Hi there! Hopefully this helps!
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Question: "Prove that a^{4} + b^{4} + c^{4} > abc(a + b + c) , where a, b, c are different positive real numbers."
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From the AM and GM inequality, we have:
a^4 + b^4 ≥ 2a^2b^2
b^4 + c^4 ≥ 2b^2c^2
c^4 + a^4 ≥ 2a^2c^2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
From adding the inequalities we have above and dividing by 2, we have:
a^4 + b^4 + c^4 ≥ a^2b^2 + b^2c^2 + c^2a^2......1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now we need to repeat the process of a^2b^2, b^2c^2, and c^2a^2 to get:
a^2b^2 + b^2c^2 ≥ 2b^2ac
b^2c^2 + c^2a^2 ≥ 2c^2ab
c^2a^2 + a^2b^2 ≥ 2a^2bc
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now, we add from what we have above and divide by 2 to get:
a^2b^2 + b^2c^2 + c^2a^2 ≥ (b^2ac + c^2ab + a^2bc) or abc(b + c + a).....2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So, from (1) and (2) it follows:
a^4 + b^4 + c^4 ≥ abc( a + b + c)
Answer:
0.5
Step-by-step explanation:
a+b+c=0—(1)
a2+b2+c2=1—(2)
We know that:
(a+b+c)2=a2+b2+c2+2ab+2bc+2ca—(3)
Substituting (1) and (2) in (3) , 0=1+2(ab+bc+ca)
=>ab+bc+ca=−0.5—(4)
Squaring: (ab+bc+ca)2=0.25
=>a2b2+b2c2+c2a2+2ab2c+2bc2a+2a2bc=0.25
=>a2b2+b2c2+c2a2+2abc(a+b+c)=0.25
Since a+b+c=0 ,
a2b2+b2c2+c2a2=0.25—(4)
squaring (2) :
(a2+b2+c2)2=12
=>a4+b4+c4+2a2b2+2b2c2+2c2a2=1
=>a4+b4+c4+2(a2b2+b2c2+c2a2)=1—(5)
Substituting (4) in (5),
a4+b4+c4+2(0.25)=1
=>a4+b4+c4=0.5
Hope this helps :D
What is h decreased by 20
Answer:
h minus 20
Step-by-step explanation:
On a map’s coordinate grid, Panthersville is located at (−3, 2), and Heel City is located at (4, 8). Falconton is the midpoint between Panthersville and Heel City. What is the approximate distance from Panthersville to Falconton? (Each unit on the grid represents 1 mile.) A. 3.25 miles B. 4.61 miles C. 5.00 miles D. 9.22 miles
Answer:
The approximate distance from Panthersville to Falconton is: B: 4.61 miles.
Step-by-step explanation:
Objective: Find the distance from Panthersville to Falconton. (Which is just half of the distance from Panthersville to Heel City because Falconton is the midpoint between both cities.)
First we need to find the distances from Panthersville to Heel City, which we are given the coordinates. ( Panthersville (-3,2) & Heel City (4, 8) )
-To find the distance between the two cities we use the distance formula:
d= √(x2 - x1) ^2 + (y2 - y1)^2 , so we set (-3,2) as x1 and y1 while (4,8) x2 and y2 and we just plug it in.
Once we plug it in we get:
d= √(4 - -3)^2 + (8 - 2) ^2
Then we solve the numbers in the parenthesis (4 - -3) = 7 and (8 - 2) = 6 so now we have:
d= √(7)^2 + (6) ^2
Next we solve for the exponents (7)^2 = (7 x 7 = 49) and (6)^2 = ( 6 x 6= 36) now it look like this:
d= √49 + 36
After that we just add both numbers together (49 + 36) = 85
d= √85
Now all we have to do is square root 85 which is just 9.219544457, just round it to the nearest hundredth and you will get 9.22.
So the distance from Panthersville to Heel City is about 9.22 miles.
Now we found the full distance we now need to find the distance from Panthersville to Falconton which is just half of that distance due to Falconton being the midpoint.
All we have to do is divide 9.22 by 2 and we get 4.61.
