The correct statements are:
1. If the product AB = 0 (zero matrix), then either A = 0 or B = 0.
4. BC = CB.
Explanation:
1. If the product of two matrices AB equals the zero matrix, it implies that at least one of the matrices A or B (or both) must be the zero matrix for the product to result in zero.
4. The statement BC = CB states that the order of multiplication of matrices B and C does not affect the resulting matrix. This property holds true for matrices of any size as long as the dimensions are compatible for matrix multiplication.
The other statements are not necessarily true in general:
2. Both BC and CB being square matrices is not guaranteed. The product of two matrices can result in a square matrix only if the number of columns of the first matrix is equal to the number of rows of the second matrix. In this case, B has 3 columns and C has 2 rows, so BC and CB are not square matrices.
3. The matrix A + BC is not defined since the addition of matrices requires them to have the same dimensions. In this case, A is a 2×2 matrix, while BC is a 2×3 matrix, so they cannot be added together.
5. The statement A = A12 = I2 implies that matrix A is equal to the 2×2 identity matrix I2. However, this is not necessarily true as the given information does not provide any details about the values or properties of matrix A.
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Plz help me on this one to plz
Answer:
The answers are............
4) D, 5) 0.75
Find the value of x when: -2(3x - 5) = 52
Answer:
-7
Step-by-step explanation:
-2(3x-5)=52
-6x+10=52
-6x=52-10
-6x=42
x=42/-6
x=-7
Marcus has 27 pairs of gym shoes total. If 9 pairs of shoes are Jordans, what is the ratio of Jordans to non-Jordan shoes?
Answer:
17 to 9
Step-by-step explanation:
I think let me know if I'm wrong
Answer:
okay 9 of marcus shoes are jordans 17 of marcus shoes arn't jordans
Step-by-step explanation:
bc if you subtract 27-9 you can get 17
Question 2. (30 points): Consider the following linear program: maxx s.t. z=4x1+3x2+3x32x1+2x2+x3≤4,x1+3x2+x3≤9,x1,x2,x3≥0. Write down the dual LP, graphically solve the dual LP, and then use complimentary slackness conditions to find the set of optimal solutions of the primal LP.
The optimal solution for the primal LP is x1 = 0, x2 = 2, x3 = 2, with a maximum value of z = 16.
Let's start by writing down the dual LP. The dual LP is obtained by interchanging the roles of variables and constraints in the primal LP. The dual variables corresponding to the constraints are y1 and y2, representing the multipliers for the first and second constraint, respectively. The objective function of the dual LP is given by minimizing 4y1 + 9y2, and the dual LP subject to the dual constraints is as follows:
min 4y1 + 9y2 subject to:
2y1 + y2 ≥ 4
3y1 + 3y2 ≥ 3
y1, y2 ≥ 0
To graphically solve the dual LP, we can plot the feasible region defined by the dual constraints and find the point that minimizes the objective function. By solving the dual LP, we obtain y1 = 1/3 and y2 = 2/3, with a minimum value of 10/3. Now, using the complementary slackness conditions, we can find the set of optimal solutions for the primal LP. The conditions state that for any optimal solution, the product of the primal constraint and the dual variable must be zero. Since the primal constraints are inequalities, we consider them as equalities to check the conditions. For the first constraint, 2x1 + 2x2 + x3 = 4, we have y1(2x1 + 2x2 + x3 - 4) = 0, which gives y1 = 0. Similarly, for the second constraint, x1 + 3x2 + x3 = 9, we have y2(x1 + 3x2 + x3 - 9) = 0, which gives y2 = 0. Hence, the optimal solution for the primal LP is x1 = 0, x2 = 2, x3 = 2, with a maximum value of z = 16, satisfying the complementary slackness conditions.
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HELPP PLEASE
GEOMETRY escape challenge G!!
Geometry escape challenges can be a fun way to develop problem-solving skills and deepen one's understanding of geometric principles. With practice and persistence, anyone can improve their geometry skills and become better equipped to tackle more complex challenges.
