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Explanation:
Consider the set
[tex]\left\{x_1,x_2,x_3,\ldots,x_n\right\}\\\\[/tex]
which has n items in it. We don't know anything about any individual item, but what we do know is that the mean is S.
So,
[tex]\text{mean} = \frac{\text{sum of values}}{\text{number of values}}\\\\\text{mean} = \frac{x_1+x_2+x_3+\ldots+x_n}{n}\\\\S = \frac{x_1+x_2+x_3+\ldots+x_n}{n}\\\\nS = x_1+x_2+x_3+\ldots+x_n\\\\x_1+x_2+x_3+\ldots+x_n = nS\\\\[/tex]
In short, the sum of the values [tex]\left\{x_1,x_2,x_3,\ldots,x_n\right\}\\\\[/tex] is exactly nS, where S is the mean of the same set.
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Next, we add 1 to [tex]x_1[/tex], add 2 onto [tex]x_2[/tex], etc to form this new set
[tex]\left\{x_1+1,x_2+2,x_3+3,\ldots,x_n+n\right\}\\\\[/tex]
Let's find the mean like so
[tex]\text{mean} = \frac{\text{sum of values}}{\text{number of values}}\\\\\text{mean} = \frac{(x_1+1)+(x_2+2)+(x_3+3)+\ldots+(x_n+n)}{n}\\\\\text{mean} = \frac{\left(x_1+x_2+x_3+\ldots+x_n\right)+\left(1+2+3+\ldots n\right)}{n}\\\\\text{mean} = \frac{nS+0.5n(n+1)}{n}\\\\\text{mean} = \frac{n(S+0.5(n+1))}{n}\\\\\text{mean} = S+0.5(n+1)\\\\[/tex]
which is why S+0.5(n+1) is the answer
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Let's look at a concrete example.
Consider the set {1,7,10} which has n = 3 items in it.
Its mean is,
S = (1+7+10)/3 = 18/3 = 6
Now increase the items in {1,7,10} by adding on the values {1,2,3} to each element in the order shown
1+1 = 2
7+2 = 9
10+3 = 13
So {1,7,10} becomes {2,9,13}
The mean of the new set {2,9,13} is...
mean = (2+9+13)/3 = 24/3 = 8
Notice how,
newMean = S + 0.5(n+1)
newMean = 6 + 0.5(3+1)
newMean = 8
which helps us see how the formula works and partially confirm the answer. While this example isn't definitive proof, it's still handy to go over. I recommend forming other sets to check to see that this formula works. Not only do I recommend trying different values, but also a different number of values as well (i.e. increase n to some larger integer).
Find the domain and range of each function
Answer:
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Step-by-step explanation:
Pls help me will pay $
Answer:
1.2 or 1.22 (Doesn't matter)
Step-by-step explanation:
Factorise
x2 - 9x - 36
Answer:
-7x - 36
Step-by-step explanation:
x X 2 - 9 x X - 36
2x - 9x - 36
Answer:
( x + 3 ) ( x - 12 )
Step-by-step explanation:
x^2 - 9x - 36
= x^2 + 3x - 12x - 36
= x ( x + 3 ) - 12 ( x + 3 )
= ( x + 3 ) ( x - 12 )
At 12 noon if the temperature is 38°C and if it decreases at the rate of 2°C per hour, then what would be the temperature at 5pm?
Answer:
38-2(5) = 28
So the temperature would be 28 degrees celsius
Answer: Teperature at 5PM will be 28°C
Ok so at 12 its 38°C
And it dcreases at 2°C an hour, we need to find the teperature at 5 o clock.
The number of hours between 12 and 5 mutiplied by 2 will give us the trail in temperature and then subtracting the trail i temperature witht the temperature a 12 will give us the teperature at 5 o clock.
SO,
hours between 12 PM and 5 PM is 5 hours
As, the temperature decreases at a uniform rate of 2°c per hour
⇒5×2°C
⇒10°C
Now the temperature at 5 PM will be 38°C-10°C=28°C
help if your good at maths
Answer:
[tex]\frac{1}{p-s}[/tex]
Step-by-step explanation:
[tex](p+s)(p^2-s^2)^{-1}[/tex]
[tex](p+s)\frac{1}{(p^2-s^2)}[/tex]
[tex]\frac{p+s}{p^2-s^2}[/tex]
[tex]\frac{p+s}{(p+s)(p-s)}[/tex]
[tex]\frac{1}{p-s}[/tex]
Airfare from Atlanta,GA to Nashville,TN was decreased from $250 to $180.By what percentage did the cost of the airfare change?