The distance from Panthersville to Falconton is 4.61 miles.
Find the volume. Show work plz
Answer:
196π or 615.75 m^3 to the nearest hundredth.
Step-by-step explanation:
This is a cone, so:
Volume = 1/3 π r^2 h
= 1/3 * π * 14^2 * 3
= 196π m^3.
How many envelopes does Jane address in a
day?
Jane addresses twice as many envelopes
as Louis in the same amount of time.
Together, they address 450 envelopes
each day.
Answer:
2x+X=450
3x=450
X=450/3
X=150
so
2x=2*150=300
X=150
so, Jane addressed 300 envelopes while Louis addressed only 150
Answer:
Jane addressed 300 envelopes while Louis addressed 150
Step-by-step explanation: Let x represent Louis's amount and 2x is Jane's amount
x+2x= 450 combine 3x =450
Divide both sides by 3.
x/3 = 450/3 x= 150. 2x = 300
If you're good at bearings pls help meeeeee
Pls show full working out ty
Answer:
201
Step-by-step explanation:
use the law of sines
sine B / b = sine C / c
sine 75 / 19.6 = sine C / 12.5
inv sine C = ( sine 75 * 12.5 ) / 19.6
C = 38
the bearing C = 180 + 59 - 38 = 201
Order of Operations - Use PEMDAS. Evaluate the expression. Show all work please!
18 - 2 (1 + 10 / 5)
Write an expression with exponents to find the total number of panes in 12 windows.
Answer:
Below
Step-by-step explanation:
Imagine our window has 4 panes (picture below)
Let T be the total number of panes:
There are 12 windows at total.
●T = 4×12
Notice that:
● 4 = 2×2
● 12 = 4×3 = 2×2×3
● T = 2×2×2×2×3 = 2^4×3
For what values of x is the value of the function f(x)=x² +3x+2 equal to zero?
Answer:
x=-2 x=-1
Step-by-step explanation:
f(x)=x² +3x+2
Set the function equal to zero
0=x² +3x+2
Factor
What 2 numbers multiply to 2 and add to 3
2*1 = 2
2+1 = 3
0 = ( x+2) (x+1)
Using the zero product property
x+2 =0 x+1 =0
x=-2 x=-1
A square has a perimeter of 8 and one vertex at (2, 2). What could be the location of another vertex of this shape? A) (1, 5) B) (-2, 2) C) (2, 3) D) (0, 0)
Answer:
D) (0,0)
Step-by-step explanation:
It is a square so each side is 2 units because
8/4 = 2
If the first point is at (2,2) we need to find which other point is 2 away from the first one. Or two away from where that point would be since there are 3 other corners.
We can rule out A and C because they are an odd number away. B is too far away because he's distance is 4.
So the other point is (0,0)
PLS HELP I NEED THIS SHSAT MATH QUESTION!!!
On Friday, Marvin sold 4 suits that had a mean sale
price of $125. On Saturday, he sold 6 suits that had
a mean sale price of $140. What was the mean sale
price, to the nearest dollar, for all 10 of the suits he
sold on Friday and Saturday?
A. $130
B. $132
C. $133
D. $134
Answer:
C.$133
Step-by-step explanation:
You have to add all numbers then divide by how many numbers there are.
So, in this case, you must add 125 and 140 to get 265
Then you must divide by 2 since there are 2 numbers
265/2 = 132.5
Round to the nearest dollar
The final answer is $133
Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the right.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the right.
Answer:
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at negative 0.5 and is pointing to the left.
Step-by-step explanation:
Required
[tex]2x - 6 \geq 6(x - 2) + 8[/tex]
Required
Determine the number line
[tex]2x - 6 \geq 6(x - 2) + 8[/tex]
Open the bracket
[tex]2x - 6 \geq 6*x - 6*2 + 8[/tex]
[tex]2x - 6 \geq 6x - 12 + 8[/tex]
[tex]2x - 6 \geq 6x - 4[/tex]
Collect Like Terms
[tex]2x - 6x \geq 6 - 4[/tex]
[tex]- 4x \geq 2[/tex]
Divide both sides by -4
[tex]\frac{- 4x}{-4} \geq \frac{2}{-4}[/tex]
[tex]x \leq -0.5[/tex]
From the list of given options, the correct answer is option C
Answer:
b
Step-by-step explanation:
Need Help! As soon as possible.
