Show that the element 0 in a vector space is unique
Answers
Showed that v = w = 0, which proves that the zero vector in a vector space is unique.
To show that the element 0 in a vector space is unique, we need to prove that if there are two elements in the vector space that both satisfy the definition of the zero vector, then they must be the same element.
Let V be a vector space over a field F. Suppose that v and w are both zero vectors in V, which means that they satisfy the following two properties
Additive identity property: For any vector x in V, we have v + x = x and w + x = x.
Additive inverse property: For any vector x in V, we have (-1)x + x = 0, where 0 is the zero vector and (-1)x is the additive inverse of x.
To show that v and w are the same element, we can use the properties of vector addition and scalar multiplication as follows:
v = v + 0 (since 0 is the additive identity in V)
= v + (w + (-w)) (since w is a zero vector)
= (v + w) + (-w) (associativity of vector addition)
= w + (-w) (since v + w = w since v is a zero vector)
= 0 (since (-w) is the additive inverse of w)
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Related Questions
What is the probability of rolling a 3 on a fair dice 50 times?
Answers
Answer: 1/50? I'm not 100% sure...Sorry..
Please help me with this question
Answers
Answer:
x = 11
Step-by-step explanation:
Since we are given triangle PQR is similar to triangle PTU, we can write a proportion to connect the side lengths:
PQ / PT = QR / TU = PR / PU
We don't really care about QR and TU because the are irrelevant to the problem, so we can remove them:
PQ / PT = PR / PU
Now, we can substitute the values given by the diagram:
70 / 30 = 49 / (x + 10)
We can cross multiply,
70(x + 10) = 30 * 49
And divide by 70 on both sides(too lazy to multiply :P)
x + 10 = 3 * 7
x + 10 = 21
x = 11
Tyler just lit a new candle and then let it burn all the way down to nothing. The initial length of the candle was 15 inches and the candle burned at a rate of 1.25 inches per hour. Write an equation for L,L, in terms of t,t, representing the length of the candle remaining unburned, in inches, tt hours after the candle was lit.
Answers
Answer:
15 in - (1.25 in/hr)t
Step-by-step explanation:
L(t) is a function of time, t: L(t) = 15 in - (1.25 in/hr)t
Note that when the candle has burned down to nothing, L(t) = 0. How long does that take? Set 15 in - (1.25 in/hr)t equal to zero and solve for t:
(1.25 in/hr)t = 15 in, or
15 in
t = ---------------- = 12 hrs
1.25 in/hr
Pls help I’ll give brainliest
Answers
Answer:
b
Step-by-step explanation:
3/2
Answer:
\(x = \frac{3}{2} \)
Step-by-step explanation:
1) Expand.
\( - 6x + 8 = - 2x + 2\)
2) Add 6x to both sides.
\(8 = - 2x + 2 + 6x\)
3) Simplify-2x + 2 + 6x to 4x + 2.
\(8 = 4x + 2\)
4) Subtract 2 from both sides.
\(8 - 2 = 4x\)
5) Simplify 8 - 2 to 6.
\(6 = 4x\)
6) Divide both sides by 4.
\( \frac{6}{4} = x\)
7) Switch sides.
\(x = \frac{3}{2} \)
Therefor, the answer is option B. 3/2.
An item cost $50. The sales tax paid was $2.30. What is the sales tax percentage?
Answers
Answer:
The answer is 4.6%
Step-by-step explanation:
$2.30 divided by $50 multiplied by 100.
Either enter an exact answer in terms of T or use 3.14 for 7 and enter your answer as a decimal.
d=2
Answers
Answer:
N CCX XN
Step-by-step explanation:
two different missiles are shot simultaneiously at a practice target. if the probability of the first one hitting the target is 1 4 and of the second one hitting is 2 5 , what is the probability that (a) both missiles will hit, (b) at least one will hit?
Answers
(a) The probability that both missiles will hit the target is 1/10.
(b) The probability that at least one missile will hit the target is 11/20.
To find the probability that both missiles will hit, we multiply the individual probabilities of each missile hitting
P(both missiles hit) = P(first missile hits) × P(second missile hits)
P(both missiles hit) = (1/4) × (2/5)
P(both missiles hit) = 2/20
P(both missiles hit) = 1/10
So the probability that both missiles will hit the target is 1/10.
(b) To find the probability that at least one missile will hit, we need to find the probability that both missiles miss and then subtract that from 1 (since the probability of either missile hitting is the complement of both missiles missing)
P(at least one missile hits) = 1 - P(both missiles miss)
P(at least one missile hits) = 1 - P(first missile misses) × P(second missile misses)
P(at least one missile hits) = 1 - (3/4) × (3/5)
P(at least one missile hits) = 1 - 9/20
P(at least one missile hits) = 11/20
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What's the principal sum?
