Please help me with this question.

Please Help Me With This Question.

Answers

Answer 1

The trigonometric function, the identity is verified.

is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here the given identity is,

=> [tex](cos \theta-5sin\theta)^2+(5cos\theta+sin\theta)^2=26[/tex]

Now using formula [tex](a-b)^2=a^2-2ab+b^2[/tex] and [tex](a+b)^2=a^2+2ab+b^2[/tex] then L.H.S

=> [tex]cos^2\theta-10cos\theta sin\theta+25sin^2\theta + 25cos^2\theta+10cos\theta sin\theta+sin^2\theta[/tex]

=> [tex]25sin^2\theta+25cos^2\theta+sin^2\theta+cos^2\theta[/tex]

=> [tex]25(sin^2\theta+cos^2\theta)+(sin^2\theta+cos^2\theta)[/tex]

We know that [tex]sin^2\theta+cos^2\theta=1[/tex] then,

=> 25(1)+1

=> 25+1

=> 26 = 26

L.H.S = R.H.S

Hence the given identity is verified.

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Related Questions

Simplify to a single power of 4:
[tex]\frac{4^7}{4^5}[/tex]

Answers

4^2


You would divide the coefficients but subtract the exponents.

What is the area and the perimeter of the shape in the screenshot?

Answers

5+2+3+7+2=19:19 is the perimeter

How can you help me with that please

Answers

The grouping of all numbers with the formula a+bi is referred to as the complex number set. If b0, the number is also referred to as an imaginary number. The quantity is referred to be a real number if b=0.

Explain about the Complex numbers and real number?

A real number and an imaginary number added together is referred to by this phrase. It is symbolized by the letter z and has the formula a + bi.

Any number that is composed of both rational and irrational numbers is considered to be real. R is used to write these numbers, which may be native or positive.

Complex numbers are those that are expressed as a+ib, where a, b are actual numbers, and I is a fictitious number termed a "iota." I = (-1) is the value. A complex number, such as 2+3i, is one where the real number 2 (Re) and the imaginary number 3 I are both present (Im).

The number that is represented by the square root of a particular negative number is referred to by this phrase.

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 For the equation: 2(x-5) = 9 - 3x +6 + 8 + 3x+ 7, the right side of the equation can be simplified by combining like terms.
Simplify 9-3x+6+8 + 3x+7:
2(x - 5) can be simplified using the Distributive Property.
Simplify 2(x - 5):
Word Bank:
136x 30x 30 2x-5 6x#30 2x+10 2x-10
Blank 1:
Blank 2:

Answers

The right side of the equation 9 - 3x +6+8 + 3x+7 can be simplified by combining like terms as: 30.

2(x - 5) can be simplified using the Distributive Property as: 2x - 10.

What is the distributive property of multiplication?

In Mathematics, the distributive property of multiplication states that when the sum of two or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Next, we would combining like terms in the right side of the equation as follows;

9 - 3x +6+8 + 3x+7 = (9 + 8 + 6 + 7) + (3x - 3x)

9 - 3x +6+8 + 3x+7 = 30.

By applying the distributive property of multiplication to left side of the equation, we have:

2(x - 5) = 2x - 10.

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Use the table to add 48 +689 vertically. The top row will be for regrouping (numbers that are "carried"). The bottom row will be for
your answer. The addends have already been filled in for you.
Hundreds
Tens
Regrouping
First Addend
Second Addend 6
Sum
4
8
Ones
8
9

Answers

The regrouping column is used to carry numbers from the ones column to the tens column. In this case, there is a 1 that must be carried from the ones column to the tens column. The sum of 48 + 689 is 737.

What is the column ?

A column is a vertical structure that acts as a support for a building or is used as a decorative object. It is commonly used in architecture and comes in many different styles, shapes, and sizes. Columns can be made from a variety of materials such as stone, marble, iron, and brass. They are often adorned with intricate carvings and detailed designs. Some ancient structures like the Parthenon in Athens, Greece, are famous for their impressive use of columns.

Hundreds

Tens

Regrouping

First Addend

Second Addend 6

Sum

4

8

Ones

7

7

The regrouping column is used to carry numbers from the ones column to the tens column. In this case, there is a 1 that must be carried from the ones column to the tens column. The sum of 48 + 689 is 737.