Answer:
Step-by-step explanation:
[tex]f^{-1}(f(58))=(fof^{-1})(58)=1_\pi(58)=58\\\\f(f(5))=f(9)=11\\[/tex]
How do I solve this
Answer:
-36
Step-by-step explanation:
[tex]-\frac{t}{2} -8 = 10\\-\frac{t}{2} = 18\\\frac{t}{2} = -18\\t = -36[/tex]
this is just a personal question if i have 47 assignments to do and i have to finish by the 20th of august how many do i need to do a day
Answer:
Hey there!
Today is August 7th, 2020.
Thus, August 20th is in 13 days.
If you have 47 assignments, you would have to do 3-4 a day to finish on time.
Hope this helps :) And good luck with your assignments.
Answer:
You have to do about 3 and a half assements a day.
Step-by-step explanation:
Just do 47 divides by 20 but since it is the 7th do 47 divides by 13
Have a nice day!
What is the volume of the following rectangular prism?
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Explanation:
Convert the mixed number 3 & 2/3 to an improper fraction
3 & 2/3 = 3 + 2/3
3 & 2/3 = 9/3 + 2/3
3 & 2/3 = (9+2)/3
3 & 2/3 = 11/3
The prism has a base area of 9 square units and a height of 11/3 units.
Multiply the base area by the height to get the volume
volume = (base area)*(height)
volume = (9)*(11/3)
volume = 99/3
volume = 33 cubic units
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You could choose to not convert to an improper fraction, and your steps may look like this
volume = (base area)*(height)
volume = (9)*(3 + 2/3)
volume = 9*3 + 9*(2/3) .... distribute
volume = 27 + 18/3
volume = 27 + 6
volume = 33 cubic units
Either way we get the same volume.
A sample is drawn from a well-shuffled deck of cards that contains 13 hearts, 13 clubs, 13 spades, and 13 diamonds. What is the best example of a representative sample? A. A sample of 10 cards that includes 3 hearts, 2 clubs, 2 spades, and 3 diamonds. B. A sample of 10 cards that includes 2 hearts, 1 club, 4 spades, and 3 diamonds. C. A sample of 10 cards that includes 1 heart, 1 club, 1 spade, 1 diamond, and the other 6 cards can be of any suit. D. A sample of 10 cards that includes 5 hearts and 5 clubs.
Answer:
D
Step-by-step explanation:
Hii! Please helpppp!! This was due like 3 days ago lol
Fergus has 3 1/4 cups of oats
= 13/4 cups of oats
Oatmeal bars = 2 2/3
= 8/3 cups of oatmeal used
Therefore cups of oats left = 13/4 - 8/3
= 39/12 - 32/12
= 7/12 cups of oats left
She borrowed 1 cup of oats from neighbour
7/12 + 1/1
= 7/12 + 12/12
= 19/12 cups of oats
Blueberry oats muffin = 1 3/4 cups of oats
= 7/4 cups of oats
Total she will have now = 19/12-7/4
= 19/12 - 21/12
= - 2/12
= -1/6
Which means she needs 1/6 cup of oats more
Therefore its option 4
Must click thanks and mark brainliest
Answer:
she needs 1/6 more so the last option! looking at the pic i dont think you need to show the work :)
Step-by-step explanation:
3. Solve for m:
-5m + 3 - 2m = -7m + 4 + m
1
m
12
m =
la
m = -1
m = 1
i need help with this question.
Missing Portion on Spinner:
So theres a circle,
2/3 is covered,
1/6 is covered,
and 1/9 is covered
what fraction is the portion that isn't covered
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Explanation:
The fractions 2/3, 1/6 and 1/9 have the denominators 3, 6 and 9. The LCM is 18, so the LCD of the fractions is 18.