Answers
The principal sum refers to the amount payable in one sum in the case of accidental death and, in some cases, accidental dismemberment.
The amount paid in the case of accident or medical insurance in the event that the insured person dies, loses a limb, or loses sight is known to be as principal sum. It means that the principal sum amount is the maximum amount paid to the insured person for all injuries resulting from the accident.
Thus, the principal sum is the amount insured to be paid by the company to the beneficiary in the case of the insured individual's accidental death as well as in the loss of limb or sight.
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2/5% as a fraction
Pld
Answers
Hey there!
2/5%
= 2/5
= 2 ÷ 5
= 0.40
= 0.40 × 100
= 40%
Therefore, your answer is: 40%
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Find The area of the figure below
Answers
Answer:
wow asphalt theme I have that too in my quizziz
ASAP Right answer only please??!!!!
Answers
Answer:
The answer is 17 or x is 17
Franco read of a chapter of his history book in § of an hour. At this rate, how many chapters of his history book
can he read in 1 hour?
Answers
Answer:
1 7/8
Step-by-step explanation:
dont know lol but trust me
How many terms are in the expression 36x^3+27x^2-18x-9
Answers
Answer:
Four (4) terms.
Step-by-step explanation:
36x³ + 27x² - \(18x^{1}\) - \(9x^{0}\)
The gives four terms.
from a population with a standard deviation of 35, a sample of 150 items is selected. at 95% confidence, what is the margin of error for the population mean? round your answer to three decimal places.
Answers
The margin of error for the population mean is 5.601
What does the term "margin of error" mean?
Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.
Given c = 0.95
The significance level is obtained as follows:
alpha = 1 - c
alpha = 1 - 0.95
alpha = 0.05
Also, it is given that n = 150 and sigma = 35 .
The critical value of Z distribution at 0.05 level of significance can be computed in MS Excel using + NORMS INV (alpha/2) function as follows:
Thus, \(Z_{0.005/2}=1.96\)
Now, the margin of error can be computed as follows: ME = Critical Value x Standard Error
\(Z_{0.005/2}*\frac{sigma}{\sqrt{n} } \\= 1.96 * \frac{35}{\sqrt{150} } \\= 5.601\)
Thus, the margin of error for the population mean is 5.601
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Opposites and absolute value mean the same thing.
True or false
Answers
Answer:
The absolute value of a number is the distance between the number and zero on a number line. In other words, a number and its opposite have the same absolute value.
Step-by-step explanation:
1 1/2
1
Emma and her 3 friends were thirsty, so she shared
2
gallon of lemonade equally among 4 people. How
much lemonade did each person get?
1
-4
2
Answers
Answer: 64 ounces each
Step-by-step explanation:
1 gallon = 128 ounces
128 ounces x 2 gallons = 256 ounces
256/4 = 64 ounces
OR
Each friend got 1/2 gallon each. If there are 2 gallons then there would be 4 'halves'. 2 halves per gallon and there are 2 gallons.
(I am not sure what the answer choices are.)
Answer:
1/8 got it right on edg
Have a good day :)))
Step-by-step explanation:
A survey asked 60 students if they play an instrument and if they are in band.
1. 35 students play an instrument.
2.30 students are in band.
3. 30 students are not in band.
Which table shows these data correctly entered in a two-way frequency table?
Answers
A table that shows these data correctly entered in a two-way frequency table is: A. table A.
What is a frequency table?In Mathematics and Statistics, a frequency table can be used for the graphical representation of the frequencies or relative frequencies that are associated with a categorical variable or data set.
Based on the information provided about this survey with respect to the 60 students, we can logically deduce that only table A represent a two-way frequency table that correctly shows the data being entered:
"35 students play an instrument."
"30 students are in band."
"30 students are not in band."
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
WILL MARK BRAINLEIST!!!
Thomas wants to start a canned food collection with his friends to help the community. They bring 2 cans of food the first day, 4 cans on the second day, 8 cans on the third day, and 16 cans on the fourth day. Thomas and his friends plan to collect cans for 10 days. Which statement describes why this sequence is a function? Select each correct answer.
A.The graph of the sequence would pass the vertical line test.
B.The graph of the sequence would pass the horizontal line test.
C.Each day corresponds to a unique amount of cans in the sequence.
D.They have a different amount of cans for the same day.
Answers
The statement that describes why this sequence is a function is given as follows:
A.The graph of the sequence would pass the vertical line test.
