To find the value of matrix A given A⁻¹ and B⁻¹, we can use the formula A = (A⁻¹)⁻¹ * B⁻¹.
Given A⁻¹ = [[2, 7], [-2, 2]] and B⁻¹ = [[2, 1], [3, 4], [4, 3], [2, 11]], we can calculate A as follows:
Step 1: Calculate the inverse of A⁻¹: (A⁻¹)⁻¹
(A⁻¹)⁻¹ = [[2, 7], [-2, 2]]⁻¹
To find the inverse of a 2x2 matrix, we use the following formula:
[[a, b], [c, d]]⁻¹ = (1 / det([[a, b], [c, d]])) * [[d, -b], [-c, a]]
Step 2: Calculate the determinant of A⁻¹: det([[2, 7], [-2, 2]])
det([[2, 7], [-2, 2]]) = (2 * 2) - (7 * -2) = 4 + 14 = 18
Step 3: Calculate the inverse of A⁻¹: (A⁻¹)⁻¹
(A⁻¹)⁻¹ = (1 / 18) * [[2, -7], [2, 2]] = [[2/18, -7/18], [2/18, 2/18]]
Step 4: Calculate A = (A⁻¹)⁻¹ * B⁻¹
A = [[2/18, -7/18], [2/18, 2/18]] * [[2, 1], [3, 4], [4, 3], [2, 11]]
Performing matrix multiplication, we get:
A = [[2/18 * 2 + (-7/18) * 3, 2/18 * 1 + (-7/18) * 4],
[2/18 * 2 + 2/18 * 3, 2/18 * 1 + 2/18 * 4]]
Simplifying the calculations, we find:
A = [[-1/3, -2/3],
[2/9, 4/9]]
Therefore, the value of matrix A is [[-1/3, -2/3], [2/9, 4/9]].
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Select the correct answer. you have 7 balls that are each a different color of the rainbow. in how many distinct ways can these balls be ordered? a. 1 b. 7 c. 49 d. 343 e. 5,040
Answer:
E. 5,040
Step-by-step explanation:
For plato users
Can one help me out with this problem it due today
Step-by-step explanation:
the solution is in the picture
the curve created by a quadratic function is called a
Answer:
A parabola
Step-by-step explanation:
A parabola is created when you create a quadratic equation, and the highest/lowest value it will reach before it dips down/up again is called the vertex; not sure what exactly you meant by this question so feel free to clarify and I can help you the best I can
The curve created by a quadratic function is called a parabola.
A parabola is a U-shaped curve that is symmetric about a vertical line called the axis of symmetry. It is defined by a quadratic equation in the form of y = ax^2 + bx + c, where "a," "b," and "c" are constants. The coefficient "a" determines whether the parabola opens upwards (if "a" is positive) or downwards (if "a" is negative).
The vertex of the parabola represents its lowest or highest point, depending on the orientation. Parabolas have various applications in mathematics, physics, engineering, and other fields due to their distinctive shape and properties.
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What do you get when you divide the circumference of your jack-o-lantern by its diameter?.
On dividing the circumference and the diameter of our Jack-o-Lantern we will get π.
A Jack-o-Lantern can be considered spherical in shape.
The circumference of a #D shape is the intersection of the 3D shape with any plane passing through its center.
Hence the circumference of a jack-o-lantern will be the perimeter of the circle that has been cut through its center.
Let the radius of our Jack-o-lantern be r cm.
The formula of a circumference of a sphere is 2πr
where r is the radius of the sphere.
The diameter of a sphere is twice its radius.
Therefore, the diameter of our jack-o-lantern will be
2r cm.
By dividing the circumference and the diameter we get
2πr cm / 2r cm
= π
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Triangles ABC and DEF are similar find d
Answer:
A=D where is picture . it is required
After buying a pair of sneakers, Ben has $12 left which is 20% of what he started with. How much money did Ben have before he bought his pair of sneakers?
Answer: $60
Step-by-step explanation:
Given that:
Amount left after purchasing sneakers = $12
$12 is equivalent to 20% of the initial starting amount
Let starting amount = x
20% of x = $12
0.2x = $12
Divide through by 0.2
0.2x / 0.2 = $12 / 0.2
x = $60
Hence, starting amount before buying sneakers is $60
How many terms are in the polynomial 3t^3 + 2t^2 + 5t - 3 ?
6
4
5
3
Answer:
4
Step-by-step explanation:
Every term is basically a part of the equation that are separated by the plus or minus signs. There are 4 terms, 3t^3, 2t^2, 5t, and 3, since they are not further simplifiable
Answer:
There are 4 terms in the given polynomial.
Step-by-step explanation:
A verandah is 40 m long and 15 m broad. It is to be paved with stones, each measuring 6
dm by 5 dm. Find the number of stones required.
