You can determine if the inverse of a polynomial function is a function by using the Horizontal Line Test on the inverse.
The Horizontal Line Test is a graphical method that can be used to determine whether a given function is one-to-one, meaning that for each output value, there is at most one input value that maps to it.
If the inverse of a polynomial function is a function, it must pass the Horizontal Line Test, meaning that no horizontal line intersects the graph of the inverse more than once.
In other words, if the inverse of a polynomial function passes the Horizontal Line Test, it is guaranteed to have an inverse, which will be a function itself. If the Horizontal Line Test fails, then the inverse is not a function and does not have an inverse.
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Additional Challenge: Khalil is working with a geometric sequence. He knows that t(0) = 3 and that the sum of the first three terms ( t(0), t(1) , and t(2) ) add up to 63 Help him figure out the sequence.
The solution is, the sequence is, {3, 31, 49, ..............}
What is Arithmetic progression?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.
here, we have,
t(0) = 3
and that the sum of the first three terms ( t(0), t(1) , and t(2) ) is 63
let, the 1st term = a
common difference = d
so, we have,
a = 3
and, a+ a+d + a+ 2d = 63
or, 9+ 3d = 63
or, 3d = 54
or, d = 18
Hence, The solution is, the sequence is, {3, 31, 49, ..............}
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A successful music app tracked the number of song downloads each day for a month for 4 music artists, represented by lines l, j, m, and d over the course of a month. Which line represents an artist whose downloads remained constant over the month?
By applying linear equation concept, it can be concluded that the line representing the artist whose downloads have remained constant over the month is the horizontal one, line m.
Linear equation is an equation that contains one or more variables, where each variable has the power of one.
Linear equation graph with a particular slope will be formed if this equation is depicted in a Cartesian diagram. The slope is usually called the gradient of the line (m), so the equation can be written as y = mx + c.
If the line graph is sloping to the right indicates that the gradient is positive. Conversely, if the line graph is sloping to the left indicates that the gradient is negative.
Therefore, the line representing the artist whose downloads have remained constant over the month is the horizontal one, line m.
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A coin is tossed three times. Find the probability of getting all heads or all tails.
Answer:
1/8
Step-by-step explanation:
The coin is flipped three times; the total number of outcomes = 2 × 2 × 2 = 8. P(X) = |X| / |Ω| = 1/8.
how to find class width
To determine the width:
By deducting the lowest point from the highest, get the range of the full data set.By how many classes there are, divide it.Round up this number (usually, to the nearest whole number).What is class width?When all the classes inside a distribution have the same width, the distance between the maximum and minimum bounds of the distribution is referred to as the class width. The distance between the bottom bounds of two successive classes is another name for the class breadth. Class width in a frequency distribution is the distance between the upper and lower limits of any class or category. Example: The first class's class breadth is 5-1, or 4. For the second class, the class size is 10-6, or 4, and so on. The size of a class interval, also known as the class width, class size, or class length, is the distance between the lower and upper class boundaries.To learn more about width, refer to:
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What is 15 1/2 - 1 11/20 and how would you solve this please do step by step!
Step-by-step explanation:
the simplest way for me is
1. to convert both terms into full fractions (not mixed numbers).
2. then to bring both fractions to the same denominator.
3. and then do the actual calculation.
and if needed, we can
4. then convert the result back into mixed numbers.
1.
15 1/2 = (15×2 + 1)/2 = 31/2
1 11/20 = (1×20 + 11)/20 = 31/20
2.
we need to convert 31/2 into a fraction .../20, so that we can actually combine it with the 31/20.
how do we get from 2 to 20 ? by multiplying by 10.
in order to keep the value of the fraction unchanged, we need to do the same multiplication also to the numerator :
31/2 × 10/10 = 310/20
3.
310/20 + 31/20 = 341/20
4.
341/20 = (17×20 + 1)/20 = 17 1/20
to get this you do an integer division and note the remainder.
341/20 = 17 remainder 1
A rectangular paperboard measuring 22 in long and 18 in wide has a semicircle cut out of it to find the area of the paperboard that remains.
