Complete the equation describing how
x and y are related.
X
0 1 2 3 4
y -1 3 7 7 11
11 15
y = [? ]x + [ ]
Enter the answer that belongs in [?].

Answer:

  e. f(x) --> -∞ as x --> -3^+ and as x --> -3^-

Step-by-step explanation:

You want to know the behavior of f(x)= (x^2 + x - 12)/(x^2 + 6x + 9) near any excluded x-values.

The function can be factored as ...

  [tex]f(x)=\dfrac{x^2+x-12}{x^2+6x+9}=\dfrac{(x+4)(x-3)}{(x+3)^2}[/tex]

The excluded values are values of x where the denominator is zero. The only excluded value is x = -3. (eliminates all answer choices except E)

At either side of x = -3, the sign of the numerator is negative and the sign of the denominator is positive. That makes f(3-) < 0 and f(3+) < 0.

f(x) will never approach +∞, but f(x) approaches -∞ as x nears -3 from either direction.

Answer:

[tex]\textsf{e)} \quad f(x) \rightarrow -\infty\;\;\textsf{as}\;\; x \rightarrow -3^+ \;\;\textsf{and as}\;\;x \rightarrow -3^-[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\dfrac{x^2+x-12}{x^2+6x+9}[/tex]

Factor the numerator:

[tex]\implies x^2+x-12[/tex]

[tex]\implies x^2+4x-3x-12[/tex]

[tex]\implies x(x+4)-3(x+4)[/tex]

[tex]\implies (x-3)(x+4)[/tex]

Factor the denominator:

[tex]\implies x^2+6x+9[/tex]

[tex]\implies x^2+3x+3x+9[/tex]

[tex]\implies x(x+3)+3(x+3)[/tex]

[tex]\implies (x+3)(x+3)[/tex]

[tex]\implies (x+3)^2[/tex]

Therefore, the rational function is:

[tex]f(x)=\dfrac{(x-3)(x+4)}{(x+3)^2}[/tex]

As the degree of the numerator is equal to the degree of the denominator, there is a horizontal asymptote at y = 1.

A vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.

[tex]\implies (x+3)^2=0[/tex]

[tex]\implies x+3=0[/tex]

[tex]\implies x=-3[/tex]

Therefore, there is a vertical asymptote at x = -3.

As there is a vertical asymptote at x = -3, the excluded x-value is x = -3.

As x approaches x = -3 from both sides, the numerator of the rational function approaches -6 and the denominator approaches a very small positive number.  Therefore, the function approaches a very large negative number.

Therefore, the end behaviour of the function as it approaches the excluded value is:

The Height of the ceiling at the center is  57.6628 feet

In geometry, an ellipse is a two-dimensional shape, that is defined along its axes. An ellipse is formed when a cone is intersected by a plane at an angle with respect to its base.

It has two focal points. The sum of the two distances to the focal point, for all the points in curve, is always constant.

The General form of ellipse is [tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

According to the question,

Length of whispering gallery is 130 feet

The foci are located 30feet from the center (0,0)

So, 2a = 130

=> a = 130/2

=> a = 65

and c = 30

As we know ,

=> c² = a² - b²

=> (30)² = (65)² - b²

=> 900 = 4225 - b²

=> b² = 4225 - 900

=> b² = 3325

=> b = 57.7 feet

Therefore , the height of the ceiling at the center is 57.6628 feet

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The restrictions on the variables x and y are given as follows:

x ∈ W, y ∈ W.

The first step in obtaining the restrictions of the variables x and y are identifying them, which is done as follows:

Then we known that we usually hear it in the news things such as this sentence:

"On the last Buffalo Bills game, 60,000 tickets were sold".

The amount of tickets sold varies, but the type of number doesn't, it is always a positive non-decimal number.

The number of ticket sold cannot assume neither negative nor decimal values, thus the variables x and y belong to the whole number set and the first option is correct.

