(7.1) basis for the nullspace of A
(7.2) basis for the column space of A
(7.3) rank and nullity of A
(7.4) subset of vectors forming a basis for the space spanned by v₁, v₂, v₃, and v₄.
Additionally, matrices B and D are row equivalent to each other.
For matrix A = [0 1 2; -2 0 3; 1 -1 1; 0 0 17/2]
To find the basis for the nullspace of A, we need to solve the homogeneous equation Ax = 0. This can be done by row reducing the augmented matrix [A | 0] and finding the special solutions. The basis for the nullspace consists of the vectors corresponding to the free variables in the row-reduced echelon form.
To find the basis for the column space of A, we can consider the pivot columns in the row-reduced echelon form of A. The column space consists of all linear combinations of these pivot columns.
The rank of A is the number of linearly independent columns in A, which corresponds to the number of pivot columns in the row-reduced echelon form. The nullity of A is the dimension of the nullspace, which is equal to the number of free variables.
To find a subset of vectors v₁, v₂, v₃, and v₄ that forms a basis for the space spanned by these vectors, we can row reduce the matrix [v₁ v₂ v₃ v₄] and identify the linearly independent columns.
The matrices B and D being row equivalent means that they can be transformed into each other by a sequence of elementary row operations. This implies that they have the same row space and nullspace, as well as the same rank and nullity.
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In a bag there are 14 blue marbles, 20 red marbles, 4 green marbles, and 12 yellow marbles, what is the probability of drawing a yellow marble?
Answer:a good chance of getting a yellow marble
Step-by-step explanation:
if anyone can answer please help meh
Answer:
1 a2 d3 c4 e5 bStep-by-step explanation:
Hope that will help youPLS HELP DUE RN Fill in the blanks with the following correct terms
Answer:
11. Coefficient
12. Monomial (Since only two terms are there)
13. Binomial (Since only one term is there)
14. Variable
15. Trinomial (Since only three terms are there)
16. Constant
Hope this helped! If not, please let me know! <3
In a class 26 of students, 12 play an instrument and 19 play a sport. There are 2 students who do not play an instrument or a sport. What is the probability that a student plays an instrument given that they play a sport?
why mathematics is neccessary for students?explain
I need help ASAP !!!plz
Answer:
80 degree angle
Step-by-step explanation:
Answer:
80 degrees
because its lower than a 90 :))
Ax + 5 = 2(3 + 2x)
X=
Answer:
Ax+5=2*3+2*2x
Ax+5-6-4x=0
x(A-4)-1=0
x=1/(A-4)
A restaurant went though 3 boxes of plastic forks over 6 months. They used ___ of a box every month.
Answer:
1/2
Step-by-step explanation:
You could formalize your answer by setting up a proportion.
3 boxes /6 months = x / 1 month
Cross multiply
3 boxes * 1 month = 6 months * x
the months cancel out.
Divide by 6
x = 3 boxes / 6
x = 1/2
Jonathan looked at the picture frame below and computed the following sum: 8 + (-4). What value did he find?
Answer:
-12
Step-by-step explanation:
you do -4 plus 8 but u count downwards from -4 so the answer is -12
4.6 + 1.2x = 68.2 -1.8x I need help please and Thank you so much!
Answer:
x = 21.2
Step-by-step explanation:
Mark me Brainliest?
Devin wants to buy some t-shirts from a store in the mall. He has $20 in his pocket and the t-shirts cost $5 each. The situation can be modeled by the function F(t) = 5t, where F(t) represents the total cost of t t-shirts. State a reasonable domain and range for this situation.
Answer:20-5t+=
Step-by-step explanation:
A teacher buys pizza for her class. There are 5 pizzas, each with 8 slices. If she has 25 students, how many slices of pizza does each student get?
Group of answer choices
Edward purchased his home for $89,000. For the first three years after
lively, so his property value grew by 4.8% every year. For the next five y
his property value grew by 2.6% every year. How much had the value of
the nearest hundred dollars?
a.$25,700
b. $27.500
$30,000
d. $13,200
Answer:
B. $25,700
Step-by-step explanation:
(sorry it took me so long to answer it was kinda hard)
Please Help!! Brainliest Answer! Thank you
Answer:
A. 4.59Step-by-step explanation:
tanФ = opp / adj.
where Ф = 74, opp = 16, adj. = x
find: x
just plugin the values into the formula
tanФ = opp / adj.
tan(74) = 16/ x
x = 16
tan(74)
x = 4.59
1. If AC=27 and BC = 9, then AB = ?
Given: F(x) = 2x and G(x) = x^2+ 2
Find F/G(-1).
