find u, v , u , v , and d(u, v) for the given inner product defined on rn. u = (5, 4), v = (−2, 0), u, v = 3u1v1 u2v2
Answers
Given that the inner product is defined as: u, v = 3u₁v₁u₂v₂and u = (5, 4), v = (-2, 0)We have to find u, v, u, v and d(u, v)We know that for any two vectors u and v in rn, the inner product is defined as:u, v = ∑uᵢvᵢ u = √41, v = 2, u = (5, 4), v = (-2, 0) and d(u, v) = √65.
where 1 ≤ i ≤ n.
Now, using the given formula for inner product,
u, v = 3u₁v₁u₂v₂= 3(5)(-2)(4)(0)= 0Therefore, u, v = 0.
Then we can compute the norm of vector u and vector v as follows:
u = ||u|| = √(∑uᵢ²) = √(5² + 4²) = √41v = ||v|| = √(∑vᵢ²) = √((-2)² + 0²) = √4 = 2
Therefore, u = √41, v = 2
Now, we have: d(u, v) = ||u - v|| = √(∑(uᵢ - vᵢ)²) = √[(5 - (-2))² + (4 - 0)²] = √(7² + 4²) = √65 Hence, u = √41, v = 2, u = (5, 4), v = (-2, 0) and d(u, v) = √65.
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Related Questions
IV. Classify the following fractions as proper fractions,
improper fractions, like fractions & unlike fractions.
Improper
fraction
8 21 4 6 7
15' 5'5'8' 2
Proper fraction Unlike fraction Like fraction
2 5 1 9 11 3 12 11 2
-
-
-
-
4'4" 7'25'8'513'21'
-
E MODEL
Answers
Improper fraction: 8 21 4 6 7 15 - This fraction is an improper fraction because the numerator (the top number in the fraction) is larger than the denominator (the bottom number in the fraction).
What is numerator?A numerator is the top number in a fraction. It is used to identify the number of parts of a whole that are being considered. For example, in the fraction 3/4, the numerator is 3, which is the number of parts being considered out of the total 4 parts.
Like fractions: 5' 5' 8' 2 - This fraction is a like fraction because the numerators and denominators are the same.
Proper fraction: 2 5 1 9 11 3 12 11 2 - This fraction is a proper fraction because the numerator is smaller than the denominator.
Unlike fraction: 4'4" 7'25'8'513'21' - This fraction is an unlike fraction because the numerators and denominators are different.
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a(n) ▼ event sample space outcome experiment is any collection of outcomes from a probability experiment.
Answers
In probability theory, an event is any collection of outcomes or results from a probability experiment. option a) is correct event
It represents a particular occurrence or set of occurrences that we are interested in studying or analyzing. A sample space (option b) is the set of all possible outcomes in a probability experiment. An outcome (option c) is a particular result of a single trial of a probability experiment. An experiment (option d) refers to the process of conducting a trial or series of trials to observe the outcomes and collect data for analysis in probability theory. Therefore, the correct answer is option a) event.
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Complete Question
A(n) _______ is any collection of outcomes from a probability experiment.
a) event
b) sample space
c) outcome
d) experiment
To summarize, an outcome is a result of an experiment, a sample space is a collection of all possible outcomes, an event is a set of outcomes chosen from the sample space, and a collection is a group of events with a common property.
An experiment in probability refers to a process of observing or measuring some phenomenon, where the outcomes are uncertain. The collection of all possible outcomes from this experiment is known as the sample space. An outcome is a particular result that occurs as a result of the experiment.
Now, a set of outcomes chosen from the sample space is known as an event. An event can be as simple as a single outcome or as complex as a combination of outcomes. For example, flipping a coin and getting heads is a simple event, while flipping a coin and getting heads or rolling a dice and getting an even number is a compound event.
Finally, a collection of events is simply a group of events that share a common characteristic or property. In probability, we use collections of events to determine the likelihood of certain outcomes occurring. This allows us to make predictions about the experiment based on the available data.