The area of the paperboard that remains is 268.83 square inches.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, a rectangular paperboard measuring 22 in long and 18 in wide has a semicircle cut out.
Area of rectangular paperboard length×width
= 22×18
= 396 square inches
Area of a semicircle = 1/2 ×πr²
Here, r=18/2 = 9 inches
= 1/2 ×3.14×9²
= 127.17 square inches
So, remaining area = 396-127.17
= 268.83 square inches
Therefore, the area of the paperboard that remains is 268.83 square inches.
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the capacity of an elevator is either children or adults. if children are currently in the elevator, how many adults can still get in?
The capacity of the elevator is 15 children or 11 adults. If 9 children are currently on the elevator, then there are 15 - 9 = 6 spots available for either children or adults.
However, since the maximum number of adults the elevator can hold is 11, the answer to the question is 11 - 9 = 2 adults can still get in.
You can act for the unknown amounts by the use of variables. Follow ignoring the description is and convert it one by one mathematically. For example, if it is asked to increase some item by 5, then you can add 5 in that item to increase it by 5.
If a thing is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
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A basketball coach determines the team has a 1 32 probability of winning a tournament. Which choice describes the probability of the coach’s basketball team winning the tournament most accurately?
The probability of the coach’s basketball team winning the tournament most accurately impossible.
What is probability ?3.03 percent Chance of A
As a result, you could say there is a 3.03% Probability instead of saying there are 1 to 32 Odds.
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
A basketball coach determines the team has a 1 32 probability of winning a tournament.
The probability of the coach’s basketball team winning the tournament most accurately impossible.
The complete question is
A basketball coach determines the team has a 1/32 probability of winning a tournament. Which choice describes the probability of the coach's basketball team winning the tournament most accurately?
answer choices
certain
impossible
likely
unlikely
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-15/4(2x-2/3)<64+11/4x help
Answer:
[-23.27 < x]
Step-by-step explanation:
Distribute -15/4 to the numbers in the parenthesis:
[tex]\frac{-15}{4}*2x[/tex] = [tex]-\frac{30}{4}[/tex]
[tex]\frac{-15}{4}*-\frac{2}{3}[/tex] = [tex]\frac{5}{2}[/tex]
[tex]-\frac{30}{4} + \frac{5}{2} < 64 + \frac{11}{4}x[/tex]
Combine like terms:
[tex]-5 < 64 + \frac{11}{4}x[/tex]
Subtract 64 from both sides:
[tex]-64 < \frac{11}{4}x[/tex]
Multiply both sides by 4:
[tex]-256 < 11x[/tex]
Divide both sides by 11:
[tex][-23.27 < x][/tex]
find equivalent fractions to compare. Then write >< or =
please tell the multiples too.
The equivalent fractions are
1.) 5/6 > 4/6
5.) 7/8 > 4/8
9.) 8/10 < 15/10
13.) 6/8 < 7/8
what is a fraction?
A fraction is a mathematical expression that represents a part of a whole or a division of one quantity into equal parts. It consists of two parts, a numerator and a denominator. The numerator represents the number of equal parts of the whole and the denominator represents the total number of parts the whole is divided into.