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The restrictions for x and y are given as follows:

3. x ∈ W, y ∈ W.

5. x ∈ W, y ∈ W.

To obtain the restrictions, the first step is classifying the variables as either discrete or continuous, as follows:

In this problem, the variables are both resumed as follows:

Number of tickets sold in the Super Bowl.

The possible values are given as follows:

0, 1, 2, ...

Which are countable values, hence discrete, and that also cannot assume negative values, hence they belong to the whole set and not the integer set, thus the restrictions are:

x ∈ W, y ∈ W.

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By using the concept of midpoint of a line, it can be concluded that-

F is the midpoint of AA' because EG bisects AA'

First option is correct

What is midpoint of a line?

Midpoint of a line is the point which divides the line into two equal parts.

ΔA'B'C' is the reflection of  ΔABC

E is the midpoint of BB'

F is the midpoint of AA'

G is the midpoint of CC'

EG is the bisector of BB', AA', CC'

F is the midpoint of AA' because EG bisects AA'

First option is correct

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Complete Question

The figure has been attached

Answer: D

Step-by-step explanation: trust

The amount must Lance Industries pay into the fund each period is $2,054.49

Define Sinking Funds

A fund set aside to cover a certain future expense is known as a sinking fund. The sinking fund can be thought of as an annuity if equal contributions are made on a regular basis; its value will rise until it is sufficient to pay the future expense.

Given,

Lance Industries borrowed = $130,000

Time = 18 years

Interest rate = 6%

The future value is,

FVₙ =PMT( (1+i/m)ⁿ - 1 ) / (i/m) )

PMT = payment fund semiannually.

i = 6% or 0.06

m = 2  (semiannually will be 2 times per year)

n = 18 * 2 = 36 periods

FV₃₆ = $130,000

Now, plug in the values in formula

FVₙ =PMT( (1+i/m)ⁿ - 1 ) / (i/m) )

130,000 = PMT ( (1 + 0.06/2)³⁶ - 1 ) / (0.06/2) )

130,000 = PMT ( (1.03)³⁶ - 1 ) / (0.03) )

PMT = 130,000 * ( 0.03 / (1.03)³⁶ - 1 ) )

        = $2,054.49

Hence, the amount must Lance Industries pay into the fund each period is $2,054.49.

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Answer:

x=4.75

Step-by-step explanation:

4x+19=8x

-4x -4x

19 = 4x

Divide 4 on each side

4.75=x or x=4.75

The Maclaurin Series of xe²ˣ: x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....

Given that,

f(x) = xe^2x

Taylor series of function f(x) at a is defined as:

f(x) = f(a) + f'(a)/1!/(x-a) +f''(a)/2! (x-a)² +....

Maclaurin series of Function F(x) is a Taylor series of Function f(x) at: a=0

f(x) = f(0) + f'(0)/1! /(x) +f''(0)/2!/ (x)² +....

Apply the Maclaurin Formula

= 0 +d/dx (xe²ˣ)(0)/1! x + d²/dx² (xe²ˣ)(0)/2! x² +....

Evaluate the derivatives :

= 0 + 1/1! x + 4/2! x² + 12/3! x³ + ...

Refine :

= x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....

So, the Maclaurin series for f(x) = xe^2x is  x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....

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When you are doing a survey of the time it takes for a person to run 100m, the unit that you would you use is seconds.

A unit of measurement is a definite magnitude of a quantity that is defined and adopted by convention or law and is used as a standard for measuring the same type of quantity. Any other such quantity can be expressed as a multiple of the unit of measurement. A length, for example, is a physical quantity.

A unit is any standard that is used to compare measurements. Unit conversions allow measurements of a property to be converted from one unit to another, such as centimeters to inches.

In this case, time is measured in seconds.

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The sum of two (63 + 7x) and (4 + x) quantities will be 8x + 67.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Let 'x' be the number.