2/3 = 12/18 after multiplying top and bottom by 6
1/6 = 3/18 after multiplying top and bottom by 3
1/9 = 2/18 after multiplying top and bottom by 2
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The three original fractions 2/3, 1/6, and 1/9 are equivalent to 12/18, 3/18, and 2/18 in that exact order.
With the fractions all having the same denominator, we can add the numerators to place over the common denominator
12/18 + 3/18 + 2/18 = (12+3+2)/18 = 17/18
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After combining all of the shaded areas, we have 17/18 of the circle shaded in with 1/18 of the circle not shaded in.
You subtract 17/18 from 1 to get 1/18
1 - (17/18) = 18/18 - 17/18 = (18-17)/18 = 1/18
You could think of it like having 18 slices of cake total, and 17 are eaten by guests, so 18-17 = 1 is left over out of the 18 overall. So 1/18 of the cake hasn't been eaten.
The required fraction is 1/18, that is not covered.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
In the given spinner,
2/3 part is covered,
1/6 part is covered,
and 1/9 part is covered.
To determine the fraction of the portion that is not covered,
Let the not covered portion is x.
Since, Total value of circle = 1
2/3 + 1/6 + 1/9 + x = 1
(4 + 1)/6 + 1/9 + x = 1
5 / 6 + 1/9 + x = 1
(15 + 2) / 18 + x = 1
17/18 + x = 1
x = 1 - 17 / 18
x = 1 / 18
The portion of the circle that is not covered is 1/18.
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The distribution of city championship wins shared by 3 HS girls basketball teams in Clayton, MO is as follows: Rockefeller HS 12, Clayton West 20, Clayton South 7. Rounded to the nearest 10%, approximately what percentage of the total wins does each team have?
Answer:
Rockefeller HS = 31%
Clayton West = 51%
Clayton South = 18%
Step-by-step explanation:
Given the following:
Championship wins shared by 3 basketball teams :
Rockefeller HS = 12
Clayton West = 20
Clayton South = 7
Percentage of total wins each team has :
Total number of wins = (12 + 20 + 7) = 39 wins
Percentage wins :
[(Number of wins per team) / total number of wins)] × 100
Rockefeller HS:
(12 / 39) * 100 = 30.769% = 31%
Clayton West :
(20/39) * 100 = 51.28% = 51%
Clayton South:
(7/39) * 100 = 17.948% = 18%
jodi has $8,525 in her savings account earning 1.8% annually. how much is in jodi’s account after 8 years? round answer to the nearest cent.
Answer: $32,207,620.36
Step-by-step explanation:
What you need to do is use the formula A = P(1+r)^n
A = Your answer
P = Is the amount Jodi started with.
R = Is the annual interest
N = Number of years
Then plug in your numbers. Always make sure you use PEMDAS. This means parenthesis, exponents, multiplication, division, addition, and subtraction. You always start with the things in the parenthesis and go on down the list. Once you finish the (1 + (1.8)) = 2.8 you will have. A = 8,535 (2.8)^8. You then multiply 2.8 with the exponent 8. Then multiply 8,535 and your answer for 2.8 times 8 and you get your answer.
Good luck on other questions kid
I would like to have some help please! ❤ thank youu I need help on the 2 question that is "write three expressions containing exponentz so that each expression equals 81."
Answer:
Below
Step-by-step explanation:
Notice that 81 = 9 * 9
So here is the first expression:
● 9^2
9 is 3^2 so 9^2 is 3^4
That's another expression
● 3^4
81 = 9*9 = 3*3*3*3 = 3^3 *3
That's another expression
● 3*3^3
You can keep manipulating the product and create many expressions like:
● 3^2 * 3^2
● 9 * 3^2
Three cyclists simultaneously start racing on a circular track at 7 am. It takes them 10 minutes, 25 minutes and 15 minutes respectively to complete the round. If all of them start at the same point and go in same direction, when will they meet again at the start point?