So, to summarize, an outcome is a result of an experiment, a sample space is a collection of all possible outcomes, an event is a set of outcomes chosen from the sample space, and a collection is a group of events with a common property.
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A pop quiz has 4 multiple choice problems, all with 3 possible answers (A, B, or C,). You need to get at least 4 correct to pass. If you are completely unprepared and have to guess on every question, what is the probability that you will pass the quiz?
Answers
Answer:
The probability is 1/4, for me if I need to guess all blankly.
But if I am unprepared but if I use my brain it can be 3/4
Sooo, hope it helps!!!
6 + 2 ÷ 4 × 3 - 7 + 6 + 5 ÷ 3 - 1 × 1
Answers
Jeremy uses 2 feet 3 inches of board for each birdhouse he builds. How many inches of board does he need to make 6 birdhouses?
Answers
Answer:
134inches
Step-by-step explanation:
Convert 2feet to inches
1foot= 12 inches
2feet= 12x2inches
=24inches
24inches is to 1 birdhouse
24inches x 6 equals six birdhouses
134inches
Answer:
He will need 162 inches
Step-by-step explanation:
6×2ft is 12 feet. Convert ft into inches for every 1 foot you have 12 inches. A total of 144in. Now multiply 6×3in which equals 18in. Add 144+18=162
To get from point A to point B you must avoid walking
through a pond. To avoid the pond, you must walk 34 meters
south and 41 meters east. To the nearest meter, how many
meters would be saved if it were possible to walk through the
pond? . To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
Answers
p
the rigth awnser is 41 meaters east to were
Step-by-step explanation:
possible to walk through the
The length of a rectangle is 4 cm more than 3 times its width. If the area of the rectangle is 15 cm², find the width.
Answers
Answer:88888888
Step-by-step explanation:
esemate 5,840 x 25 i need help please
Answers
Answer:
146,000
Step-by-step explanation:
Simple math let me know if you need anymore help honey, have a nice day!
|x-b|=c, only one solution is -3
Answers
Answer:
x-b=-3
Step-by-step explanation:
1. Simplify
|x-b|=c
x-b=c
If c=-3 then,
Answer= x-b=-3
Bracelets are on sale for 3 for $15. How much do 5 bracelets cost?
Answers
Answer:
25
Step-by-step explanation:
15 divided by 3 is 5. Meaning, each bracelet cost $5. 2 bracelets cost 10 more dollars since 5x2 is equal to $10. 15+10=25
PLEASE HELP
Kira created two patterns. pattern g starts at 2 and increases by 2 each time. pattern h starts at 4 and increases by 4 each time
when the number in Pattern H is 48, what is the corresponding term in Pattern G?
Answers
Answer:
when pattern H is 48, pattern G is 24
what is the volume of a cube with sides of 10 cm in length after removing half a spehere with a diamtere of 10 cm
Answers
The volume of the cube after removing a sphere of diameter 10cm from it = 476.67 cm³
What is the volume of a cube?Volume of a cube = \(side^{3}\) (side = side of the cube)
What is the volume of a sphere?
Volume of a sphere = \(\frac{4 \pi (radius)^{2} }{3}\) (radius = radius of the sphere)
Given:
Side of cube = 10cmDiameter of sphere = 10cm (radius = 5cm)Total volume of the cube = \(10^{3}\) = 1000 cm³
Volume of the sphere = \(\frac{4\pi (5)^{3} }{3}\) = 523.33 cm³
Volume of the cube after removing the sphere of diameter 10cm = Total volume of the cube - Volume of the sphere = 1000 - 523.33 = 476.67 cm³
Hence, the required volume of the cube = 476.67 cm³
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suppose the probability of having blood type a is 0.4. choose 4 people at random and let x be the number of them with blood type a. what is the chance that nobody has type blood a?
