Answer:
10
Step-by-step explanation:
you put the answer on the board
Let A and B be symmetric nxn matrices. For each of the following, determine whether the given matrix must be symmetric or could be nonsymmetric.a) C = A + Bb) D = A^2c) E = ABd) F = ABAe) G = AB + BAf) H = AB-BA
The matrices C, D, F, and G are symmetric while matrix H is skew-symmetric and matrix E is non-symmetric.
A matrix is an array of elements(numbers) in a peculiar order. A matrix with m rows and n columns is said to be of order m × n.
As it is known that [tex](A + B)^t = A^t + B^t[/tex] and [tex](AB)^t = B^t A^t[/tex] for any n × n matrices A and B.
Also, if matrices A and B are symmetric, then
[tex]A^t = A[/tex] and [tex]B^t = B[/tex].
a) Given that
C = A + B
Take the transpose of matrix C,
[tex]C^t = (A + B)^t[/tex]
[tex]= A^t + B^t \\= A + B = C[/tex].
Hence, matrix C is symmetric.
b) Given that
D = A²
Take the transpose of matrix D,
[tex]D = (A^2)^t[/tex]
[tex]= (AA)^t \\= A^t A^t \\= AA \\= A^2 = D[/tex].
Hence, matrix D is symmetric.
c) Given that
E = AB
Let's take an example,
A = [tex]\left[\begin{array}{cc}1&2&2&1\end{array}\right][/tex] and
B = [tex]\left[\begin{array}{cc}1 &-1 &-1&2\end{array}\right][/tex]
So,
E = AB
[tex]=\left[\begin{array}{cc}1&2&2&1\end{array}\right] \times \left[\begin{array}{cc}1 &-1 &-1&2\end{array}\right]\\= \left[\begin{array}{cc}-1&3&1&0\end{array}\right][/tex]
Clearly, matrix E is non-symmetric.
d) Given that
F = ABA
Take the transpose of matrix F,
[tex]F^t = (ABA)^t[/tex]
[tex]= A^t B^t A^t\\ = ABA = F[/tex].
Hence, matrix F is symmetric.
e) Given that
G = AB + BA
Take the transpose of matrix G,
[tex]G^t = (AB + BA)^t[/tex]
[tex]= (AB)^t + (BA)^t \\= B^t A^t + A^t B^t \\= BA + AB = G[/tex].
Hence, matrix G is symmetric.
f) Given that
H = AB-BA
Take the transpose of matrix H,
[tex]H^t = (AB - BA)^t[/tex]
[tex]= (AB)^t - (BA)^t \\= B^t A^t - A^t B^t \\= BA - AB = -H[/tex].
Hence, matrix H is skew-symmetric.
Thus, the matrices C, D, F, and G are symmetric while the rest are not.
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33
56
Find the unknown side length, x. Write your answer in simplest radical form.
A 2047
B. 60
С.
5169
D. 65
Answer:
D. 65Step-by-step explanation:
The question lacks the appropriate diagram. Find the diagram attached.
The triangle is a right angled triangle that is made of of three sides namely the opposite, the adjacent and the hypotenuse (the longest side). According to the diagram, the longest side is the side with length x. To get the side length x, we will use the Pythagoras theorem as shown;
hyp² = opp²+adj²
hyp² = 33²+56²
x² = 1089+3136
x² = 4225
take the square root of both sides
√x² = √4225
x = 65
Hence the unknown side length x is 65
Help i dont understand this someone help me pls :(
Answer:
10
Step-by-step explanation:
Seven more than three times a number is 25. What is the number?
3. Two fair dice are thrown once, find the probability of getting a total score greater than 5
Answer:
26/36
Step-by-step explanation:
The probability of something = the amount of favourable outcomes/total possible outcomes.
The total number of dice combinations is 36 (6x6).
In this case there are more outcomes more than 5 than less than 5 so for the sake of simplicity we are going to find the number of outcomes less than 5 and then find the inverse.
There are only 10 possible dice combos which add to totals 5 or under:
1,1 1,2 2,1 1,3 3,1 1,4 4,1 2,2 2,3 and 3,2
That means there is a 10/36 probability of getting a total score less than 5 so to get the probability of getting more than 5, we just do 36/36 - 10/36 (because all probabilities add to 1)
Therefore there is a 26/36 probability that the toatals will add to greater than 5.
Alternatively you could also draw up a possibilities table and count the favourable outcomes.
Hope this helped!
Answer:
13/18.
