Answer:
To solve the equation, we need to isolate the square root term and square both sides of the equation. We have:
1 + √n + 11 = n
√n = n - 12
Squaring both sides:
n = (n - 12)^2
n = n^2 - 24n + 144
n^2 - 25n + 144 = 0
Factorizing the quadratic equation:
(n - 16)(n - 9) = 0
Therefore, n = 16 or n = 9. We need to check these solutions in the original equation to see if they are valid.
For n = 16:
1 + √16 + 11 = 16
1 + 4 + 11 = 16
16 = 16
The solution n = 16 satisfies the equation.
For n = 9:
1 + √9 + 11 = 9
1 + 3 + 11 = 9
15 = 9
The solution n = 9 does not satisfy the equation.
Therefore, the only real solution is n = 16, which corresponds to option C: -2 is an extraneous solution and 5 is a real solution.
Hope This Helps!
Is 3x-2x+ 0.5x equivalent to 0.5x
no
calculating the equation, you haft to simplify it gives 1.5
it's 1.5x
a sum of 8000 is compounded annually for 3 years if the rate of interest in 10% per annum for the first year 12% per annum for the second year and 15% per annum for the third year then what is the amount at the end of 3rd years?
Answer:
the amount at the end of the third year is A3 = $11,330.40.
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
For the first year, the interest rate is 10%, so we have:
A1 = 8000(1 + 0.1/1)^(1*1)
A1 = 8800
After the first year, the principal becomes 8800. For the second year, the interest rate is 12%, so we have:
A2 = 8800(1 + 0.12/1)^(1*1)
A2 = 9856
After the second year, the principal becomes 9856. For the third year, the interest rate is 15%, so we have:
A3 = 9856(1 + 0.15/1)^(1*1)
A3 = 11330.4
Therefore, the amount at the end of the third year is A3 = $11,330.40.
In summary, the initial amount of $8,000 is compounded annually for three years at different interest rates. By using the formula for compound interest, we find that the amount at the end of the third year is $11,330.40.
Maths. Please help me as best as you can.
Answer:
Step-by-step explanation:
She is traveling via Bootle.
Crosby to Bootle is 4 miles.
Bootle to Speke is 12 miles.
That is 16 miles each way.
16 times 2 = 32 miles per day
5 times 32 for the work week.
5 times 32 = 160 miles per week
Nolan is trying to pick out an outfit for the first day of school. He can choose from 6 pairs of pants, 3 t-shirts, 3 sweaters or hoodies, and 5 pairs of shoes. How many different outfits does Nolan have to choose from?
Nolan has 270 different outfits to choose from.
What is permutation?
Ways" or permutation refers to the number of different possible outcomes or arrangements in a situation. For example, if you have 3 different shirts and 4 different pants, there are 12 ways (3 x 4) to choose one shirt and one pant. The concept of "ways" is often used in combinatorics, which is the branch of mathematics that deals with counting and arranging objects.
To find the total number of different outfits that Nolan can choose from, we need to multiply the number of options for each clothing item:
Total number of outfits = number of pants x number of t-shirts x number of sweaters or hoodies x number of shoes
Total number of outfits = 6 x 3 x 3 x 5 = 270
Therefore, Nolan has 270 different outfits to choose from.
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Guys please I need help
B
East Indians and Chinese because they are both in the continent of Asia, which is where P and Q are located.
algebra 1 mid term help!!
Answer:
Yes,
Step-by-step explanation:
Because no x- Values repeat.
Graph the inverse of the provided graph on the accompanying set of axes. You must
plot at least 5 points.
*Click the graph to make a point. Click it again to erase.
The inverse of the provided graph is shown in the image attached below.
What is an inverse function?In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value). By critically observing the graph, we can logically deduce the following points;
Vertex (h, k) = (-4, 6)
y-intercept (x, y) = (0, 8)
y-intercept (x, y) = (0, 4)
Point (x, y) = (5, 9)
Point (x, y) = (5, 3)
By swapping both the input value (x-value) and output value (y-value), we have:
Vertex (h, k) = (6, -4)
x-intercept (x, y) = (8, 0)
x-intercept (x, y) = (4, 0)
Point (x, y) = (9, 5)
Point (x, y) = (3, 5)
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preform the indicated operation
(1)/(x^(2)-6x)=(x)/(x^(2)-36)+2
solve for x
[ sorry if im missing anything ]
The solutions to the equation are x = -11/3 and x = 6.