When does a relation represents a function?A relation represents a function when each value of the input is mapped to a single value of the output.
In this problem, the input is the number of days, while the output is the number of cans. There are no repeated inputs, which means that this relation is a function.
On the graph, a relation being a function means that a vertical line will intercept the graph of the function only once, and thus option A is correct.
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Which of the following best explains why one graph appears skewed and one graph appears symmetrical? The scale of the box-and-whisker plot does not start at zero. The interval of the box-and-whisker plot is too large. The interval of the stem-and-leaf plot is not consistent. The scale of the stem-and-leaf plot is too small for the set of data.
Answers
The statement that best explains why one graph appears skewed and one graph appears symmetrical is given by: Option C: The interval of the stem-and-leaf plot is not consistent.
What is a symmetric distribution?A symmetric distribution oftenly refers to the distribution which looks symmetric about a fixed line.
For this case, the missing image is attached below.
The stem leaf plot represents the considered bar plot.
But stem leaf plot seems symmetric whereas the box plot isn't.
This is because the stem and leaf plot is missing '5' in its stem, making the interval inconsistent.
Doing inconsistant graphing isn't allowed as that represents distorted data, as for this case, the data seems symmetric when it isn't.
Thus, the statement that best explains why one graph appears skewed and one graph appears symmetrical is given by: Option C: The interval of the stem-and-leaf plot is not consistent.
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Answer:c edge
Step-by-step explanation:
What is the probability of getting ALL 2 red balls in a bag containing 24 balls?
Answers
Answer:
1 / 276
Step-by-step explanation:
The total Number of balls in the bag = 24
Number of red balls = 2
Assume the number of picks required = 2 and selection is performed without replacement ;
The probability of :
Choosing a red on first pick = (number of red balls / total number of balls) = 2 / 24
After first pick, red balls left = 1 ; total number of balls = 23
Choosing a red on second pick = (number of red balls / total number of balls = 1 / 23
Hence,
(2/24) * (1/23) = 2 / 552 = 1/276
AI's Auto Shop charges $149 for parts and $53 per hour of labor for a repair job. Edna's Engine Repair charges a flat fee of $280 for the same job.
a. Write a system of equations to represent the situation.
b. Graph the system of equations.
c. Which shop is cheaper if the job takes 2 hours? 3 hours?
Answers
Answer:
AI's Auto Shop: y = 149 + 53x
Edna's Engine Repair: y = 280
Explanation:
The system of equations represent the costs of the two different repair shops. The first equation, y = 149 + 53x, represents the total cost of AI's Auto Shop. The variable x represents the number of hours of labor required, and the variable y represents the total cost. The second equation, y = 280, represents the flat fee charged by Edna's Engine Repair.
The graph of the system of equations would show two lines, one for each equation. The line for AI's Auto Shop would have a slope of 53 and a y-intercept of 149, representing the cost of parts and hourly labor. The line for Edna's Engine Repair would be a horizontal line at y = 280, representing the flat fee charged.
When the job takes 2 hours, AI's Auto Shop would charge $149 + $53*2 = $255 and Edna's Engine Repair would charge $280. So, AI's Auto Shop would be cheaper.
For a job that takes 3 hours, AI's Auto Shop would charge $149 + $53*3 = $308 and Edna's Engine Repair would charge $280. So, AI's Auto Shop would be more expensive.
Find all values of k so that Polynomial Can be factored using integers
X^2 - 8x + k, k > 0
Answers
Answer:
the crisis point b 2000 white white x converse
the study would use a . the study would use simple random sampling because it would be easy to randomly select of . b. the study would use a . the study would use cluster sampling because the of fall into naturally occurring subgroups. c. the study would use a . the study would use stratified sampling because it would be important to have members from each segment of the population. d. the study is a , because the population is for it to be practical to record all of the responses.
Answers
The study would use a simple random sampling because it would be easy to randomly select. The study would use cluster sampling because the of fall into naturally occurring subgroups. The study would use stratified sampling because it would be important to have members from each segment of the population.
The study is a sample survey, because the population is for it to be practical to record all of the responses.
a. The study would use a simple random sampling because it would be easy to randomly select members of the population. Simple random sampling is a type of probability sampling that is used when the population is homogenous and every member has an equal chance of being selected for the sample.
b. The study would use cluster sampling because the members of the population fall into naturally occurring subgroups. Cluster sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into naturally occurring subgroups.
c. The study would use stratified sampling because it would be important to have members from each segment of the population. Stratified sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into segments or strata based on certain characteristics.
d. The study is a sample survey, because the population is too large for it to be practical to record all of the responses. Sample survey is a type of survey that collects data from a sample of the population, rather than the entire population. This is often done when the population is too large or when it is not practical to survey the entire population.