1.) 5/6 ___ 2/3
To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 6 and 3 is 6. So, to make the denominator of 2/3 equal to 6, multiply both the numerator and denominator by 2:
2/3 * 2/2 = 4/6
Now, both 5/6 and 4/6 have a common denominator of 6. So, we can easily compare:
5/6 __ 4/6
5/6 is greater than 4/6, so the answer is 5/6 > 4/6
5.) 7/8 ___ 1/2
To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 8 and 2 is 8. So, to make the denominator of 1/2 equal to 8, multiply both the numerator and denominator by 4:
1/2 * 4/4 = 4/8
Now, both 7/8 and 4/8 have a common denominator of 8. So, we can easily compare:
7/8 __ 4/8
7/8 is greater than 4/8, so the answer is 7/8 > 4/8
9.) 8/10 ___ 3/4
To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 10 and 4 is 10. So, to make the denominator of 3/4 equal to 10, multiply both the numerator and denominator by 5/5:
3/4 * 5/5 = 15/10
Now, both 8/10 and 15/10 have a common denominator of 10. So, we can easily compare:
8/10 __ 15/10
8/10 is less than 15/10, so the answer is 8/10 < 15/10
13.) 3/4 ___ 7/8
To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 4 and 8 is 8. So, to make the denominator of 3/4 equal to 8, multiply both the numerator and denominator by 2:
3/4 * 2/2 = 6/8
Now, both 6/8 and 7/8 have a common denominator of 8. So, we can easily compare:
6/8 __ 7/8
6/8 is less than 7/8, so the answer is 6/8 < 7/8
Hence, the equivalent fractions are
1.) 5/6 > 4/6
5.) 7/8 > 4/8
9.) 8/10 < 15/10
13.) 6/8 < 7/8
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parametrize the portion of the parabola, x=2y^2-4 where -1
The portion of the parabola from t=-1 to t=1 can be parametrized as x=2t²-4 and y=t.
A parabola is a symmetrical and U-shaped curve that is defined by a mathematical equation.
In this case, we will use the variable t to represent the y-coordinate and find the corresponding x-coordinate. The equation becomes y=t, and substituting this into the original equation, we get
=> x=2t²-4.
To find the portion of the parabola where -1≤t≤1, we can plot the points (x, y) for various values of t in this range.
when t=-1,
=> x=2(-1)²-4 = 0.
And when
t=1, x=2(1)²-4 = -2.
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A number is a restriction on a rational expression if the number makes the denominator of the rational expressionTrueFalse
Answer: The values that make the denominator equal to zero for a rational expression are known as restricted values. How do you identify restrictions in rational expressions? The restriction is that the denominator can not be equal to zero. So in this problem, since 4x is in the denominator it can not equal zero.
trigonometric ratios in right triangles calculator
A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.
Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:
1. Enter the lengths of the sides of the right triangle into the calculator.
2. Select the angle for which you want to find the trigonometric ratios.
3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.
Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.
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A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.
Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:
1. Enter the lengths of the sides of the right triangle into the calculator.
2. Select the angle for which you want to find the trigonometric ratios.
3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.
Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.
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GEOMETRY Triangle KLM is shown. Graph the image of the triangle after a dilation centered at the origin with a scale factor of 2
When ΔKLM is dilated with a scale factor of 2 the new ΔK'L'M' has vertices K'(4,10), L'(8,4) and M'(4,4).
What is dilation?
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.
The ΔKLM has the coordinates of vertices - K(2,5), L(4,2) and M(2,2)
If the scale factor is 2, then every coordinate point of the original triangle is multiplied by the scale factor 2.
When the triangle is dilated with the scale factor of 2, the coordinate points formula becomes -
(x,y) → (2x,2y)
So, obtain the new triangle ΔK'L'M' -
K(2,5) → [2(2),2(5)] → K'(4,10)
L(4,2) → [2(4),2(2)] → L'(8,4)
M(2,2) → [2(2),2(2)] → M'(4,4)
The graph for the new coordinates have been ploted.
Therefore, the new coordinates are K'(4,10), L'(8,4) and M'(4,4).
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in chemistry class, a student has earned scores of 64, 69, and 73 on three tests. they must maintain an average of 70 to pass the course. what score must the student earn on the final exam to pass the course?
The student must earn a 74 on the final exam to pass the course with an average of 70.
The student's current average score is (64 + 69 + 73) / 3 = 66.
To find the score the student needs to earn on the final exam to maintain an average of 70, we can set up an equation:
(64 + 69 + 73 + x) / 4 = 70
Where x is the score the student needs to earn on the final exam.
Solving for x:
(64 + 69 + 73 + x) = 280
x = 280 - 64 - 69 - 73 = 74
So, the student must earn a 74 on the final exam to pass the course with an average of 70.