Describe Equation?In mathematics, an equation is a statement that two expressions are equal. It consists of two sides separated by an equal sign (=). The expression on the left side of the equal sign is usually called the left-hand side (LHS), while the expression on the right side is called the right-hand side (RHS).
Equations can take many different forms and can involve various types of functions and operators, such as addition, subtraction, multiplication, division, exponentiation, logarithms, trigonometric functions, and more. They can also involve one or more variables, which can be solved for to obtain a specific value or range of values that make the equation true. Equations are used extensively in mathematics, science, engineering, economics, and many other fields.
To solve the equation for x, we can start by simplifying both sides of the equation and bringing all the terms to one side:
(1)/(x²-6x) - (x)/(x²-36) = 2
We can simplify the left side of the equation by finding a common denominator:
[(1)(x-6) - (x)(x+6)] / [(x-6)(x+6)] = 2
Expanding the numerator and simplifying, we get:
(-x² + 7x - 6) / [(x-6)(x+6)] = 2
Multiplying both sides by the denominator, we get:
-x² + 7x - 6 = 2(x-6)(x+6)
Expanding the right side, we get:
-x² + 7x - 6 = 2(x² - 36)
Simplifying and rearranging, we get:
3x² - 7x - 66 = 0
We can solve this quadratic equation by factoring or using the quadratic formula:
3x² - 7x - 66 = (3x + 11)(x - 6) = 0
So either 3x + 11 = 0 or x - 6 = 0:
3x + 11 = 0 => x = -11/3
x - 6 = 0 => x = 6
Therefore, the solutions to the equation are x = -11/3 and x = 6.
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30 points to whoever solves
Answer:
Step-by-step explanation:
its a 12/14 probabiloty or a 92.5%
Step-by-step explanation:
I'll try:
7 boys choose 5 = 7! / (5!2!) = 21 ways
4 girls choose 2 = 4 ! / (2! 2!) = 6 ways
6 x 21 = 126 ways to choose 5 boys and 2 girls
11 cats total choose 7 = 11! /( 7! 4!) = 330 ways to choose 7 cats
126 of these will be 5 boys and 2 girls
126 out of 330 = 126/330 = .382
Rachel is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $104 and allows unlimited mileage.
Company B has an initial fee of $65 and charges an additional $0.60 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
Answer:
To find out for what mileages Company A will charge less than Company B, we need to set up an inequality using the given prices and the number of miles driven, m.
For Company A, the cost is a flat rate of $104 regardless of the number of miles driven. Therefore, the inequality is simply:
104 < 65 + 0.60m
We can simplify this inequality by subtracting 65 from both sides:
39 < 0.60m
To isolate m, we can divide both sides by 0.60:
65 < m
So, Company A will charge less than Company B for any mileage greater than 65 miles. If Rachel plans to drive more than 65 miles, she should choose Company A to save money. However, if she plans to drive less than 65 miles, Company B may be the cheaper option.
from a population of 600 elements, a sample of 100 elements is selected. it is known that the variance of the population is 900. find the approximate standard error of the mean.
The approximate standard error of the mean is 3.
Here is how to find the approximate standard error of the mean from a population of 600 elements, where a sample of 100 elements is selected, and it is known that the variance of the population is 900.
Determine the sample size n, which is 100
Find the population variance, which is 900.
Compute the population standard deviation, which is the square root of the variance, as follows:
σ = √900σ
= 30
Compute the standard error of the mean as follows:
SEM = σ/√nSEM
= 30/√100SEM
= 3
The standard error of the mean (SEM) can be calculated using the formula:
SEM = σ / √n
where σ represents the population standard deviation, and n represents the sample size. In this case, we know that the population variance is 900.
To find the standard deviation, take the square root of the variance:
σ = √900 = 30
Now, we can plug in the values into the formula:
SEM = 30 / √100
SEM = 30 / 10
SEM = 3
The approximate standard error of the mean for this sample is 3.
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in the year 2015, the timss ranking and average scores of math achievement for fourth-graders were lowest for: korea. russia. kuwait. iran.
