The size of a matrix is its dimension,
AB and BA are of size 4 x 4 and 2 x 2 respectively
Matrix A has dimension 4 x 2 and matrix B has dimension 2 x 4
Matrix:
In mathematics, a matrix (multiple matrices) is a rectangular array or table of numbers, symbols, or formulas, arranged in rows and columns, used to represent mathematical objects or properties of such objects .
Product of Matrix:
Multiplication of two matrices is defined only if the number of columns in the left matrix equals the number of rows in the right matrix. If A is an m-by-n matrix and B is an n-by-p matrix, then its matrix product AB is an m-by-p matrix whose entries correspond to the corresponding rows of A in the matrices.
A column of B whenever a product of different sizes is such that it is defined. The product AB can be defined without BA being defined. That is, if A and B are m-by-n and n-by-k matrices, respectively, and m ≠ k. In general, even if both products are defined, they need not be the same. So, AB ≠ BA,
Product AB:
The dimensions of AB are the rows of matrix A multiplied by the columns of matrix B.
Matrix A has 4 rows and Matrix B has 4 columns.
Therefore, the dimension of the matrix AB is 4 x 4.
Product BA:
The dimensions of matrix BA are the rows of matrix B multiplied by the columns of matrix A.
Matrix B has 2 rows and Matrix A has 2 columns.
Therefore the dimension of the matrix BA is 2 x 2.
Therefore, the sizes of AB and BA are 4 x 4 and 2 x 2 respectively.
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I WILL GIVE BRAINLIEST PLEASE ANSWER!!
△ABC has the verticies at A(4,5) B(-3,6) and C(-1,8)
the following transformations have been done to the triangle in that order...
rotated 90 degrees
reflected across the line y=0
then translated according to the rule (x+3,y-3)
Once all transformations are complete what are the final points?
Answer:
o answer this question, we need to apply the transformations in the reverse order. So first, we need to apply the translation according to the rule (x+3,y-3). This means that the coordinates of the triangle will become A'(7,2), B'(0,3), and C'(2,5). Next, we need to reflect the triangle across the line y=0. This means that the y-coordinates of the triangle will become negative. So the coordinates of the triangle will become A''(7,-2), B''(0,-3), and C''(2,-5). Finally, we need to rotate the triangle 90 degrees. In a standard cartesian coordinate system, a rotation of 90 degrees counterclockwise is equivalent to the transformation (x, y) -> (-y, x). So the final coordinates of the triangle will be A'''(-2,7), B'''(-3,0), and C'''(-5,2).
Given the linear function equation state the function rate.
y = -7x + 1
m=?
Answer:
In the linear function equation y = -7x + 1, the value of m (the slope of the line) is -7. The slope of a line represents the rate at which the y-value changes as the x-value changes. In this case, for every unit increase in the x-value, the y-value decreases by 7 units. Therefore, the function has a rate of -7.
To find the slope of a line from a linear function equation, you can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. In this case, we can choose any two points on the line and substitute their coordinates into the formula to find the slope. For example, if we choose the points (1, -6) and (2, -13), we get:
m = (-13 - (-6)) / (2 - 1) = -7
Alternatively, we can use the fact that the slope of a line is equal to the coefficient of the x-term in the linear function equation. In this case, the coefficient of the x-term is -7, so the slope of the line is also -7.
Step-by-step explanation:
if the numbers denoting the perimeter and area of the square are equal, what is the length of the diagonal?
If the numbers denoting the perimeter and area of the square are equal, the length of the diagonal will be 4√2 units.
What are Area and Perimeter?
An object's shape defines a region as its area. The area of a figure or any other two-dimensional geometric shape is how much space it takes up in a plane.
The whole length encircling a shape is referred to as its perimeter. Simply put, if a shape is stretched into a linear form, its perimeter is its length. In a two-dimensional plane, a shape's perimeter is the sum of its total dimensions.
Let the side of the square to be 'a'.
If Area and Perimeter of a square are equal then,
So, Area = Perimeter
a^2 = 4a
we get, a = 4 units.