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ABC has vertices A (0, -1), B (3,4), and C (3,1).
Reflect it across x-axis
Need as soon as possible...

Answers

ABC has vertices A (0, -1), B (3,4), and C (3,1). The coordinates of the image after reflection over the x axis is

A' (0, 1)B' (3, -4)C' (3, -1)

How to find the coordinate's after reflection

Reflection is a method of transformation that creates mirror image.

The transformation rule for reflection over the x axis is as below

(x, y) → (x, -y)

Applying the rule we have

A (0, -1), B (3, 4), and C (3, 1) will result to

A' (0, 1), B' (3, -4), and C' (3, -1)

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translate the sentence into equation
Twice the difference of a number and 8 is 7.

Answers

Answer:

x = 11.5  This is the answer to the equation.

Step-by-step explanation:

2 · (x - 8) = 7  This is the equation as it is written.

x - 8 = 7/2

Write down the percentage multiplier to find 26% of an amount
pls do simple steps/working out :)

Answers

The percentage multiplier to find 26% of an amount is, 0.26.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We know that;

Percentage multiplier calculates the percentage of an amount. It is also used to increase or decrease an amount by a percentage.

Now, In order to find the percentage multiplier of 26% of an amount we can multiply the number by a multiplier.

⇒ 26%

⇒ 26/100

⇒ 0.26

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please help me will give u extra points :)

Answers

Therefore , the solution of the given problem of compound sentence's comes out to be { x|–2< x < 5}

What is Compound Inequalities?

Indicated by the conjunction "or," the compound sentence is true as long as either of the two statements is true. In other words, it is the union or combination of the solution sets for each unique assertion. The term "conjunction" refers to a compound inequality that contains the word "and". The words "and" and "or," which are considered to be variables of speech, have a different meaning in mathematics than they do in grammar.

Here,

Given :

=> On the number line

=> -5 to -2

and 5 to infinity .

So,

Both x| x > -2 and x < 5

The following is another method to state this solution set:

{ x|–2< x < 5}

It is assumed that the word "and" will always be used in compound inequality expressions when neither "and" nor "or" is explicitly used. You say, "x is more than  -2 and (reading to the right) x is less than 4," reading from the "x" position as "x|-2" "x," "x," and "x," respectively. This is the solution set's graph.

The Complete Question.

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Exercise 2: A researcher collected data from college students on the number of hours they slept
the night before a major exam. He collected the following set of data:
2 6 4 4 3 6 7 5 4 8
4 5 8 3 5 5 7 6 1 4
a) What is the sample size? (n = ?)
b) Organize the data in the frequency distribution table below. Start with the highest X
value. Then, compute proportions, relative frequencies, and percentages

Answers

For the given frequency distribution table the answer of the following questions are:

a. sample size is equal to n = 20.

b. Proportion , relative frequency , and the percentage are :

 f           Proportion                Relative frequency              Percentages

1                 0.05                        0.05                                     5

2               0.1                            0.1                                        10

3                0.15                           0.15                                    15

4                 0.2                            0.2                                    20

5                 0.25                         0.25                                   25

a. Sample size of the number of hours students slept before exam is :

n = 2+ 2 + 3+ 4+ 5 + 2+ 1+ 1

   = 20

b. Organization of the data in the form of frequency distribution table form is:

X       f           Proportion                Relative frequency              Percentages

8        2           2/20 = 0.1                   2/ 20 = 0.1                      0.1 × 100 = 10

7        2            2/20 = 0.1                   2/ 20 = 0.1                     0.1 × 100 = 10

6        3           3/20 = 0.15                   3/ 20 = 0.15                 0.15 × 100 =15

5        4           4/20 = 0.2                  4/ 20 = 0.2                     0.2 × 100 = 20

4        5          5/20 = 0.25                  5/ 20 = 0.25               0.25 × 100 = 25

3        2         2/20 = 0.1                   2/ 20 = 0.1                      0.1 × 100 = 10

2        1          1/20 = 0.05                   1/ 20 = 0.05                0.05 × 100 =5

1        1         1/20 = 0.05                   1/ 20 = 0.05                0.05 × 100 =5        

         20

Therefore, the sample size of the frequency distribution is 20 and the proportion , relative frequency ,and percentage are shown in the above table.