2/3
-2/3
-2
Answer:
second option
Step-by-step explanation:
F (-1) = 2 (-1)
= -2
G (-1) = (-1)^2 + 2
= 1 + 2
= 3
Start by graphing either y= x
1
or y= x 2
1
and modify that function to create the graphs of other algebraic functions with the following properties:
one vertical asymptote (no horizontal asymptote)
one horizontal and two vertical asymptotes
one horizontal asymptote (no vertical asymptote). Ensure that the entire function 2c is in the positive halfplane.
For each of the three graphed functions, list its equation, domain, range, and asym
1. There are no asymptotes for this function.
2. Vertical asymptote at x = 0, no horizontal asymptote
3. Vertical asymptotes at x = 2 and no horizontal asymptote
4. Horizontal asymptote at y = 0, no vertical asymptote
Let's start by graphing the function y = x^2.
Graph of the function y = x^2:
Equation: y = x^2
Domain: All real numbers (-∞, ∞)
Range: All non-negative real numbers [0, ∞)
Asymptotes: There are no asymptotes for this function.
Modifying the function to create a graph with one vertical asymptote (no horizontal asymptote):
Equation: y = 1/x
Domain: All real numbers except x = 0 (-∞, 0) U (0, ∞)
Range: All real numbers except y = 0 (-∞, 0) U (0, ∞)
Asymptotes: Vertical asymptote at x = 0, no horizontal asymptote
Modifying the function to create a graph with one horizontal and two vertical asymptotes:
Equation: y = 1/(x - 2)
Domain: All real numbers except x = 2 (-∞, 2) U (2, ∞)
Range: All real numbers (-∞, ∞)
Asymptotes: Vertical asymptotes at x = 2 and no horizontal asymptote
Modifying the function to create a graph with one horizontal asymptote (no vertical asymptote):
Equation: y = 2/(x + 1)
Domain: All real numbers except x = -1 (-∞, -1) U (-1, ∞)
Range: All real numbers (-∞, ∞)
Asymptotes: Horizontal asymptote at y = 0, no vertical asymptote
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Allison can sew three scarves in 75 minutes. How many scarves can she sew in four hours?
Answer:
2.4
Step-by-step explanation:
75/3=25.
So she can do 1 scarf in 25mins
60/25=2.4
she can do 2.4 scarfs in one hour
Answer:
9.6 or 9 whole scarves
Step-by-step explanation:
You have to change the 4 hours into 240 minutes.
You can set it up as a proportion.
[tex]\frac{3}{75}[/tex] and [tex]\frac{x}{240}[/tex]
Then you need to set it up as:
75 x = 240 · 3
Then you get:
75 x = 720
Now you set it up as:
x = 720 ÷ 75
When you divide you get 9.6.
So, X = 9.6.
Allison can sew 9 whole scarves in four hours. The answer could also be 9.6 scarves. Not sure which one you need.
help !!!! I will mark as brainliest 20 points !!!! solve both of question !!!
pls show work !!! thanks
Answer:
a). k ≥ -1
b). k < 5
c). k ≤ 2
d). k > -3
Step-by-step explanation:
a). k ≥ - 3 + 2
k ≥ -1
b). 3k < 16 - 1
3k < 15
k < 5
c). -4k ≥ -5 - 3
4k ≤ 8
k ≤ 2
d). 3k > -10 + 1
3k > -9
k > -3
Answer:
solution is on the picture attached
Hope this helps
PLEASE ANSWER ASAP!!!! HELP DESPERATELY NEEDED!!!
Answer:
it's wrong because he put a closed circle on the nine when he was supposed to put an open circle because nine is not less than itself but the thing that he did right wad that he went to the left if it was a greater than or equal symbol then it would be correct
Happy :) have a good day lol
Step-by-step explanation:
Your answer
b. To find 36 x 19, I find 36 times 20 and remove 1 group of 36. *
Your answer
Answer:
684
Step-by-step explanation:
36
x19
let calculator do the rest and then ur done
helppp !! what is the domain of the function shown in the table?
х
2
4
6
8
y
3
4
5
6
A. {2, 3, 4, 5, 6, 8}
B. {3, 4, 5, 6}
C. (2,3), (4,4),(6,5), (8, 6)
D. {2, 4, 6, 8}
Answer:
D is the correct answer i think
Step-by-step explanation:
Domain of the function is option (D) {2, 4, 6, 8}
What is Domain?The domain of a function is the set of inputs accepted by the function.