The first number is given as,

⇒ 7(9 + x)

⇒ 63 + 7x

The second number is given as,

⇒ 4 + x

Then the sum of two numbers is given as,

⇒ 63 + 7x + 4 + x

⇒ 8x + 67

The sum of two (63 + 7x) and (4 + x) quantities will be 8x + 67.

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Answer:

27°

Step-by-step explanation:

Let h = highest temperature

h = -15 + 42

h = 27°

The maximum revenue of the problem given at the end of the answer is of: $144.

$28,125.

The break-even point is of:

(50, 25000) and (80, 28000).

The revenue function is given as follows:

R(x) = -5x² + 750x.

Which is a quadratic equation with the coefficients given as follows:

a = -5, b = 750.

Then the x-coordinate of the vertex is of:

x = -b/2a = -750/-10 = 75.

Thus the maximum revenue is of:

R(12) = -5(75)² + 750(75) = $28,125.

The break-even points are the points of intersection of the revenue and of the cost functions, given as follows:

From the intersection of the graph given at the end of the answer, these points are of:

(50, 25000) and (80, 28000).

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Q falls to 251,400 to 201,400 which means a fall of 50,000 which should be counteracted by advertising. If advertising expenditure becomes 30,000 it will raise the Q again to 251,400.

Given that,

One of a travel company's main products, a guided tour to a specific country, was the subject of a demand analysis by a management consulting firm for 26 regional markets. The consultant estimates the following equation using data:

Q=1500−4P+5A+10I+3PY

Q is the quantity of the product that is demanded;

P represents the item's monetary price;

A represents advertising costs in thousands of dollars;

I represents income expressed in dollars;

PY is the cost of a different travel product provided by a rival travel agency.

We have to find

(a) Utilizing the information below, determine the amount demanded for this product:

P = $400

A = $20,000

I = $15,000

PY=$500

Q = 1,500 - 4 × 400 + 5 × 20,000 + 10 × 15,000 + 3 × 500

= 1,500 - 1,600 + 100,000 + 150,000 + 1,500

= 251,400

(b)  In Income falls to 10,000

Q = 1,500 - 4 × 400 + 5 × 20,000 + 10 × 10,000 + 3 × 500

= 1,500 - 1,600 + 100,000 + 100,000 + 1,500

= 201,400

Q falls to 251,400 to 201,400 which means a fall of 50,000 which should be counteracted by advertising. If advertising expenditure becomes 30,000 it will raise the Q again to 251,400.

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Answer:

25!

in this type of questions you need to find 10 makers ( it's means you need to find numbers which has 2 or 5 in their prime factors) obviously there is a bunch of numbers which has 2 in their prime factors.

so we need to find multiples of 5. But you should be aware that some numbers have more than one prime factors of 5 e.g. 25 .

ok let's go back to the question.

starting from 1 , we've got 5, 10 , 15 ,20 &25(5²)

so the answer is 25!

Given Statement (a!)b = ab! is false becuase it is not appropriate to represent factorial like this.

What is Factorial?

In mathematics, the term "Factorial" refers to the sum of all positive integers that are less than or equal to a certain positive integer, which is followed by an exclamation point. Thus, factorial seven is denoted by the symbol 7!, which stands for 1*2*3*4*5*6*7. Factorial 0 is equivalent to 1 by definition.

(a!)*b = ab!

this depends on the value of a and b.

I'm not sure if the phrase "ab!" means to multiply a by b and then compute the factorial of the resulting product, as in (ab)!, or to compute the factorial of b first and then multiply this by a, as in a(b!). Either way, the assertion is false.

Given Question is incomplete Complete Question here:

assume that a and b are positive integers. for each statement below, determine whether the statement is true or false, and indicate your answer in the appropriate box  (a!)b = ab!  

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The VO2max test resulted by z score should result in a minimum score of 36 for 84% of college students.