Step-by-step explanation:
The favourable outcomes are (1,5) (1,6) (2,4) (2,5) (2,6) (3,3) (3,4) (3,5) (3,6) (4,2)(4,3) (4,4) 4,5) (4,6) 5,1) (5,2) 5,3) (5,4) (5,5) (5,6 )(6,1) to (6,6).
= total of 26.
As the total of all possible outcomes is 36 the answer is 26/36
= 13/18.
400 thousands + 600 thousands in standard form
Answer: 1 million
Step-by-step explanation:
Answer:
1,000,000
Step-by-step explanation:
Step 1:
400,000 + 600,000 = 1,000,000
Answer:
1,000,000
Hope This Helps :)
4 - m/2 = 10
Please help!!
Answer:
M=3
Step-by-step explanation:
4-m/2=10subtract 4 from each sideget m/2=6then divide 2 from 6 and get m=3Hope this helps:)
Write the following set using roster notation. Do not include repeats.
A is the set of odd integers between 4 and 12.
Answer:
The Set of Natural Numbers: {1, 2, 3, 4, 5, . . .}
The Set of Whole Numbers: {0, 1, 2, 3, 4, 5, . . .}
The Set of Integers: {. . . , −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, . . .}
Step-by-step explanation:
Given A is between Y and Z and YA= 14x, AZ= 10x, and YZ= 12x + 48, find AZ
Answer:
96
Step-by-step explanation:
The value of AZ will be 40.
A is a point between Y and Z and YA = 14x , AZ = 10x and YZ = 12x + 48.
We have to calculate the value of AZ.
What is the value of MP , if N is the midpoint of M and P ?
The value of MP will be equal to the summation of NM and NP i.e., MP = NP + NM .
As per the question ;
A is the midpoint of Y and Z.
⇒ AZ + YA = YZ
⇒ 10x + 14x = 12x + 48
⇒ 24x = 12 x + 48
⇒ 12x = 48
⇒ x = 4
So ,
The value of AZ will be ;
AZ = 10 × 4
AZ = 40
Thus , the value of AZ will be 40.
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While riding her bike to the ocean and back home 6 times, Mandi timed herself at 52min, 54min, 53min, 51min, 53min, and 43min. She had set a goal of averaging 51 minutes for her rides. How many minutes will she need to spend on her seventh ride to attain her goal?
Answer:
306 min
Step-by-step explanation:
If the ratio of boys to girls at the school is 2:5 and there are 40 boys how many girls are there?
Answer:
100 girls
Step-by-step explanation:
The ratio of boys : girls is 2 : 5.
In other words, boys are 2 parts of the school while girls are 5 parts of the school.
Since there are 40 boys, 2 parts of the school is 40. Thus:
[tex]2p = 40\\p = 20[/tex]
1 part is 20.
Since there are 5 parts girls, there are
[tex]5p = 5*20 = 100[/tex]
100 girls.
Answer: 100 girls
The total number of students in school is 140 and number of girls at the school is equal to 100.
What do you mean by ratio ?
Ratio is the quantitative relationship between two values indicating how frequently one value contains or is contained within the other.
It is given that the ratio of boys to girls at the school is 2:5.
Let's assume the total number of students in school is x.
We now need to find the number of girls in the school but before that we must try to find the total number of students in the school.
Sum of ratios = 2 + 5 = 7
It is given that there are 40 boys in students.
2/7 of the total number of students are boys.
i.e., the expression can be written as :
2x / 7 = 40
2x = 40 × 7
2x = 280
x = 140
The total number of students in school is 140.
So , the number of girls in school is :
= 140 - 40
= 100
There are 100 girls in the school.
Therefore , the total number of students in school is 140 and number of girls at the school is equal to 100.
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5. The Robin's Nest Nursing Home had a fundraising goal of $9,500. By the
end of the fundraiser, they had exceeded their goal by $2,100. How much
did they raise?
During its first year in business, Alice's restaurant shows a loss of $12,000. During its second year, the restaurant makes a profit of $23,200, and during its third year, the restaurant shows a loss of $1,200. What is the net profit of the restaurant during its first three years in business?
Answer:
$10,000
Step-by-step explanation:
-12,000+23,200-1,200= 10,000
The profit of the restaurant during it's first 3 years is 9800 dollars.
What is profit and loss ?When the amount of money we get is more than what we have invested is more we have profit and when the amount of money we get is less than what we have invested we have loss.
Let us assume Alice start with a net profit or or of 0 dollars.
