The standard deviation of the sampling distribution of the sample mean is equal to the standard deviation of the population (or random variable) divided by the square root of the sample size.
When a random sample of size n is obtained from a population (or a random variable) with a known standard deviation, the sampling distribution of the sample mean refers to the distribution of all possible sample means that could be obtained from samples of the same size. The standard deviation of the sampling distribution of the sample mean is a measure of the variability or spread of these sample means.
The standard deviation of the sampling distribution of the sample mean, often denoted as the standard error, is equal to the population (or random variable) standard deviation divided by the square root of the sample size. Mathematically, it can be represented as σ/√n, where σ represents the standard deviation of the population and n is the sample size.
This relationship can be explained by the concept of the Central Limit Theorem. According to this theorem, as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. The standard deviation of the sampling distribution decreases as the square root of the sample size increases, indicating that larger sample sizes lead to more precise estimates of the population mean.
The standard deviation of the sampling distribution of the sample mean, often denoted as the standard error, is equal to the population (or random variable) standard deviation divided by the square root of the sample size. Mathematically, it can be represented as σ/√n, where σ represents the standard deviation of the population and n is the sample size.
This relationship can be explained by the concept of the Central Limit Theorem. According to this theorem, as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. The standard deviation of the sampling distribution decreases as the square root of the sample size increases, indicating that larger sample sizes lead to more precise estimates of the population mean.
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find x
answer choices
6
7
9
10
8
The answer should be 10
Find (f+g)(x).
f(x) = 1
-
x
g(x) = x^2 + 2x-5
Answer:
(f + g)(x) = x² + x - 4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
f(x) = 1 - x
g(x) = x² + 2x - 5
(f + g)(x) is f(x) + g(x)
Step 2: Solve
Substitute in functions: (f + g)(x) = (1 - x) + (x² + 2x - 5)Combine like terms (x): (f + g)(x) = x² + x - 5 + 1Combine like terms: (f + g)(x) = x² + x - 4PLEASE HELP FAST NEED IT FAST =)
Which pair of triangles demonstrates congruence with the AAS Postulate?
Answer:
B
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
brainliest?
In a lab, Andrew is studying the growth of a particular species of bacteria. The bacteria in the petri dish started at 300. After 2 days he realizes that the number of bacteria is about 480. After another 2 days he realizes that the number of bacteria in the dish is 288 more than what it was two days ago. a.) Give an equation to estimate the amount of bacteria in the dish after every day. b.) At what rate would the bacteria be growing c.) How many days would it take for the bacteria to reach almost 1229. d.) Find the average rate of change between 6 days and the first day
a) The equation to estimate the amount of bacteria in the dish after every day is N = 90t + 210.
b) The coefficient is 90, indicating that the bacteria is growing at a rate of 90 per day.
c) It would take approximately 11.32 days for the bacteria to reach almost 1229.
d) Average rate of change = (N₂ - 300) / (6 - 1)
a) Let's denote the number of bacteria in the dish after a certain number of days as N. We can create an equation to estimate the amount of bacteria in the dish after every day based on the given information.
On the first day, the initial number of bacteria is 300. After 2 days, the number of bacteria is approximately 480. This gives us two data points: (1, 300) and (3, 480).
To find the equation for estimating the number of bacteria, we can use the two-point form of the linear equation:
N - 300 = ((480 - 300) / (3 - 1))(t - 1)
Simplifying the equation, we get:
N = 90t + 210
Therefore, the equation to estimate the amount of bacteria in the dish after every day is N = 90t + 210.
b) The rate at which the bacteria is growing can be determined from the coefficient of t in the equation. In this case, the coefficient is 90, indicating that the bacteria is growing at a rate of 90 per day.
c) We can use the equation N = 90t + 210 to find the number of days it would take for the bacteria to reach almost 1229. We substitute N = 1229 into the equation and solve for t:
1229 = 90t + 210
1019 = 90t
t ≈ 11.32
Therefore, it would take approximately 11.32 days for the bacteria to reach almost 1229.
d) To find the average rate of change between 6 days and the first day, we need to calculate the change in the number of bacteria divided by the change in time:
Average rate of change = (N₂ - N₁) / (t₂ - t₁)
Here, N₁ is the number of bacteria on the first day (300), t₁ is the first day (1), N₂ is the number of bacteria on the sixth day, and t₂ is the sixth day.