To find the answer, we will use the z-score formula:

z = (x - μ)/σ

We will use the given values for the mean (μ = 44), the standard deviation (σ = 8), and the value we are looking for (x = 36).

z = (36 - 44) / 8

z = -1

We can then look up the percentage of values equal to or below -1 on the standard normal distribution table. This value is 84%. Therefore, we should expect 84% of college students to score at least 36 on the VO2max test.

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As proportional relationship, the amount decreasing at a rate milligrams per hour expression P(t) = 500 + e⁻⁰²ˣ

Proportional relationship:

In math, the relationships between two variables where their ratios are equivalent is known as proportional relationship.

Given,

Here we have the rate at which the= drug leaves the bloodstream proportional to the amount of the drug bloodstream: The amount of the drug in the bloodstream can be modeled by K; where constant and- time; hours At time 500 milligrams of the drug was administered. At the moment when the amount of the drug in the bloodstream 50 milligrams, the amount decreasing at a rate milligrams per hour.

Here we need to find the expression.

While we looking into the given question, we have identified the following details,

=> Bloodstream = 500 milligrams

Here they state that the bloodstream 50 milligrams, the amount decreasing at a rate milligrams per hour.

So, the expression for this proportional relationship is written as,

=> P(t) = 500 + e⁻⁰²ˣ

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Indefinite integral using integration by parts from x2 ln(x) dx is

[tex]\frac{1}{3}[/tex] [tex]X^{3\\}[/tex] (ln(x) - [tex]\frac{1}{3}[/tex]) + C

The given choice of u and dv

∫ [tex]x^{2} ln(x) dx[/tex]

we can use the formula

∫ u dv = uv - ∫ v du

Then split the component

u =  [tex]ln(x)[/tex]     du = [tex]\frac{1}{x}[/tex][tex]dx[/tex]

dv = [tex]x^{2}[/tex]         v = [tex]\frac{1}{3}x^{3}[/tex]

∫ u dv = uv - ∫ v du

∫ [tex]x^{2} ln(x) dx[/tex]   =  ln(x) [tex]\frac{1}{3}x^{3}[/tex] - ∫ [tex]\frac{1}{3}x^{3}[/tex] [tex]\frac{1}{x}[/tex] dx

                    = [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{3}[/tex] [tex]\frac{1}{x}[/tex] dx

                    = [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{3} . x^{-1}[/tex] dx

                    = [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{2}[/tex] dx     ----> ∫ [tex]x^{2}[/tex] dx = [tex]\frac{1}{3} x^{3} + C[/tex]

                    =  [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] [tex]\frac{1}{3} x^{3} + C[/tex]

                    = [tex]\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C[/tex]

Therefore Indefinite integral using integration by parts

∫ [tex]x^{2} ln(x) dx[/tex]  is  [tex]\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C[/tex]

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The translation rule that maps A(-4, -2), B(-2, 6) and C (4, 4) to A' (-2, -2) B' (0, -10) and C' (6, -8) is

(x + 2, y + 4)

The transformation rule is solved by comparing the both preimage and image transformations as follows

preimage  image

A(-4, -2)   A' (-2, -2)

B(-2, 6)     B' (0, -10)

C (4, 4)     C' (6, -8)

x direction

-4 + x = -2, x = -2 + 4 = 2

-2 + x = 0, x = 0 + 2 = 2

4 + x = 6, x = 6 - 4 = 2

y direction reflection on the x axis leads to change of sign

preimage  image

A(-4, -2)   A' (-2, 2)

B(-2, 6)     B' (0, 10)

C (4, 4)     C' (6, 8)

-2 + y = 2, y = 2 + 2 = 4

6 + y = 10, y = 10 - 6 = 4

4 + y = 8, y = 8 - 4 = 4

The transformation rule is (x + 2, y + 4)

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Answer:

Samuel's watch is slower than the actual time 10 seconds.

Step-by-step explanation:

30 - 20 = 10 (seconds)

So Samuel's watch is slower than the actual time 10 seconds.