During its first year in business, Alice's restaurant shows a loss of 12,000 dollars.
∴ He is in loss of (0 - 12000) dollars which is
= - 12000 dollars.
During its second year, the restaurant makes a profit of 23200 dollars.
∴ His net profit is
= ( -12000 + 23000 ) dollars.
= 11000 dollars.
During its third year, the restaurant shows a loss of 1200 dollars so his ne profit is
= ( 11000 - 1200 ) dollars
= 9800 dollars.
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Evaluate the expression when a=2 and b=20
What number belongs in the box to make the equation true? 2 7 3 5
Select the relationship that does represent a function
the 4th one is a relationship that is a fuction I think
Answer:
4th image
Step-by-step explanation:
the others cannot be functions since one domain cannot be in two ranges
Simon used 13 pears and 9 apple to make fruit salad. What was the ratio of the number of apple to the number of fruit in the fruit salad?
Answer:
13:9
Step-by-step explanation:
The ratio of the number of apples to the number of fruits in the fruit salad is given by the equation A = 9 : 22
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the ratio of number of apples to the number of fruits be A
Now , the proportion will be
The number of pears = 13 pears
The number of apples = 9 apples
Now , the number of fruits = number of pears + number of apples
Substituting the values in the equation , we get
The number of fruits = 13 + 9 = 22
Now , the proportion of apples to fruits A is
Ratio of the number of apples to the number of fruits in the fruit salad A = number of apples : number of fruits
Substituting the values in the equation , we get
Ratio of the number of apples to the number of fruits in the fruit salad
A = 9 / 22
A = 9 : 22
Therefore , the value of A is 9 : 22
Hence , the proportion is 9 : 22
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Sally hopes to buy a 10 - kayak for $15,000. Describe all the numbers that when round to the nearest hundred are 15,000
Answer:
All the numbers ranging from 14,500 to 15444 would be rounded to 15000
Step-by-step explanation:
All the numbers ranging from 14,500 to 15444 would be rounded to 15000.
How this is possible.
1) all the numbers from 0-4 are not counted as the next number when rounded off.
2) all the numbers from 5-9 are counted as the next number when rounded off.
Example Suppose we have numbers from 15- 19.
These numbers can be rounded off to 20
But numbers from 10-14 would never be rounded off to 20 instead they are rounded as 10.
Same happens in the hundreds case.
If we have numbers from 450 - 499 they can be rounded as 500
And numbers from 400 - 444 cannot be rounded as 500 but the number 445 may be rounded as 450 . When we carry 5 from units place and replace it as 450 then again 450 can be rounded to 500.
Same happens with 15000 but when are rounding nearest hundred not ten.
Thus all the numbers ranging from 14,500 to 15444 would be rounded to 15000.
What are the graphs to these?
Answer:
The graph is in the image
Step-by-step explanation:
[tex]y = \frac{3}{5} x -3\\\\2x -y =-4\\\\y=-6,\:x=-5\\[/tex]
John has a 4 litre bottle of water. One mug holds one half of a litre of water. Jane drinks 3 mugs of water, how many mugs would the remaining water fill
Answer:
the answer is 3.5
Step-by-step explanation:
1. the total is 4
2.each mug = .5 of a litre
3.jane drinks 3 mugs which=1.5
4.she drinks 1.5 litres which is 3.5 of the whole bottle
5.so the remaining will be 3.5 which is what remains after she drank 1.5 litres of the whole bottle
Need help thank you!
Answer:
$216
Step-by-step explanation:
We know that the cost of an outfit for one team member is 10 + 26 + 18 = $54, therefore, the cost of outfits for all 4 team members will be 54 * 4 = $216.
Jamie invests part of $10,000 at 9% annual interest and the rest at 8%. If his annual income from
these investments is $860, how much does he invest at 8%?
Answer:
$4000
Step-by-step explanation:
Assuming a = money invested at 9%
Assuming b = money invested at 8%
then we can form am equation from the question given
1) a + b = $10000, also
0.09a + 0.08b = $860 -> multiply by 100
2) 9a + 8b = $86000
Next we try to solve both equations simultaneously. We multiply both the left hand side and the right hand side of the first equation by 8. We have
3) 8a + 8b = $80000, now we subtract 3 from 2
9a + 8b = $86000
-8a - 8b = -$80000
a = $6000.
Then, we plug this in any of the first 2 equations, to get b
9 * $6000 + 8b = $86000
$54000 + 8b = $86000
8b = $86000 - $54000
8b = $32000
b = $32000/8
b = $4000.
