(-1)^{3}]^{6} find the value of
Answers
The value of Exponent \((-1^{3}) ^{6}\) is 1
Exponent:
A number's exponent indicates how many times we multiply a number by itself. For example, \(3^{4}\) indicates that we have multiplied 3 four times. The expanded form is 3×3×3×3. An exponent is also known as a number's power. It can be an integer, a fraction, a negative number, or decimals.
Law of Power of a Power: \((x^{a}) ^{b}\)=\(x^{ab}\) {Here a,b can be an integer, a fraction, a negative number, or decimals}
Given question is \((-1^{3}) ^{6}\)
⇒\((-1^{3}) ^{6}\)=\((-1)^{6.3}\){ using Law of Power of a Power}
⇒\((-1)^{18}\)=1 { -1 raised any even number= positive one}
Therefore,The value of Exponent \((-1^{3}) ^{6}\) is 1
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Related Questions
Decrease £16855.21 by 13.5%
Give your answer rounded to 2 DP.
Answers
Answer:
£ 14,579.75Step-by-step explanation:
= £16855.21 - ( £16855.21 x 13.5% )
100
= £ 14,579.75
A ______ can have one of two values, true or false, and is often used in if statements.
Answers
A boolean expression can have one of the two values, true or false and is often used in if statements.
Given: To identify what is used in if statements that has either of the two values, true or false.
What are boolean expressions?
Boolean expressions are logical statements that can either be true or false.
Boolean expressions are used to compare different values which are of the same domain and to verify if the condition of comparison is true or false.
For example: 4 > 5 , is this statement true? With the help of boolean variables "true" and "false" we can say that 4 > 5 is "false"
NOTE: There are two boolean variables : TRUE and FALSE
The boolean value TRUE is equivalent to 1 in the integer domain.
The boolean value FALSE is equivalent to 0 in the integer domain.
The common operators that are often used in boolean expressions are OR, AND and NOT.
For example: 7 > 6 OR 0 < 90
Now 7 > 6 is TRUE, also 0 < 90 is TRUE
So, TRUE OR TRUE gives TRUE
Hence 7 > 6 OR 0 < 90 is TRUE, the condition is verified.
The "if" statement is a conditional statement in programming which when TRUE performs certain given information and if FALSE it either terminates or performs some other statements that may be defined in the else or the FALSE part.
"if" statements works on boolean values TRUE and FALSE.
It's like IF this is TRUE do this or ELSE do that.
The structure of if statement is:
if <condition>
//statements [executed if condition is TRUE]
else
//statements [executed if condition is FALSE]
Hence a boolean expression can have one of the two values, true or false and is often used in if statements
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A Boolean expression can have one of the two values, true or false and is often used in if statements.
We are given a statement about an expression which can have the values as true or false and is mostly used in the if statements.
We need to identify the expression that they are talking about.
We get that, they are talking about the Boolean expression as it is the only expression that has the values as True or False and is often used in the if statements to know whether those statements are correct or not.
Therefore, a Boolean expression can have one of the two values, true or false and is often used in if statements.
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what is the probability that if 7 letters are typed, no letters are repeated? write your answer in decimal form, rounded to the nearest thousandth.
Answers
To calculate the probability that no letters are repeated when 7 letters are typed, we need to consider the number of possible arrangements without repetition and divide it by the total number of possible arrangements with repetition. The probability can be determined by calculating the ratio of these two quantities.
When 7 letters are typed without repetition, the first letter can be chosen from all 26 alphabets, the second letter from the remaining 25, the third from 24, and so on. This can be calculated as 26 x 25 x 24 x 23 x 22 x 21 x 20 = 17,748,480.
On the other hand, if 7 letters are typed with repetition allowed, each letter can be chosen from the 26 alphabets independently, resulting in 26 x 26 x 26 x 26 x 26 x 26 x 26 = 26^7 = 8,031,810,176.
Therefore, the probability that no letters are repeated is given by 17,748,480 / 8,031,810,176 ≈ 0.002213 (rounded to the nearest thousandth).
