Let B = {b1, b2} and C = {c1, c2} be bases for R2. Find the change-of-coordinates matrix from B to C and then from C to B.b1 = matrix(2,1,[1,1]) , b2 = matrix(2,1,[1,2]) , c1 = matrix(2,1,[2,3]) , c2 = matrix(2,1,[3,4])
Answers
The change-of-coordinates matrix from B to C is P_B→C, and the change-of-coordinates matrix from C to B is P_C→B.
To find the change-of-coordinates matrix from B to C, we need to express each vector in the basis C as a linear combination of the vectors in the basis B.
We can represent this relationship using a matrix called the transition matrix.
Given B = {b1, b2} and C = {c1, c2}, with b1 = [1,1], b2 = [1,2], c1 = [2,3], and c2 = [3,4], we can set up the following system of linear equations:
c1 = a * b1 + b * b2
c2 = c * b1 + d * b2
Solving this system, we get a = 1, b = 1, c = 2, and d = 1.
Thus, the transition matrix from B to C, denoted as P_B→C, is: P_B→C = | 1 2 | | 1 1 |
To find the change-of-coordinates matrix from C to B (P_C→B), we simply find the inverse of P_B→C:
P_C→B = (P_B→C)^(-1) = | 1 -2 | | -1 1 |
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Related Questions
Plss help its due in 6 hours
Answers
Answer:
1. 1/25
2. 3x3x3x3=81
3. (25)(625)=15,625
4. 7^4x2/ 7^5=343
5. 3
6.64
A builder is using the drawing below to build a house. If the owner decides to increase the living room dimensions by 20%, what is the new length and width of the living room floor?
A.14.4 feet x 9.6 feet
B.144 feet x 96 feet
C.13.2 feet x 8.2 feet
D.10 feet x 8 feet
Answers
Percentage increment means the part of original value is added to the value. The new length of the living room is 14.4 feet long and new width of the living room is 1.6 feet long. The option A is the correct option.
What is the percentage of a number?
Percentage of a number or ratio is fraction of hundred. It is expressed with the sign "%".
Given information-
The length of the living room is 12 feet.
The width of the living room is 8 feet.
The owner increases the 20 percent of length and 20% width.
Suppose new length is feet long. As the owner increases the 20 percent of length. Thus the new length will be sum of original length and the 20 percent of it. Hence,
Thus the new length of the living room is 14.4 feet long.
Suppose new width is feet long. As the owner increases the 20 percent of width. Thus the new width will be sum of original width and the 20 percent of it. Hence,
Thus the new width of the living room is 1.6 feet long.
Hence the new length of the living room is 14.4 feet long and new width of the living room is 1.6 feet long. The option A is the correct option.
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Which expression is equivalent to 10>5/154x8? assume x>=0
Answers
The expression that is equivalent to 10 > 5/154x8 is x > 1/ 2464 or 2464x > 1.
To see why this works, we can first simplify 5/154x8 . We can then simplify this to 5/1232x, by multiplying 5/(154*8) by x and simplifying the result. We can then substitute this expression into the original inequality to get:
10 > 5/1232x
x > 0, which means that x is a positive number
Divide both sides by 10 and multiply by x, then
x > 5/(1232*10)
x > 1/ 2464
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Sophia owns a small business selling used books. She knows that in the last week 15 customers paid cash, 50 customers used a debit card, and 15 customers used a credit card. Based on these results, express the probability that the next customer will pay with a debit card as a decimal to the nearest hundredth.
Answers
The probability that the next person will pay with a debit card is:
P = 0.63
How to find the probability?
We want to find he probability that the next customer will pay with a debit card.
That probability can be estimated as the quotient between the number of customers that paid with debit card and the total number of customers.
We know that:
15 paid in cash.
50 paid with debit card.
15 paid with credit card.
For a total of 15 + 50 + 15 = 80
Then the probability is:
P = 50/80 = 0.63
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If the product of the extremes is 8,then the geometric mean is
~2
~4
~2(square root sign)2
Answers
The geometric mean of two numbers is the square root of their product:
\(GM(a,b)=\sqrt{ab}\)
So, if the product is 8, the geometric mean is \(\sqrt{8}=2\sqrt{2}\)
What is the actual length of the living space if the length in the scale drawing is 16. 8 in the scale
Answers
The actual length of the living area is 134.4 feet if the length in the scale drawing is 16.8 in the scale.