Therefore, he invested $4000 at 8%
i already know the answer, its increasing by 4 but i dont know how to write the answer.
Answer: m+3
Step-by-step explanation:
Since the jump from each number increases by 3, you would write m+3, since m is indicated in the pattern.
−2(2x + 5) − 3 = −3(x − 1)
Answer:
x =-16
Step-by-step explanation:
[tex]-2(2x + 5) - 3 = -3(x -1)[/tex]
Expand
[tex]\mathrm{Expand\:}-2\left(2x+5\right)-3:\quad -4x-13\\\\\mathrm{Expand\:}-3\left(x-1\right):\quad -3x+3\\\\-4x-13=-3x+3[/tex]
Collect like terms and simplify
[tex]-4x+3x =3+13\\-x =16\\[/tex]
Divide both side by -1
[tex]\frac{-x}{-1}=\frac{16}{-1}\\\\x =-16[/tex]
Consider the composite function (g (x) ) = StartRoot StartFraction 1 Over x squared minus 3 EndFraction EndRoot. If g(x) = x2 – 3, what is f(x)?
Answer:
C ON EDGE 2020
The function f(x) = [tex]\sqrt{1/x}[/tex] if, F[g(x)] = [tex]\sqrt{(1/x^2 - 3)}[/tex], g(x) = x² - 3, so option C is correct.
What is a function?
The function is a relationship between a set of potential outputs and a set of possible inputs, where each input has a single relationship with each output. This means that if an object x is present in the set of inputs (also known as the domain), then a function f will map that object to exactly one object f(x) in the set of potential outputs (called the co-domain).
Given:
F[g(x)] = [tex]\sqrt{(1/x^2 - 3)}[/tex]
g(x) = x² - 3
Put the value of g(x) in all the options and check whether it is equal to F[g(x)] as shown below,
Put it in option 3,
f{g(x)} = [tex]\sqrt{(1/x^2-3)}[/tex]
Thus, f(x) = [tex]\sqrt{1/x}[/tex]
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If (42)P = 414, what is the value of p?
7 8 12 16
Answer:
c
Step-by-step explanation:
Which inequality is true?
O A n-3>1
B. 9n> 27
c. 9/3n> 1
O D. N+7<10
Answer:
c.
Step-by-step explanation:
You are trying to estimate the average amount a family spends on food during a year. In the past the standard deviation of the amount a family has spent on food during a year has been approximately $900. If you want to be 99% sure that you have estimated average family food expenditures within $50, how many families do you need to survey? Round your answer up to the nearest whole number, if necessary.
Answer:
the number of families needed for the survey is 2,157
Step-by-step explanation:
The computation of the number of families needed for the survey is shown below:
Given that
The Standard deviation is $900
Service level = 99%
z value at 99% = 2.58
Expenditures = $50
Based on the above information
The number of families needed for the survey is
[tex]n = (\frac{zs}{E})^2\\\\= (\frac{2.58\times 900}{50})^2[/tex]
= 2,157
Hence, the number of families needed for the survey is 2,157
Simplify the following:
1.4 : 0.21
best answer gets brainliest.
Answer:
1.4/0.21= 140/21= 20/3
Step-by-step explanation:
Answer:
20:3
Step-by-step explanation:
decimal points can't be ratios so we have to convert to whole numbers:
so 1.4:0.21 becomes:
140:21
after simplifying fully( i divided both sides by 7) we come to 20:3.
The average cost of an item is defined as the total cost to produce divided by the number produced.A shoe company that pays $240,000 in rent and employee salaries per year figures it also must pay $3.50 in materials per shoe set it produces Write the equation needed to solve the problem. Use the equation to find the number of shoe sets the company would need to produce for the average cost of each set to be $7.50. Work out the problem, show all of your steps, and provide explanations.
Answer:
Step-by-step explanation:
Average cost = Total cost to produce / number of items produced
Fixed cost per year = $240,000
Variable cost = $3.50s
Where s = number of shoes produced
Total cost= fixed cost + variable cost
Total cost = $240,000 + $3.50s
When average cost = $7.50
Average cost = Total cost to produce / number of items produced
7.50 = $240,000 + $3.50s / s
Cross product
7.50s = $240,000 + $3.50s
Collect like terms
7.50s - 3.50s = 240,000
4s = 240,000
divide both sides by 4
s = 240,000 / 4
= 80,000
s = 80,000