Answer:
52
Step-by-step explanation:
The minimum of the data set is the smallest number. Therefore, the minimum is 52.
take a square of arbitary measure assuming its area is one square unit.divide it in to four equal parts and shade one of them.again take one shaded part of that square and shade one fourth of it.repeat the same process continuously and find the sum area of shaded region
Answer:
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.[1][2] The order of the magic square is the number of integers along one side (n), and the constant sum is called the magic constant. If the array includes just the positive integers {\displaystyle 1,2,...,n^{2}}{\displaystyle 1,2,...,n^{2}}, the magic square is said to be normal. Some authors take magic square to mean normal magic square.[3]
The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3
Magic squares that include repeated entries do not fall under this definition and are referred to as trivial. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant we have semimagic squares (sometimes called orthomagic squares).
The mathematical study of magic squares typically deals with its construction, classification, and enumeration. Although completely general methods for producing all the magic squares of all orders do not exist, historically three general techniques have been discovered: by bordering method, by making composite magic squares, and by adding two preliminary squares. There are also more specific strategies like the continuous enumeration method that reproduces specific patterns. Magic squares are generally classified according to their order n as: odd if n is odd, evenly even (also referred to as "doubly even") if n is a multiple of 4, oddly even (also known as "singly even") if n is any other even number. This classification is based on different techniques required to construct odd, evenly even, and oddly even squares. Beside this, depending on further properties, magic squares are also classified as associative magic squares, pandiagonal magic squares, most-perfect magic squares, and so on. More challengingly, attempts have also been made to classify all the magic squares of a given order as transformations of a smaller set of squares. Except for n ≤ 5, the enumeration of higher order magic squares is still an open challenge. The enumeration of most-perfect magic squares of any order was only accomplished in the late 20th century.
Magic squares have a long history, dating back to at least 190 BCE in China. At various times they have acquired occult or mythical significance, and have appeared as symbols in works of art. In modern times they have been generalized a number of ways, including using extra or different constraints, multiplying instead of adding cells, using alternate shapes or more than two dimensions, and replacing numbers with shapes and addition with geometric operations.
The sum area of shaded region is [tex]\frac{1}{3}[/tex].
Summation formula for geometric progressionThe formula to find the sum of infinite geometric progression is
[tex]S_{n}=\frac{a_{1}(1-q^{n}) }{1-q} \ \ q \ne 1[/tex]
Given
S = [tex]\frac{1}{4} +\frac{1}{16} +\frac{1}{64} +.........[/tex]
Using geometric progression
S = [tex]\lim_{h \to \infty} [\frac{1}{4} +(\frac{1}{4} )^{2} +(\frac{1}{4} )^{3} +.........+(\frac{1}{4} )^{n}][/tex]
Using summation formula for geometric progression
[tex]S_{n}=\frac{a_{1}(1-q^{n}) }{1-q} \ \ q \ne 1[/tex]
= [tex]\lim_{h \to \infty} \frac{\frac{1}{4} (1-(\frac{1}{4} )^{n} }{1-\frac{1}{4} }[/tex]
= [tex]\lim_{h \to \infty} \frac{\frac{1}{4} (1-\frac{1}{4^{n} }) }{\frac{3}{4} }[/tex]
= [tex]\lim_{h\to \infty} \frac{1}{3}(1-\frac{1}{4^{n} } )[/tex]
[tex]\lim_{h\to \infty} \frac{1}{4^{n} }[/tex] = 0
S = [tex]\frac{1}{3}(1-0) = \frac{1}{3}[/tex]
The sum area of shaded region is [tex]\frac{1}{3}[/tex].
Find out more information about summation formula for geometric progression here
brainly.com/question/27438806
#SPJ2
Marla noticed that her friend Ron had three times as many pieces of candy as she did. She told him, "If you give me seven pieces of your candy, we'll have exactly the same number of pieces." Ron responded, "I didn't know that until you mentioned it. But I'll make you a deal: If you can show me how to solve this puzzle using algebra, I'll give you the seven pieces. "One minute later, Ron was shocked to see that Marla had solved it perfectly. Can you do the same?
Answer:
This question seems to be asking for the work, so I put it below.
Anyhow, Marla had 3.5 candies, and Ron had 10.5.