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Together Pam, Dan, and Sam have $31.00. How many dollars does Sam have if Dan has $3.00 less than Pam, and Sam has $1.00 more than Pam and Dan combined?
Answer:
Let x be the amount Pam has, then Dan has x - $3.00 and Sam has x + x - $3.00 + $1.00 = 2x + $1.00
The total amount of money they have is x + x - $3.00 + 2x + $1.00 = 31.00
So, 4x + $1.00 = 31.00
Subtracting $1.00 from both sides gives 4x = 30.00
Finally, dividing both sides by 4 gives x = $7.50
So Pam has $7.50, Dan has $7.50 - $3.00 = $4.50, and Sam has $7.50 + $4.50 + $1.00 = $13.00.
Solve each equation, and write the algebraic reason for each step.
1. 3y+5=2y-8
2. -2(x-1)=3x-13
3. 3b+4+b=16
The equations are solved to give
1. y = 13
2. x = 3
3. b = 3
How to determine the solution to the expressionsIt is important to note that algebraic expressions are expressions composed of variables, terms, factors, constants and coefficients.
From the information given, we have that the expressions are;
3y+5=2y-8
Now, collect like terms
3y - 2y = -8 - 5
subtract the like terms
y = 13
-2(x-1)=3x-13
expand the bracket
-2x + 2= 3x - 13
collect like terms
-2x -3x = -13 - 2
subtract the like terms
-5x = -15
x = 3
3b+4+b=16
collect like terms
4b = 12
b = 3
Hence, the values are 13. 3 and 3
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Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
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The function f(x) = x + 6 represents the length of a rectangle, and the function g(x) = 9x − 4 represents the width of the rectangle. What is the area of the rectangle if x = 2?
168
112
22
−144
Answer:
A = 112
Step-by-step explanation:
Area of rectangle = LW
x = 2
L = x + 6 = 2 + 6 = 8
W = 9x − 4 = 9(2) − 4 = 18 - 4 = 14
A = LW = 8(14) = 112
Answer: A = 112
Your welcome for the help
What is the best answer to report for (515 x 0.0025) + ?24.57 25.86 26 25.8575 25.9
The best way to report for (515 x 0.0025) is 25.86 and it is done using the concept of significant figures.
Given (515 x 0.0025) + 24.57
We are asked to report the answer in the best way. This can be done using the concept of significant figures.
We can see that 515 has 3 significant figures
0.0025 has 4 significant figures ( we have to consider the zeros after the decimal)
24.57 has 4 significant figures
Thus the best answer will have 4 significant figures.
(515 * 0.0025 ) + 24.57 = 25.8575 = 25.86
We have to round off the answer to 4 significant figures, thus it'll be 25.86 ( 5 becomes 6 because the figure next to 5 is 7, thus 5 will be rounded off to 6 )
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nth taylor polynomial about 0 e^x
The function to derive an nth Taylor polynomial is y = nthTaylorPolyExp( n, x )
%y = nthTaylorPolyExp( n, x )is a function that returns 3rd Taylor polynomial of exponential function at x=0.
% n is an input argument, which indicates the degree of Taylor
% polynomial.
% x is an input argument
% y is the output.
y=zeros('like',x);
% ============= YOUR CODE HERE ==============
% Instructions: Return nth Taylor polynomial of exponential function at x=0.
% You can use built-in function factorial(n) to return n!,
% and use for loop to get the sum.
for i = 0:n
% y = y + (-1)^i * (x.^(2 * i)) / factorial(2 * i); is my version, but its incorrect.
end
Thus, the function to derive an nth Taylor polynomial is y = nthTaylorPolyExp( n, x )
Complete question: How do I write the function to derive an nth taylor polynomial?
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Geometry worksheet. Can someone help please?
For the given geometry the perimeter is 37 units, area is 118.55 square units and the type is pentagon.