Geometry is a branch of mathematics that deals with the study of shapes, sizes, relative positions of objects, and the properties of space. It has applications in various fields like engineering, art, architecture, and science.
To solve geometry problems, one needs to have a solid understanding of geometric principles and formulas and develop problem-solving skills that enable them to visualize and manipulate 2D and 3D objects.
Escape challenges are games designed to test one's logical thinking and puzzle-solving abilities. In the context of geometry, an escape challenge may involve finding solutions to problems or uncovering hidden clues that help players move through various levels of the game.
To succeed in escape challenges, one needs to be observant, analytical, and creative. Some common strategies for tackling geometry escape challenges include breaking down complex problems into smaller components, using visual aids to help visualize concepts, and testing multiple solutions until the correct one is found.
In conclusion, geometry escape challenges can be a fun way to develop problem-solving skills and deepen one's understanding of geometric principles. With practice and persistence, anyone can improve their geometry skills and become better equipped to tackle more complex challenges.
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HELP NOW PLEASE I WILL GIVE BRAINLIEST IT'S URGENT!!!!!!
I need help filling in the equation for #30. My teacher asked me to fill in the blank.
y = ___ - 4x
Answer:
y=24-4x
Step-by-step explanation:
If you use this equation on any problem, you can see it will work. For (1,20) plug in the x and y variable, which is 20=24-4(1)
4(1)=4, so the equation is 20=24-4
24-4=20
20=20
the single factor that made the hindu arabic number system superior to the other number systems is the
Answer:
invention of 0
Step-by-step explanation:
shows that it is possible to have nothing
Paul is adding mulch along the edge of his driveway. There are 8 black fish, 5 white fish, and 3 gold fish. What is the ratio of gold fish to total fish? Select all that apply.
A: 3:16
B: 16:3
C: 3 to 16
D: 16 to 3
E: 3/16
F: 16/3
Marking brainlest if you answer ASAP!!!!plsss
Answer:
Add up the number of chocolate chips and then just search up waht is the median of ____.
Step-by-step explanation:
Hope this helped
Consider the following data:
x 1 2 3 4 5
P(X=x) 0.1 0.2 0.3 0.2 0.2
Step 3 of 5:
Find the standard deviation. Round your answer to one decimal place.
Step 4 of 5:
Find the value of P(X≥5)P(X≥5). Round your answer to one decimal place.
Step 5 of 5:
Find the value of P(X≤3)P(X≤3). Round your answer to one decimal place.
The standard deviation is approximately 1.3, rounded to one decimal place. The values for P(X≥5) and P(X≤3) are approximately 0.2 and 0.6, respectively, rounded to one decimal place.
To determine the standard deviation, we first need to calculate the mean. We can do this by multiplying each value of 'x' by its corresponding probability and summing them up:
Mean (μ) = (1*0.1) + (2*0.2) + (3*0.3) + (4*0.2) + (5*0.2) = 0.1 + 0.4 + 0.9 + 0.8 + 1.0 = 3.2
Next, we can calculate the variance (σ^2) by squaring the differences between each 'x' value and the mean, multiplying by their probabilities, and summing them up:
Variance (σ²) =
[tex][(1-3.2)^2 * 0.1] + [(2-3.2)^2 * 0.2] + [(3-3.2)^2 * 0.3] + [(4-3.2)^2 * 0.2] + [(5-3.2)^2 * 0.2]= \\(-2.2)^2 * 0.1] + [(-1.2)^2 * 0.2] + [(-0.2)^2 * 0.3] + [(0.8)^2 * 0.2] + [(1.8)^2 * 0.2]= \\4.84 * 0.1 + 1.44 * 0.2 + 0.04 * 0.3 + 0.64 * 0.2 + 3.24 * 0.2= 0.484 + 0.288 + 0.012 + 0.128 + 0.648 \\= 1.56[/tex]
Finally, the standard deviation (σ) is the square root of the variance:
Standard Deviation (σ) = √1.56 ≈ 1.25 (rounded to one decimal place)
To find P(X≥5), we add up the probabilities of all 'x' values greater than or equal to 5:
P(X≥5) = P(X=5) = 0.2
To find P(X≤3), we add up the probabilities of all 'x' values less than or equal to 3:
P(X≤3) = P(X=1) + P(X=2) + P(X=3) = 0.1 + 0.2 + 0.3 = 0.6
Therefore, the values are:
Standard Deviation ≈ 1.3
P(X≥5) ≈ 0.2
P(X≤3) ≈ 0.6
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How is a sample related to a population?