Step-by-step explanation:
x = 3x - 7 (lets set this as "a") { a = 3x - 7}
x + 7 = 3x -7 + 7
x + 7 = 3x
( x + 7 ) / 3 = 3/3x
( x + 7 ) / 3 = x = *(same as "a") {a}
( x + 7 ) / 3 = 3x - 7
( x + 7 ) / 3 * 3 = ( 3x - 7 ) * 3
x + 7 = 9x - 21
x - x + 7 = 9x - x - 21
7 = 8x - 21
7 + 21 = 8x - 21 + 21
28 = 8x
28 / 8 = 8/8x
3.5 = x
We can plug this back into the original equation and find that it is correct because:
x = 3x - 7
x = 3.5 =====
3.5 = 3( 3.5 ) - 7
3.5 = 10.5 - 7
3.5 = 3.5
Answer:
Marla has 7 and Ron has 21
Step-by-step explanation:
lets take
no. of candies Marla has as "x"
and no. of candies Ron has will be "3x"
Marla says if Ron gives her seven candies, they will have the same no. of candies
so your equation will be -
x + 7 = 3x - 7 (as Marla gets the candy, Ron loses the candy)
3x - x = 7 + 7
2x = 14
∴x = 7
and 3x = 3 x 7 = 21
YOUR WELCOME
any 5
algebraic formulas
Answer:
a2 – b2 = (a – b)(a + b)
(a + b)2 = a2 + 2ab + b2
a2 + b2 = (a + b)2 – 2ab
(a – b)2 = a2 – 2ab + b2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
a4 – b4 = (a – b)(a + b)(a2 + b2)
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4
Answer:
a2 – b2 = (a – b)(a + b)
(a + b)2 = a2 + 2ab + b2
a2 + b2 = (a + b)2 – 2ab
(a – b)2 = a2 – 2ab + b2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
a4 – b4 = (a – b)(a + b)(a2 + b2)
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
URGENT PLS HELP<3 Each person needs to rent a helmet for $5. Write the expression for the total cost for the helmets.
Answer:
5n
Step-by-step explanation:
cost of one helmet = $5
let 'n' be the number of person that is n=1,2,3,4........
note that the value of n is always a natural number
therefore the expression = 5n
where 5 is the cost one helmet
n is the number of persons
(Picture) Could someone help me solve this I need to use Inverse Operations but I don't fully understand? I'll mark brainliest, 10 Points.
Answer:
[tex]x = - 8[/tex]
Step-by-step explanation:
First,Step write the given equation.
[tex] \frac{x}{2} + 7 = 3[/tex]
In Algebra, we learn how to solve for a missing term called a variable. We must use inverse operations to undo terms to isolate our variable. Inverse operations means that we do the opposite of the given.
Opposite of Addition is Subtraction, vice versa.Opposite of Multipication is Division, vice versa.For example, say we have a equation
[tex]x + 2 = 3[/tex]
We would subtract 2 from both sides. E.g( remember the golden rule of algebra). What we do to one side, we do the other. This applies when we solving for a variable.
This means that
[tex]x = 1[/tex]
And if we substitute 1 in for x, it is indeed true.
[tex]1 + 2 = 3 = 3[/tex]
Now, back to the question.
[tex] \frac{x}{2} + 7 = 3[/tex]
First, we subtract 7 from both sides to get rid of the 7 on the left side. Also remeber to undo terms that aren't included in the variable when solving these problems.
So now we got
[tex] \frac{x}{2} = - 4[/tex]
Then we multiply 2 by both sides since that the opposite of division.
[tex] \frac{x}{2} \times 2 = x = -4 \times 2 = - 8[/tex]
So this means that
[tex]x = - 8[/tex]
If we plug this in, this is true.
[tex] \frac{ - 8}{2} + 7 = 3[/tex]
can someone pls help w finding the x and y intercepts of this?
y=x^2-2x
Answer:
y-intercept is 0, x-intercept is 0 and 1
Step-by-step explanation:
For y-intercept, x=0 :
[tex]{ \tt{y = {(0)}^{2} - 2(0) }} \\ { \tt{y = 0}}[/tex]
For x-intercept, y=0 :
[tex]{ \tt{0 = {2x}^{2} - 2x }} \\ { \tt{2x(x - 1) = 0}} \\ { \tt{x = 0 \: \: and \: \: 1}}[/tex]
2. In a certain company, the senior employees have an average of 16 years of work experience and the junior employees have an average of 4 years of work experience. If the average number of years of experience for all the senior and junior members is 7 years, then what is the ratio of senior members to junior members at the company
Answer:
The ratio of senior members to junior members at the company is 1 : 3
Step-by-step explanation:
The given average number of years of experience of the senior employees, x = 16 years
The given average number of years of experience of the junior employees, y = 7 years
Let a represent the number of senior employees in the company, and let b represent the number of junior workers in the company, we have;
(16·a + 4·b)/(a + b) = 7
∴ (16·a + 4·b) = (a + b) × 7 = 7·a + 7·b
16·a - 7·a = 7·b - 4·b
9·a = 3·b
a/b = 3/9 = 1/3
a/b = 1/3
The above equation, expressed as a ratio is, a : b = 1 : 3
Therefore;
The ratio of senior members to junior members at the company, a : b = 1 : 3.
