Based upon the central limit theorem, what is the standard deviation of a sample distribution? The sample distribution standard deviation is the population standard deviation divided by the square roo
Answers
The standard deviation of a sample distribution, according to the central limit theorem, is equal to the population standard deviation divided by the square root of the sample size.
The central limit theorem states that when independent random variables are added, their sum tends toward a normal distribution, regardless of the shape of the original variables' distribution. This holds true under certain conditions, such as a sufficiently large sample size.
To calculate the standard deviation of a sample distribution, we divide the population standard deviation by the square root of the sample size. This adjustment accounts for the fact that as the sample size increases, the variability of the sample means decreases.
In summary, the standard deviation of a sample distribution is obtained by dividing the population standard deviation by the square root of the sample size. This relationship is based on the central limit theorem, which allows us to make inferences about a population based on a sample.
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Related Questions
2-simplifica
1)x²-5x-16
x+2=
2)6an²-3b²n²
b4-4ab²+4a²=
3)4x²-4xy+y²
5y-10x
4)n+1-n³-n²
n³-n-2n²+2=
5)17x³y4z6
34x7y8z10=
6)12a²b³
60a³b5x6=
Answers
1. x² - 5x - 16 can be written as (x - 8)(x + 2).
2. 6an² - 3b²n² = n²(6a - 3b²).
3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².
4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).
5. 17x³y⁴z⁶ = (x²y²z³)².
6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.
Let's simplify the given expressions:
Simplifying x² - 5x - 16:
To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.
Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).
Simplifying 6an² - 3b²n²:
To simplify this expression, we can factor out the common term n² from both terms:
6an² - 3b²n² = n²(6a - 3b²).
Simplifying 4x² - 4xy + y²:
This expression represents a perfect square trinomial, which can be factored as (2x - y)².
Simplifying n + 1 - n³ - n²:
Rearranging the terms, we have -n³ - n² + n + 1.
Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).
Simplifying 17x³y⁴z⁶:
To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:
17x³y⁴z⁶ = (x²y²z³)².
Simplifying 12a²b³:
To simplify this expression, we can multiply the exponents of a and b with the given expression:
12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.
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Write the equations in cylindrical coordinates.
9x2 − 3x + 9y2 + z2 = 9
// I keep getting z^2=9-3r(3r-cos (theta))
Answers
The equation \(9x^2 − 3x + 9y^2 + z^2 = 9\) can be written in cylindrical coordinates as \(z^2\) = 9 - 3r(3r - cos(theta)).
to express the equation in cylindrical coordinates, we need to substitute the Cartesian variables (x, y, z) with their corresponding cylindrical variables (r, theta, z).
In cylindrical coordinates, the relationship between Cartesian and cylindrical variables is given by:
x = rcos(theta)
y = rsin(theta)
z = z
Substituting these expressions into the equation, we have:
\(9(rcos(theta))^2 -3(rcos(theta)) + 9(rsin(theta))^2 + z^2\) = 9
Simplifying the equation, we get:
\(9r^2cos^2(theta) - 3rcos(theta) + 9r^2sin^2(theta) + z^2\)= 9
Using the trigonometric identity \(cos^2(theta) + sin^2(theta)\) = 1, we can further simplify the equation to:
\(9r^2 + z^2 - 3rcos(theta)\) = 9
Finally, rearranging the terms, we obtain:
\(z^2 = 9 - 3r(3r - cos(theta))\)
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select all the quations that would be correct with fraction 2/9 81x_=18
900x_=200
72x_=16
450x_=100
Answers
The equations that would be correct with fraction 2/9 are:
81*x=18
45*x=100
900*c=200
How can the fractions be known?Based on the given equation from the question, it can be seen that the fraction that is needed to complete the X is required, that will give the correct answer to each of the equation.
From the question, we can see that if we put X= 2/9 into the space above, we will have the correct solution. which is been performed below.
81*2/9=18
45*2/9=100
900*2/9=200
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The weight of chocolate bars from a particular chocolate factory has a mean of 8 ounces with a standard deviation of 0. 1 ounces. What is the z-score corresponding to a weight of 8. 17 ounces? What percent of chocolate bars weigh less than 8. 17 ounces. Show and explain your work
Answers
95.54% of the chocolate bars at the factory weigh less than 8. 17 ounces
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
z score shows by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean)/standard deviation
Given that mean = 8, standard deviation = 0.1
For x < 8.17 ounces:
z = (8.17 - 8) / 0.1 = 1.7
From the normal distribution table:
P(z < 1.7) = 0.9554 = 95.54%
The probability that the chocolate bars weigh less than 8. 17 ounces is 95.54%
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Please answer fast!