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(1, 3) and (-3, -5) write in slope intercept form
Answers
Answer:
y = 2x + 1
Step-by-step explanation:
The slope intercept form is represented in: y=mx+b
m = slope
b = y-intercept
let's find slope:
(1, 3)(-3, -5)
m = -5 - 3 / -3 - 1 = - 8 / -4 = 2
Therefore,
let's find b using (1, 3)
y = 2x + b
3 = 2 + b
b = 1
y = 2x + 1
Factor −4x2 + 12x. PLease help
Answers
Answer:
-4x(x-3)
Step-by-step explanation:
-4x^2+12x
divide by -4x
-4x(x-3)
whats a interger with your words
Answers
Answer:The first graders began to count, naming each integer up to 100.
Step-by-step explanation:
Answer:
one of the positive or negative numbers 1, 2, 3, etc., or zero.Compare whole number.
Step-by-step explanation:
Write an expression to represent the area of a right triangle with legs length as follow: 2x-2 and 4x+2
Answers
A=ab/2
(2x-2)(4x+2)/2
(8x^2+4x-8x-4)/2
(8x^2-4x-4)/2 take common term 2
2(4x^2-2x-2)/2
So A=4x^2-2x-2
Expression to represent the area of a right triangle with legs length as 2x-2 and 4x+2 is 4x² - 2x - 2.
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.
For example, x + y is an expression, where x and y are terms having an addition operator in between.
Given,
legs length of a right angle triangle = 2x-2 and 4x+2
Area of the right angle triangle = (length of leg a × length of leg b)/2
= (2x-2)(4x + 2)/2
= 2(x - 1)(4x + 2)/2
= (x - 1)(4x + 2)
Area of the right angle triangle = 4x² - 2x - 2
Hence, 4x² - 2x - 2 is the expression for area of right triangle.
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Suppose the time it takes a child to eat a donut is uniformly distributed between 0.5 and 4 minutes, inclusive. Calculate the probability that a randomly selected child takes more than two minutes to eat a donut given that the child has already been eating the donut for more than 1.5 minutes. Comment with your answer.
Answers
The probability that a randomly selected child takes more than two minutes to eat a donut given that the child has already been eating the donut for more than 1.5 minutes is approximately 0.5714 or 57.14%.
To calculate the probability that a randomly selected child takes more than two minutes to eat a donut given that the child has already been eating the donut for more than 1.5 minutes, we need to find the conditional probability.
Let's denote:
A = Event that a child takes more than two minutes to eat a donut
B = Event that a child has already been eating the donut for more than 1.5 minutes
We want to calculate P(A|B), which represents the probability of event A occurring given that event B has already occurred.
The time it takes a child to eat a donut is uniformly distributed between 0.5 and 4 minutes, inclusive. Since the distribution is uniform, the probability density function (PDF) is constant within the interval.
To find P(A|B), we need to consider the intersection of events A and B, which corresponds to the portion of the time interval where both conditions are satisfied. In this case, the intersection is the interval from 2 minutes to 4 minutes.
The length of the entire time interval is 4 - 0.5 = 3.5 minutes.
The length of the intersection interval is 4 - 2 = 2 minutes.
Therefore, P(A|B) = (length of intersection interval) / (length of entire interval) = 2 / 3.5 ≈ 0.5714.
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Which of the following is a fundamental difference between the t statistic and a z-score?
The t statistic uses the sample variance in place of the population variance.
Answers
The fundamental difference between t-test and z-score is: t-test is used to determine the difference in data sets, the standard deviation and the z-score is used to to draw data from a given population with different means and standard deviation. A) The t statistic uses the sample mean in place of the population mean
How to know the use of t-test and z-score?T-test is a statistic model which is used to find how averages of different data sets differ in case the standard deviation and Z-scores statistic helps to draw data from populations with different means and standard deviations and also place them on a common scale.
The z-core formula is:
Z₁=\(\frac{x-m}{s}\)
Therefore the fundamental difference is that the t-test uses the variance in place of the population variance.
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Complete question:
Which of the following is a fundamental difference between the t statistic and a z-score?
A) The t statistic uses the sample mean in place of the population mean
B) All of the choices are differences between t and z.
C) The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n.
D) The t statistic uses the sample variance in place of the population variance.
What is the linear distance traveled in one revolution of a 36-in diameter wheel.
Answers
The linear distance traveled in one revolution of a wheel can be calculated using the formula:
Circumference = π * Diameter
Given that the diameter of the wheel is 36 inches, we can substitute the value into the formula:
Circumference = π * 36 inches
Using an approximate value of π as 3.14159, we can calculate the circumference:
Circumference ≈ 3.14159 * 36 inches
Circumference ≈ 113.09724 inches
Therefore, the linear distance traveled in one revolution of a 36-inch diameter wheel is approximately 113.09724 inches.
suppose that 30% of new yorkers own a dog, 25% of new yorkers own a cat and 15% of new yorkers own a cat given they own a dog. a new yorker is chosen at random and reported to own a cat. what is the probability they also own a dog?