Substituting the values into the formula, we get:
Average rate of change = (N₂ - 300) / (6 - 1)
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PLEASE HELPP!!!!
The wingspan of a hawk is the distance from the end of one spread-out wing to the end of the other spread-out wing. A scientist measured the wingspans of a random sample of hawks at a national park. Based on the median wingspan of the sample, the scientist estimates that the median wingspan of all hawks in the national park is 40 inches. Which graph most likely represents the data from the scientist's sample?
Answer:
D)
Step-by-step explanation:
It looks like the most sense
Write an expression that can be used to find the length of JH and an expression that can be used to find the length of GJ.
Answer: JH = 9 sin(35)
not sure about GH...
Step-by-step explanation:
The ratio of opposite side of the triangle hypotenuse side of triangle is equal to sine of angle.
The expression required to fine the length of GJ is,
[tex]\sin 35=\dfrac{GJ}{9}\\[/tex]
The length of the [tex]GJ[/tex] is 5.162 units.
What is right angle triangle?A right angle triangle is the triangle in which measure of one of the angle is equal to the 90 degrees.
The ratio of opposite side of the triangle hypotenuse side of triangle is equal to sine of angle.
Given information-
In the given triangle shown in the figure,
[tex]\angle JGH=35[/tex]
The angle [tex]\angle HJG[/tex] is right angle, which is equal to the 90 degrees.
As the sum of all the angles of a triangle is equal to the 180 degrees. Thus,
[tex]\angle JGH+\angle HJG+\angle GHJ=180\\[/tex]
Put the values,
[tex]35+90+\angle GHJ=180\\125+\angle GHJ=180\\\angle GHJ=180-125\\\angle GHJ=55[/tex]
In the given triangle, the side [tex]GJ[/tex] is the opposite side of the triangle and [tex]GH[/tex] is the hypotenuse side of the triangle.
Thus the length of the [tex]GJ[/tex] for the right triangle can be given as,
[tex]\sin 35=\dfrac{GJ}{9}\\[/tex]
This is the required expression,
[tex]GJ=\sin 35\times9\\GJ=0.574\times9\\GJ=5.162[/tex]
Thus the length of the [tex]GJ[/tex]5.162 units.
The expression required to fine the length of GJ is,
[tex]\sin 35=\dfrac{GJ}{9}\\[/tex]
The length of the [tex]GJ[/tex]5.162 units.
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Find the equation for the
following parabola.
Focus (3, 4)
Directrix y = 2
A. (x-3)2 = 2(y-2.5)
B. (x-3)2 = 4(y-3)
C. (x-3)2 = (y-4)
D. (y-3)2 = 4(x-3)
Option A is correct.The equation for the parabola is A.(x - 3)^2 = 2(y - 2.5)
The equation for a parabola with a focus (h, k) and a directrix y = a can be expressed as:
(x - h)^2 = 4a(y - k)
The focus is (3, 4) and the directrix is y = 2, we can substitute these values into the equation:
(x - 3)^2 = 4(2)(y - 4)
Simplifying:
(x - 3)^2 = 8(y - 4)
The correct equation for the parabola is:
(x - 3)^2 = 8(y - 4)
Therefore, the answer is option A. (x - 3)^2 = 2(y - 2.5)
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what is the answer someone help me!!!
Answer:
14.4in so your radius is your third answer
Good art is art that allows you to enter it from a variety of angles and to
emerge with a variety of views."" what is you insights about this quotes?
