Answers
1, 2, 3, 3, 3, 2, 1, 1, 2, 3, 5, 3, 2, 1
i) the mean of x is:
[tex] \displaystyle{\frac{1+2+3+3+3+2+1+1+2+3+5+3+2+1}{14}= \frac{32}{14}= 2.3[/tex]
ii)
to find the variance,
1.we find the difference of each value to the mean.
2. we square each of these differences
3.we find the mean of the squared differences
as follows:
i)
1-2.3=-1.3, 2-2.3=-0.3 3-2.3=0.7 5-2.3=2.7
ii)
[tex](-1.3)^2=1.69\\\\(-0.3)^2=0.09\\\\(0.7)^2=0.49\\\\(2.7)^2=7.29[/tex]
iii)
we have 4-1's, 4-2's, 5-3's, and 1 5,
so the mean of the differences squared is :
[tex]\displaystyle{ \frac{4\cdot1.69+4\cdot0.09+5\cdot0.49+7.29}{14}= \frac{16.86}{14}= 1.2[/tex]
Answer:
mean = 2.3
variance = 1.2
Related Questions
One of the events at the circus starred Gabriella the Human Cannonball. On Saturday she performed in four shows. Shot from a cannon, her distances measured 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters. What was the total distance Gabriella flew that day?
Answers
In this case, Gabriella flew 4 times with different distance. To answer this question you just need to add all the distance, The calculation would be:
Total distance = distance 1 + distance 2 + distance 3 + distance 4
Total distance = 8.05 meters+ 17.71 meters + 14.38 meters + 19.35 meters= 59.49 meters.
The total distance Gabriella flew that day with distances measuring 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters is,
⇒ 51.44 meters
The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that,
On Saturday she performed in four shows.
Shot from a cannon, her distances measured 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters.
Now, To find the total distance Gabriella flew that day with distances measuring 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters we can add all the distances,
⇒ 8.05 m + 17.71 m + 14.38 m + 19.35 m
⇒ 51.44 meters
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Write an expression, that when using the Distributive Property, can be simplified to 12a + 18b - 6c.
Answers
Find a number that will go into all evenly. 6 will go into all of them evenly
[tex]\frac{12a + 18b - 6c}{6}[/tex]
6(2a + 3b - c)
What is the value of x in the equation 3x – y = 18, when y = 27?
a.5
b.7
c.45
d.63
Answers
Answer:
5
Step-by-step explanation:
will give BRAINEST
Use the elimination method to solve the system of equations. Choose the correct ordered pair.
x + y = 8
x – y = 6
Answers
Explanation:
Test all the ordered pairs in the equations. The one that fits in both is the answer.
(9, 3)
9 + 3 = 8 12 ≠ 8 no
9 - 3 = 6 6 = 6 yes
(6, 0)
6 + 0 = 8 6 ≠ 8 no
6 - 0 = 6 6 = 6 yes
(8, 2)
8 + 2 = 8 10 ≠ 8 no
8 - 2 = 6 6 = 6 yes
(7, 1)
7 + 1 = 8 8 = 8 yes
7 - 1 = 6 6 = 6 yes
Given a sphere with volume V, the formula
r = 0.62V
1
3
may be used to approximate the sphere's
radius r.
Find the approximate radius of a sphere that has a volume of
512 in3.
The approximate radius of a sphere that has a radius of
512 in3
is ___ in
Answers
Solving for V, we divide 0.62 from both sides, getting r/0.62=512/0.62=around 825.8
In a recent survey 7 out of 10 people prefer coffee in the morning the rest said they prefer tea if 27 people said they prefer tea how many people were interviewed
Answers
A total of 90 people were interviewed in the survey, which was determined by setting up a proportion based on the information that 7 out of 10 people prefer coffee and the remaining prefer tea, with 27 people preferring tea.
To solve the problem, we need to determine the total number of people surveyed based on the information given about their preferences for coffee and tea in the morning.