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Consider the following.
f(x) = x − 4
f(x) = x2 + 5x − 36
Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.)
Identify any discontinuities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
x =
If the function has any discontinuities, identify the conditions of continuity that are not satisfied. (Select all that apply. Select each choice if it is met for any of the discontinuities.)
There is a discontinuity at x = c where f(c) is not defined.
There is a discontinuity at x = c where lim x→c f(x) ≠ f(c).
There is a discontinuity at x = c where lim x→c f(x) does not exist.
There are no discontinuities; f(x) is continuous.

Answers

1. The function is continuous everywhere because it is defined for all values of x, and there are no points where f(x) is undefined or where the limit as x approaches a specific value does not exist.

2. Interval of continuity: (-∞, ∞)

Discontinuities: None

Conditions of continuity not satisfied: None

Hence, option (d) is correct.

If and only if a function is continuous on every point in the open interval (a,b), it is continuous over that interval (a,b).

If and only if it is continuous on (a,b), then is continuous over the closed interval [a,b].

The right-sided limit of at x=a is (a), while the left-sided limit of at x=b is (b).

If a function is continuous across the whole open interval, it is said to be continuous over the interval. If it is continuous at each point in its interior and at both of its ends, it is continuous over a closed interval.

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Find an equation of a horizontal line containing the point (−1,4)

Answers

Answer:

  y = 4

Step-by-step explanation:

You want the equation of the horizontal line containing the point (-1, 4).

Horizontal line

On a horizontal line, the y-coordinates of every point are the same. The equation can be written ...

  y = constant

Application

In order for the horizontal line to go through a point with y-coordinate 4, the constant must be 4. The equation is ...

  y = 4

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12 is 2% of_________

Answers

twelve is two percent of six hundred

A circle has a radius of 22 centimeters. Arc has a length of centimeters. What is the radian measure of the corresponding central angle?

Answers

Answer:

The radian measure of a central angle of a circle can be found using the formula:

Radian measure = Arc length / Radius

In this case, the radius is 22 centimeters, and the arc length is x. So,

Radian measure = x / 22

Step-by-step explanation:

Answer:

Step-by-step explanation:

d

17. ______________________ the set of all the possible outcomes in a probability experiment.

Answers

A sample space the set of all the possible outcomes in a probability experiment.

How to complete the statement

The sample space in probability theory is the set of all possible outcomes of a random experiment.

It is the set of all possible results of an action, experiment, or random process. In other words, it is the set of all possible values that a random variable can take.

For example, in a coin flip experiment, the sample space could be defined as the set {heads, tails}.

In a dice roll experiment, the sample space could be defined as the set {1, 2, 3, 4, 5, 6}.

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Mr. Phan fills a portion of his pool with water on Monday. Then on Tuesday, he fills the pool with water coming from a hose at a constant rate. The table shows the number of feet of water in the pool as a function of time on Tuesday. Write an equation in slope- intercept form (y=mx+b) that represents this function.

Time on Tues. after 9 AM (hr) 0 1 2 Amount of Water in Pool (ft) 1.1 1.7 2.3​

Answers

The equation in slope - intercept form would be y = 0.6x + 1.1.

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Mr. Phan fills a portion of his pool with water on Monday. Then on Tuesday, he fills the pool with water coming from a hose at a constant rate. The table shows the number of feet of water in the pool as a function of time on Tuesday -

Time on Tuesday after 9 AM (hr) →   0    1      2

Amount of Water in Pool (ft) →          1.1   1.7   2.3​

Let the equation be -

y = mx + c

We can write the slope as -

{m} = (1.7 - 1.1)/(1 - 0)

{m} = 0.6

and

{c} = 1.1        

So, the equation in slope - intercept form would be -

y = 0.6x + 1.1

Therefore, the equation in slope - intercept form would be y = 0.6x + 1.1.

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the following are the weights (in pounds) of seven people: 100, 115, 135, 140, 180, 197, 230. find the 36th percentile? A.175 B.227 C.140 D.197

Answers

In the weights of seven people, the 36th percentile is 135.

The following are the weights (in pounds) of seven people:

100, 115, 135, 140, 180, 197, 230

We have to determine the 36th percentile.

The term "percentile" describes how a score contrasts with other scores from the same collection. The percentage of values in a set of data scores that fall below a specific value is a typical way to represent percentile, despite the fact that there is no single meaning for this term.