Answer:
Step-by-step explanation:
My insight on this quote is that a good piece of art can tell various stories. Maybe there are various characters in the art and each on shows different actions and emotions. Or maybe the art is abstract and the emotions that it triggers in a person can tell a story all on its own. In a way these various angles are the different ways that the art makes us feels that allows us to view it in such a way. Yet these views can change if we look at the art in a different perspective.
Which of the following statistical information about the data is calculated by the Column Statistics tool? Select the two correct answers ,Threshold calculation,Date analysis,Regression analysis,Median calculation
The correct answer is: Median calculation and Threshold calculation.
Median calculation: The Column Statistics tool can calculate the median of a dataset. The median is the middle value in a sorted dataset. It is a measure of central tendency that divides the data into two equal halves. Calculating the median can provide insights into the central value of a dataset and is less sensitive to extreme values compared to other measures like the mean.
Threshold calculation: The Column Statistics tool can calculate thresholds or cutoff points based on the data. These thresholds define certain conditions or ranges in the data. For example, you can set a threshold to identify data points above a certain value as outliers or flag data points that fall within a specific range. Threshold calculations can be useful for data cleansing, anomaly detection, or creating categorical variables based on certain conditions.
The other options, Date analysis and Regression analysis, are not typically calculated by the Column Statistics tool. Date analysis involves examining patterns and trends related to dates or time, which may require specialized techniques such as time series analysis or date-specific functions. Regression analysis is a statistical technique used to model the relationship between variables and requires more advanced tools or methods beyond basic column statistics.
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Write the first four terms of the sequence{an}defined by the following recurrence relation.
an+1=2a2n-1;a1=0
The first 4-terms of sequence {aₙ} defined by recurrence-relation : aₙ₊₁ = 2aₙ²-1; a₁ = 0 are 0, -1, 1 and 1.
To find the first four terms of the sequence {aₙ} defined by the recurrence relation aₙ₊₁ = 2aₙ² - 1, with the initial-condition a₁ = 0, we apply the recurrence relation,
Starting with a₁ = 0, we can find the subsequent terms as follows:
⇒ a₂ = 2a₁² - 1 = 2(0)² - 1 = -1
⇒ a₃ = 2a₂² - 1 = 2(-1)² - 1 = 1
⇒ a₄ = 2a₃² - 1 = 2(1)² - 1 = 1
Therefore, the first four terms of the sequence are : a₁ = 0, a₂ = -1, a₃ = 1
and a₄ = 1.
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The given question is incomplete, the complete question is
Write the first four terms of the sequence {aₙ} defined by the following recurrence relation.
aₙ₊₁ = 2aₙ²-1; a₁ = 0.
you are part of a group of tourists in Yosemite National Park who want to rent bikes to ride around the valley floor. you arrive at the bicycle rental shop and see that there are two different rental plans:
Plan A: $15 initial fee, plus $2 per hour
Plan B: $5 initial fee, plus $4 per hour
The group doesn't know which plan is best for each person, but you volunteer to use your algebra skills to analyze the situation. Define two variables, write and solve a system of equations to answer the following questions.
a) For which people is plan A best? For which people is plan B best?
b) When are the costs of the two plans the same and what is the cost?
Answer:
a
Step-by-step explanation:
Question 3
1 pts
meters, will the period of a pendulum be 3 seconds? Use the formulas T = a[.where the proportionality constant,
The acceleration of gravity on Mars is 3.69 For what length
2 TT
a. depends on the acceleration of gravity: a =
vg
0.92 meters
0.84 meters
0.66 meters
find the area of the rectangle PLUM khan academy
Answer:
Length x Breadth
Step-by-step explanation:
Let x = 9a - 7, where a is an integer. What is x mod 3?
For x = 9a - 7, where a is an integer, the value of x mod 3 is determined using the remainder when x is divided by 3, and it is equal to 2.
To find the value of x mod 3, we need to determine the remainder when x is divided by 3.
The expression x = 9a - 7, where a is an integer, allows us to calculate x mod 3.
To find x mod 3, we substitute the given expression x = 9a - 7 into the equation:
x mod 3 = (9a - 7) mod 3.