In the year 2015, the times ranking and average scores of math achievement for fourth-graders were option (c) Kuwait
According to the Trends in International Mathematics and Science Study (TIMSS) report for 2015, the lowest ranking and average scores of math achievement for fourth-graders were found in Kuwait. Kuwait ranked 48th out of the 49 countries that participated in the study.
It's worth noting that while Korea, Russia, and Iran also participated in the study, they did not have the lowest ranking or scores. Korea, in fact, ranked 5th overall with an average math score of 608, while Russia ranked 12th with an average math score of 544, and Iran ranked 24th with an average math score of 474.
The reasons for Kuwait's low ranking and scores in math achievement could be due to various factors, such as inadequate resources for education, lack of effective teaching methods, or low investment in STEM (science, technology, engineering, and mathematics) education.
Therefore, the correct option is (c) Kuwait
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with a rancher is to buy steers at each and cows at each. if the number of steers and the number of cows are both positive integers, then:
The solution is that the rancher should buy 26 steers and 13 cows
Let's start by setting up a system of equations based on the given information.
The total amount of money the rancher has is $1000, and they plan to buy steers at $25 each and cows at $26 each. Let's say they buy s steers and c cows, then we have:
$25s + $26c = $1000 (Total amount spent)
We also know that s and c are both positive integers (whole numbers greater than zero).
We can solve for s and c by using some algebraic techniques. First, let's simplify the equation by dividing both sides by $1 to get rid of the dollar sign
25s + 26c = 1000
Now we can use a technique called "integer division" to solve for s and c. We'll start by assuming that the rancher buys all steers and no cows, which gives us
25s + 26(0) = 1000
25s = 1000
s = 40
So the rancher could buy 40 steers with their $1000. However, we need to account for the fact that they can also buy cows. Let's say they buy c cows, then we can set up another equation based on the total number of animals they buy
s + c = Total number of animals
Since we don't know the total number of animals, we'll leave that as a variable for now. We can use this equation to solve for c in terms of s:
c = Total number of animals - s
Now we can substitute this expression for c into the first equation:
25s + 26c = 1000
25s + 26(Total number of animals - s) = 1000
25s + 26Total number of animals - 26s = 1000
-Taking 25s to the right side
26Total number of animals = 1000 + s
dividing both sides by 26
Total number of animals = 38 + s/26
So the total number of animals must be a whole number, which means that s/26 must be a positive integer. We can try different values of s to see which ones work
If s = 26, then s/26 = 1 and Total number of animals = 39. This gives us c = 39 - 26 = 13, so the rancher would buy 26 steers and 13 cows.
If s = 52, then s/26 = 2 and Total number of animals = 40. This gives us c = 40 - 52 = -12, which doesn't make sense since c must be a positive integer.
If s = 78, then s/26 = 3 and Total number of animals = 41. This gives us c = 41 - 78 = -37, which again doesn't make sense.
So the only solution that works is when the rancher buys 26 steers and 13 cows. This would cost
25(26) + 26(13) = $650 + $338 = $988
So the rancher would have $12 left over from their $1000 budget.
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The given question is incomplete, the complete question is:
With $1000 a rancher is to buy steers at $25 each and cows at $26 each. If the number of steers s and the number of cows c are both positive integers, what is the solution?
In this Magic Square, every row, column, and diagonal adds to 0. Copy and complete this square
A Magic Square is a square grid of numbers in which the sum of every row, column, and diagonal is equal.
One way to approach this is to start with the center number and work outwards.
Since every row, column, and diagonal adds up to 0, the center number must be 0.
From there, we can fill in the rest of the numbers systematically.
For example, in the top row, we need to find two numbers that add up to 0.
We could choose 1 and -1, or 2 and -2, or any other pair of opposite numbers.
Let's choose 1 and -1 for the top row.
Then, we can fill in the bottom row with the same numbers in reverse order.
Next, we can fill in the left and right columns.
Since every column must add up to 0, we need to choose numbers that add up to 0 in each column.
Let's choose 3 and -3 for the left column, and 2 and -2 for the right column.
Finally, we can fill in the diagonals with the remaining numbers.
In this particular Magic Square, every row, column, and diagonal adds up to 0.
We can choose 4 and -4 for one diagonal, and 5 and -5 for the other diagonal.