The formula is:

= Percentile/100 × Total number of weights

There have total weights of 7 people and percentile is 36.

Now putting the value

= 36/100 × 7

= 2.52

= 3(approx)

To find the percentile value we count from left to right.

The 3rd number from left to right is 135.

So the 36th percentile is 135.

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What is a major goal of the federal government when managing land resources?

A) conversation


B) land sales


C) residential development


D) privatization ​

Answers

A) Conservation is the answer
A.conservation isthe answer

what is the probability that vowels occupy even places in 'jvuyojzrxccome'

Answers

Answer: The probability that vowels occupy even places in the word "jvuyojzrxccome" is 3/7.

Step-by-step explanation:

1) To find the probability that vowels occupy even places in the word "jvuyojzrxccome", we can use the following steps:

2) Break down the word into individual characters: "jvuyojzrxccome"

3) Identify the vowels in the word: "u, o, o, e"

4) Count the number of vowels in the word: 4

5) Count the number of even-positioned characters in the word: (1st, 3rd, 5th, 7th, 9th, 11th, 13th) 7

6) Identify the vowels in the even positions: "u, o, e"

7) Count the number of vowels in the even positions: 3

Use the formula for probability: P(vowels in even positions) = (number of favorable outcomes) / (number of total outcomes)

8) P(vowels in even positions) = 3/7

Therefore, the probability that vowels occupy even places in the word "jvuyojzrxccome" is 3/7.

–10x + 4y + 14 = 0 in slope intercept form

Answers

Slope intercept form is written as follows:

[tex]y=mx+b[/tex]

With this information, isolate y on the left side of the provided equation:

[tex]4y=10x-14[/tex]

Now, divide both sides of the equation by 4:

[tex]y=\frac{10}{4} x-\frac{7}{2}[/tex]

This equation cannot be simplified anymore, and is therefore the answer!

[tex]y=\frac{10}{4} x-\frac{7}{2}[/tex]

Answer:

y = (5/2)x - (7/2)

Step-by-step explanation:

–10x + 4y + 14 = 0

                 -14     -14

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

-10x + 4y = -14

+10x                 + 10x

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

4y = 10x - 14

÷4    ÷4     ÷4

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

y = (10/4)x - (14/4)

simplified

y = (5/2)x - (7/2)

I hope this helps!

A pasty chef needs 90 milliliters of batter to produce one cupcake. How many cupcakes can be produced from a recipe that yields 18 liters of batter?

Answers

Answer:

Step-by-step explanation:

i don't know convert

The total worldwide box-office receipts for a long-running movie are approximated by the following function where T(x) is measured in millions of dollars and x is the number of years since the movie's release.
T(x) =
120x2
x2 + 4
How fast are the total receipts changing 1 yr, 5 yr, and 7 yr after its release? (Round your answers to two decimal places.)

Answers

The total receipts after the end of 1,5,7 years are 124 , 604, 844 million respectively.

What are functions?

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The function T(x)= 120x²+4

Thus after 1 year the receipts is T(1)=120×1+4

                                                          =124 million

After 5 years T(5)=120×5+4

                            =600+4

                            =604 million

Similarly for t=7 years T(7)=840+4

                                          =844 million

Hence, The total receipts after the end of 1,5,7 years are 124 , 604, 844 million respectively.

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the whole numbers are written consecutively in rows as shown. each row contains two more numbers than the previous row. 123{,}000 is the m th number in the n th row (counting from the left). enter the values of m and n in this order, separated by a comma.

Answers

The number of terms in the nth row is n + 1. The sum of the terms in the first n rows is equal to the sum of the first n + 1 triangular numbers, which is given by the formula n(n + 1)(n + 2)/6.

So to find m and n, we need to solve the following two equations simultaneously:

n(n + 1)(n + 2)/6 + m = 123000

n + 1 = 2m

Substituting the second equation into the first equation, we get:

m(2m + 1)(2m + 2)/6 = 123000

We can then solve for m using a numerical method, such as the bisection method or Newton-Raphson method. The solution is approximately m = 142.

So the values of m and n are 142 and 284, respectively.

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The following is the number of minutes to commute from home to work for a group of college students.
Determine the class interval.