To simplify the expression, we can use the properties of modular arithmetic.
First, we can rewrite 9a as (3 × 3a) and distribute the modulus operator:
(9a - 7) mod 3 = ((3 × 3a) - 7) mod 3.
Next, we can separate the modulus operation:
((3 × 3a) - 7) mod 3 = ((3 × 3a) mod 3 - 7 mod 3) mod 3.
Since 3 is congruent to 0 mod 3, the first term becomes 0:
((3 × 3a) mod 3 - 7 mod 3) mod 3 = (0 - 7 mod 3) mod 3.
The second term, 7 mod 3, can be simplified as the remainder when 7 is divided by 3, which is 1:
(0 - 7 mod 3) mod 3 = (0 - 1) mod 3 = -1 mod 3.
Finally, we can find the remainder when -1 is divided by 3, which is 2:
-1 mod 3 = 2.
Therefore, x mod 3 is equal to 2.
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CAN SOMEONE IN THIS APP HELP PLEASE
Answer:
15 feet
Step-by-step explanation:
The distance from the foot of the ladder to the person is 6 feet. The person is also 6 feet. Therefore that mini triangle's length and width are both 6 feet.
The distance from the foot of the ladder to the wall is 15 feet. This is now a simple ratio. The length of the mini triangle is 6 to length of the larger triangle, 15. The height ratio is the mini triangle is 6 to the bigger triangle, x.
The height of the bigger triangle is the height of the wall. (Since the two are similar, then we can automatically deduce the height is 15.) But if you wanted to work out the ratio above ^^ you would multiply the 6 diagnol to the 15 and then divide by the last 6 to get 15.
In 2015, Mrs. Jonos paid $630 in Medicare
taxes. This represents 1% of her salary. What
was Mrs. Jones's gross income in 2015?
A submarine was situated 475 feet below sea level. if it ascends 150 feet, what is its new position relative to the sea level?
Answer:
325 feet below sea level i believe
Step-by-step explanation:
Question is in picture
Answer:
The answer is 32 inches
65 - 33 = 32
Ahh i hate math fr someone help
1. What does PEMDAS stand for?
P:
E:
M:
D:
A:
S:
Answer:
P- arenthesis
E- xpontent
M- ultiplication
D- ivision
A- ddition
S- ubtraction
Answer:
Step-by-step explanation:
p=parentheses
e=exponents
m=multiplication
d=division
a=addition
s=subtraction
Type a digit that makes this sentence true!
Answer:
1
best answer ever be amazing
phoebe compared the cost of books in 9 different stores. $2, $8, $4, $7, $8, $5, $8, $4, $6 what is the median cost of the books?
The median cost of the books is $6.
To find the median, we first arrange the costs of the books in ascending order: $2, $4, $4, $5, $6, $7, $8, $8, $8. Next, we determine the middle value. Since there are nine values, the middle value is the fifth one, which is $6. Therefore, the median cost of the books is $6.
The median is a statistical measure that represents the middle value of a dataset when it is arranged in ascending or descending order. It is useful in situations where there are outliers or extreme values that could skew the average. By using the median, we can get a better representation of the typical value in the dataset.
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Oliver just accepted a job at a new company where he will make an annual salary of
$54000. Oliver was told that for each year he stays with the company, he will be
given a salary raise of $3000. How much would Oliver make as a salary after 6 years
working for the company? What would be his salary after t years?
Answer:
After 6 Years: 54000*6 + 3000*5 = 339,000
After t years: 54000*t + 3000*(t-1) = 57000 t - 3000
==============
Please give brainliest, I really want to rank up, thank you!
Answer:
$358,000
Step-by-step explanation:
He makes $54k dollars "annual" = per year
Each year he stays he gets $3k worth of a raise
He stays 6 years so
3000 x 6 = 18k
54,000 x 6= 340,000
so then you just add
18,000 + 340,000=
358,000
I hope that helps :D
Can someone help me with this. Thank you.