By following this systematic approach, we can complete the Magic Square with the following numbers:
3 2 -1
0 0 0
-3 -2 1
This Magic Square is a great example of the fascinating patterns and mathematical properties that can be found in numbers. It is also a fun puzzle to solve and can provide hours of entertainment for people of all ages.
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State what each variable may be so that the equation is true. You must have at least one negative number. Explain how you chose the values for a and b. 2^a • 2^b = 2^0
Answer:
[tex] {2}^{a} \times {2}^{b} = {2}^{a + b} = {2}^{0} [/tex]
From this, a + b = 0, meaning a and b are additive inverses of each other.
As an example, let a = 1, so b = -1.
HELP ASAP A hockey season ticket holder pays $136.98 for her tickets plus $2.50 for a program each game. A second person pays $17.72 for a ticket to every game, but doesn't buy programs. In how many games will they have paid the same amount?
Therefore, they will have paid the same amount after attending 9 games.
What is equation?An equation is a mathematical statement that expresses the equality between two expressions or values. It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, as well as other mathematical functions. An equation typically includes an equal sign (=) that indicates that the two sides of the equation are equal in value.
Here,
Let's start by setting up an equation to represent the total cost for each person after attending a certain number of games:
For the season ticket holder: Total Cost = 136.98 + 2.5x, where x is the number of games attended
For the second person: Total Cost = 17.72x
To find the number of games at which they will have paid the same amount, we can set the two equations equal to each other and solve for x:
136.98 + 2.5x = 17.72x
136.98 = 15.22x
x = 9
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Hello everyone, can you help me please?
-where n is an integer,
-Which of the following is the result of the process?
Answer:
A) -1
Step-by-step explanation:
[tex] \dfrac{i^{2n - 3} \times i^{3n - 1}}{i^{5n - 2}} = [/tex]
[tex] = i^{2n - 3 + 3n - 1 - (5n - 2)} [/tex]
[tex] = i^{2n - 3 + 3n - 1 - 5n + 2} [/tex]
[tex] = i^{-2} [/tex]
[tex] = \dfrac{1}{i^2} [/tex]
[tex] = \dfrac{1}{-1} [/tex]
[tex] = -1 [/tex]
Find the area of the parallelogram. 8 cm 9 cm 24 cm
Answer:
we know the area of the parallelogram is given by a=b×h
An oil tanker is approximately 1500 feet long. How far would 8500 oil tankers span if you placed them end to end?
Answer:
12,750,000ft
Step-by-step explanation:
1,500 * 8,500 = 12,750,000
factor the polynomial, please.
1. 2p^2+7p-6
2. -5v^2+31v-6
3. -6v^2-11v-4
explain how to take a systematic sample of 100 companies from the 1,803 companies that are members of an industry trade association. state important numerical values used in the process.
To take a systematic sample of 100 companies from a population of 1,803 companies, determine the sampling interval (k) which is N/n, choose a random starting point between 1 and k, and select every kth company until 100 companies are sampled.
To take a systematic sample of 100 companies from the 1,803 companies that are members of an industry trade association, follow these steps
Determine the sampling interval (k), which is the number of companies in the population divided by the desired sample size. In this case, k = 1803/100 = 18.03. Round this number up or down to the nearest whole number based on your sampling preferences.
Choose a random starting point between 1 and k. For example, you could randomly select a number between 1 and 18.
From the starting point, select every kth company in the list of members until you have 100 companies. For example, if the starting point is 4, you would select companies 4, 22, 40, 58, 76, 94, 112, and so on until you reach 100 companies.
Important numerical values used in this process are:
Population size (N) = 1,803 companies
Desired sample size (n) = 100 companies
Sampling interval (k) = N/n = 1803/100 = 18.03
Random starting point (any number between 1 and k, depending on sampling preference)
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Three ballet dancers are positioned on stage. Max is 2 feet straight behind Kenji and 4 feet directly left of Lindsey. When the music begins, Max twirls to Lindsey's position, then leaps to Kenji's position, and finally walks back to his original position. How far did Max travel? If necessary, round to the nearest tenth.
The total distance traveled by Max is approximately 2 + 4.5 + 4.5 = 11 feet/.
What is Cartesian plane?
The Cartesian plane, also known as the coordinate plane, is a two-dimensional plane that is used to represent and graph mathematical equations and functions. The plane is named after the French mathematician and philosopher René Descartes, who developed the concept in the 17th century.