According to the survey, 7 out of 10 people prefer coffee. The rest, which is 3 out of 10, prefer tea. We are told that 27 people prefer tea. To find the total number of people surveyed, we set up a proportion where 3 people out of 10 is equivalent to 27 people out of the total number of people interviewed:
Let x represent the total number of people interviewed.Set up the ratio: 3/10 = 27/x.Cross multiply to solve for x: 3x = 270.Divide both sides by 3 to find x: x = 90.So, a total of 90 people were interviewed.
It takes joey 1/16 of an hour to write one thank you note. How many cards can he write in 3/4 of an hour
Answers
divide 3/4 by 1/16
3/4 / 1/16 =
3/4 * 16/1 =
48/4 = 12
he can write 12
Suppose you want to cut 1515 identical boards of length 33 feet. the procedure is to measure and cut the first board, then use the first board to measure and cut the second board, then use the second board to measure and cut the third board, and so on. answer parts a and
b.
a. what are the possible lengths of the 1515th board if, each time you cut a board, there is a maximum error of plus or minus±one third 1 3 inch? the board could be as short as nothing inches or as long as nothing inches. (simplify your answer. type integers or decimals rounded to the nearest hundredth as needed.)
Answers
The lengths of the 1515th board could range from 32.51 feet to 33.49 feet, considering the maximum measurement error of plus or minus one third inch per cut.
Explanation:To find the possible lengths of the 1515th board, we need to consider the maximum error in each board measurement. Each time a board is cut, there is a maximum error of plus or minus one third inch. So, the 1515th board could be as short as 33 feet minus 1515 multiplied by one third inch, and as long as 33 feet plus 1515 multiplied by one third inch. Simplifying this, the 1515th board could be as short as 32.51 feet and as long as 33.49 feet.
Estimate the value of 9.9 squared x 1.79
Answers
The estimation of 9.9 squared multiplied by 1.79 is 180.
To estimate the value of 9.9 squared multiplied by 1.79, use rounded numbers to simplify the calculation.
First, round 9.9 to 10 and calculate 10 squared, which is 100.
Next, we round 1.79 to 1.8.
Now, we can perform the multiplication:
100 x 1.8 = 180
Therefore, an estimation is 180.
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The value of 9.9 Squared x 1.79 is 175.59
Let's calculate
[tex]9.9^{2}[/tex]×1.79 let's break it down step by step:
[tex]9.9^{2}[/tex] means 9.9 [tex]\times[/tex] 9.9 multiplied by itself:
9.9×9.9, which equals 98.01
Now, multiply
98.01 × 1.79 = 175.5879
Rounded to a reasonable precision, the value is approximately
175.59
The process involves squaring
9.9 first and then multiplying the result by
[tex]1.79.9.9^{2}[/tex] gives us 98.01 and then that result is multiplied by
1.79 to obtain 175.59.
The explanation illustrates the order of operations: performing the exponentiation before the multiplication. This follows the basic principles of arithmetic, ensuring each step is carried out accurately to arrive at the final result.
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The Nygen family wants to put a circular fence around their pool. They want it to be exactly 11 feet from the center of the pool. How many feet of fencing do they need to buy?
Answers
r = radius = 11
[tex]p = 2\pi r[/tex]
[tex]p = 2\times\pi\times 11[/tex]
p = 69.115
If we round
p = 69.12
multiply 5 × 381 using place value and expanded form
Answers
Drag the correct tiles that match.?
Answers
Olivia has taken out a $13,100 unsubsidized Stafford loan to pay for her college education. She plans to graduate in four years. The loan has a duration of ten years and an interest rate of 7.6%, compounded monthly. By the time Olivia graduates, how much greater will the amount of interest capitalized be than the minimum amount that Olivia could pay to prevent interest capitalization? Round all dollar values to the nearest cent.
a. $654.45
b. $477.27
c. $995.60
d. $354.22
Answers
If Olivia wants to prevent interest capitalization, she must pay the accrued interest each month. That amount is
... I = Prt = $13,100×0.076×(1/12) = $82.97
Over 4 years (48 months), these payments total $82.97×48 = $3982.56.
_____
If no payments are made, the loan balance grows by the multiplier (1 +r/12) each month. Then the amount of interest that will be capitalized at the end of 48 months is ...
... $13,100×((1 +0.076/12)^48 -1) = $4637.01
The difference in these amounts is ...