What is Function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
From the given table,
Domain of the function is {2, 4, 6, 8}
Because the domain of a function is the set of inputs accepted by the function.
Hence, Domain of the function is option (D) {2, 4, 6, 8}
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Solve the equation 4a – (6 – 5a) + 12 = 3a + 2(2a – 4) for a.
Could you help me?
There are no options for this answer. It must be solved
Answer:
a = -7
Step-by-step explanation:
4a – (6 – 5a) + 12 = 3a + 2(2a – 4)
x and y together represent what?
Answer:
xy
Step-by-step explanation:
or like a graph, I think you need more. or they represent the x axis and the y axis
Imagine that owners of lemons are willing to sell for $2500 and owners of plums are willing to sell for $5000. Imagine that purchasers are willing to pay up to $2700 for a lemon and up to $6000 for a plum. Assume that sellers know what kind of car they have, but buyers can't tell. All buyers know is that one third of all used cars are lemons.
What is the maximum price that the buyers would be willing to pay for a car. (upto two decimal places)
The maximum price that buyers would be willing to pay for a car is $4900.
The maximum price that buyers would be willing to pay for a car can be determined by considering the expected value of the car. Since one third of all used cars are lemons, buyers would expect that there is a one-third chance of purchasing a lemon and a two-thirds chance of purchasing a plum.
Based on this information, we can calculate the expected value by considering the prices of lemons and plums and their respective probabilities.
The expected value is calculated as follows:
Expected value = (Probability of getting a lemon * Maximum price for a lemon) + (Probability of getting a plum * Maximum price for a plum)
In this case, the probability of getting a lemon is 1/3 and the probability of getting a plum is 2/3. The maximum price for a lemon is $2700 and the maximum price for a plum is $6000. Substituting these values into the formula, we can calculate the expected value:
Expected value = (1/3 * $2700) + (2/3 * $6000)
Simplifying the equation, we get:
Expected value = $900 + $4000
Expected value = $4900
Therefore, the maximum price that buyers would be willing to pay for a car is $4900. This price takes into account the probabilities of getting a lemon or a plum and the respective maximum prices buyers are willing to pay for each type of car. Buyers would consider this price as the maximum they are willing to pay, as it represents the expected value of the car considering the lemon-plum distribution and their respective preferences and valuations.
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(PowerToys) PowerToys Inc. produces a small remote-controlled toy truck on a conveyor belt with nine stations. Each station has, under the current process layout, one worker assigned to it. Stations and processing times are summarized in the following table: a. What is the bottleneck in this process? b. What is the capacity, in toy trucks per hour, of the assembly line? c. What is the direct labor cost for the toy truck with the current process if each worker receives $15 /hour, expressed in dollars per toy truck? d. What would be the direct labor cost for the toy truck if work would be organized in a work cell, that is, one worker performs all tasks? Assume that the processing times would remain unchanged (i.e., there are no specialization gains). e. What is the utilization of the worker in station 2 ? Because of a drastically reduced forecast, the plant management has decided to cut staffing from nine to six workers per shift. Assume that (i) the nine tasks in the preceding table cannot be divided; (ii) the nine tasks are assigned to the six workers in the most efficient way possible; and (iii) if one worker is in charge of two tasks, the tasks have to be adjacent (i.e., one worker cannot work on tasks 1 and 3 ). f. How would you assign the nine tasks to the six workers? g. What is the new capacity of the line (in toy trucks per hour)?
The bottleneck in the process is Station 5, with a processing time of 8 minutes. The capacity of the assembly line is approximately 1.76 toy trucks per hour.
a. The bottleneck in this process is the station with the longest processing time. In this case, Station 5 has the longest processing time of 8 minutes. The bottleneck is the station that limits the overall capacity of the assembly line because it takes the longest time to complete its task.