Answer:
percentage cost of airfare change= (difference in cost / original cost )×100
% age = (250-180/ 250) ×100
=70/250 ×100
7000/250
= 28%
HELPPP MY MATH HOMEWORK!!!
I dont know how to answer number 12 but number 13 is the first one 3x + 15 = 17
please answer this question
Domain in numerical order: {-7, -1, 0, 1}
Range in numerical order: {-1, 0, 1, 2, 7}
Which number is not part of the range of this relation? = -7
Hope this helps!
HI PLEASE ANSWER BEFORE 12:00a.m. EST
Answer:
D
Step-by-step explanation:
Amanda's unit rate would be
s=50m
while Mary's is
s=60m
60-50 is 10, meaning the answer would be D.
Mary saves $10 more than Amanda every month.
Hope this helps! :)
Hi there!
We can find an equation that models Amanda's savings using the equation:
y = km, where:
k = rise / run (Amount/months)
Plug in a set of values from the table:
k = 100/2 = 50
y = 50m
We know that Mary saves y = 60m dollars a month, so we can determine the correct comparison by plugging in a value of 1 month into both equations:
Amanda:
y = 50(1) = $50
Mary:
y = 60(1) = $60
The difference between Mary's and Amanda's savings is $60 - $50 = $10, so each month, Mary saves $10 more than Amanda.
The correct answer is D.
Unit Ra 1. Walmart sells a 6oz bottle of laundry detergent for $4.80. What is the price per ounce? 2 A. $0.80 B. $0.08 C. $8 D. $0.88
you have to explain and show me how you solve it
$0.80 because 4.80/6=0.8
Reduce 40/100 please helppp
Answer:
2/5
Step-by-step explanation:
40 and 100 can both be divided by 20. 40 divided by 20 equals 2 and 100 divided by 20 equals 5
Answer:
2/5 (0.4)
Step-by-step explanation:
We can reduce this by first looking at the fraction. [tex]\frac{40}{100}[/tex]
We can first divide by 10 on both sides to get a better number: [tex]\frac{4}{10}[/tex]
We can simplify both by 2 since thats another common number: [tex]\frac{2}{5}[/tex]
That is the most we can go to!
If this answer helped, consider marking this as brainliest!
Cheers!
Today every thing at a store is on sale. The store offers a 20% discount. Write an equation to represent how much someone would pay
Error Analysis Jessie incorrectly said the rate
1/6 / 1/24
can be written as the unit rate
gallon
1/144
pound per gallon. What is the correct unit rate? What was Jessie's likely error?
Answer:
4
Step-by-step explanation:
she multiplied 6x24, got 144 and said 1/144
parallel to y = -2/5 and passes through 2, -8
Answer:
y = -8
Step-by-step explanation:
When y = -2/5, the slope is 0.
Seeing this, we can make the equation the same as the y-value of the point given.
Hence,
y = -8
Feel free to mark this as brainliest! :D
May I please receive help?
Answer:
3
Step-by-step explanation:
(-3/4) (-4/7) (-2/3) = ??
(-2/3) (-3/4) (4/5) = ??
(2/3) (-9/10) (5/6) = ??
answer has to be a fraction
Answer:
Step-by-step explanation:
2/5 và -1/2
What is the slope of this line? −2/3 2/3 3/2 I don't know. Graph of a line on coordinate plane. Axes are labeled x and y. Three points are shown, labeled with ordered pairs 2 comma 3, 5 comma 5, and 8 comma 7. The line passes through these three points.
Answer:
2/3 is your answer
Step-by-step explanation:
Hope this helps
P.S.(from k12)
The slope of the line is 2/3.
Here,
Graph of a line on coordinate plane. Axes are labeled x and y.
Three points are with ordered pairs (2, 3), (5, 5), and (8, 7) and the line passes through these three points.
We have to find the slope of the line.