To determine the actual length of the living space from a scale drawing, we need to use the scale factor, which is the ratio of the length in the drawing to the actual length. If the length in the scale drawing is 16.8 inches and the scale is given as a ratio of 1 inch in the drawing to 8 feet in actual size, we can set up a proportion:
1 inch (drawing) / 8 feet (actual)
= 16.8 inches (drawing) / x (actual)
We can cross-multiply and simplify to find x's value:
1 inch × x = 8 feet × 16.8 inches
x = (8 feet × 16.8 inches) / 1 inch
x = 134.4 feet.
Therefore, the actual length of the living space is 134.4 feet.
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an employee group requires 6 people be chosen for a committee from a group of 12 employees. determine the following probabilities of randomly drawn committee of 6 employees. write your answers as percents rounded to 4 decimal places. the employee group has 9 women and 3 men. what is the probability that 3 of the people chosen for the committee are women and 3 people chosen for the committee are men? % the committee requires that exactly 2 people from human resources serve on the committee. there are 4 people in human resources. what is the probability that exactly 2 of the people chosen for the committee are from human resources? %
Answers
The probability of choosing 3 men and 3 women to form the committee is 0.4329 and the probability to select exactly 2 people from the human resources is 0.4545.
It is given that there are 12 employees.
The number of male employees is 6
number of female employees is 6
A committee of 6 is to be formed. We need to find the probability that out of 6, 3 are male and 3 are female.
Let A be the event of having 3 men and 3 women on the committee
The total number of ways to choose 6 people is
¹²C₆
Probability = number of favorable outcomes / total number of outcomes
n(A) = ⁶C₃ X ⁶C₃
Therefore,
P(A) = (⁶C₃ X ⁶C₃) / ¹²C₆
= (20 X 20) / 924
= 400/924
= 0.4329
It is given that the number of employees in human resources from the group is 4
Let B be the event to choose exactly 2 employees from the human resource
n(B) = ⁴C₂ X ⁸C₄
P(B) = ⁴C₂ X ⁸C₄ / ¹²C₆
= 6 X 70 / 924
= 420 / 924
= 0.4545
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A diver leaps off of cliff, modeled by the equation y =-16x^{2}-8x+120. When will the diver reach a height of 72 feet
Answers
The diver reaches a height of 72 feet after 1.5 seconds.
Given that, a diver leaps off of cliff, modeled by the equation,
y = -16x²- 8x +120.
We need to time taken by the diver to reach a height of 72 ft.
72 = -16x²- 8x + 120.
-16x²- 8x + 48 = 0
2x² + x - 6 = 0
Factorizing,
2x² + 4x -3x - 6 = 0
2x(x+2) -3(x+2) = 0
(2x-3)(x+2) = 0
x = -2, x = 1.5
Since, time cannot be negative so neglecting x = -2
Hence, the diver reaches a height of 72 feet after 1.5 seconds.
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Samuel has 1 cup of rubbing alcohol and will use the entire amount. He plans to store the cleaning solution in containers that each hold a maximum of 6 cups. How many containers does he need.
Answers
Samuel needs a total of 6 containers for his plan
How to determine the number of container he needs?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
1 cup of rubbing alcohol = 1/(1/2) = 2 shares
Also, we have
1 cup of rubbing alcohol contains = 1 + 1/2 + 16 = 17.5
For the 2 shares calculated above, we have
2 shares = 17.5 * 2
Evaluate
2 shares = 35
Given that each can hold a maximum of 6 cups, the number of containers needed is
Container = 35/6
This gives
Container = 5.83
Round up
Container = 6
Hence, he needs 6 containers
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Pls help me I will make you as Brainly
Wendy plans to her first 5k, in two months, and she needs to prepare. She has a busy schedule, though, and needs to select the best way for her activity for her heart. Which way should Wendy pick.
Answers
Answer:
it is the first option as they are intense exercises
2. Help me find the mode of these data set: 12, 10, 10, 10, 13,12, 11, 13, 10
(2 Points)
1. 10
2. 10 & 12
3. no mode
4. 12
Answers
Answer:
10 is the answer for this
please mark me as brilliant
Please answer! Will give brainliest!
Answers
The required linear functions are A(t) = 50t + 100 and B(t) = 25t + 200 which are represented in the attached graph. Company A is cheaper if the time is less than 4 hours.
As per the given question, we can write the linear functions as:
A(t) = 50t + 100
B(t) = 25t + 200
We can determine time t when both companies charge the same rate by equating the two equations.