PLEASE GIVE ME BRAINLIEST IF THIS IS THE CORRECT ANSWER! THANKS!

Answer: 240 seconds

Step-by-step explanation:

So, here Samuel's watch gains 20 seconds every hour with respect to the alarm clock.

Also, alarm clock lags by 30 seconds every hour with respect to the actual time.

Therefore, Samuel's watch lags by (30-20) seconds every hour with respect to the actual time.

30-20=10 seconds

In 1 hour Samuel watch deviate by 10 seconds, then in 24 hours, it deviates by 24*10 seconds= 240 seconds..

Answer:

(36, 13)

Step-by-step explanation:

to find the midpoint you have the add the x and the y and then divide by two

to find one of the endpoints you just do the opposite

you multiply the midpoint by 2

and then subtract the remaining endpoint from it

(11, -1) --> (22, -2)

now subtract T from it

(36, 13)

that is your answer

The stock yield for the stocks will be 4.8%. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

To get the stock to yield use this formula - annual dividend / current stock price or share price

Substitute the dividend of $.88 and the closing price of $18.33 to the formula above. Divide and simplify.

Stock yield = .88 / 18.33

Stock yield = 0.0480 x 100

Stock yield = 4.8%

Therefore, the stock yield for the stocks will be 4.8%. The correct option is A.

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As per the concept of linear regression, the equation of the data is y ​= 133.1807 − 6.3096x.

The term linear regression means to determine the character and strength of the association between a dependent variable and a series of other independent variables.

Here we have given that mathematics and statistics teacher rex boggs, from Australia, weighed the bar of soap in his shower stall before showering in the morning. And the data on day and soap weight (in grams) appear in the table.

Here we need to find the linear regression equation that represents the given situation.

Based on the concept of linear regression, we know the the general formula for the regression is written as,

=> y = a + bx

FRom the given data, we have identified the value of the functions as,

a = 133.1807

b = -6.3096

r² = 0.9962

r = -0.9981

When we apply these values on the formula, then we get the equation as,

Then it implies the regression line is,

=> ŷ = a + bx = 133.18076.3096x

here a represents the day and y represents the weight in grams.

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The principal investment required to get an accrued amount of $5,000.00 in 821 days is  $4,494.52.

Simple interest is expressed as;

A = P(1 + rt)

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that;

Plug the given values into the above formula and solve for principal P.

A = P(1 + rt)

P = A / (1 + rt)

P = $5,000.00 / ( 1 + ( 0.05 × 821/365 ) )

P = $5,000.00 / ( 1 + 821/7300 )

P = $5,000.00 / ( 8121/7300 )

P = $4,494.52

Therefore, the principal required is $4,494.52.

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As per the unitary method, it take 3 minutes will it take John to reach the flagpole.

The term unitary method in math is defined as in which the value of one article is first obtained to find out the value of any required articles.

Here we have given that John is jogging on a straight jogging trail toward a flagpole at a speed of 500 ft/min. He is currently 1500 feet from the flagpole. And here we have to write an absolute value function that models John's distance from the flagpole after x minutes.

Here let us consider x be the time taken by John to reach the flagpole.

And here we know that

speed = 500 ft/min

height = 1500 feet

Then the absolute function for the given situation is written as,

=> f(x) = 500|x|

Apply the value of f(x) as 1500, then we get

=>  1500 = 500|x|

=> x = 3

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The perimeter of the square will be equal to 31.96 meters.

The perimeter of the square is defined as the sum of all the sides of the square. The perimeter of the square when the diagonals of the square are given will be calculated by the product of 2√2 with the diagonal magnitude.

Given that the diagonal of the square is 11.3 meters. The perimeter of the square will be calculated as,

P = 2√2 x d

P = 2√2 x 11.3

P = 31.96 meters

Therefore, the perimeter of the square will be equal to 31.96 meters.

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Answer:

1.14x = 19.38

$17

Step-by-step explanation:

Let the price before delivery charge = x.