Please help me out!!!!!!
Answer:
200 stones.
Step-by-step explanation:
Given that the verandah is 40 meters long by 15 meters wide, and that it is going to be paved with stones that measure 6 decimeters by 5 decimeters, to determine the amount of stones that should be used, the following calculation must be performed:
1 m = 10 dm
Verandah's surface: 40 x 15 = 600m2
Stones' surface: 6 x 5 = 30dm2 = 3m2
600/3 = X
200 = X
Therefore, 200 stones should be used to pave the entire verandah.
Suppose the vectors \( \bar{i}, \bar{j}, \bar{p} \) and \( \bar{q} \) are all unit vectors and the angle \( \theta=222^{\circ} \). Find the cartesian vector form of \( \bar{F}=(-31 \bar{i}+102 \bar{j}
The cartesian vector form of \(F\) is \(F = (-31cos(\alpha )i + 102sin(\alpha )j)\). We call x + yi the Cartesian form for a complex number.
Given that \(i,j,p\) and \(q\) are unit vectors and the angle \(\alpha = 222\)°, we can express the cartesian vector form of \(F\) as \(F = (-31cos(\alpha )i + 102sin(\alpha )j)\).
To calculate the components of \(F\) , we use the trigonometric functions \(cos(\alpha )\) and \(sin(\alpha )\) with the given angle \(\alpha = 222\)°.
\(cos(222) = -0.766\\sin(222) = -0.643\)
Substituting these values into the cartesian vector form, we have:
\(F = (-31cos(222)i + 102sin(222)j)\\F = (-31 * -0.766i + 102*-0.643j)\\F = (23.746i - 65.586j)\)
Therefore, the cartesian vector form of \(F\) is \(F = (23.746i - 65.586j)\).
The cartesian vector form of \(F = (23.746i - 65.586j)\)
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Find an equation of the plane through the given point and parallel to the given plane. origin 3x - y + 3z = 4
An equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4 is 3x - y + 3z = 0.
To find an equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4, we can use the fact that parallel planes have the same normal vector.
Step 1: Find the normal vector of the given plane.
The normal vector of a plane with equation Ax + By + Cz = D is . So, in this case, the normal vector of the given plane is <3, -1, 3>.
Step 2: Use the normal vector to find the equation of the parallel plane.
Since the parallel plane has the same normal vector, the equation of the parallel plane passing through the origin is of the form 3x - y + 3z = 0.
Therefore, an equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4 is 3x - y + 3z = 0.
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The value of the sample mean will remain static even when the data set from the population is changed.
True or False?
False. The value of the sample mean is not static and can change with different data sets.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
False.
The value of the sample mean is calculated based on the data in the sample, and it can change if the data set from which the sample is drawn changes.
For example, suppose we have a population with a certain mean and take a random sample from that population to calculate the sample mean. If we take a different sample from the same population, we may get a different sample mean. Similarly, if we take a sample from a different population with a different mean, we will get a different sample mean.
Therefore, the value of the sample mean is not static and can change with different data sets.
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Determine which of the following discrete-time, causal systems are stable. 1. y[n+1] - 3y[n] = x[n] 2. y[n+1] - 0.3y[n] = x[n] 3. y[n+1] + 3y[n] = x[n] 4. y[n+1] + 0.3y[n] = x[n] A. 1 and 2 B. 1 and 3 C. 1 and 4 D. 2 and 3 E. None of the above
The stable discrete-time, causal systems are options A. 1 and 2. The stable systems among the given options are 1 (unstable) and 2 (stable), leading to option A. 1 and 2 as the correct answer.
A discrete-time system is stable if its output does not grow unbounded for bounded inputs. One way to determine stability is by examining the poles of the system's transfer function. In this case, we can rewrite the given equations in the form of a transfer function. Let's assume Y(z) and X(z) represent the z-transforms of y[n] and x[n], respectively.
For the first system, the equation y[n+1] - 3y[n] = x[n] can be rearranged as Y(z)(z - 3) = X(z). The transfer function of this system is H(z) = Y(z)/X(z) = 1/(z - 3). The pole of this transfer function is z = 3. Since the pole is outside the unit circle in the z-plane, this system is unstable.
For the second system, the equation y[n+1] - 0.3y[n] = x[n] can be rearranged as Y(z)(z - 0.3) = X(z). The transfer function of this system is H(z) = Y(z)/X(z) = 1/(z - 0.3). The pole of this transfer function is z = 0.3. Since the pole is inside the unit circle in the z-plane, this system is stable.
Therefore, the stable systems among the given options are 1 (unstable) and 2 (stable), leading to option A. 1 and 2 as the correct answer.
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what is a point-slope equation of the line with slope -12 that goes through the point (5,3)?