50t + 100 = 25t + 200
Subtract 25t from both sides and subtract 100 from both sides
25t = 100
Divide both sides by 25
t = 4
At 4 hours both companies charge the same rate. So Company A is cheaper if the time is less than 4 hours.
After 4 hours, company B is cheaper.
Since both functions are linear, we only need two points to plot each one onto a graph.
Thus, the required linear functions are A(t) = 50t + 100 and B(t) = 25t + 200 which are represented in the attached graph.
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Two identical regular hexagons are joined together as shown in the diagram.
Work out the size of angle x
Answers
Answer:
120
Step-by-step explanation:
Please help and show the formula used, along with all substitutions and calculations needed
Answers
Answer:
The given triangle is right.
Step-by-step explanation:
The Pythagorean converse theorem states the following: if one can substitute the sides of a triangle into the following formula:
\(a^2+b^2=c^2\)
If the equation formed is a true statement, then the triangle is right, if it is not, then the triangle is not right. In this case, one is not given the angle that has the right angle, however, the hypotenuse is the longest side in a right triangle. Therefore, if the triangle is right, then the hypotenuse is the longest, then side (c) is the longest side in the given triangle. Then side (a) and (b) are the legs, the sides adjacent to the right angle. It doesn't matter which sides one substitutes for these parameters.
Substitute in the given values and solve to prove the triangle is right,
\(a^2+b^2=c^2\\\)
Substitute,
\((9.6)^2+(12.8)^2=(16)^2\)
Simplify,
\(92.16+163.84=256\)
\(256=256\)
The given triangle is right since its sides follow the Pythagorean converse theorem.
Can someone help me with this question plz
Casey starts with $180 in
her bank account. She
withdraws $90, and then
she deposits $50. Mitchell
starts with $120 in his bank
account. He deposits $75,
and then he withdraws $45.
Who has more money in
the bank at the end?
Please explain or show work.
Answers
180-90= 90
90+50=140
Mitchell:
120+75=195
195-45=150
In the end Mitchell has more by $10
Find the zero of f(x)=-3x-18
Answers
Answer:
2 and -3
Step-by-step explanation:
The reason why these are the answers is because if you put it in your graphics calculator then you can see the only points where the diagram intersects with the x-axis would be at points 2 and -3 :)
What is the percent of decrease from 6,000 to 600?
Answers
Answer:
Percentage Calculator: What is the percentage increase/decrease from 6000 to 600? = -90.
Step-by-step explanation:
What is the solution to the equation
X/6 = 4/12
X=1
x= 2
x=4
x = 6
Answers
Answer:
x = 2
because we have the same question and i got it right its hard to explain but trust me its x = 2
The solution to the given equation is 2. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is x/6 = 4/12.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Now, x/6 = 4/12
By cross multiplication, we get
12x=24
⇒ x=2
The solution to the given equation is 2. Therefore, option B is the correct answer.
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A rectangular building ha a bae that i 255ft long, 255 feet wide, and the building i 42 ft tall. Find the unit for the volume of the building
Answers
The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.
The volume of the building will be calculated by the formula -
Volume = length × breadth × height
Thus, keeping the value of each component of building in the formula to find the volume of the building.
Volume of building = 255 × 255 × 42
Performing multiplication on Right Hand Side of the equation to find the value of volume
Volume of building = 2,731,050 feet³
Therefore, the volume of the building is 2,731,050 feet³.
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Find the exact value of tan A in simplest radical form
Answers
Answer:
12.68 de
Step-by-step explanation:
The function in the table is linear.
a. Determine the slope of the function. Show your work.
b. Write an equation for the function. Use function notation. Show your work.
Answers
Answer:
Step-by-step explanation:
Function given by the table represents a linear function.
a). Since, slope of a linear function passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is,
Slope = \(\frac{y_2-y_1}{x_2-x_1}\)
Slope of the linear function passing through two points (0, -5) and (2, 1) will be,
Slope = \(\frac{1+5}{2-0}=3\)
b). Let the equation of the function is,
y = mx + b
Where m = slope of the function
b = y-intercept
Here slope of the function 'm' = 3
y-intercept of he function = -5 [y-value of the function at x = 0]
Therefore, the function is,
y = 3x - 5
Perform the indicated operation:
-5(4a- 6b)
Answers
Answer:
-20a+30b
.......................