... $4637.01 -3982.56 = $654.45 . . . . . matches selection a.
Answer:
A
Step-by-step explanation:
654.45
chose the graph that represents the equation y=|x-4|
Answers
Why not graph y=|x-4| yourself, to help you choose the correct answer?
First, graph y=|x|. It looks like a "v" opening up, with the vertex at (0,0).
Next, move the whole "v" graph 4 units to the right.
Compare your result to the given answer choices.
Answer:
V shape.
Vertex at (4,0)
Intersect with y axis at (0,4)
Step-by-step explanation:
In order to solve this you just ahve to search fo the graph that grows like a V because when you deal with functions that have absolute values you can have negative and positive values for the independent variable but not for the dependent, in this case x is the independent so x will have negative and positive values while Y will only grow in the postives, now the vertex of the function is found where Y=0 so to calculate that you equal the function to 0
y=|x-4|
0=|x-4|
x=4
So the vertex will be at (4,0) and the intersect with the y axis will be located where x=0, so you evaluate the function for 0:
y=|x-4|
y=|o-4|
y=|-4|
y=4
So the intersect with the y axis will be at (0,4).
The sum of two consecutive integers is −225. Find the two integers
Answers
2x = -226. Thus, x = -113 and x+1 = -113+1 + -112.
The two consecutive integers are -112 and -113. Adding these together results in -225, as we had hoped.
ABC Office Supply offers an electric typewriter for $129.95. If ABC received a 15% markup on cost by selling the typewriter at this price, what was the cost of the typewriter to ABC?
Answers
Mark up=15%
x=at cost price to ABC
Set up proportion:
129.95 x
--------- = ---------- (Got 1 from 100% which is the cost to ABC and 1.15 from 100%
1.15 1 +15% which is the cost to customer then changed to
decimal form.) Cross multiply
129.95=1.15x
129.95/1.15=1.15x/1.15
113=x
Cost to ABC is $113
Amy is just learning how to rock climb. Her instructor takes her to a 26 ft climbing wall for her first time. She climbs up 5 ft in 2 min. But then slips back 2 ft in 10 sec. This pattern (up 5 feet down 2 ft) continues until she reaches the top. How long will it take her to reach the very top?
Answers
Speed going up = 5 ft/(2min * 60 s/1 min) = 1/24 ft/s
Speed going down = 2 ft/10 s = 0.2 ft/s
Net speed = 1/24 ft/s - 0.2 ft/s = 5/24 ft/s
Using this net speed, we can already calculate for the total time:
Speed = Distance/Time
5/24 ft/s = 26 ft/Time
Time = 124.8 seconds or 2.08 minutes
Final answer:
Amy needs to cover 23 feet through 7 full cycles of climbing and slipping, followed by a final climb of 5 feet without slipping. It takes her 15.17 minutes for the cycles and an additional 2 minutes for the final climb, summing up to a total of 17.17 minutes to reach the top.
Explanation:
Amy is learning how to rock climb and faces a challenge of climbing a 26 ft wall by moving up 5 ft in 2 minutes, then slipping back 2 ft in 10 seconds. To calculate the total time it will take her to reach the top, we can start by finding the net distance she covers in each cycle of climbing and slipping.
During each cycle, Amy climbs 5 ft but then slips back 2 ft, making her net gain per cycle 3 ft (5 ft up - 2 ft back). To reach the top of the 26 ft wall, she doesn't slip back after the final climb, so the last part of the climb she only needs to cover the distance that takes her to 26 ft without slipping back.
Let's consider the entire climb except the final push to the top:
Total distance to cover without the last climb: 26 ft - 3 ft = 23 ft.
Number of full cycles to cover 23 ft: 23 ft / 3 ft per cycle = 7.67 cycles. Since she can't do a partial cycle, we round down to 7 full cycles, covering 21 ft (7 cycles * 3 ft/cycle).
Remaining distance after 7 cycles: 26 ft - 21 ft = 5 ft, which she covers in her last climb.