Evaluate 2(n+3) if n= -14
Answers
Answer:
-22
Step-by-step explanation:
2(n + 3) when n = -14
~Substitute
2(-14 + 3)
~Add
2(-11)
~Multiply
-22
Best of Luck!
For a given calendar year, Mrs. Terry pays the first $2,500 of her medical expenses plus 20% of all medical expenses
over $2,500. In the equation shown, y represents the amount that she pays when x is the total dollar amount of her
medical expenses for the year.
V = 2,500 + 0.2 (x - 2,500)
for x ≥ 2,500
If y = $2,632 for this year, what is x, Mrs. Terry's total medical expenses?
Answers
Using proportions, Mrs. Terry total medical expenses are of $2,526.4.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, her expenses are divided as follows:
All of the first $2,500.20% of the remaining 2632 - 2500 = $132.Hence her total medical expenses are given as follows:
2500 + 0.2 x 132 = $2,526.4.
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I need help with finding 12x+3y=-3 on a graph.
Answers
Let's graph the equation
\(12x+3y=-3\)Notice that this equation corresponds to a line.
1. First, let's clear y, so we can get the equation of the line in the slope-intercept form:
\(\begin{gathered} 12x+3y=-3 \\ \rightarrow3y=-12x-3 \\ \rightarrow y=-4x-1 \end{gathered}\)This way, he equation of the line in the slope-intercept form is
\(y=-4x-1\)2. Now, we have to expose two points contained in the line. To do so, we give x any value we want and we calculate the corresponding y value.
Let's do this with x = 0 and x = 1
\(\begin{gathered} y=-4x-1 \\ \\ x=0\Rightarrow y=-4(0)-1\rightarrow y=-1 \\ \text{This way, the point} \\ (0,-1) \\ \text{Belongs to the line} \\ \\ x=1\Rightarrow y=-4(1)-1\rightarrow y=-5 \\ \text{This way, the point } \\ (1,-5) \\ \text{belongs to the line} \end{gathered}\)3. Put those points in the cartesian plane:
4. Draw a straight line that passes through both points. This will be the graph of the line
2(x-3)+7 as a verbal expression
Answers
Answer:
Two, times a number minus three, plus seven.
Hope this is what you were looking for.
an organization will give a prize to a local artist. the artist will be randomly chosen from among 7 painters, 4 sculptors, and photographers. what is the probability that the artist chosen will be a painter or a 5 photographer? write your answer as a fraction.
Answers
The probability that the artist chosen will be a painter or a photographer is 3/4
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
To solve this exercise the formula and the procedure that we have to use for probability is:
probability= (achieving success / possible outcomes)
Achieving success = 7 painters + 5 photographer = 12
Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16
Applying the formula to calculate the probability we get:
probability= (achieving success / possible outcomes)
probability= 12/16
Simplifying:
probability= 3/4
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3x + 1,2x, 3x - 7 If the value of x is 3, write down 3the first three terms?
Answers
Answer:
10 , 6 ,2
Step-by-step explanation:
x = 3
3x +1 = 3*3 + 1 = 9 + 1 = 10
2x = 2*3 = 6
3x - 7 = 3*3 - 7 = 9 - 7 = 2
Find the dependent values if the independent values are 2 and 4
Answers
Answer:
it is very easy for even a third grader 2x4=8
What is the solution to this system of equations?
y=1/3x+4
y=1/6x+3
Answers
Help which ones are it ?
Answers
Answer:
A, B, and D
Step-by-step explanation:
Help please.
Simplify: 5i/ 3 + 2i
Answers
Answer:
10+15i/13
Step-by-step explanation:
This question is about complex numbers.
so,
in this type of questions we have to multiply this fraction by the conjugate of the denominator
conjugate of the denominator is 3-2i
1) 5i(3-2i)/(3+2i)(3-2i)
2) 15i-10i^2/9-4i^2 ( we know that i^2 = -1 )
3) 15i+10/9+4
4) 15i+10 / 13
-3x + 14 = 26
pls answer asap, i will give brainliest award also please answer with step-by-step explanation!