The charge is 14%, so it is 14% of x, or 0.14x.

The original price plus charge is x + 0.14x, or 1.14x.

1.14x = 19.38

x = 19.38/1.14

x = 17

The price is $17

Answer:

θ = 2 π n_1 + π/3 for n_1 element Z

or θ = 2 π n_2 + (5 π)/3 for n_2 element Z

or θ = π n_3 for n_3 element Z

θ = π n_3 for θ element Z and cos(θ)!=0 and n_3 element Z

Step-by-step explanation:

Solve for θ:

tan(θ) - 2 sin(θ) = 0

Factor sin(θ) from the left hand side:

sin(θ) (sec(θ) - 2) = 0

Split sin(θ) (sec(θ) - 2) into separate parts with additional assumptions.

Assume cos(θ)!=0 from sec(θ):

sec(θ) - 2 = 0 or sin(θ) = 0 for cos(θ)!=0

Add 2 to both sides:

sec(θ) = 2 or sin(θ) = 0 for cos(θ)!=0

Take the reciprocal of both sides:

cos(θ) = 1/2 or sin(θ) = 0 for cos(θ)!=0

Take the inverse cosine of both sides:

θ = 2 π n_1 + π/3 for n_1 element Z or θ = 2 π n_2 + (5 π)/3 for n_2 element Z

or sin(θ) = 0 for cos(θ)!=0

Take the inverse sine of both sides:

θ = 2 π n_1 + π/3 for n_1 element Z

or θ = 2 π n_2 + (5 π)/3 for n_2 element Z

or θ = π n_3 for cos(θ)!=0 and n_3 element Z

The roots θ = π n_3 never violate cos(θ)!=0, which means this assumption can be omitted:

Answer: θ = 2 π n_1 + π/3 for n_1 element Z

or θ = 2 π n_2 + (5 π)/3 for n_2 element Z

or θ = π n_3 for n_3 element Z

Solve for θ over the integers:

tan(θ) - 2 sin(θ) = 0

Factor sin(θ) from the left-hand side:

sin(θ) (sec(θ) - 2) = 0

Split sin(θ) (sec(θ) - 2) into separate parts with additional assumptions.

Assume cos(θ)!=0 from sec(θ):

sec(θ) - 2 = 0 or sin(θ) = 0 for cos(θ)!=0

Add 2 to both sides:

sec(θ) = 2 or sin(θ) = 0 for cos(θ)!=0

Take the reciprocal of both sides:

cos(θ) = 1/2 or sin(θ) = 0 for cos(θ)!=0

Take the inverse cosine of both sides:

θ = 2 π n_1 + π/3 for θ element Z and n_1 element Z or θ = 2 π n_2 + (5 π)/3 for θ element Z and n_2 element Z

or sin(θ) = 0 for cos(θ)!=0

The roots θ = 2 π n_1 + π/3 violate θ element Z for all n_1 element Z:

θ = 2 π n_2 + (5 π)/3 for θ element Z and n_2 element Z

or sin(θ) = 0 for cos(θ)!=0

The roots θ = 2 π n_2 + (5 π)/3 violate θ element Z for all n_2 element Z:

sin(θ) = 0 for cos(θ)!=0

Take the inverse sine of both sides:

Answer: θ = π n_3 for θ element Z and cos(θ)!=0 and n_3 element Z

As the number of degrees of freedom for t-distribution increases, the difference between the t-distribution and standard deviation becomes smaller. The correct answer is B.

A t-distribution is described by one parameter, that is, degrees of freedom (df) v = n – 1, where n is the sample size. Its variance = v, where v represents the number of degrees of freedom and v ≥ 2.

To calculate degrees of freedom of a 1-sample t-test, we have to determine the size of our sample (N). Then, subtract 1. The result is the number of degrees of freedom.

Learn more about degrees of freedom at: https://brainly.com/question/27811227

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