Now, we can find the diagonal by using Pythagoras theorem,
We know that, Hypotenuse^2 = Base^2 + Perpendicular^2
Here, the hypotenuse will be the diagonal of the square.
So, We have,
Diagonal^2 = 4^2 + 4^2
= 16 + 16
= 32
∴ Diagonal = √32 = 4√2 units.
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What is the equation of a line perpendicular to y = - 1/4 x + 6 and goes through the point (2, 9) ?
Using the slope formula, the required equation is y = -4x + 1.
What is the slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
The slope of a line can be used to gauge how steep it is.
The slope is theoretically determined as "rise over run" (change in y divided by change in x).
So, slope formula: m = y2 - y1/x2 - x2
Now we have: y = - 1/4 x + 6 and points (2, 9)
Now, substitute as follows:
(y-9) = -4(x+2)
In order to convert this equation into the slope-internet form, we can additionally solve it for y:
(y-9) = (-4*x+(4*2)
(y-9) = -4x - 8
y - 9 + 9 = -4x - 8 + 9
y - 0 = -4x + 1
y = -4x + 1
Therefore, using the slope formula, the required equation is y = -4x + 1.
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PLEASE HELP ME PLEASE!!!!!!!!!!!
Answer:
(6,12)
Step-by-step explanation:
(Hopefully you can see the work if not then sorry)
the amount of money spent by a customer at a discount store has a mean of and a standard deviation of . what is the probability that a randomly selected group of shoppers will spend a total of more than ? (hint: the total will be more than when the sample mean exceeds what value?)
The probability that a randomly selected group of shoppers will spend a total of more than is 7.86%.
Standard deviation = √n × σ
= √50 × 30
= 212.1320
P( Σx > 5300) = P( Σx - nu / √n * σ > 5300 - 5000/212.1320)
= P(z > 1.414)
= 1 - P( z< 1.414)
= 0.078621
= 7.86%
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How can you tell if a formula represents length, an area, or volume? what do you look for in the formula?.
60 people attend a game night. Everyone chooses to play chess, a two-player game, or cribbage, a four-player game. All 60 people are playing either chess or cribbage.
1.Complete this table showing some possible combinations of the number of each type of game being played:he equation. Enter only 1 term in each blank.
2.Write an equation to represent the situation illustrated in the table
3.There are 3 more games of cribbage being played than games of chess being played. Write an equation to represent this relationship. 4.Solve the system of equations you just wrote. There were
chess games, and
cribbage games.
Answer:
8 chess games are being played while 11 cribbage games are being played.
Let x represent the number of chess games and y represent the number of cribbage games.
Since there are 60 people, chess is a two-player game and cribbage is a four-player game, hence:
2x + 4y = 60 (1)
There are 3 more games of cribbage than games of chess, hence:
y = x + 3
-x + y = 3 (2)
Solving equations 1 and 2 simultaneously gives:
x = 8, y = 11
Therefore 8 chess games are being played while 11 cribbage games are being played.
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Step-by-step explanation:
Super easy question
Answer: The correct answer is A. Addition
Step-by-step explanation:
Let's solve for x in 2x+4y=10
Step 1: Add -4y to both sides.
2x+4y+−4y=10+−4y
2x=−4y+10
Step 2: Divide both sides by 2.
2x/2 = −4y+10/2
x = −2y +5
Now let's solve for x in 5x+4y = -12
Step 1: Add -4y to both sides.
5x+4y+−4y=−12+−4y
5x=−4y−12
Step 2: Divide both sides by 5.
5x/5 = −4y−12/5
x = −4/5y + −12/5
Here is what solving for Y looks like
Let's solve for y in 2x+4y=10
Step 1: Add -2x to both sides.
2x+4y+−2x=10+−2x
4y=−2x+10
Step 2: Divide both sides by 4.
4y/4 = −2x+10/4
y = −1/2x + 5/2
Now let's solve for y in 5x+4y = -12
Step 1: Add -5x to both sides.
5x+4y+−5x=−12+−5x
4y=−5x−12
Step 2: Divide both sides by 4.