Answer:
y-3=-12(x-5)
Step-by-step explanation:
y-y1=m(x-x1)
y-3=-12(x-5)
Help with this question
Help me plsas fast as you can :) tyyyy
(A) Create and label a circle graph based on the percentages in the table.
(B) How much money did the family spend on each category for the party?
A. A labeled circle graph to represent the percentages in the table is shown below.
B. The amount of money this family spent on each category for the party are;
Drinks = $192.Food = $228.Entertainment = $108.Decorations = $72.How to create a circle graph based on the percentages?In this scenario and exercise, we can make use of an online graphing calculator or Microsoft Excel to create and label a circle graph based on the percentages shown in the table. You should type in the various categories and input values (percentages) in columns and then click on insert (charts).
Part b.
Next, we would calculate the amount of money the family spent on each category for the party are as follows;
Drinks = 32/100 × 600
Drinks = $192.
Food = 38/100 × 600
Food = $228.
Entertainment = 18/100 × 600
Entertainment = $108.
Decorations = 12/100 × 600
Decorations = $72.
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1. Simplify the fraction: 14/63
Answer:
2/9 is the simplified fraction (14/63 = 2/9)
Answer:
2/9
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator GCD of 14 and 63 is 7.
Divide both the numerator and denominator by the GCD 14 ÷ 7 / 63 ÷ 7.
Reduced fraction: 2 / 9 Therefore, 14/63 simplified to lowest terms is 2/9.
Can you help me solve this problem??
The function that models the averageTannual cost of owning a small dog for x years is f(x) = (180 + 400x) / x
How to depict the functionThe total cost of owning a small dog for x years can be expressed as the sum of the one-time cost and the continuing costs for x years, which is:
Total Cost = One-time Cost + Continuing Costs for x years
Total Cost = $180 + $400x
In this case, to find the average annual cost, we divide the total cost by the number of years:
Average Annual Cost = Total Cost / x
Average Annual Cost = ($180 + $400x) / x
Therefore, the function that models the average annual cost of owning a small dog for x years is: f(x) = ($180 + $400x) / x
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The weekly marginal revenue from the sale of x pairs of tennis shoes is given by the equation below, where R() is revenue in dollars. R'(x)= 48 -0.03x +600/( x + 1). R(0)=0.
Find the revenue function. Find the revenue from the sale of 1,000 pairs of shoes. (Round to the nearest cent as needed.)
Given, the weekly marginal revenue from the sale of x pairs of tennis shoes is given by the equation below, where R() is revenue in dollars. R'(x)= 48 -0.03x +600/( x + 1). R(0)=0. We need to find the revenue function and the revenue from the sale of 1,000 pairs of shoes.
Steps to find the revenue function:
R'(x) = 48 -0.03x + 600/(x+1)∫ dR(x)/dx = ∫ [48 -0.03x + 600/(x+1)]dx R(x) = ∫ [48 -0.03x]dx + ∫ [600/(x+1)]dx R(x) = 48x - 0.015x^2 + 600ln(x+1) + C (where C is a constant of integration).
Now, R(0) = 0C = 0. Therefore, the revenue function is R(x) = 48x - 0.015x^2 + 600ln(x+1).
Revenue from the sale of 1,000 pairs of shoes is R(1000) = 48(1000) - 0.015(1000)^2 + 600ln(1000+1) = $44,097.51 (rounded to the nearest cent).
Therefore, the revenue from the sale of 1,000 pairs of shoes is $44,097.51.
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An Amtrak official obtains data on a particular day concerning the length of time (in minutes) that the metroliners leaving New York take to reach Philadelphia, with the following results:
93 89 91 87 91 89
Find the sample variance.
a. 3.6
b. 5.6
c. 6.8
d. 7.6
e. 4.4
The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.
The sample variance is a measure of how much the individual data points in a sample vary from the mean.
It is calculated by finding the average of the squared differences between each data point and the mean.
To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:
Calculate the mean (average) of the data set:
Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90
Subtract the mean from each data point and square the result:
(93 - 90)^2 = 9
(89 - 90)^2 = 1
(91 - 90)^2 = 1
(87 - 90)^2 = 9
(91 - 90)^2 = 1
(89 - 90)^2 = 1
Calculate the sum of the squared differences:
9 + 1 + 1 + 9 + 1 + 1 = 22
Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):
Variance = 22 / 5 = 4.4
It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.
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I need help please ASAP
Answer:
for # 1 it is 9
#2 is 21
Step-by-step explanation:
What is the solution to this system of equations?
y=1/3x+4
y=1/6x+3
what is the degree of -7xyz^2
Answer:
The degree is 4
Let me know if it helped :)
What is the solution to the equation
Answer:
The answer to your question is C D=1
Step-by-step explanation:
i'm new to brainly but I'm also really smart in math have a nice day glad to help
In a class of 29 students, 19 are female and 14 have an A in the class. There are 8 students who are male and do not have an A in the class. What is t
If In a class of 29 students, 19 are female and 14 have an A in the class then 2 male students have an A in the class.