Answer:
A sample is a subset of a population.
Step-by-step explanation:
Solve the system by substitution.
12x + 6y + 72 = -35
7x - 5y – 6z= 200
x+y= -10
Step-by-step explanation:
12x+6y+72=-35
12x+6y=-35-72
12x+6y=-107 equation i
X+y=-10 equation ii
multiply by 6 on equation ii and subtract from equation i
12x+6y=-107
-6x-6y=60
6x=47
X=7.83333333
put the value of X on equation i
12×7.83333333+6y=-107
6y=-107-94
y=33.5
now
put the value of X and y on equation iii
7×7.83333333-5×33.5+6z=200
54.8333331-167.5+6z=200
-112.666667+6z=200
6z=200+112.666667
z=52.1111112
i am thinking of a number. my number is a multiple of 6. what three other numbers must my number be a multiple of?
find the constant of variation k for the direct variation
Answer:
The constant of variation is k = -2 ⇒ (B)
Step-by-step explanation:
The equation of the direct variation is y = k x, where
k is the constant of variationThe constant of variation k = [tex]\frac{y}{x}[/tex]The given table has 4 points (-1, 2), (0, 0), (2, -4), (5, -10)
We can use one of the points [except point (0, 0)] to find the value of k
∵ (-1, 2) is a given point
∴ x = -1 and y = 2
∵ k = [tex]\frac{y}{x}[/tex]
→ Substitute the values of x and y in the relation above
∴ k = [tex]\frac{2}{-1}[/tex]
∴ k = -2
The constant of variation is k = -2
PLSSS HELP....Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with x-axis labeled study time in hours and y-axis labeled grade percent. Points are plotted at 1 comma 50, 2 comma 50, 2 comma 60, 2 comma 70, 3 comma 70, 3 comma 80, 4 comma 85, and 4 comma 90, and a line of fit drawn passing through the points 0 comma 30 and 2 comma 60
Determine the equation of the line of fit.
y = 15x + 60
y = 15x + 30
y = 30x + 60
y = 30x + 30
The equation of the Line of fit is y = 15x + 30.
The equation of the line of fit, we can use the two given points: (0, 30) and (2, 60).
First, we find the slope (m) of the line using the formula:
m = (change in y) / (change in x)
m = (60 - 30) / (2 - 0) = 30 / 2 = 15
The slope of the line is 15.
Next, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
Using the point (2, 60):
y - 60 = 15(x - 2)
Simplifying the equation:
y - 60 = 15x - 30
Now, we can isolate y:
y = 15x - 30 + 60
y = 15x + 30
Therefore, the equation of the line of fit is y = 15x + 30.
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Which statement best describes a difference between electromagnetic waves and mechanical waves?
Answer: D
Step-by-step explanation: I just answered the question on the quiz and got it wrong (from a p e x)
2
Type the correct answer in each box. Use numerals instead of words.
Complete the area model representing the polynomial x2 - 11x + 28. What is the factored form of the polynomial? Use the model to rewrite the
expression
X
-7
X
X2
-4X
(x+
(
-7)
Reset
Next
Answer:
blank 1 (in the graph) : -7x
blank 2 (in the graph) : 28
blank 3 (next to the graph) :-4
on the bottom equation blanks: -4 and then 7
bottom equation blanks should look like:
(x+-4) (7-7)
True or False?