Each cycle takes 2 minutes and 10 seconds (2 minutes for climbing up 5 feet and 10 seconds for slipping back 2 feet). Since 10 seconds is 1/6 of a minute, each cycle takes 2 + (1/6) = 2.167 minutes. For 7 cycles, the time is 7 cycles * 2.167 minutes/cycle = 15.17 minutes. The final climb of 5 ft takes an additional 2 minutes, resulting in a total time of 17.17 minutes to reach the top.
what is the cube root of 4096
Answers
6 divided by 1/3 equals
Answers
6 divided by 1/3 equals 6 times 3
6*3 = 18
First, let's write the problem.
[tex]\frac{6}{\frac{1}{3}}[/tex]
In this case, we multiply outer numbers by outer numbers and inner numbers by inner numbers.
[tex]=\frac{3\cdot \:6}{1}[/tex]
Simplify the numerator.
[tex]=\frac{18}{1}[/tex]
Our final answer would be,
[tex]=18[/tex]
You can feel free to let me know if you have any questions regarding this!
Thanks!
- TetraFish
what is
4 group of _ tenths is 2.8
Answers
Same as
0.7 x 4 is 2.8
That's the answer 0.7
What is the least common multiple of 27,48, and 66
Answers
The LCM would most likely be: [tex]4.752 [/tex]
So, go through all of your factors to find your [tex]answer[/tex] of those [tex]numbers [/tex]
[tex]MeIsKaitlyn:)[/tex]
~
what is 10 1/3 as a improper fraction and show your if you can.
Answers
10(3)= 30+1= 31
2. Put the 31 over 3.
31/3
The improper fraction of 10 1/3 is 31/3.
Hope this helps!
What is the equation of the following graph in vertex form?
Answers
Vertex form is the same as standard form or y=a(x-h)^2+k where h and k are the x and y values of the vertex. a stretches or compressed the graph. In this case, a = 1
Substitute for the point (0.1):-
1 = a * 1^2
so a = 1
Answer is y = (x + 1)^2
WORLD'S HARDEST MATH QUESTIONS
Scientists released 6 rabbits into a new habitat in year 0. Each year, there were four times as many rabbits as the year before. How many rabbits were there after x years? Write a function to represent this scenario.
Answers
in year 1, the number of rabbits is 4*6 which is 6*(4)^1
in year 2, the number of rabbits is (4*6) from year one multiplyed by 4, so a total of rabbits is 4*6*4 which is 6*(4)^2
in year 3, the number of rabbits is 6*(4)^2 from year two multiplyed by 4, so a total of rabbits is 4*6*4*4 which is 6*(4)^3
The sequence will continue in the same way.
Therefore, for year x:
f(x) = 6 * (4)^x which is choice A
If a person starts investing $100 per month starting at age 21, and that money earns a 7% return every year, how much will this person have when turning 70 years old? For ease of calculation, assume starting balance of $0 and annual contributions of $1,200 (12*$100
Answers
Fv=pmt [((1+r)^(n)-1)÷r]
Fv future value?
PMT yearly payment 1200
R interest rate 0.07
N time 49 years (70-21)
Fv=1,200×(((1+0.07)^(49)−1)÷(0.07))
Fv=454,798.80
Hope it helps!
The amount of money the person will have is [tex]\fbox{\begin\\\ \bf \$454,800\\\end{minispace}}[/tex].
Further explanation:
In the question it is given that the amount of money invested per month is [tex]\$100[/tex].
So, the total amount of money invested in [tex]1[/tex] year or [tex]12[/tex] months is calculated as follows:
[tex]\fbox{\begin\\\ 100\times 12=1200\\\end{minispace}}[/tex]
This implies that the total amount of money invested in [tex]1[/tex] year is [tex]\$1200[/tex].
Amount of money invested grows at a rate of [tex]7\%[/tex] per year.
A person started investing the money at an age of [tex]21[/tex] years and decided to withdraw the money at the age of [tex]70[/tex] years.
So, the total time for which the money was invested is calculated as follows:
[tex]\fbox{\begin\\\ 70-21=49\\\end{minispace}}[/tex]
The formula to obtain the future value of the invested money is as follows:
[tex]\fbox{\begin\\\ FV=PV\left[\dfrac{(1+r)^{t}-1}{r}\right]\\\end{minispace}}[/tex]
Substitute [tex]1200[/tex] for [tex]PV[/tex], [tex]0.07[/tex] for [tex]r[/tex] and [tex]49[/tex] for [tex]t[/tex] in the above equation.