What is area of a pentagon?The space enclosed by a pentagon's sides is referred to as the pentagon's area. Various techniques can be used to compute it depending on the dimensions that are known. The kind of pentagon also makes a difference. For instance, if it is a normal pentagon, the area can be determined using a single formula; but, if it is an irregular pentagon, we must divide it into various polygons and add their areas to determine the pentagon's area.
The perimeter is the sum of length of all the sides of a pentagon.
P = 5s
P = 5(7.4) = 37 units.
The area of the pentagon is given as:
A = 1/2 (P)(a)
Substitute the value of P = 37 and a = 6.4086:
A = 1/2 (37)(6.4086) = 118.55 square units.
Type: Pentagon.
Hence, for the given geometry the perimeter is 37 units, area is 118.55 square units and the type is pentagon.
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let matrices a, b be where i^2=-1. find the order of the group generated by a and b under matrix multiplication
The order of the group generated by matrices a and b under matrix multiplication is a process of multiplying the matrices and counting the number of distinct matrices that can be produced.
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
The order of a group generated by matrices a and b refers to the number of distinct matrices that can be produced by multiplying a and b a certain number of times.
To find the order of the group, we need to start by multiplying a and b and see if we get any new matrices. If we do, we keep multiplying those matrices until we get back to the original matrices a and b.
The order of the group is the number of distinct matrices we get in this process.
It is important to note that matrix multiplication is associative, which means that the order in which we multiply the matrices does not affect the result. Also, the identity matrix is a special matrix that, when multiplied by any matrix, produces the same matrix.
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Find the total surface area of this prism where the cross-section is an isosceles triangle.
Perpendicular Height: 5cm
Base Length: 24cm
Base Side Length: 10cm
Answer:
Step-by-step explanation:
620 cm^2
Step-by-step explanation:
Area of isosceles triangles:
A = (b×h) ÷ 2
Substitute
(24 × 5) ÷ 2
120 ÷ 2 = 60 cm^2
There are 2 triangles so:
60 × 2 = 120 cm^2
Area of 2 identical rectangles:
- They are identical and this is shown by the two short lines which indicate that this is an isosceles triangle. They have 2 identical sides.
A = L × W
Substitute
10 × 13 = 130
Because there are two:
130 × 2 = 260 cm^2
Area of the rectangle at the bottom:
- Let's not forget the rectangle at the bottom of this shape.
A = L × W
Substitute
24 × 10 = 240 cm^2
Add these all together to get the total surface area:
120 + 260 + 240 = 620 cm^2
Answer: 620 cm^2
Answer:
620cm squared
Step-by-step explanation:
a=bxh/2
so this means
24x5/2=area of one triangle(60cm squared)
since there are two .that means the area for both triangles is 120cm squared
for the recatngles:
a=lxw
Substitute
10 × 13 = 130
since there are 2 of them,
130 × 2 = 260 cm^2
the rectangle on the bottom:
a=lxw
24x10=240cm squared
240+260+120=620
how can you plot a one dimensional vector field on the real line for a differential equation in python
Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.
Can Python solve differential equations?Using the Scipy.integrate package and the functions odeint or solve ivp, one can use Python to solve differential equations. t: Time points at which the solution should be reported To maintain the precision of the answer, additional internal points are frequently calculated but are not reported.Differential equations can be solved using the Python library diffeqpy. Its basic routines use DifferentialEquations. jl to provide high performance solving of a variety of differential equation types, such as: Function mapping and discrete stochastic (Gillespie/Markov) simulations are examples of discrete equations.ODE gives us a technique to represent the dynamic changes in specified variables numerically. Imagine taking a picture of the outdoors; this image lacks any motion, making it a static system. A static system is the reverse of that.Here i attached answer.