11
24
21
5
16
6

33
34
27
47
41
9

18
22
17
22
2
37

21
41
5
36
16
28

16
42
29
34
21
16

Answers

The class intervals would be:

Class 1: 2-10

Class 2: 11-19

Class 3: 20-28

Class 4: 29-37

Class 5: 38-46

How did we get the values?

Class interval can be determined by dividing the range of the data by the desired number of intervals (also known as classes).

First, we need to find the range of the data:

Maximum value: 47

Minimum value: 2

Range: 47 - 2 = 45

For this example, let's choose 5 classes.

Class interval = Range / Number of classes = 45 / 5 = 9

The class intervals would be:

Class 1: 2-10

Class 2: 11-19

Class 3: 20-28

Class 4: 29-37

Class 5: 38-46

Note: The upper limit of each class is always rounded up.

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The Lorenz curve of income distribution of a small island nation is

f(x) = 0.3x^4 +0.3x³ +0.4x²

The Gini coefficient (index) of inequality for this nation is...

Answers

The Gini coefficient for this nation cannot be calculated from the given information

How to determine the Gini coefficient

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

f(x) = 0.3x^4 +0.3x³ +0.4x²

The Gini coefficient for this nation cannot be calculated from the given information.

This is so because the Lorenz curve which is a graphical representation of the income distribution of a population is required

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based on sample data, newborn males have weights with a mean of 3260.1 g and a standard deviation of 761.9 g. Newborn females have weights with a mean of 3080.7 g and a standard deviation of 523.1 g. who has the weight that is more extreme relative to the group from which they came: male who weights 1600 g or a female who weights 1600 g?

Answers

The z-score for the male is more than the z-score for the female.

What is the z-score?

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The z-score for males is given as,

z = (1600 - 3260.1) / 761.9

z = - 1660.1 / 761.9

z = - 2.179

The z-score for females is given as,

z = (1600 - 3080.7) / 523.1

z = - 1480.7 / 523.1

z = - 2.830

The z-score for the male is more than the z-score for the female.

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What is the slope of the equation y – 5 = –3x?

Answers

Answer:

-3

Step-by-step explanation:

Write the equation in slope -intercept form: y = mx + b

where m is the slope.

       y - 5 = -3x

            y = -3x + 5

Slope = -3

Answer:

Step-by-step explanation:

1. Write the equation.

[tex]y-5 =-3x[/tex]

2. Add "5" on both sides of the equation.

[tex]y-5+5 =-3x+5\\ \\y=-3x+5[/tex]

3. Identify the slope.

The slope of a linear equation will always be the coefficient of the "x" variable when the equation is equalled to "y". The coefficient is just the number that multiplies the variable. Hence, the coefficient of this line is "-3". Check the attached image.

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Please help me with this question.

Answers

The solution for the equation 2cos4x - 1 = 0 is x = 3π/35.

How to evaluate for the solution of the equation

For the values:

x = π/5 + 2kπ and also;

x = π/7 + kπ

then we can solve for k as follows:

π/5 + 2kπ = π/7 + kπ

collect like terms

2kπ - kπ = π/7 - π/5

kπ = (5π - 7π)/35 {simplifying the right hand side to a single fraction}

kπ = -2π/35

k = -2/35 {divide through by π}

put -2/35 for k in the equation x = π/7 + kπ to get the value of x;

x = π/7 - 2π/35 {simplifying the right hand side to a single fraction}

x = (5π - 2π)/35

x = 3π/35

Therefore, the solution for the equation 2cos4x - 1 = 0 is x = 3π/35.

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Suppose X1 ...... Xn is a random sample from the uniform distribution on [a; b].
(a) Find the method of moments estimators of a and b.
(b) Find the maximum likelihood estimators of a and b.

Answers

The method of moment estimators of a and b are [tex]\hat{a}=\bar{X}-\sqrt{3}S_x[/tex] and[tex]\hat{b}=\bar{X}+\sqrt{3}S_x[/tex] . And, the maximum likelihood estimators of a and b are  [tex]\hat{b}=x(n)[/tex] and [tex]\hat{a}=x(1)[/tex].