4y/4 = −5x−12/4
y = −5/4 x−3
addition. thanks for the points. /j
one assumption underlying linear regression is that the x values are normally distributed. true false
One assumption underlying linear regression is that the x values are normally distributed.
This above statement is true.
Linear regression:Linear regression is a linear approach for modeling the relationship between a scalar response and one or more explanatory variables (also called dependent and independent variables). When there is one explanatory variable, it is called simple linear regression. If there are more than one, the process is called multiple linear regression. This concept differs from multivariate linear regression, which predicts multiple correlated dependent variables instead of a single scalar variable.
In linear regression, relationships are modeled using a linear predictor function in which the unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response is assumed to be an affine function of the values of the explanatory variables (or predictors) given those values. In rare cases, a conditional median or another quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response variable given the values of the predictor variables, rather than the joint probability distribution of all variables, which is the domain of multivariate analysis.
Assumption:1. Weekly Exogeneous:
It means that we can treat the predictor variable x as a fixed value rather than as a random variable. This means, for example, that the predictor variables are assumed to be error-free, ie not contaminated with measurement error. This assumption is not realistic in many situations, but omitting it makes the within-variable error model much more difficult.
2. Linearity:
This means that the mean response variable is a linear combination of the parameters (regression coefficients) and the predictor variables. . The predictor variables themselves can be arbitrarily transformed. In fact, we can add multiple copies of the same underlying predictor variable, each transformed differently.
3. Constant variance or Homogeneity:
This means that the error variance does not depend on the values of the predictor variables. Therefore, for any given fixed value of the predictor, the variability of the response is the same no matter how large or small the response is. This is often not the case because variables with large mean values usually have more variance than variables with small mean values.
4. Independence from:
This assumes that the response errors are uncorrelated. (True statistical independence is a stronger condition than just lack of correlation and is often unnecessary, but can be exploited when it is known to hold.) Generalized least squares, etc. Some methods in can handle correlated errors, but this usually requires significantly more data unless some kind of regularization is used to bias the model to accept uncorrelated errors Bayesian linear regression is a popular method for handling this problem.
5. Lack of Multicollinearity:
Predictors are not fully multicollinear. For the standard least-squares estimation method, the design matrix X must have perfect column rank p. Otherwise, the predictors are perfectly multicollinear, meaning there is a linear relationship between two or more predictors. This can be caused by erroneously duplicating variables in the data, using linear transformations of the variables together with the original variables, or using multiple variables in the model. It can be caused by inserting a linear combination. as their average. It is also possible that too little data is available relative to the number of estimated parameters.
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Is dilatation the same as dilation?
Answer:
no
Step-by-step explanation:
Dilatation is acutally for medicine and dilation is actually for phycology.
Find the demand function for the marginal revenue function. recall that if no items are sold, the revenue is 0. R′(x)=0.06x2−0.05x+138
The revenue function for the given marginal revenue function
R'(x) = 0.06x² - 0.05x + 138 be
R(x) = 0.02x³ - 0.025x² + 138x
Given, a marginal revenue function,
R'(x) = 0.06x² - 0.05x + 138
we have to find the demand function
as, we know that the demand function can be find by integrating the marginal revenue function with respect to the variable x.
So, as the marginal revenue function is given,
R'(x) = 0.06x² - 0.05x + 138
On integrating with respect to x, we get
R(x) = 0.06x³/3 - 0.05x²/2 + 138x + C
where C is an arbitrary constant.
Also, it is given that
R(0) = 0
So, R(0) = 0.06(0) - 0.05(0) + 138(0) + C
0 = C
R(x) = 0.06x³/3 - 0.05x²/2 + 138x + 0
R(x) = 0.02x³ - 0.025x² + 138x
So, the revenue function be R(x) = 0.02x³ - 0.025x² + 138x
Hence, the revenue function be R(x) = 0.02x³ - 0.025x² + 138x
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On Monday, Jake could lift 25 lbs. One
year later, the weight he could lift
increased by 30%. What is the number
of pounds he can lift a year later?