Answers
Answer:15
Step-by-step explanation:it just is the answer
The coefficient part of a number
written in scientific notation is
between which numbers?
A. 1 and 10
B. -1 and -10
C. Both A and B
Answers
Answer:
A
There are two parts to a number written in Scientific Notation. The first is the coefficient and the second part is a power of ten. In order for the number to be correctly written it has to be between 1 and 10.
The coefficient part of the scientific notation is required.
The correct option is A. 1 and 10
Scientific notation is written in the form of
\(m\times 10^n\)
The coefficient part (m) is written as absolute value between 1 and 10.
n is the exponent and an integer.
Let us write a negative number in scientific form.
\(-53000\\ =-(m\times 10^n)\\ =-(5.3\times 10^{5})\\ =-5.3\times 10^5\)
So, the coefficient part is a number that lies in \(1\leq m<10\)
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What is the equation of a line, in point- slope form, that passes through (5, −3)and has a slope of 2/3?
A. y - 5 = 2/3(x + 3)
B. y + 5 = 2/3 (x - 3)
C. y + 3 = 2/3 (x - 5)
D. y - 3 = 2/3 (x + 5)
Answers
Ava borrowed some money from her friend in order to help buy a new video game system. Ava agreed to pay back $2 per week and after 5 weeks, Ava still owe her friend$10
Answers
Answer:70
Step-by-step explanation:
Answer: -2t+20
Step-by-step explanation:
I just did it
sarah is playing a game in which she rolls a number cube 20 times the results are recorded in the chart below. what is the experimental probability of rolling a 1 or a 2? answers 0.3, 0.45, 0.65, 1.25.
Answers
The experimental probability of rolling a 1 or a 2 is 0.2.
Hence, Option A is correct.
We know that,
The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.
In this case,
The event is rolling a 1 or a 3,
Which occurred ⇒ 3 + 1
= 4 times.
Given that there are total number of trials = 20.
Therefore,
The experimental probability of rolling a 1 or a 3 = 4/20,
= 1/5
= 0.2
Hence, the required probability is 0.2.
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The complete question is:
Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?
Number on cube:1,2,3,4,5,6
Number of times event occurs:3,6,1,5,3,2
A.0.2
B.0.3
C.0.6
D.0.83
11)
If y varies directly as and y= 10 when x = 2, then what is the value of y when x = 4?
A)
2.5
B)
20
C)
40
D)
80
Answers
If x goes from 2 to 4 it was multiplied by 2. you would do the same to the y. 10*2=20
Answer:
B)20
Step-by-step explanation:
y=10 when x=2 and varies directly so y=5*x
when x=4 then y=5*x=5*4=20
helppppppppppp me pleaseeee
Answers
You are selling lemonade for $1.50, a bag of kettle corn for $3, and a hot dog for $2.50 at a fair. Write and simplify an expression for the amount of money you receive when p people buy one of each item
Answers
Answer:
1.5p + 3p + 2.5p
Step-by-step explanation:
This expression, 1.5p + 3p + 2.5p, will represent the amount of money received when p people buy one of each food item.
Since the price of each is the coefficient for p, this will represent how much money will be gained from each food item. All 3 terms will be added together to represent the total amount of money gained from selling all 3 items.
You know that the average college student eats 0.75 pounds of food at lunch. If the standard deviation is 0.2 pounds of food, then what is the total amount of food that a cafeteria should have on hand to be 90 percent confident that it will not run out of food when feeding 50 college students?
Answers
Answer: $53.95
Step-by-step explanation:
Given: \(\mu=0.75\) pounds
\(\sigma= 0.2\) pounds
n= 50
Two tailed critical z-value for 90% confidence level = 1.645
Let x be the total amount of food that a cafeteria should have on hand to be 90 percent confident that it will not run out of food .
z-score = \(\dfrac{x-\mu}{\sigma}\) \(=\dfrac{x-0.75}{0.2}\)
Then, \(\dfrac{x-0.75}{0.2}=1.645\)
\(x-0.75=1.645\times0.2\\\\\Riightarrow\ x-0.75=0.329\\\\\Rightarrow\ x= 0.329+0.75\\\\\Rightarrow\ x= 1.079\)
Foe 50 students, total amount of food = 1.079 x 50 = $53.95
hence, the cafeteria should have food of amount $53.95 so that it is be 90 percent confident that it will not run out of food.