b. To calculate the capacity of the assembly line, we need to determine the cycle time, which is the time it takes for one complete cycle of the assembly line. The cycle time is equal to the sum of the processing times at each station. In this case:
Cycle time = 1 + 2 + 3 + 4 + 8 + 6 + 5 + 3 + 2 = 34 minutes
To calculate the capacity in toy trucks per hour, we need to convert the cycle time from minutes to hours:
Capacity = 60 minutes / 34 minutes = 1.76 toy trucks per hour
c. The direct labor cost for the toy truck with the current process can be calculated by multiplying the number of workers assigned to each station by their hourly wage, and then dividing it by the number of toy trucks produced per hour. Since there is one worker per station and each worker receives $15 per hour, the direct labor cost per toy truck can be calculated as follows:
Direct labor cost = (Number of workers × Hourly wage) / Capacity
= (9 workers × $15/hour) / 1.76 toy trucks per hour
≈ $80.68 per toy truck
d. If the work were organized in a work cell, with one worker performing all tasks, the direct labor cost would remain the same. Each worker would still receive $15 per hour, regardless of the number of tasks they perform. There would be no specialization gains in this scenario, so the direct labor cost per toy truck would still be approximately $80.68.
e. To determine the utilization of the worker in station 2, we need to compare the processing time at that station to the cycle time of the assembly line. The processing time at station 2 is 2 minutes, and the cycle time is calculated as 34 minutes (as mentioned in point b).
Utilization = Processing time at station 2 / Cycle time
= 2 minutes / 34 minutes
≈ 0.059 or 5.9%
This means that the worker in station 2 is only utilized for about 5.9% of the cycle time, indicating that they spend most of their time waiting for the other stations to complete their tasks.
f. With the reduced staffing from nine to six workers per shift, the tasks should be assigned to the six workers in the most efficient way possible. One possible assignment could be as follows:
Worker 1: Stations 1 and 2
Worker 2: Stations 3 and 4
Worker 3: Stations 5 and 6
Worker 4: Stations 7 and 8
Worker 5: Station 9
Worker 6: No assigned task (idle)
g. To calculate the new capacity of the line with six workers, we need to determine the total processing time for the new assignment. The total processing time would be the sum of the processing times at each station assigned to a worker:
Total processing time = 1 + 2 + 6 + 5 + 3 + 2 = 19 minutes
The new capacity of the line would be the reciprocal of the total processing time:
Capacity = 60 minutes / 19 minutes = 3.16 toy trucks per hour
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Write an expression that represents the perimeter of the triangle?
Answer:
(3m - 2) + (5m - 2) + (2m + 7)
Step-by-step explanation:
When you add all the sides together, you get the perimeter.
The expression of the perimeter of the triangle is 10m + 3.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The three sides of the triangle are:
2m + 7
3m - 2
5m - 2
Now,
The perimeter of the triangle.
= Sum of all the sides
= 2m + 7 + 3m - 2 + 5m - 2
= 10m + 7 - 4
= 10m + 3
Thus,
The perimeter of the triangle is 10m + 3.
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Ben, Cam, and Justin are lumberjacks. The number of trees they chop down is given by b + 2 c + 3 j b+2c+3jb, plus, 2, c, plus, 3, j where b bb is the number of hours Ben spends chopping, c cc is the number of hours Cam spends chopping, and j jj is the number of hours Justin spends chopping.
Consider the complete question is "Ben, Cam, and Justin are lumberjacks. The number of trees they chop down is given by b+2c+3j, where b is the number of hours Ben spends chopping, c is the number of hours Cam spends chopping, and j is the number of hours Justin spends chopping. How many trees do they chop down after Ben spends 8 hours chopping, Cam spends 3 hours chopping, and Justin spends 4 hours chopping?"
Given:
Total number of trees chopped by them = [tex]b+2c+3j[/tex]
b = number of hours Ben spends chopping = 8
c = number of hours Cam spends chopping = 3
j = number of hours Justin spends chopping = 4
To find:
The numerical value of total number of trees chopped by them.
Solution:
Total number of trees chopped by them = [tex]b+2c+3j[/tex]
Put [tex]b=8, c=3[/tex] and [tex]j=4[/tex] in the given expression.
[tex]Total=8+2(3)+3(4)[/tex]
[tex]Total=8+6+12[/tex]
[tex]Total=26[/tex]
Therefore, total number of trees chopped by them is 26.
One hundred less than a twice a number is five
Answer:
52.5
Step-by-step explanation:
52.5 times 2 is 105 and 100 less than this is 5.
It can also be set out in the equation 2x-100=5
need to know now!!! giving 10 points what -6+8
Answer:
the answer is 2...................
Step-by-step explanation:
-6+8=2
Answer:
-6+8= 2 draw a line then write at the center 0 to the left write negative integers to your write positive integers-6 +8 move 8 steps forward from-6 and you will be at 2 that's the answer