A retailer bought 1000 glass tumblers at rs 80 each.50 glass tumblers were broken and he sold the rest at Rs 96 each .find his profit or loss percent
Step-by-step explanation:
Soln
Given
Cp of 1 glass tumbler=80.1000
=Rs 80000
Number of broken glass tumbler=50
Number of remaining glass tumbler=1000-50
=950
Sp of one glass tumbler=96
Sp of 950 glass tumbler=96.950
=91200
Now
Sp > Cp so it is profit
Profit%=sp-cp/cp.100
=91200-80000/80000.100
=11200/80000.100
=14%
Answer:
14%profit
Step-by-step explanation:
Cost of 1000 tumblers=1000×80=80,000
50 of them were broken: 1000-50=950
: He sells 950 tumblers of rs.96 each= ( 950×96)
S.P=91200
We can clearly see he gains for rs.11200.
P%=gain/C.P×100
11200×80000×100
=14%
evaluate the expression. check all possible sets that the solution may belong in. 40-5^2
Answer:
15
Step-by-step explanation:
following PEMDAS, we don't have () so we move on to exponents
5^2 is equal to 5 x 5 which is 25
40-25=15
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{40 - 5}\mathsf{^2}\\\\\\\large\textsf{5}\mathsf{^2}\\\large\textsf{= 5}\times\large\textsf{5}\\\large\textsf{= \bf 25}\\\\\\\large\textsf{= 40 - 25}\\\\\\\large\textsf{= \bf 15}\\\\\\\\\\\\\boxed{\boxed{\huge\textsf{Therefore your answer is: \bf 15}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\textsf{Amphitrite1040:)}[/tex]
f(x) = 2x + 7 with domain: x = {2, 3, 5, 9}
Answer:
2(2)+7=11
2(3)+7=13
2(4)+7=15
2(5)+7=17
2(9)+7=25
Step-by-step explanation:
2(2)+7
4+7=11
2(3)+7
6+7=13
2(4)+7
8+7=15
2(5)+7
10+7=17
2(9)+7
18+7=25
lvan earned $8 each time he walks his neighbor's dog. he already walked the dog 5 times.
How many more times does her need to walk the dog to earn enough money to buy a game that costs $88
__? more times
Complete the tables, and the graph… HELPPP
Answer:
answer is - 1
Step-by-step explanation:
- x + y = 3
x = 4
- ( - 4 ) + y = 3
4 + y = 3. take 4 to the right
y = 3 - 4
y = - 1
I hope this answers your question.
Find X in the picture
Find the place value of 8 in 2456.1387.
Tenths
Hundredths
Thousandths
Thousands
Answer: Third Choice. Thousandths
Step-by-step explanation:
Concept:
Here, we need to know the order and name of each place value.
Please refer to the attachment below for the specified names.
Solve:
STEP ONE: Orde and name each place
2 ⇒ One Thousands
4 ⇒ Hundreds
5 ⇒ Tens
6 ⇒ Ones
.
1 ⇒ Tenths
3 ⇒ Hundredths
8 ⇒ One Thousandths
7 ⇒ Ten Thousandths
STEP TWO: Find the number [8] in the number
As we can see from the list above, 8 is at the right of the decimal point, thus, the place value is Thousandths.
Hope this helps!! :)
Please let me know if you have any questions
What is the constant of proportionality in the equation x 2
—- = ——
Y 9
Answer:
The Constant is 9/2
What is the measure of m?
5
15
E
n
m = [?]
====================================================
Explanation:
The two smaller triangles are proportional, which lets us set up this equation
5/n = n/15
Cross multiplying leads to
5*15 = n*n
n^2 = 75
----------
Apply the pythagorean theorem on the smaller triangle on top, or on the right.
a^2+b^2 = c^2
5^2+n^2 = m^2
25+75 = m^2
100 = m^2
m^2 = 100
m = sqrt(100)
m = 10
1. The product of two consecutive numbers is 42. What are the numbers?
Answer:
6, 7
Step-by-step explanation:
6 x 7 = 42
Find the length of each side and the
perimeter.