We can calculate the number of students who are male and have an A in the class by subtracting the given values from the total number of students.
Total students = 29
Female students = 19
Male students = Total students - Female students = 29 - 19 = 10
Students with an A = 14
Male students without an A = 8
To calculate the number of male students with an A, we subtract the number of male students without an A from the total number of male students.
Male students with an A = Male students - Male students without an A = 10 - 8 = 2
Therefore, there are 2 male students who have an A in the class.
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he - Venn diegram below describes the probablity of students who wlll lake Chem istry = and Spanish at Jafferson High School next year; Where A Student takes chemistry and B Students takes Spanish_ Suppose one student Is chosen at random Use Ihe above vann dlagram . Find the value of P(A L 8) and describe In words. a.) 0.6; The probability that the student takes both chemistry and Spanish. b.) 0.1; The probability that the student takes both chemistry and Spanish_ c.) 0.1; The probability that the student takes either chemistry or Spanish; bul not both. d.)0.6; The probability that the student takes either chemistry or Spanish, or both.
From the Venn diagram , the value of required probability P(A∪B) is given by :
Option a). 0.6 . The probability that students takes both Spanish and Chemistry.
Let us consider 'A' be the probability of the students who takes Chemistry.
And 'B' be the probability of the students who takes Spanish.
From the Venn diagram we have,
Probability of A 'P(A) ' = 0.2 + 0.1
= 0.3
Probability of B 'P(B)' = 0.3 + 0.1
= 0.4
Probability of A∩B 'P(A∩B)' = 0.1
Probability of A∪B is given by :
P(A∪B) = P(A) + P(B) - P(A∩B)
Substitute the value we get ,
⇒ P(A∪B) = 0.3 + 0.4 - 0.1
⇒ P(A∪B) = 0.6
P(A∪B) represents the probability of the students that takes both Chemistry and Spanish.
Therefore, the value and explanation of P(A∪B) is equal to :
Option a). 0.6 , the probability of the students that takes both Chemistry and Spanish.
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The above question is incomplete , the complete question is:
The - Venn diagram below describes the probability of students who will take Chemistry and Spanish at Jefferson High School next year, where A Student takes chemistry and B Students takes Spanish. Suppose one student is chosen at random Use the attached Venn diagram .
Find the value of P(A∪B) and describe in words.
a.) 0.6; The probability that the student takes both chemistry and Spanish.
b.) 0.1; The probability that the student takes both chemistry and Spanish.
c.) 0.1; The probability that the student takes either chemistry or Spanish; but not both.
d.)0.6; The probability that the student takes either chemistry or Spanish, or both.
Venn diagram is attached.
strengths and limitations of visually interpreting histograms
Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.
Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.
Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.
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Sam bought a television for $535. The tax rate in Pennsylvania is 6%. What is the total amount Sam paid for the television? (Round your answer to the nearest cent.)
\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 535}}{\left( \cfrac{6}{100} \right)535}\implies 32.10~\hfill \underset{ \textit{total amount} }{\stackrel{ 535~~ + ~~32.10 }{\text{\LARGE 567.10}}}\)
A music store marks up the instruments it sells by 40%. If the store bought a guitar for $35, what will be its store price? If the price tag on a trumpet says $104, how much did the store pay for it? If the store paid $75 for a clarinet and sold it for $100, did the store mark up the price by 40%?
Answer:
a. $49
b. $74.28
c. No
Step-by-step explanation:
The computation is shown below:
a. The store price is
= Purchase price + markup
= $35 + $35 × 40%
= $35 + $14
= $49
b. The price paid is
Since there is a markup of 40% and when it is added to 100% of cost so the selling price is 140% of the cost or 1.40 of the cost
Now the price paid is
$104 = 1.40 × cost
So, the cost is
= $104 ÷ 1.40
= $74.28
c. Now the markup is
= $100 - $75
= $25
The markup percentage is
= $25 ÷ $75
= 33.33%
No the store does not markup the price by 40%
What is the measure of Zx?
Angles are not necessarily drawn to scale.
Answer:
the answer is 78*
Step-by-step explanation:
31 and 47 is 78...
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i want to know if i am right
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Calculate the mean and median of: 202, 199, 223, 198, 223, 223, 301, 199.
Answer:
mean =225.25, median= 212.5
Step-by-step explanation:
You add all the numbers and divided by the total numbers to get mean, and for get the median you need to put them in order and get the number that is between all the number it be the 202 and 223 so you divide the two number with two and it will be 212.5
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