The union of two or more sets is the set of all elements that belong
to either one set or the other set or to both sets.
Answer:
Its false im pretty sure i hope this helped
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
I believe that it is FALSE
Hope this helped
Solve Z/5 - 4 = 2 1/3.
Z=
PLEASE HELP
Answer:
Z= 31.6666666666666666
Step-by-step explanation:
x/5 - 4 = 2 1/3
x/5 = 6 1/3
x=6 1/3 times 5
x=31.66 repeated
is y=10x a function?
Answer:
Yes
Step-by-step explanation:
HELP!!! 10 points and marked brainliest
Answer:
m=2
Step-by-step explanation:
RS=2m+2
ST=3m+3
RT=15
m=2
RS=2(2)+2
RS=4+2
RS=6
ST=3(2)+3
ST=6+3
ST=9
Because S is in the middle of RT, if you add RS and ST together, you will get the length of RT.
6+9=15
Solve the following, show all work for thumbs
up!
Calculate the matrix elements of a 4x4 matrix given
the following basis states and Hamiltonian where first term in the
Hamiltonian is the hopping
+ + H = =+ (C₁F C²₂₁ +²₁ √ (₂²) + C₂₁ C₁p + C₂ C₁4) +Unit+1^₂)) Hopping i hopp. interaction; int. where ris: Cis Cis is number operator Using the following information: 11)
Answer:
Yes
Step-by-step explanation:
2.95x+28=50
Please help
Answer:
x = 22 / 2.95 :)
Step-by-step explanation:
Alright, so 2.95x + 28 = 50.
This means, (subtracting 28) that
2.95x = 50 - 28 = 22
2.95x = 22
So...
x = 22 / 2.95 :)
When viewed from the front, the rope used to tie down a tent forms a pair of supplementary angles with the ground. Find $m\angle ABC$ .
Answer:
<ABC = 49°
Step-by-step explanation:
The sum of two supplementary angle is 180. From the diagram, the two angles are 3x+4 and 8x+11. IF this two angles are supplementary then;
3x+4+8x+11 = 180
11x+15= 180
11x = 180-15
11x = 165
x = 165/11
x = 15
From the attached diagram, <ABC = 3x+4
<ABC = 3(15)+4
<ABC = 45+4
<ABC = 49°
use it the number line to answer the following 2 questions . How many groups of 9 over 5 are in 1. Evaluate 6 divided by 9 over 5
Answer: The answer to your second question is 2/15
Step-by-step explanation:
6/9=2/3 and 2/3 divided by 5 or multiplied by 1/5 is 2/15
(b) Ten men can assemble 400 cycles in 8 days. How many cycles 5 men will
assemble if they work for 16 days?
Answer:
400
Step-by-step explanation
First, find how many cycles 5 man can make in 8 days.
400/2=200 (/ means divide)
Next, mutliply the answer to find out how many cycles 5 man can make in 16 days.
200x2=400
pleaseeeeeeeeeee hellllllllppppppppp
two no are in ratio 5:3 if diffrence is 18 find no.
Answer:
[tex]5..3 = 18..x[/tex]
[tex] \frac{5}{3} = \frac{18}{x} [/tex]
Cross Multiply ✖
[tex]5(x) = 18(3)[/tex]
[tex]5x = 54[/tex]
Dividing both sides by 5 ⚄
[tex]x = \frac{54}{5} [/tex]
[tex]x = 10.8[/tex]
OR
[tex]10 \times \frac{4}{5} [/tex]
[tex]10 \frac{4}{5} [/tex]
MARNIE OUT !
A team won 12 games and lost 4 games, what is their win-loss ratio?
please help!!!
Example and Answer
Answer:
y=3x
Step-by-step explanation:
Can some help me please because I got the correct answer but is saying it incorrect !
Answer:
i got 7 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