Answers
The probability that a New Yorker who possesses a cat also owns a dog is 0.103. if a new yorker is chosen at random.
New Yorkers own a dog (D) = 30%
New Yorkers own a cat (C) = 25%
New Yorkers own a cat and dog = 15%
This problem can be calculated using Bayes' theorem, which notes that the possibility of an event A given event B is equal to the possibility of event B given A times the probability of A, divided by the probability of event B.
P(D) = 0.30
P(C) = 0.25
P(C|D) = 0.15
Using Bayes' theorem:
P(D|C) = P(C|D) * P(D) / P(C)
P(C) = \(P(C|D) * P(D) + P(C|not D) * P(not D)\)
P(C) = \(P(C|D) * P(D) + P(C) * P(not D)\)
P(C) =\(P(C|D) * P(D) / (1 - P(D) * P(C|not D))\)
Now we can substitute these values into the Bayes' theorem formula:
P(D|C) = P(C|D) * P(D) / P(C)
P(D|C) = \(0.15 * 0.3 / (P(C|D) * P(D) + P(C) * P(not D))\)
P(D|C) = \(0.15 * 0.3 / (0.15 * 0.3 + P(C) * 0.7)\)
P(C) = \(0.15 * 0.3 / (1 - 0.3 * 0.25)\)
P(C) = 0.16
P(D|C) = \(0.15 * 0.3 / (0.15 * 0.3 + 0.16 * 0.7)\)
P(D|C) = 0.103
Therefore, we can conclude that the probability that a New Yorker who owns a cat also owns a dog is 0.103.
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Determine whether the integral is convergent or divergent. 5 lovst dx - X convergent divergent If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) 4.38602 x
Answers
The given integral is ∫(5/√x - x)dx, with the limits of integration not provided. To determine if the integral is convergent or divergent, we need to consider the behavior of the integrand.
First, let's examine the individual terms: 5/√x and -x. The term 5/√x represents a power function with a negative exponent, while -x represents a linear function.
When considering the convergence or divergence of an integral, we need to focus on the behavior of the integrand as x approaches the limits of integration.
For the term 5/√x, as x approaches 0 from the right, the value of 5/√x becomes infinitely large, indicating divergence. On the other hand, for -x, the value remains finite as x approaches 0.
Since the integrand exhibits divergence at x = 0, the integral is divergent.
Therefore, the integral ∫(5/√x - x)dx is divergent.
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PLS HELP ILL GIVE U POINTS :)
Explain how you know the following system of equations has at most 2 solutions.
Solve the system algebraically. Show your work.
Solve the system by graphing.
y= 2x-1
y= x^2-9
Answers
Answer:
Step-by-step explanation:
Answer:
The said explanation is the answer.
Step-by-step explanation:
1) Graphing the first function (y = 2x-1). When the exponents of the variables are all 1, that is there are no square, cubes, etc. the equation is a line. Then it is enough to find two points to draw it. We can calculate two points assigning a number to x and calculating the corresponding number for y. For example, when x= 0 y= 2 times 0 -1 = -1. Then the line will pass from the point (0,-1). We need a second point, we can take x=1, then y = 2 times 1 -1 = 1. The line will pass from (1,1). We can mark the two points on the plane and draw the line from these two points.
2) Graphing the second function (y = x^2-9). A quadratic equation is of the form: ax^2+bx+c= 0. We have: y= f(x) -9. Set y=0. We have the quadratic equation: x^2-9=0. Using the algebraic identity: a^2-b^2=(a+b)(a-b). We can rewrite x^2-9=0 as x^2-3^2=0: [(x+3)(x-3)=0] - [(x+3)=0,(x-3)=0] - [x= -3, x= 3]. Hence, there are two solutions for x. So we have two x-intercepts: (-3,0) and (3,0). To find the y-intercept, set x=0: [(y = (0)^2-9=0)] - [(y=-9)]. Hence the y-intercept: (0,-9)
In conclusion, this system of equations at most has two real solutions, since two points of both functions intersect each other.