At noon, a tank contained 6 in. of water. After several hours, it contained 3 in. of water. What is the percent decrease of water in the tank
The percent decrease of water in the tank is 50%.
What is the percent decrease?
The difference between starting and final numbers is the percentage drop. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decline.
We have,
a tank contained 6 in. of water.
After several hours, it contained 3 in. of water.
percent decrease of water in the tank?
A tank contained 6 in of water.
After several hours, it contained 3 in of water
So, decrease in water = 6 in - 3 in = 3 cm
The percent decrease of water in the tank = (change in amount of water/initial amount) * 100
The percent decrease of water in the tank = (3/6) * 100
= 50
Hence, the percent decrease of water in the tank is 50%.
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Tara and Edward each painted their bedrooms. They finished in the same amount of time, even though Edward's bedroom is bigger. They have 4 hours to start painting the basement before dinner is ready. Who will likely paint a larger part of the basement?
can someone help me with this
How do you find the equation of a plane passing through two points and perpendicular to another plane?
To find the equation of a plane passing through two points and perpendicular to another plane, use the cross product.
First calculate the vector between the two given points,
then use the cross product to find a vector that is perpendicular to both the vector between the two points and the equation of the other plane.
Finally, use the two points and the perpendicular vector to find the equation of the plane.
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Help I’m struggling
After the discount and the tax, the total cost will be $24.19
How to find the total cost?
So, suppose we have a known price P.
If we apply a discount of X (in percentage) then the new price will be:
P' = P*(1 - X/100%)
If instead, we apply an increase of X, the new price willbe:
P' = P*(1 + X/100%).
In this case the original price is $30, then we apply a discount of 25% and then an increases of 7.5%, then the total cost will be:
C = $30*(1 + 7.5%/100%)*(1 - 25%/100%)
C = $30*(1 + 0.075)*(1 - 0.25) = $24.19
That is the final cost of the jeans.
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Determine the slope of the line that contains the points (15,7) and (6, 13).
Answer: -0.66667
Step-by-step explanation:
answer or im crying myself asleep
Answer:
154.64 m-----------------------------
We see that triangles MNO and MPQ are similar.
Corresponding sides of similar triangles are proportional:
MN/MP = NO/PQ(65 + 110)/110 = NO/97.2175/110 = NO/97.2NO = 175*97.2/110NO = 154.6363 ≈ 154.64 m
The size of a large milkshake is 1. 4 times the size of a small milkshake. Write a percent that compares the size of the large milkshake to the size of the small milkshake.
The percentage comparing the size of the large milkshake to the size of the small milkshake is 140%.
Let the size of small milkshake he x. So, the size of large milkshake will be 1.4x. Now, for percentage calculation the formula will be -
Percentage = size of large milkshake/size of small milkshake × 100
As we need to find the percentage of ratio, we need to simply take large and small size of milkshake.
Keep the values in formula -
Percentage = 1.4x/x ×100
Cancelling x from numerator and denominator
Percentage = 1.4 ×100
Performing multiplication
Percentage = 140%
Hence, the percentage is 140%.
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P(4,6), over the x-axis
The image of point P(4,6) after a reflection over the x-axis is given as follows:
P'(4,-6).
How to obtain the image of point P?The coordinates of the point P in this problem are given as follows:
P(4,6).
Meaning that:
The x-coordinate is of 4.The y-coordinate is of 6.The rule for a reflection over the x-axis is given as follows:
(x,y) -> (x,-y).
Meaning that the x-coordinate remains constant, while the y-coordinate has the signal exchanged.
Applying the rule, the coordinates of the image are given as follows:
x-coordinate of 4, as it remains constant.y-coordinate of -6, as the signal is exchanged.Then the coordinates of the image after the reflection are given as follows:
P'(4,-6).
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How can you solve multi-step equations that include parentheses?
Answer:
Use PEMDAS to solve by simplifying and isolating the variable.