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Whole numbers between 63 and 101
Answers
Answer:
64,81,100
Step-by-step explanation:
Answer: 64,81 and 100
Step-by-step explanation: 8^2=64, 9^2=81 and 10^2=100
True or False: If there are multiple operations inside a parentheses, you do not need to complete these in the order of PEMDAS.
Answers
Answer:
False
Step-by-step explanation:
I would say false. The operations inside should always go by PEMDAS unless instructed otherwise
Answer:
FALSE
Step-by-step explanation:
Within a set of parentheses, the order of operations should be followed. This is because you will get the wrong answer if you don't.
You use a tape measure to measure the dimensions of a rug, as shown. Estimate the area of the rug.
Answers
Answer:
its impossible since i cant see this rug.
Step-by-step explanation:
to find the area of the rug, determine the width and length
Brian is building a rectangular pool that has a circular island in the middle. If he wants the length to be 25ft long, the width to be 15ft wide, and the island to have a diameter of 4ft, then what will the area of Brian's pool be, not including the island?
Answers
Answer:
368.72 ft^2
Step-by-step explanation:
25x15-2π
=375-2π
~368.72
Marilyn is having shelves installed to create a corner pantry. The length of one wall is 21 inches and the measure of the angle opposite the short side of the pantry, m∠A = 40°. The contractor who is making the shelves, which are shaped like right triangles, needs to know the length of the other wall. The length of the other wall is inches. Round your answer to the nearest integer.
Answers
Answer:
40° or 40.03 degrees or 25 inches as nilla mentioned.
PLEASE HELP.
50 POINTS IF U ANSWER ALL QUESTIONS
Answers
(a) Fill in the table using the given rules for scoring. For example, if the coin shows heads and the die shows 1, then the score is 2 × 1 = 2; if the coin shows tails and die shows 1, then the score is 1 + 1 = 2.
\(\begin{array}{c|cccccc} & 1 & 2 & 3 & 4 & 5 & 6 \\ \text{heads} & 2 & 4 & 6 & 8 & 10 & 12 \\ \text{tails} & 2 & 3 & 4 & 5 & 6 & 7 \end{array}\)
(b) A score of 4 can happen if the outcome is either
• heads and 2, or
• tails and 3
These events are mutually exclusive, meaning
Pr[(heads and 2) or (tails and 3)] = Pr[heads and 2] + Pr[tails and 3]
The coin toss and die roll are independent, so
Pr[heads and 2] = Pr[heads] × Pr[2] = 1/2 × 1/6 = 1/12
Pr[tails and 3] = Pr[tails] × Pr[3] = 1/2 × 1/6 = 1/12
Then
Pr[(heads and 2) or (tails and 3)] = 1/12 + 1/12 = 1/6
Put another way, there are 12 possible outcomes of the coin toss and die roll, and each has the same probability of occurring, 1/12. (This is because the results of the coin toss have equal probability, 1/2, and so do the results of the die roll, 1/6; by independence, each outcome can occur with probability 1/2 × 1/6 = 1/12.)
(c) Scoring 10 points has a probability of 1/12. Out of 60 games, George can expect to win 10 points 60 × 1/12 = 5 times.
Kiki has 1/6 pound of blueberries and 5/8 pound of raspberries. What is the most accurate estimate for the difference between the pounds of berries? 1/6 is closest to , and 58 is closest to. So the difference is closest to the Response area. 101/2
Answers
The most accurate estimate for the difference between the pounds of berries is 0.46 pounds, which is closest to the response area of 10.5 or 101/2 (depending on the formatting).
To find the difference between 1/6 pound of blueberries and 5/8 pound of raspberries, we need to subtract the two quantities:
5/8 - 1/6
To subtract these fractions, we need a common denominator. The least common multiple of 6 and 8 is 24, so we can rewrite the fractions as:
5/8 = 15/24
1/6 = 4/24
Now we can subtract:
15/24 - 4/24 = 11/24
So the difference between 5/8 pound of raspberries and 1/6 pound of blueberries is 11/24 pounds.
However, since the question asks for an estimate, we can use the given approximations to get a rough idea of the answer. We can round 1/6 to 0.17 and 5/8 to 0.63, since these are the closest values given. Then we can find the difference:
0.63 - 0.17 = 0.46
So the most accurate estimate for the difference between the pounds of berries is 0.46 pounds, which is closest to the response area of 10.5 or 101/2 (depending on the formatting).
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