Here's the graph:
A recreational court is four times as long as it is wide. If the perimeter is295 ft , find the dimensions of the court.
Answers
The width of the recreational court is 29.5 feet and the length is 118 feet.
What are the dimenstions of the recreational court?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
The perimeter of a rectangle is expressed as;
P = 2(length + width )
Let's represent the width of the recreational court as "w".
Since the length is stated to be four times the width, we can represent the length as "4w".
Plug in the values into the above formula:
P = 2(length + width )
295 = 2( 4w + w )
Simplifying the equation:
295 = 8w + 2w
2w + 8w = 295
10w = 295
w = 295/10
w = 29.5 ft
Now that we know the width, we can find the length:
Length = 4w
Length = 4 × 29.5
Length = 118 ft
Therefore, the width measure 29.5 ft and the length measure 118 ft.
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Which graph shows the line of best fit for the data ?
Answers
Answer:
Bottom left
Step-by-step explanation:
It covers the most points
is 7/25 supposed to be a fraction or decimal?
Answers
Answer:
7/25 is a fraction
Step-by-step explanation:
7/25 is a fraction and 7/25 in decimal form is 0.28
To turn into decimal 7 divide by 25 =0.28
[RevyBreeze]
Answer:
7/25 supposed to be a fraction
Step-by-step explanation:
its decimal form is 0.28
Sarah has $240 and she gives her mum $80 what fraction of the money does Sarah have left give the fraction in its simplest form
Answers
Answer:
\(\frac{2}{3}\)
Step-by-step explanation:
$240 - $80 = 160
\(\frac{160}{240} = \frac{2}{3}\)
\(\frac{160 | 80}{240 | 80}\) = 2/3
explanation:
240-80=160 so
140/240 simplified= 2/3
Michael wants to make 5 shirts. Each shirt takes ⅘ yards of fabric to make. How much fabric will he need?
Answers
Answer:
4
Step-by-step explanation:
answer is 5*0.8=4 yards of fabric
Answer:
4 yards
Step-by-step explanation:
He need 4/5 yards to make 5 shirts. Multiply the two to find your answer
4/5 * 5 = 4
He will need 4 yards of fabric to make 5 shirts.
The Staeb company manufactures headphones. The company's total cost function is C(h)=−0.002h 2
+75h+2200 and revenue is given by R(h)=140h (both in dollars), where h is the number of pairs of headphones. What is the company's profit function, P(h) ? (Simplify your expression) P(h)=
Answers
The company's profit function, P(h), is given by P(h) = -0.002h^2 + 65h - 2200.
The profit function, P(h), can be calculated by subtracting the total cost function, C(h), from the revenue function, R(h).
Profit (P) = Revenue (R) - Total Cost (C)
Given:
R(h) = 140h
C(h) = -0.002h^2 + 75h + 2200
Substituting these values into the profit formula:
P(h) = R(h) - C(h)
= 140h - (-0.002h^2 + 75h + 2200)
= 140h + 0.002h^2 - 75h - 2200
Simplifying further:
P(h) = -0.002h^2 + 140h - 75h - 2200
= -0.002h^2 + 65h - 2200
Therefore, profit function obtained is -0.002h^2 + 65h - 2200.
The profit function P(h) allows the company to assess its financial performance and make informed decisions regarding pricing, production levels, and resource allocation.
By understanding the relationship between the number of headphones sold, production costs, and revenue, the company can determine the level of output that yields the highest profit.
This information is crucial for effective business planning, maximizing profitability, and ensuring the company's long-term success in the highly competitive headphone market.
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A random sample of 12 joggers was asked to keep track and report the number of miles they ran last week. The responses are
5.5 7.2 1.6 22.0 8.7 2.8
5.3 3.4 12.5 18.6 8.3 6.6
a. Compute the three statistics that measure central location.
b. Briefly describe what each statistic tells you.
Answers
a. The three statistics that measure central location are:
Mean = 8.825 miles.Mode = no modeMedian = 7.95 miles.b. The mean tells us the average number of miles jogged by the sample of 12 joggers last week. Median tells us the midpoint of the data. The mode give us insight into what distance is most frequently jogged by the sample
a. Mean: average of the data = (5.5 + 7.2 + 1.6 + 22.0 + 8.7 + 2.8 + 5.3 + 3.4 + 12.5 + 18.6 + 8.3 + 6.6) / 12 = 8.825 miles.
Median: middle value of the data when arranged in order = 7.95 miles.
