selling exactly 4 hours in one day ?
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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Determine whether the lines L1(t) = ⟨3 − t, 8 − 3t, 1 − t⟩ and
L2(s) = ⟨−1 − 2s, 3 + s, s⟩ intersect. If they do, state where they
intersect.
The answer of lines intersect at the point is (1, 2, -1)
To determine whether the lines L1(t) = ⟨3 − t, 8 − 3t, 1 − t⟩ and L2(s) = ⟨−1 − 2s, 3 + s, s⟩ intersect, we need to find a value of t and s that make the x, y, and z components of both lines equal.
First, let's set the x components of both lines equal to each other:
3 − t = −1 − 2s
Next, let's set the y components of both lines equal to each other:
8 − 3t = 3 + s
Finally, let's set the z components of both lines equal to each other:
1 − t = s
Now we can solve for t and s. From the first equation, we get:
t = 4 + 2s
Substituting this value of t into the second equation, we get:
8 − 3(4 + 2s) = 3 + s
Simplifying this equation gives us:
-4 − 6s = 3 + s
Solving for s gives us:
s = -1
Substituting this value of s back into the first equation gives us:
t = 4 + 2(-1) = 2
So the lines intersect at t = 2 and s = -1. To find the point of intersection, we can substitute these values back into either line equation. Substituting into L1(t) gives us:
L1(2) = ⟨3 − 2, 8 − 3(2), 1 − 2⟩ = ⟨1, 2, -1⟩
Therefore, the lines intersect at the point (1, 2, -1).
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Find a function f whose graph is a parabola with the given vertex and that passes through the given point. vertex (−1, 3); point (−2, −2)
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
After a number of months, a bank balance was -$46. 83. Each month, the bank charges a $5. 95 fee for having a negative balance. Write an inequality to determine at most how many months the fee was charged. Let x be how many months the fee was charged
If x is the number of months the fee was charged, then the inequality to determine at most months the fee was charged is x ≥ (y + 46.83)/5.95 .
Let x be the number of months the fee was charged.
Let y be the initial balance before the fee was charged.
So, we can write the inequality as : y - 5.95x ≤ -46.83
where y is = positive number representing the initial balance.
Since the initial balance is "y" , we can determine the value of x that satisfies this inequality.
The inequality is represented as : x ≥ (y + 46.83)/5.95 .
Therefore, the inequality to determine number of months is x ≥ (y + 46.83)/5.95.
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The regular price of a pair of sneakers is 40 dollars. The sale price is 25 percent off. what is the sale price?
Answer:
30
Step-by-step explanation:
40/4=10
25%=10
40-10=30
Someone help me please, I am struggling with this
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°
Four more than the quotient of a number and 8 is equal to 2
guys i need this asap PLEASE
12 cm
12 cm
Work out the area of the
yellow part of the pattern
This is a pattern that is
being used to make a
patch quilt. Each pattern is
a square, measuring 12cm
by 12cm square. These are
the measurements of each
trapezium
3 cm
3 cm
9 cm
The area of the yellow part of the pattern is found as: 72 cm²
Explain about the square shape?It has four vertices and four sides. Its sides all equal in length. Since all interior angles being equal as well as right angles, they are all 90° in length. 360° is the total of all interior angles.In geometry, a square is a flat shape with 4 separate sides plus four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle .The dimension of the square: 12 x 12
Area of yellow part = Area of triangle with base height equals side of square.
Then,
Area of yellow part = 1/2 * B * H
Area of yellow part = 1/2 *12 *12
Area of yellow part = 72 cm²
Thus, the area of the yellow part of the pattern is found as: 72 cm².
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The correct question is-
Work out the area of the yellow part of the pattern. This is a pattern that is being used to make a patch quilt. The pattern is a square, measuring 12cm
by 12cm square.
Suppose a city with population 500,000 has been growing at a rate of 2% per year. If this rate continues, find the population of this city in 25 years
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &500000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=\textit{elapsed time}\dotfill &25\\ \end{cases} \\\\\\ A = 500000(1 + 0.02)^{25} \implies A=500000(1.02)^{25}\implies A \approx 820303[/tex]
Let X be a random variable whose characteristic function ∅ satisfies ∫▒〖|∅(t)|dt< [infinity].〗 . Show that (2π)^(-1) ∫▒〖e^(-√(-1) xt)∅(t)dt〗 is the Lebesgue density of X.