Answer:
All are true
Step-by-step explanation:
2) True
3) True
4) True
Adjustment for Merchandise Inventory Using T Accounts: Periodic Inventory System
Ibby Smith owns and operates Ibby’s Ice Cream Cones. Her beginning inventory as of January 1, 20--, was $45,000, and her ending inventory as of December 31, 20--, was $57,000. Set up T accounts for Merchandise Inventory and Income Summary and perform the year-end adjustment for Merchandise Inventory.
Use the labels shown.
(a) Remove the beginning balance in Merchandise Inventory.
(b) Add the new balance in Merchandise Inventory.
The Income Summary will be credited for $12,000 in the T account.
The journal entry to remove the beginning balance in Merchandise Inventory is as follows:
Merchandise Inventory Debit $45,000
Opening Inventory Credit $45,000
In the T account of Merchandise Inventory, the beginning balance of $45,000 will be subtracted from the total of the debit amounts in the account.
ii. Add the new balance to Merchandise Inventory
The journal entry to add the new balance to Merchandise Inventory is as follows:
Closing Inventory Debit $57,000
Merchandise Inventory Credit $57,000
In the T account of Merchandise Inventory, the ending balance of $57,000 will be added to the total of the credit amounts in the account.
The year-end adjustment entry for Merchandise Inventory is:
Merchandise Inventory Dr. $57,000 ($57,000 - $45,000)
Income Summary Cr. $57,000 ($57,000 - $45,000)
In the Merchandise Inventory T account, the ending balance is $12,000 (credit balance) since the credit amount of $57,000 exceeded the debit amount of $45,000 by $12,000.
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Can you help me in this please No links or spams or bots or report
Answer:
Monday - 7 hr 30 mins
Wednesday - 9 hr 30 mins
Friday - 7 hr
Saturay - 5 hr 30 mins
---------------------------------------------------------------
If you earn $12.40 per hour, first you must find how many hours you worked total - in this case, 29 hr and 30 mins.
So you would be making $359.60 per week.
Find the smallest sample size needed to estimate the percentage of Americans who prefer to watch the news rather than read or listen to it. Use a 0.03 margin of error and a confidence level of 99%. From a previous poll, it was found that 47% of the American respondents prefer to watch the news rather than read or listen to it.
To estimate the percentage of Americans who prefer to watch the news rather than read or listen to it with a 0.03 margin of error and 99% confidence level, the smallest sample size needed is 1,060.
To calculate the sample size, we can use the formula:
n = (Z² * p * (1 - p)) / E²
where:
n = sample size
Z = Z-score corresponding to the desired confidence level (in this case, for a 99% confidence level, Z ≈ 2.576)
p = estimated proportion of the population with the characteristic of interest (based on the previous poll, p = 0.47)
E = margin of error (E = 0.03)
Substituting the values into the formula, we have:
n = (2.576² * 0.47 * (1 - 0.47)) / 0.03²
n ≈ 1060
Therefore, the smallest sample size needed to estimate the percentage of Americans who prefer to watch the news rather than read or listen to it, with a 0.03 margin of error and 99% confidence level, is approximately 1,060. This means that a sample of at least 1,060 individuals should be surveyed to obtain reliable estimates with the desired level of confidence.
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Nahla Burtoni is buying her first home for $125,000. She has been granted
a mortgage loan at an annual interest rate of 8.5% for 20 years with a
$25,000 down payment. Closing costs are 2% of the amount of the
mortgage loan and will be financed as part of the mortgage. What is the
actual amount financed with the mortgage?
O $100,000
O $102,000
O $120,000
O $125,000
Answer: the answer is B!!!!!!!!!!!!!!
Step-by-step explanation:
What is the area of this quadrilateral?
4 ft
3 ft
10 ft
10 ft
31
4 ft
Answer:
42
Step-by-step explanation:
Answer:
42 square feet
Step-by-step explanation:
add all of the square feet together, including the sides parallel that don't tell you how many inches. What I mean by parallel is the sides across from it.