Mode: most common value in the data set = there is no mode since no value is repeated.
b. The mean shows us how many miles on average the sample of 12 joggers covered last week. The median provides the data's midpoint, which is helpful when the mean may be impacted by extreme numbers. When it is present, the mode can help us understand what distance the sample covers most frequently. Since there is no mode in this instance, this number is useless.
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can someone please explain what i have to do.
Answers
Answer:
(4,5)
Step-by-step explanation:
The equation of the graph is y=x+1
Basically, if you plug in the x coordinate and add one, you will get the y coordinate.
This question is asking what the y coordinate would be if x is equal to 4
y=x+1
y=4+1
y=5
Therefore the ordered pair would be (4,5)
It’s (4,5) because the slope is 1/1 meaning up one and right one. So when you graph up one and right one you get (4,5)
To get the slope from y=x+1 you always look at what’s in front of x
In this case it’s just x so there’s an imaginary 1 in front of it and for a slope it’s rise over run so it’s 1/1
Hope that’s easy to understand
What is 64^2/4 in a fraction?
Answers
Answer:
128/4 or 32
Step-by-step explanation:
b) 10x-8 = 8x
e) 2x+3 = x-9
h) 5x+8 = 7x-32
Answers
Answer:
b) x = 4
e) x = -12
h) x = 20
Step-by-step explanation:
b) 10x - 8 = 8x
10x - 8 + 8 = 8x + 8
10x = 8x + 8
10x - 8x = 8x + 8 - 8x
2x = 8
\(\frac{2x}{2} = \frac{8}{2}\)
x = 4
e) 2x +3 = x - 9
2x +3 -3 = x - 9 -3
2x = x - 12
2x -x = x -12 -x
x = -12
h) 5x + 8 = 7x - 32
5x + 8 - 8 = 7x -32 -8
5x = 7x - 40
5x - 7x = 7x - 40 -7x
-2x = -40
\(\frac{-2x}{-2} = \frac{-40}{-2}\)
x = 20
What is the optimal solution for the following problem?
----------------------------------------------------
Maximize P =4x + 12y
subject to
3x + 5y ≤ 12 6x + 2y ≤ 10
and x ≥ 0, y ≥ 0.
Answers
The maximum value of P is 20.68, which occurs when x = 1.67 and y = 1.07.
The optimal solution, we need to first graph the constraints and determine the feasible region.
The first constraint is 3x + 5y ≤ 12, which represents a line with a y-intercept of 2.4 and a slope of -3/5.
The second constraint is 6x + 2y ≤ 10, which represents a line with a y-intercept of 5 and a slope of -3.
Plotting these lines on a graph, we get:
The feasible region is the shaded region that satisfies both constraints and lies in the first quadrant.
Next, we need to evaluate the objective function at each corner point of the feasible region to find the maximum value of P.
The corner points are:
(0, 2.4)
(1.67, 1.07)
(1.43, 0)
(0, 0)
Evaluating P at each of these points, we get:
(0, 2.4):
P = 9.6
(1.67, 1.07):
P = 20.68
(1.43, 0):
P = 17.72
(0, 0):
P = 0
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a committee of congressmen will be selected from a group of democrats and republicans. find the number of ways of obtaining exactly one .
Answers
The number of ways of obtaining exactly one Democrat is 504
We are choosing 6 committee members, and exactly 1 of them must be a Democrat, which leaves 5 members to be selected from the Republicans. The number of ways to select 5 Republicans from 9 Republicans is 9 choose 5, which is 9! / (5! * (9-5)!).
Therefore, the total number of ways to form a committee with exactly 1 Democrat and 5 Republicans is 4 * (9 choose 5) = 4 * 126 = 504. or
There are a total of 13 members (4 Democrats and 9 Republicans), so the number of combinations that can be chosen is 13C6, or 1716. Since we are looking for a committee with exactly one Democrat, we need to subtract the total number of combinations with no Democrats (9C6, or 84) from the total number of combinations, giving us 1716-84 = 504 ways of obtaining exactly one Democrat.
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Your question is incomplete but probably the full question was:
A committee of six Congressmen will be selected from a group of four Democrats and nine Republicans. What is the number of ways of obtaining exactly one Democrat?
The volleyball team is selling raffle tickets for $1. 50 each. It wants to make at least $250 from the sales. Assume everyone buys the same number of tickets. If there are 75 people at the fundraiser, what is the least number of tickets each person needs to buy to meet that goal?.