(5n -17) cm
(2n + 1) cm
n cm
7n-16
Step-by-step explanation:
Sry can u give me the picture
A girl bought x kg of green apples and 3 kg of red apples. What was the total mass of all the apples she bought
Answer:
Total = x+3 kg
Step-by-step explanation:
Green apples = x kg, Red apples = 3 kg
what value of x is in the solution set of -5-15>10+20x
Answer:
-3/2 >x
Step-by-step explanation:
-5-15>10+20x
Combine like terms
-20 > 10 +20x
Subtract 20 from each side
-20 -10 > 10+20x-10
-30> 20x
Divide by 20
-30/20 >20x/20
-3/2 >x
Answer:
-3/2 > x
Step-by-step explanation:
-5 - 15 > 10 + 20x
^ ^
-20
-20 > 10 + 20x
-10 -10
---------------------
-30 > 20x
----- -------
20 20
-3/2 > x
Hope this helped.
cho tứ giác ABCD. Gọi M,N,P,Q là trung điểm của các cạnh AB, CD, AD, BC. Chứng minh rằng vecto MP = vecto QN, vecto MQ = vecto PN
Answer:
Step-by-step explanation:
Xét tam giác DAB có: P là trung điểm AD, M là trung điểm AB
=> MP là đường trung bình của tam giác DAB => MP//BD và MP=[tex]\frac{1}{2}[/tex]BD (1)
Xét tam giác DBC có: N là trung điểm DC, Q là trung điểm BC
=> QN là đường trung bình của tam giác DBC => QN//BD và QN=[tex]\frac{1}{2}[/tex]BD (2)
Từ (1) và (2) => vecto MP song song cùng chiều với vecto QN
và độ dài MP = độ dài QN = [tex]\frac{1}{2}[/tex]BD
=> vecto MP = vecto QN
Tương tự xét các tam giác DAC và tam giác ABC => vecto MQ = vecto PN
find the radius of a circle for which an arc 6 cm long subtends an angle of 1/3 radians at the center?
plz some one can help to solve the question??
Step-by-step explanation:
Eueydhhdgdgdbdbddbdbhd
Answer:
Hello,
[tex]R=\dfrac{18}{\pi}\ (cm)[/tex]
Step-by-step explanation:
[tex]Formula: \ L=\theta*R\\[/tex]
[tex]R=\dfrac{6}{\dfrac{\pi}{3} } =\dfrac{6*3}{\pi} =\dfrac{18}{\pi}\ (cm)[/tex]
ayudenme pls aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
aslo bien jjjjjjj
Step-by-step explanation:
Which of the following intervals is the graph decreasing?
Answer:
B
Step-by-step explanation:
Values of y are decreasing where x is in the range (-4;02)
Four times an angle is equal to half of its supplement. Find the measures of both angles.
Answer:
The bigger angle is 144 degrees and the smaller one is 36 degrees
(2x+1)(x-4)
(6x-5)(3x+2)
Answer:
2x^2 + 9x - 4
18x^2 - 3x - 10
Step-by-step explanation:
use foil method
The amount of money lana earns for tutoring is proportional to the time she spends tutoring. She earns $24 for tutoring 1 1/2 hours. what is the constant of proportionality for the relationship between dollars earned and number of hours?
Answer:
y=16x
Step-by-step explanation:
24=1 1/2x=3/2x
x=24*(2/3)=16
y= total money earned; x=number of hours worked
factorize = n!+(n-1)!
Answer:
Hello,
Step-by-step explanation:
n! + (n-1)!
=(n-1)! * n+ (n-1)!
=(n-1)! * (n+1)
(3 1/3) (6) What is the answer?
Answer:
20
Step-by-step explanation:
(6x3=18) (6x1/3=2) (18+2=20)
First things first!
Multiply 6 by 3 (18).
Mulitply 6 by 1/3 (2).
Add 18 and 2, and ... *drum roll*, the final answer is 20!
Hope this helps :)
(84)/(12)+(5-7)^(2)-72-6x2
Answer:
[tex]-73[/tex]
Step-by-step explanation:
Note: My explanation is based of the order-of-operations
First, using the order-of-operations, we evaluate the expressions in parentheses. Fully simplifying [tex](5-7)^2[/tex] gives us: [tex](5-7)^2 = -2^2 = 4[/tex].
Next, we do [tex]6\cdot2[/tex] giving us [tex]12[/tex]. So far, our expression is simplified to [tex]\frac{84}{12} + 4 - 72 - 12[/tex].
We also know that [tex]\frac{84}{12}[/tex] is just [tex]7[/tex] so we can replace that value in the expression leaving us with: [tex]7+4-72-12[/tex]. Now, we can solve it in simple steps!
1) [tex]7+4=11[/tex]
3) [tex]11-72=-61[/tex]
4) [tex]-61-12=-73[/tex]
Our answer is [tex]-73[/tex]
Hopefully this helped you out! Please (please) tell me if their is a mistake in the solution and I will correct it as fast as possible for me.