We can use the Pythagorean theorem to find the distance between Max and Kenji, and between Max and Lindsey. Let's assume that the stage is a coordinate plane, with Max's original position at (0,0), Kenji's position at (0,2), and Lindsey's position at (-4,0).
The distance between Max and Kenji is the length of the hypotenuse of a right triangle with legs of length 2 and 4. Using the Pythagorean theorem, we have:
sqrt(2² + 4²) = sqrt(20) ≈ 4.5
So the distance between Max and Kenji is approximately 4.5 feet.
The distance between Max and Lindsey is the length of the hypotenuse of a right triangle with legs of length 4 and 2. Using the Pythagorean theorem, we have:
sqrt(4² + 2²) = sqrt(20) ≈ 4.5
So the distance between Max and Lindsey is also approximately 4.5 feet.
To find the total distance traveled by Max, we can add up the distances traveled during each part of his dance:
Twirling from Lindsey's position to Kenji's position: This distance is the same as the distance between Lindsey and Kenji, which is 2 feet.
Leaping from Kenji's position back to Max's original position: This distance is the same as the distance between Max and Kenji, which we found to be approximately 4.5 feet.
Walking from Max's final position back to his original position: This distance is the same as the distance between Max and Lindsey, which we also found to be approximately 4.5 feet.
So the total distance traveled by Max is approximately 2 + 4.5 + 4.5 = 11 feet. Rounded to the nearest tenth, this is 11.0 feet.
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m∠CBD=6x+27 ∘ so you have to find C B D with this
For the given triangle, m∠CBD = 63 degrees.
What is triangle?
A triangle is a two-dimensional geometric shape with three sides and three angles. It is one of the basic shapes in geometry and is formed by connecting three non-collinear points with line segments.
In a triangle, the sum of the angles is always 180 degrees.
So, we can write:
m∠ABD = m∠ABC + m∠CBD
Substituting the given values, we get:
96 = (7x - 9) + (6x + 27)
Simplifying the equation:
96 = 13x + 18
Subtracting 18 from both sides:
78 = 13x
Dividing by 13:
x = 6
Therefore:
m∠ABD = 96 degrees
m∠CBD = 6x + 27 = 6(6) + 27 = 63 degrees
m∠ABC = 7x - 9 = 7(6) - 9 = 33 degrees
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Arianna measured a boarding school and made a scale drawing. The scale of the drawing
was 3 millimeters = 9 meters. What is the scale factor of the drawing?
() Simplify your answer and write it as a fraction.
Videa
Answer:
The scale factor would be 3,000
Step-by-step explanation:
3(3000) = 9000 millimeters
9000 x [tex]\frac{1}{1000}[/tex] = 9 to convert to meters
Helping in the name of Jesus.
example: marlon jogs two miles to the park in 25 minutes, turns around, and takes another 55 minutes to walk the same path back to his house. what is the average speed of the round-trip?
The average speed of the round-trip for same path back to his house is given by 3 miles per hour.
The mean value of a body's speed over a period of time is its average speed. As a moving body's speed is not constant over time and fluctuates, the average speed formula is required. The values of total time and total distance travelled may be employed even when the speed varies, and with the aid of the average speed formula, we can identify a single number that sums up the whole motion.
So the average speed is simply: [tex]\frac{distance}{time}[/tex]
In case, the total time = 25 minutes + 55 minutes
which is a total of 80 minutes, or 1.33 hours.
The total distance traveled is two miles + two miles, since he jogged two miles to the park, and then he turns around and walks the same path.
So in total he traveled 4 miles.
Plugging this in to the formula gives you the equation:
[tex]v = \frac{d}{t} \\= \frac{4\ miles}{4/3 \ hour} \\= \frac{4 \ miles}{1} * \frac{3}{4} hours\\= 3mph[/tex]
Therefore, average speed of the round-trip is 3 mph.
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1) Evaluate. Help me plsss
The logarithm expression is approximately 4.6.