Answers
The least number of tickets each person needs to buy to meet that goal of volleyball team is 3 tickets.
What is an algebraic expression?The algebraic expression are used to represent the general problem in the mathematical way to solve them to find the value of unknown variable.
Let suppose the number of tickets sold are n. As the volleyball team is selling raffle tickets for $1.50 each and the total fund raised by selling the ticket is $250.
Thus, the number of tickets sold are,
\(n=\dfrac{250}{1.5}\\n\approx167\)
Now everyone buys the same number of tickets and there are 75 people at the fundraiser. Thus, the number of tickets purchased by each fundraiser is,
\(x=\dfrac{167}{75}\\x=2.23\)
The number of tickets should be more than 2.23 buy by each people to earn the profit at least or more than $250.
Hence, the least number of tickets each person needs to buy to meet that goal of volleyball team is 3 tickets.
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What is the solution to the system of equations graphed below?
y=-x+2
y = 5x + 28
O A. (-8,4)
B. (0,2)
C. (-4,8)
D. (4,8)
Answers
Answer:
Y=-3/2x+2 y=5x+28 so -3/2x+2=5x+28
Solve: -13/2x=26 x= -2/13 (26)= -4 The right answer is C (-4,8)
Step-by-step explanation:
circle p is described by the equation (x3)(y2)25. which of the following lines are tangent to p?
Answers
To determine which of the given lines are tangent to circle p, we need to first find the equation of the circle.
The equation given is (x^3)(y^2)=25, which can be rewritten as y^2=25/(x^3).
Taking the derivative of this equation with respect to x,
we get: 2y(dy/dx) = -(75)/(x^4).
Simplifying this, we get dy/dx = -(75y)/(2x^4).
Now we can substitute the slope of each given line into this equation and find the corresponding value of y. If this value of y satisfies the equation of the circle, then the line is tangent to the circle at that point. We find that only the line y = 5x + 1 satisfies this condition, and therefore it is the only line that is tangent to circle p.
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If y varies directly as x andx = 12 when y = 24, what is x when y = 8? (I just need to know the rate of change, y-intercept, x-intercept, what m & b are, & what the equation is in slope-intercept form.)
Answers
If y varies directly as x and x = 12 when y = 24, what is x when y = 8.?
So, y = c * x
where c is constant
x = 12 when y = 24
so,
24 = c * 12
c = 24/12 = 2
so,
y = 2x
Now, need to find x when y = 8
so,
8 = 2x
x = 8/2 = 4
===============================================================
From the graph:
y-intercept = 3 , it is the value of y when x = 0
the general form of the line: y = mx + b
where b is y-intercept
So, y = mx + 3
to find m, choose point like (2 , 2) and substitute with it
so, y = 2 when x =2
2 = 2m + 3
2m = -1
m = -1/2 = -0.5
so, y = -0.5x + 3
so, to find x-intercept is the value of x when y = 0
so, 0 = -0.5x + 3
0.5x = 3
x = 3/0.5 = 6
m is the slope = -0.5
b is y-intrcept = 3
A random sample of 40 ucf students has a mean electricity bill of $112. Assume the population standard deviation is $19. 20. Construct a 90% confidence interval for the mean electricity bill of all ucf students. Round final answer to two decimal places.
Answers
The 90% confidence interval for the mean electricity bill of all UCF students is discovered using the t-distribution to be (117.06, 106.94).
The standard deviation for the sample has been provided to us, so the t-distribution is employed to address this issue.
The information given is:
Sample mean of : x = 112
Sample standard deviation : s = 19
Sample size of : n = 40
The confidence interval is: \(\bar{x}\pm t\cdot\frac{S}{\sqrt{n} }\)
Using a t-distribution calculator, the critical value is t = 1.6854 for a two-tailed 95% confidence interval with 40 - 1 = 39 df.
Hence:
Upper bound = 112 + 1.6854 × 19 / √40 = 117.06
Lower bound = 112 - 1.6854 × 19 / √40 = 106.94
A confidence interval is a range of estimates for an unknown parameter (CI). The most common confidence level is 95%, but when calculating confidence intervals, other levels, such 90% or 99%, are also occasionally employed.
The 90% confidence interval for the mean electricity bill of all UCF students is discovered using the t-distribution to be (117.06, 106.94).
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