What’s the sum of the number m and the number after it?
Answers
Answer:
wat number put the value there
The required sum of the number m and the number after it 2m + 1.
Given that,
To determine the sum of the number m and the number after it.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Let the number m and the number after m is m+1
Now the sum = m + m + 1
= 2m + 1
Thus, the required sum of the number m and the number after it 2m + 1.
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a manager receives 9 applications for a specific position. she wants to narrow it down to 4. in how many ways can she rank 4 applications?
Answers
The number of ways that can she rank 9 applications should be 126.
What is the definition of combination in math?
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.
Calculation of the number of ways:
Since A manager receives 9 applications for a specific position. She wants to narrow it down to 4.
So here we do apply the permutation here:
9*8*7*6/ 4*3*2
=126
Hence, The number of ways that can she rank 4 applications should be 126
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explain the difference between using the tangent ratio to solve for a missing angle in a right triangle versus using the cotangent ratio
Answers
The tangent ratio is used to solve for a missing angle in a right triangle by dividing the length of the side opposite the angle by the length of the side adjacent to the angle.
Using the tangent ratio, we can find a missing angle in a right triangle by taking the inverse tangent (arctan) of the ratio. For example, if we know the length of the side opposite an angle and the length of the side adjacent to the angle, we can use the tangent ratio to find the value of the angle.
Using the cotangent ratio, we can also find a missing angle in a right triangle by taking the inverse cotangent (arccot) of the ratio. If we know the length of the side adjacent to an angle and the length of the side opposite the angle, we can use the cotangent ratio to find the value of the angle.
The main difference between using the tangent ratio and the cotangent ratio is the order of the sides in the ratio. The tangent ratio involves the opposite side divided by the adjacent side, while the cotangent ratio involves the adjacent side divided by the opposite side.
Both the tangent and cotangent ratios are useful tools for solving right triangles and finding missing angles. The choice between using one or the other depends on the given information and the specific problem at hand.
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A group of people were asked il they had run a red light in the last year. 377
responded yes and 166 responded no. Find the probability that if a person is
chosen at random, they have run a red light in the last year.
Answers
The probability that a person chosen at random has run a red light in the last year is 69.4%.
To find the probability that a person chosen at random has run a red light in the last year, we need to divide the number of people who said "yes" by the total number of people who were asked. In this case, 377 people said "yes" out of a total of 543 people who were asked.
1. Determine the total number of people who responded: 377 (yes) + 166 (no) = 543 people
2. Find the number of people who responded yes (ran a red light): 377 people
So the probability is:
Calculate the probability by dividing the number of people who ran a red light by the total number of people who responded: 377 / 543
377/543
Which simplifies to:
0.694 or 69.4%
Therefore, the probability that a person chosen at random has run a red light in the last year is 69.4%.
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Evaluate 2/3 - 1/6.
1/6
1/2
5/6
1
Answers
Answer:
1/2
Step-by-step explanation:
first find the least. common multiple of the denominators(LCM)
this is 18
18
divide each denominator with the lcm
then multiply the answers you get by the numerators...
e.g2/3. 18÷3×2=12. 1/6. 18/6x1 which is 3
then 12-3 which is 9 over the lcm which is 18
the. simplified form of the answer is
1/2
What is the slope of the line that passes through the points (−5, −8) and (−5, 1)?
Answers
Answer: Undefined
Step-by-step explanation:
Based on the points, I can tell that the line is a vertical line
All vertical lines have an undefine slope
Answer: undefined (0)
Step-by-step explanation:
m= y1-y2/ x1-x2
m= -8-1/-5-(-5)
m= -9/0
m= 0
Kailynn has a bag with an equal number of red, yellow, and blue marbles. She
makes a tree diagram to show the sample space if she randomly selects two
marbles out of the bag.
What is the probability that both marbles selected are different colors?
Answers
Answer:
6/9
Step-by-step explanation:
Probability is the likelihood or occurrence of an event. Probability is the ratio of the total number of possible outcomes to the total outcomes. That is:
Probability = total possible outcomes / total outcomes
From the tree diagram we can see that:
total outcomes = {RR, RY, RB, YR, YY, YB, BR, BY, BB} = 9
getting different colors = {RY, RB, YR, YB, BR, BY} = 6
Therefore, the probability that both marbles selected are different colors = number of different colors / total outcomes
The probability that both marbles selected are different colors = 6 / 9