Answer:
9:30 am
Step-by-step explanation:
factors of 10; 5 and 2
factors of 15; 5 and 3
factors of 25; 5 and 5
calculate lcm so, 5x5x3x2 =150
150 mins = 2hr 30mins
7am+2hr30min = 9:30 am
PLEASE HELP I WILL GIVE BRAINLIEST!!!!! The box plots below show attendance at a local movie theater and high school basketball games: Two box plots are shown. The top one is labeled Movies. Minimum at 100, Q1 at 130, median at 165, Q3 at 185, maximum at 200. The bottom box plot is labeled Basketball games. Minimum at 135, Q1 at 225, median at 248, Q3 at 275, maximum at 300. Which of the following best describes how to measure the spread of the data? The IQR is a better measure of spread for movies than it is for basketball games. The standard deviation is a better measure of spread for movies than it is for basketball games. The IQR is the best measurement of spread for games and movies. The standard deviation is the best measurement of spread for games and movies.
Correct option is Option B: The standard deviation is a better measure of spread for movies than it is for basketball games.
Visual analysis for movies:
Movies data is more centric to mean and not skewed on a particular side.
Visual analysis for Basketball games:
Basketball games data is not centric to mean but is skewed or say more dense in right then left.
Property of standard deviation and its limitation:
Standard deviation just measures the deviation or spread with respect to mean of collected data. It is non- sensible for skewness of the data and thus more information is needed in such case.
Property of IQR and its limitation:
IQR is interquartile range. IQR generally is less powerful than standard deviation, but more powerful if the data is skewed and its variability has to be measured. It measures the range or say difference between [tex]Q_3 \: and \: Q_1[/tex]
In the movies data, the data is more collected and barely visible to be skewed. Thus standard deviation is best suited for this dataset.
In the basketball data, the standard deviation will fail to give good information about the data. The IQR, is better here since we've to measure variability or dispersion of data which is skewed.
Thus, option B: The standard deviation is a better measure of spread for movies than it is for basketball games; is correct option.
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What is the area of triangle PQR to the nearest tenth of a square meter? Drawing is not to scale. A. 24.1 m2 B. 34.4 m2 C. 48.2 m2 D. 68.8 m2
Answer:
b
Step-by-step explanation:
The area of triangle PQR which is an SAS triangle, to the nearest tenth, is: A. 24.1 m²
What is the Area of an SAS Triangle?The area of an SAS triangle = ½ × bc × sin(A).
Given the following:
PQ (b) = 14 mRQ (c) = 6 mAngle Q (A) = 35°Area of triangle PQR = ½ × (14)(6) × sin(35)
Area of triangle PQR = 24.1 m²
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I WILL GIE BRAINLY AND 50 POINTS PLZ PLZ PLZ HELP ME
Select the correct scientific notation form of this numeral using only 2 significant figures.
8,421,032.9266
84 × 10 9
8.4 × 10 10
8.4 × 10 6
None of these
Answer:
8.4 × 10^6
Step-by-step explanation:
Use floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10 (as in 1.591 × 10−20)
Hope this helps <3
CAN SOMEWON HELP ME PLZ I NEED HELP
Answer:
1.791875241e13
Step-by-step explanation:
5.67811 x 10⁵ = 567811
3.15576 x 10⁷ = 31557600
31557600 x 567811 = 1.791875241e13
Answer:
1.791875241e13
Harrison saved $48.97 from his first paycheck and $67.09 from his second paycheck. How much did he save from the paychecks?
Answer:
$116.06
Step-by-step explanation:
48.97 + 67.09 = 116.06
Answer:
$116,06
Step-by-step explanation:
48,97 + 67,09
The angles of a pentagon are in ratio
9:10:12:14:15. What is the sum of measures of
the smallest and largest angles?
Answer:
216°
Step-by-step explanation:
The ratio of the sum of smallest and largest to the total of all angles is ...
(9 +15)/(9 +10 +12 +14 +15) = 24/60 = 0.4
__
The total of all angles in an n-gon is 180°(n -2), so the total of all angles in a pentagon is ...
180°(5 -2) = 540°
Then the sum of smallest and largest angles is ...
0.4(540°) = 216°