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use implicit differentiation to find an equation of the tangent line to the graph of the equation at the given point.1 ln 7xy = e7x − y, (1/7, 1)
The equation of the tangent line to the graph of the equation at the given point (1/7, 1) is [tex]y = 7x - 6/7 + 1.[/tex]
[tex]y' = (7e7x + 7x - 1)/7xy[/tex]
1. Use implicit differentiation to differentiate both sides of the equation with respect to x:
[tex]ln 7xy = e7x − y ln 7xy + (7xy) (y') = (7e7x) + (e7x)(7)[/tex]
2. Solve for y':
[tex]y' = (7e7x + 7x - 1)/7xy[/tex]
3. Plug in the given point to find the slope at that point:
[tex]y' = (7e(1/7) + (1/7) - 1)/(7*(1/7)*1) = (7 + 1 - 1)/1 = 7[/tex]
4. Use the point-slope form of a line to find the equation of the tangent line:
[tex]y - 1 = 7(x - 1/7)y = 7x - 6/7 + 1[/tex]
The equation of the tangent line to the graph of the equation at the given point (1/7, 1) is[tex]y = 7x - 6/7 + 1.[/tex]
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Is this the answer anyone???
The number of hot dogs will Team A need to sell to reach its goal is 690.
What is the linear equation in one variable?
A linear equation in one variable is an equation that can be written in the form: y = mx + b,where "x" is the independent variable, "y" is the dependent variable, "m" is the slope of the line, and "b" is the y-intercept.
Let the number of dogs be x.
1.48x - 20 = 1000
1.48x = 1020
x = 1020/1.48
x = 690
Hence, the number of hot dogs will Team A need to sell to reach its goal is 690.
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discuss how discrete mathematics led to fewer cultural distinctions and where mathematics became more a unifying language of its own.
Discrete mathematics is a branch of mathematics that deals with objects that can assume only distinct, separated values and can be counted. It has played a significant role in reducing cultural distinctions by providing a unifying language for the field of mathematics and a common understanding for solving problems across cultures.
Through discrete mathematics, people from different backgrounds and cultures can communicate and collaborate more effectively, breaking down cultural barriers and promoting unity.
For example, discrete mathematics has been used to create algorithms that solve complex problems in computer science, cryptography, and optimization, making it possible for people from different cultures to work together to solve these problems.
Additionally, the standardization of mathematical language and symbols through discrete mathematics has made it easier for people to understand and share mathematical ideas across cultures, further promoting unity and reducing cultural distinctions.
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Consider the system modeled by the following difference equation. y(n) = 3y(n-1) + x(n − 2)
Assume the underlying system is casual with zero initial conditions. What is the transfer function?
Assuming the underlying system is casual with zero initial conditions, the transfer function is Y(z)/X(n) = 1/([tex]z^2[/tex] - 3z).
The differential equation is y(n) = 3y(n-1) + x(n − 2).
Since there are no initial conditions, the underlying system is known to be casual.
Considering the Transfer function.
Z transform properties are used
y(n-1) = [tex]z^{-1}[/tex]Y(z)
y(n) = Y(z)
x(n-2) = [tex]z^{-2}[/tex]X(n)
Now putting the value in the equation
Y(z) = 3[tex]z^{-1}[/tex]Y(z) + [tex]z^{-2}[/tex]X(n)
Multiply by [tex]z^2[/tex] on both side, we get
[tex]z^2[/tex]Y(z) = 3zY(z) + X(n)
Subtract Y(z) 0n both side, we get
[tex]z^2[/tex]Y(z) - 3zY(z) = X(n)
Y(z)([tex]z^2[/tex] - 3z) = X(n)
Divide by ([tex]z^2[/tex] - 3z) on both side, we get
Y(z) = X(n)/([tex]z^2[/tex] - 3z)
Divide by X(n) on both side, we get
Y(z)/X(n) = 1/([tex]z^2[/tex] - 3z)
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the statistic x¯ is used as an estimator for which of the following?
As a point estimator for, we utilise x-bar (sample mean) (mu, population mean)
What is mean or average?The average value in mathematics is the middle number, which is calculated by dividing the total number of numbers by the sum of all the numbers. A set of data's average is calculated by adding up all the values and dividing the result by the total number of values.
We use the x-bar (sample mean) as a point estimator for (mu, population mean). As long as the sample is random, this estimator's impartial long-run distribution is centred at (mu).
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