[tex]\begin{aligned}FV&=1200\left[\dfrac{(1+0.07)^{49}-1}{0.07}\right]\\&=1200\left[\dfrac{(1.07)^{49}-1}{0.07}\right]\\&=1200\left[\dfrac{26.53}{0.07}\right]\\&=1200\times379\\&=454800\end{aligned}[/tex]
Therefore, the future value of the invested money is [tex]\$454,800[/tex].
Thus, the amount of money the person will have is [tex]\fbox{\begin\\\ \bf \$454,800\\\end{minispace}}[/tex].
Learn more:
A problem on coordinate geometry https://brainly.com/question/4057490A problem on linear function https://brainly.com/question/9801816A problem on linear equation https://brainly.com/question/1761434Answer details:
Grade: College
Subject: Mathematics
Topic: Time value of money
Keywords: Future value, present value, interest, time period, investment, money, 7 percent, $100, amount, invested money, formula.
If the probability that the Cavaliers will win the NBA championship this year is 7/11, what are the odds that the Cavaliers will lose the NBA championship?
Answers
So, subtract 1 and 7/11 to get your answer
The answer is 4/11.
Hope this helped!
Answer:
4 out of eleven
Step-by-step explanation:
DIVIDING ALGEBRAIC FRACTIONS HELPP!!!!
8/9-a^2 divided by 4a^2-4a-24/a^2-6a+9
Answers
-8/(a-3)(a+3) • (a-3)(a-3)/4(a-3)(a+2)
Erica has a box with 10 pencils in it. she wants to give 0.3 Of the pencils in the box to her sister. which model represents the number of pencils Erica have to her sister
Answers
At 12:30 pm on august 2, the surface receives 789 wm−2 and reflects 110 wm−2. what is the surface albedo?
Answers
Math Please Help!!!!
Answers
Part A
Slope:
m = (y2-y1)/(x2-x1)
m = (9-5)/(4-2)
m = 4/2
m = 2
Use this slope to find the y intercept b
y = mx+b
5 = 2(2)+b
5 = 4+b
b = 1
Therefore the equation is y = 2x+1
-------------------
Part B
Slope:
m = (y2-y1)/(x2-x1)
m = (20-10)/(4-2)
m = 10/2
m = 5
Use this slope to find the y intercept b
y = mx+b
10 = 5*2+b
b = 0
Therefore the equation is y = 5x
===============================================
Problem 7
A) The coefficients are 7, 25, and -2. These are the values in front of the variables
-------------------
B) The variables are m, y, and y^3. Basically any term with a letter in it.
-------------------
C) The constant is 44. This is the term without any variables (letters) attached.
-------------------
D) There are four terms and the four terms are: 7m, 25y, 44 and -2y^3
-------------------
E) 25y and 2y^3 are NOT like terms. We cannot combine unlike terms. It's like trying to add 25a and 2b. We could think of it as having 25 apples and 2 bananas. We can't combine them to get 27a (there aren't 27 apples, only 25). Likewise we can't add them to get 27b (there aren't 27 bananas, only 2). Saying 27ab is also incorrect.
===============================================
Problem 8
Plug in n = 1
2^2*(n+3)
2^2*(1+3)
4*(1+3)
4*4
16
So the output is 16
-------------------
Plug in n = 3
2^2*(n+3)
2^2*(3+3)
4*(3+3)
4*6
24
So the output is 24
-------------------
Plug in n = 4
2^2*(n+3)
2^2*(4+3)
4*(4+3)
4*7
28
So the output is 28
-------------------
Plug in n = 6
2^2*(n+3)
2^2*(6+3)
4*(6+3)
4*9
36
So the output is 36
See the image attachment for the completed table.
===============================================
Problem 9
Plug in d = 6 and evaluate
C = 40 + 8(d-3)
C = 40 + 8*(d-3)
C = 40 + 8*(6-3) ... Replace d with 6
C = 40 + 8*(3)
C = 40 + 24
C = 64
It will cost 64 dollars.