How to evaluate the expression with which logarithmic identity?To evaluate 9㏒₉⁵ - ㏒₃3⁵, we can use the logarithmic property that states:
㏒ₐ(b^c) = c x ㏒ₐ(b)
Using this property, we can simplify the expression as follows:
9㏒₉⁵ - ㏒₃3⁵
= ㏒₉(95^9) - ㏒₃(35)
= ㏒₉(1423892081) - ㏒₃(35)
We can evaluate these logarithmic terms using the change of base formula, which states:
㏒ₐ(b) = log(b) / log(a)
Using this formula, we get:
㏒₉(1423892081) = 8.032
㏒₃(35) = 3.432
Substituting these values back into the expression, we get:
9㏒₉⁵ - ㏒₃3⁵ = 8.032 - 3.432
= 4.6
The above answer is in response to the question below;
Evaluate
9㏒₉⁵ - ㏒₃3⁵
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Mack, Nina, Samuel, and Tara play a board game. Each of them is equally likely to go first in the game. Also, each of them is equally likely to win the game. Winning the game is independent of going first. What is the probability Samuel goes first and wins the game?
A0
B0.0625
C0.25
D0.5
The probability that Samuel goes first and wins the game is 1/16 (0.0625). The Option B is correct.
What is the probability in this case?The probability that Samuel goes first is 1/4, since there are four players and each is equally likely to go first.
The probability that Samuel wins the game, given that he is playing, is also 1/4, since each player is equally likely to win and there are four players in total.
To find the probability that Samuel goes first and wins the game, we need to multiply these two probabilities:
P(Samuel goes first and wins) = P(Samuel goes first) x P(Samuel wins | Samuel is playing)
= (1/4) x (1/4)
= 1/16
= 0.0625
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There is a screenshot below showing my question. Please help asap, will name branliest plus its 10 points :)
Answer:
h = 9km
Step-by-step explanation:
area of a trapezoid= ½ x (a+b) x h
117 = (2+2+11 +11) / 2 x h
h = 117 / 26÷2
h = 9km
2. a college admissions director wishes to estimate the mean age of all students currently enrolled. in a random sample of 20 students, the mean age is found to be 22.9 years. from past studies, the standard deviation is known to be 1.5 years and the population is normally distributed. (a) (2 points) construct a 90% confidence interval of the population mean age. then calculate a 95% confidence interval, and a 99% confidence interval. (b) (2 point) construct a 90% confidence interval for this case, assuming that the given standard deviation of 1.5 years came from the sample instead of the population. (c) (1 point) suppose that the distribution of the population is not specified. do we have enough information to form a confidence interval in that case?
a) For a 90% confidence interval [22.25, 23.55].
For a 95% confidence interval [22.10, 23.70].
For a 99% confidence interval [21.97, 23.83].
b) For a 90% confidence interval [22.25, 23.55].
a) To construct a confidence interval for the population mean age, we can use the formula: CI = x* ± tα/2 * (σ / sqrt(n)), where x* is the sample mean age, σ is the population standard deviation, n is the sample size, and tα/2 is the critical value of the t-distribution with n-1 degrees of freedom and a given level of confidence α/2.
For a 90% confidence interval, α = 0.1 and tα/2 = 1.725, so the interval is: 22.9 ± 1.725 * (1.5 / sqrt(20)) = [22.25, 23.55].
For a 95% confidence interval, α = 0.05 and tα/2 = 2.093, so the interval is: 22.9 ± 2.093 * (1.5 / sqrt(20)) = [22.10, 23.70].
For a 99% confidence interval, α = 0.01 and tα/2 = 2.861, so the interval is: 22.9 ± 2.861 * (1.5 / sqrt(20)) = [21.97, 23.83].
b) If the given standard deviation of 1.5 years came from the sample instead of the population, we need to use a t-distribution with n-1 degrees of freedom to construct the interval. The formula is the same as before, but we replace σ with s, the sample standard deviation.
For a 90% confidence interval, the critical value is still 1.725, so the interval is: 22.9 ± 1.725 * (1.5 / sqrt(20)) = [22.25, 23.55].
c) If the distribution of the population is not specified, we can still form a confidence interval if we have a large enough sample size (typically, n >= 30) due to the central limit theorem. In this case, we have n = 20, so we may not have enough information to form a confidence interval if we cannot assume the population is normally distributed.
To know more on central limit theorem
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Answer:
The answer is B
Step-by-step explanation:
These are triangles are similar and because of that:
x/6 = (x+2.5)/(6+4)
x/6 = x/10 + 0.25
x = 6x/10 + 1.5
4x/10 = 1.5
4x = 15
x = 3.75