What is the slope of the line?
Let two points (x₁, y₁) and (x₂, y₂) are on the line, then slope of the line is calculated as;
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Now,
Three points are passes through the line are (2, 3), (5, 5), and (8, 7).
To find the slope, Let any two point from three given points.
Let (2, 3) and (5, 5) on the line.
Hence, Slope is calculated as,
⇒ [tex]m = \frac{5-3}{5-2} = \frac{2}{3}[/tex]
Therefore, The slope of the line is 2/3.
Learn more about the slope of the line visit:
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use the equation below to find y,if m=4,x=5, and b=9. y=mx-b
Step-by-step explanation:
Y=4(5)-9
=11
you must follow the formula given
Answer:
y=11
Step-by-step explanation:
y=mx-b
mx-b=y
4 * 5 - 9 = y
20 - 9 = y
11 = y
Complete the statement with always, sometimes, or never. Explain your reasoning.
1. A line ____________ has endpoints.
2. Two points ____________ determine a line.
[tex]\sqrt{25} =5[/tex]
What is the reciprocal of -5 5/6
Answer:
Well simplified it is 35/6
Then flip it an it is 6/35
Step-by-step explanation:
Hope this helps!
1. Jasmine has two more than five times the number of books that Steven has. She has at
least 15 books.
x= how many books Steven has
Write out inequality
Fairview and Rockview are 104 m from each other. How apart would the cities be on a map that has a scale of 1 cm : 13 m?
Answer:
They would be 8 cm apart
Step-by-step explanation:
104 divided by 13 equals 8
Emma and her 3 friends did chores for Emma's dad on Saturday. They earned 55 and split evenly. How much money did each of the 4 children get?
Emma and her 3 friends did chores for Emma's dad on Saturday. They earned 55 and split evenly. How much money did each of the 4 children get? Each of them got 13.75
In an examination of final year students of a school, 60 offered history, 50 offered economics, and 48 literature. 30 offered history and economics 16 offered history and literature, 22 offered economics and literature. If 10 candidates offered all the 3 subjects find the number that offered:
1)
a) History only
b) Economics only
c) Literature only
2) How many candidates sat for the examination assuming that each candidate sat for at least one subject.
REPRESENT IN VENN DIAGRAM
Answer:
Step-by-step explanation:History(H),Economics(E),Literature(L)
1a).To find History(H) only is
H only =H-HE-HL+HEL
H only =60-30-16+10=24
b).E only=50-30-22+10=8
c). L only=48-22-16+10=20
2).no of candidates who sat for the exam is 24+8+20=52
"In an examination of final year students of a school, 60 offered history, 50 offered economics, and 48 literature." The Vein diagram is attached below.
What is a Vein diagram?A Venn diagram is a diagram that utilizes circles to demonstrate the similarities and contrasts between two or more items.
Generally, the equation for History students only is mathematically given as
HisO=His-His Eco-His Lie+HisEcoLie
Therefore
HisO=60-30-16+10
HisO=24
EcoO=50-30-22+10
EcoO=8
LieO=48-22-16+10
LieO=20
In conclusion, candidates that sat for at least one subject
At least HEL= 24+8+20
At least HEL=52
Read more about the vein diagram
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How do you solve 5[2p−4(p+5)]=25 properly?
Answer:
Step-by-step explanation:
5[2p-4(p+5)]=25
or, 2p-4(p+5)=5
or, 2p-4p-20=5
or, -2p=5+20
or, -2p=25
or, 2p=-25
or, p=25/2
so, p=12.5
340,250 rounded to the nearest thousand?
Answer:
340,000
Step-by-step explanation:
Answer:
340,000
Step-by-step explanation:
in 340,250, you would round down because the 2 in ,250 is less than 5, and you can only round up if the number is more than 5.
Between which two values is the square root of 75?
Answer:
Between 8 and 9
Step-by-step explanation:
Square root of 75 is 8.66025403784
I just need the answers
Answer:
Sana makatulong
Solve w=x/y-x for x.
Answer:
Rewrite the equation as x+xyz=wx+xyz=w.
x+xyz=wx+xyz=w
Subtract xx from both sides of the equation.
xyz=w−xxyz=w-x
Divide each term by xzxz and simplif