(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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A "pool toy" is thrown into a swimming pool, but floats on the surface of the water. It displaces 200mL of water in the pool. Use this information to select a correct conclusion.
(a) The toy weighs 200 grams. (b) The toy absorbed 200 mL of water. (c) The toy has a surface area of 200 cm². (d) The toy has a volume of 200 cm³.
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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0.4 in sin degrees in trigonometry
The value of angle XYZ is 0.020 degrees using the cosine function.
What are inverse trigonometric functions?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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Write and solve the inequality.
Eight more than the quotient of a number b and 45 is greater than 6.
Fill in the boxes.
b
45
+8
b
45
6
-2
b
(Type integers or fractions.)
The answer choice which represents the solution to the inequality given as required is; b > -90.
What is the solution for b in the inequality?Quotient refers to a number resulting from the division of one number by another.
As evident in the task content; the given inequality is;
Eight more than the quotient of a number b and 45 is greater than 6.
The symbols of inequalities are;
Greater than >
Less than <
Equal to =
Greater than or equal to ≥
Less than or equal to ≤
Therefore, the algebraic expression is;
b/45 + 8 > 6
Therefore; b/45 > -2
b > -90.
Ultimately, the required inequality is; b/45 + 8 > 6 and it's solution is; b > -90.
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Solve the following system of linear equations by the Gauss-Jordan elimination method 7x7 + 7x4 + 7x3 = 0 2x: + 2x2 - 4x + 6x4 - 2xy = 0 X1 + X2 - 2x3 - x5= 0 + x = 0
2X1 + 2X2 - x3 + x5= 0
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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Choose all the expressions that are equal to 1/6. A. 6÷1 B. 3÷18 C. 2÷ 1/3 D. 1÷6 E. 1/3 ÷ 2
We can state this by responding to the provided question B, D, and E are expressions the expressions that have values of 1/6.
what is expression ?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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FAMILY The table below shows the predicted annual cost for middle income family to raise a child from birth until adulthood. Draw a scatter plot and describe what relationship exists within the data
you have too draw a scatter
Please help quickly! Both circles have the same center. The circumference of the inner circle is 125.6 inches. What is the area of the shaded region?
Use 3.14 for pi. Write your answer as a whole number or decimal rounded to the nearest hundredth.
Answer: 43.96 inches^2
Step-by-step explanation:
(a) Show that the F statistic for testing that all effects equal
0 has expression in terms of the R2 value as
(b) Show that the F statistic for comparing nested models has
expression in terms of the
(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.
To know more about F statistic refer here:
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I need help with this question can you also go step by step because tomorrow I have a quiz?
Answer:
3/5
Step-by-step explanation:
In your problem you have a right triangle.
For this problem, you need to know what sine is. Sin is [tex]\\\frac{opposite}{hypotenuse}[/tex]
In this problem we know that the hypotenuse is 20, but we do not know the opposite. The opposite refers to the side that is opposite to the angle. In this case, the angle we are using is c. Also, in this case, the name of the opposite side is ED. To figure out that side, we need to use the pythagorean theorem.
[tex]a^{2} +b^{2} =c^{2}[/tex]
A is 16, c is 20
Therfore we can plug those values into our formula
[tex]16^{2} +b^{2}=20^{2}[/tex]
Simplify:
[tex]256 + b^{2} =400[/tex]
Simplify even more:
[tex]b^{2} = 144[/tex]
Square root both sides:
[tex]b = 12[/tex]
Now we Know all 3 sides of our triangle: 20, 16, and 12.
Sin refers to OPPOSITE/HYPOTENUSE
Our opposite is 12, and our hypotenuse is 20.
Plugging those values into our formula gives us:
12/20
Simplify:
3/5.
THERFORE, THE ANSWER IS 3/5
**Also, this whole process seems long, but in reality it is very short and you'll master it in no time!