Part of the population of 7,000 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 7 of them are infected. How many elk are likely to be infected?
Answers
Answer:
620
Explanation:
When the sample is given, the number of elk are likely to be infected is to be considered as the 620.
Calculation of the number of elk:
Since the population is 7,750.
The random sample is 50.
So here be like
= 620
hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 620.
Let \(f(x)=-5x+3\) and \(g(x)=6x-2\). Find f times g and its domain.
Answers
The result of f times g is; -30x² + 28x - 6 while it's domain as required is the set of all real numbers.
What is the domain of f times g?As evident in the task content;
f(x) = -5x + 3 while g(x) = 6x - 2.
Hence, the result of f times g is; (-5x + 3) (6x - 2).
open parenthesis
f × g = -5x(6x) - 5x(-2) + 3(6x) + 3(-2)
= -30x² + 10x + 18x - 6
f × g = -30x² + 28x -6.
By observation, the function above is a quadratic function and hence, it's domain is the set of all real numbers.
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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
Answers
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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Mr. Ashton has a 4-foot by 8-foot sheet of plywood that weighs 46.2 pounds. How many pounds would 14.5 sheets of plywood weigh
Answers
If the area of the sheet is 14.5 square feet. Then the weight of the sheet of plywood will be 20.93 pounds.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
A sheet of plywood measuring 4 feet by 8 feet and weighing 46.2 pounds belongs to Mr. Ashton.
The weight of the sheet of plywood in the unit square foot is given as,
⇒ 46.2 / (4 x 8)
⇒ 1.44375
If the area of the sheet is 14.5 square feet. Then the weight of the sheet of plywood is given as,
⇒ 1.44375 x 14.5
⇒ 20.93 pounds
If the area of the sheet is 14.5 square feet. Then the weight of the sheet of plywood will be 20.93 pounds.
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Every day, Kathleen‘s burritos stand uses 3/8 of a bag of tortillas. For how many days will 1 1/8 bag of tortillas last.
Answers
Answer:
3 days
Step-by-step explanation:
x is the number of days Kathleen's burritos stand use
3/8x = 1 1/8
x = (1 1/8)/(3/8) = (9/8)/(3/8) = (9/8)x(8/3) = 9/3 = 3
Answer:
3 days.
Step-by-step explanation:
1 1/8 / 3/8
= 9/8 / 3/8
= 9/8* 8/3
= 9/3
= 3.
The perimeter of a rectangle is 320 feet. Find the length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.
Answers
The length of rectangle is 25 feet and the width of rectangle is 135 feet.
According to the question,
The perimeter of a rectangle is 320 feet. The length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.
Odd integers that follow each other and they differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers. The perimeter of a rectangle is 320 feet. Let the length of a rectangle is x. The next consecutive odd integer is x+2.width = 5(x+2)
=5x+10.
Let, Length - l:Width - w; l = 5w and the perimeter of a rectangle is 320 feet. Formula for perimeter of rectangle is 2(Length + Breadth). Perimeter of a rectangle is the sum of the length of all sides of the rectangle. The perimeter of a rectangle formula is,
P = 2(l + b)
In words, it is equal to the sum of two times the length and two times the breadth of the rectangle. Perimeter for any figure is defined as the length of its boundary.
2(length + width) = 320
Length+ width=160
x+5x+10=160
6x=150
x=25
Length = 25 feet
width = 5(25+2)=135 feet.
Hence, the length of rectangle is 25 feet and the width of rectangle is 135 feet..
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The sum of two consecutive integers is 75. What are fhe two integers?
Answers
Answer:
The numbers are 37 and 38.
Step-by-step explanation:
Forming the equation,
→ x + (x + 1) = 75
→ 2x + 1 = 75
Now the value of x will be,
→ 2x + 1 = 75
→ 2x = 75 - 1
→ x = 74/2
→ [ x = 37 ]
The another number will be,
→ x + 1
→ 37 + 1 = 38
Hence, numbers are 37, 38.
Members of a baseball team raised $1128.75 to go to a tournament. They rented a bus
for $856.50 and budgeted $24.75 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Equation:
Answers
The baseball team can bring 11 players to the tournament based on their budget.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of players the team can bring to the tournament. They rented a bus for $856.50 and budgeted $24.75 per player for meals, hence:
24.75x + 856.5 = 1128.75
x = 11
The baseball team can bring 11 players to the tournament based on their budget.
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