The random sample given is X₁, X₂, X₃,..........., Xₙ from the uniform distribution on [a, b]. The probability density function (pdf) of this is written as,

[tex]f(x)=\begin{cases} \frac{1}{b-a},&a < x < b\\0,&\text{otherwise} \end{cases}[/tex]

a) Now, let's calculate the expected value of X E(X). We get,

[tex]\begin{aligned}\mu _1=E(X)&=\int_a^b x\cdot\frac{1}{b-a}\;dx\\&=\frac{1}{b-a}\left[\frac{x^2}{2}\right]_a^b\\&=\frac{b+a}{2}\end{aligned}[/tex]

Let's calculate the second moment of X. We get,

[tex]\begin{aligned}\mu_2=E(X^2)&=\int^b_ax^2\cdot\frac{1}{b-a}\;dx\\&=\frac{1}{b-a}\left[\frac{x^3}{3}\right]_a^b\\&=\frac{b^3-a^3}{3(b-a)}\\&=\frac{b^2+a^2+ab}{3}\end{aligned}[/tex]

From the above values, variance is calculated as follows,

[tex]\begin{aligned}\mu_2-\mu_1^2=E(X)-E(X^2)&=\frac{b^2+a^2+ab}{3}-\frac{a^2+b^2+2ab}{4}\\&=\frac{4(b^2+a^2+ab)-3(a^2+b^2+2ab)}{12}\\&=\frac{b^2-2ab+a^2}{12}\\&=\frac{(b-a)^2}{12}\end{aligned}[/tex]

Now, using the method of moment, we denote [tex]E(X^2)=\mu_r[/tex] and [tex]M_n=\frac{1}{n}\sum_{i=1}^{n}X_i^2[/tex]. Then, [tex]\hat{\mu_r}=\frac{1}{n}\sum_{i=1}^{n}{X_i} ^r[/tex].

When [tex]\hat{a}[/tex] and [tex]\hat{b}[/tex] are the method of moment estimator of a and b, then, [tex]\hat{\mu_1}=\frac{\hat{a}+\hat{b}}{2}=\bar{X}[/tex] and [tex]\hat{\mu_2}=\frac{1}{n}\sum_{i=1}^{n}{X_i}^{2}[/tex].

Then,

[tex]\begin{aligned}\hat{\mu_2}-\hat{\mu_1^2}&=\left(\frac{1}{n}\sum_{i=1}^{n}({X_i}^{2}\right)-\bar{X}^2\\&=\frac{1}{n}\sum_{i=1}^{n}(X_i-\bar{X})^2\\&={S_x}^{2}\\\frac{(\hat{b}-\hat{a})^2}{12}&={S_x}^{2}\end{aligned}[/tex]

From [tex]\hat{b}+\hat{a}=2\bar{X}[/tex] and [tex]\hat{b}-\hat{a}=\sqrt{12{S_x}^{2}}=2\sqrt{3}S_x[/tex].

Then, the moment estimators of a and b are [tex]\hat{a}=\bar{X}-\sqrt{3}S_x[/tex] and[tex]\hat{b}=\bar{X}+\sqrt{3}S_x[/tex] .

b) Using the joint distribution of [tex]X=(X_1,........, X_n)[/tex] be

[tex]\begin{aligned}L(x_i\; a,b)&=\frac{1}{(b-a)^n}, a < x_i < b\\&=\frac{1}{(b-a)^n}, a < x(1) < x(n) < b\\&=\frac{1}{(b-a)^n}\cdot I\{x(n) < b\}\cdot I\{x(1) > a\}\end{aligned}[/tex]

where [tex]I_A=\begin{cases}1\;\text{if A is true}\\0\;\text{if not}\end{cases}[/tex]

The joint distribution of likelihood is maximum when b-a is minimum under the constraints b>x(n) and a<x(1). Then, [tex](b-a) > x(n)-x(1)[/tex]. So the minimum value is attained when [tex]b-a=x(n)-x(1)[/tex] that is [tex]\hat{b}=x(n)[/tex] and [tex]\hat{a}=x(1)[/tex]. Hence, the maximum likelihood estimate of a and b.

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Please help.
Complete the equation for the function that is represented by the graph.
f(x)=?
Does this represent exponential growth or exponential decay?

Answers

The function represents an exponential decay, as it is a decreasing function.

How to classify a function as exponential growth or exponential decay?

A function is classified as exponential growth if it is an increasing function, that is, the function is increasing over it's entire domain.

A function is classified as exponential decay if it is an decreasing function, that is, the function is decreasing over it's entire domain.

As the function in this problem is decreasing, it is an exponential decay function.

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