Step-by-step explanation:
Simplify both sides of the equation. You can use PEMDAS to do this (parentheses, exponets, multiplication, division, addition, subtraction). That is the order to simplify in. Also dont forget to distribute any signs infront of the parentheses to the values in the parentheses.After both sides are simplified and all like terms are combined isolate the variable. (get it by itself)after it is by itself simplify it if it has anything attached to it like it being multiplied or divided by a value.then you should have your answer (x=value)The students at a certain high school have an elective period, where each student chooses an elective from among four options. The following table shows the number of students who selected each elective for the 1,500 students at the high school.
If each student can only choose one elective, picking both is impossible, making the probability 0.
There is no chance of picking a single kid for music and art electives (0).
Information disclosed:
A high school's students are participating in electives.
Since each student is only allowed to choose one elective course from the options provided, they can either choose music or art as their elective.
Therefore, it is impossible to choose a student who has chosen to study art and music.
As a result, there is no chance of picking a student for whom both music and art are electives (0).
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ways that Canada and Australia can reduce their dependence on fossil fuels.
Answer:using gas
Step-by-step explanation:
How much pizza sauce is needed to cover a 16" pizza? (Note: 16" is the diameter of the pizza.)
Responses
A 200.96 in2200.96 in 2
B 803.84 in2803.84 in 2
C 50.24 in250.24 in 2
D 3215.36 in2
Answer:
It is difficult to give a precise answer without more information, such as the thickness of the sauce and the desired coverage. However, if we assume that the sauce is being applied evenly and that a thin layer is desired, the amount of sauce needed to cover a 16" pizza would be approximately 50.24 in2. This is because the area of a circle with a diameter of 16" is approximately 50.24 in2. To calculate the area of a circle, you can use the formula A = πr^2, where A is the area, π is approximately 3.14, and r is the radius of the circle (which is half the diameter). In this case, the radius would be 8" and the area would be approximately 50.24 in2.
Step-by-step explanation:
Find the slope between the
following points:
(-6,0), and (1,-14)
Answer:
gradient = -2
Step-by-step explanation:
gradient = difference of y-coordinates / difference of x-coordinates
gradient = (y2-y1) / (x2-x1)
gradient = (-14)-0 / 1-(-6)
gradient = (-14)/7
gradient = -2
Solve for X in Circle A
The value of x, if In triangle ABC, AC = 18, BC = 30 is 24.
What is circle?A circle is a two-dimensional shape created by a collection of points that are spaced uniformly or uniformly apart from a fixed point (center) on the plane.
Given:
In triangle ABC, AC = 18, BC = 30
As we know, if a tangent is drawn from the circle then it will form a right-angled triangle thus, ∠ ABC = 90°,
Calculate the value of x by using Pythagoras' theorem as shown below,
[tex]AB^2 = BC^2 - AC^2[/tex]
Substitute the values
x² = 30² - 18²
x = √(900 - 324)
x = √576
x = 24
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Helppppppppppppppp I need helppp
Answer:
4. (2) 0
5. (1) 1/25
Step-by-step explanation:
Definition: a^0 = 1
4.
8(x + 11)^0 - 2x^0 + 6x =
= 8 × 1 - 2 × 1 + 6 × (-1)
= 8 - 2 - 6
= 0
5.
[(5^3)^2]/[(5^2)^4] =
= 5^6 / 5^8
= 5^(-2)
= 1/5^2
= 1/25
what is the standard deviation of the sample means called? what is the formula for this standard deviation?
The term "standard error of the mean" refers to the sample mean's standard deviation. And the formula for the standard deviation is σ/√n.
What is a standard deviation?The square root of a random variable's variance is the standard deviation of a sample, statistical population, data collection, or probability distribution. Compared to the average absolute deviation, it is algebraically easier but less reliable in practice. The standard deviation has the advantage of being represented in the same unit as the data, unlike the variance, which is a desirable characteristic.
The standard error of a statistic (such the sample mean) is related to the standard deviation of a population or sample, however they are very different. Standard deviation of the population divided by the square root of sample size yields the standard deviation of the sampling distribution of means. "Standard error of the mean" is the term for the sampling distribution's standard deviation.
The term "standard error of the mean" refers to the sample mean's standard deviation.
And the formula for the standard deviation is given by σ/√n.
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