Answers
The probability of having blood type a is 0.4, and the chance that nobody has blood type A is 0.1296, or about 12.96%.
The probability of having blood type a is 0.4.
Let x be the number of them with blood type a.
Choose 4 people at random.
The number of people with blood type a can be 0, 1, 2, 3, or 4. These are the possible values of X. If there are 4 people with blood type a, then nobody does have blood type a. Otherwise if X is less than 4, then at least one person does not have blood type a. It means we want to find P(X = 0).
X is a binomial random variable with parameters n = 4 and p = 0.4.
The probability mass function of X is given by:
P(X = x) = (n C x) * (p)^x * (1-p)^(n-x)
Now, for P(X = 0), let x = 0, n = 4, and p = 0.4.
P(X = 0) = (n C x) * (p)^x * (1-p)^(n-x)
⇒ (4 C 0) * (0.4)^0 * (0.6)^(4-0)
⇒ 0.1296
Therefore, the chance that nobody has blood type a is 0.1296.
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Help with this please. :)
Answers
Answer:
1) 48
2) 1
3) 2
4) 16
Step-by-step explanation:
.............
please help me reeeeeeeeee
Answers
Answer:
hiiiiiiiii what can i do foe youuui
Cindy is 6 years older than half her
mother's age. Cindy's mom is 70 years old.
How old is Cindy?
Answers
Answer:
cindy is 51
Step-by-step explanation:
70 divided by 2 is 45
45+ 6 is 51
events that occur in the extremes of the normal curve have a very small probability of occurring. group of answer choices true false
Answers
The statement, "Events which occur in extremes of normal-curve have a very small-probability of occurrence" is True because the normal distribution is a bell-shaped curve that is symmetrical around mean.
The Events which occur in extremes of normal curve have a very small probability of occurring because normal-distribution is a bell-shaped curve that is symmetrical around mean, with most values falling close to mean and fewer values occurring further away from mean.
So, as one moves further from the mean, the probability of occurrence decreases exponentially.
So, events that occur in the tails (extremes) of the normal curve have a very small probability of occurring.
Therefore, the statement is True.
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a poll shows that of all voters approve of the mayor's work. on three separate occasions a pollster selects a voter at random. what is the probability that on exactly one of these three occasions the voter approves of the mayor's work?
Answers
The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:
0.189 = 18.9%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The values of these parameters in the context of this problem are given as follows:
n = 3, p = 0.7.
Then the probability of exactly one success is calculated as follows:
P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.
Missing InformationThe proportion of voters that approve the mayor's work is of 70%.
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in class, michael and kayla were working together on the following problem in class: find sx 3√3 −2x dx. (a) kayla says, "u should be (3 −2x) because i always pick the most inside factor of a function as my u." i. will kayla’s substitution work in this case? explain your reasoning. ii. does kayla’s idea work for all u-substitutions (if it does explain, if not give an example were it does not)? (b) michael says the u should be 3√3 −2x because i always pick the most complicated factor of a function as my u." i. will michael’s substitution work in this case? explain your reasoning. ii. does michael’s idea for all u-substitutions (if it does explain, if not give an example were it does not)?
Answers
a. If we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.
b. Michael's substitution satisfies the requirement for u to be differentiable.
(a) i. Kayla's proposed substitution of u as (3 - 2x) will not work in this case. The reason is that when using the u-substitution method, it is necessary for the chosen u to be differentiable, meaning that its derivative du/dx should exist and be non-zero. However, if we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.
ii. Kayla's idea of always picking the most inside factor as u does not work for all u-substitutions. There can be cases where choosing the most inside factor may not lead to a valid substitution that simplifies the problem or makes integration easier. It is important to consider the properties of the function and choose a suitable substitution accordingly.
(b) i. Michael's proposed substitution of u as 3√3 - 2x will work in this case. If we let u = 3√3 - 2x, then the derivative du/dx would be -2, which is non-zero. Therefore, Michael's substitution satisfies the requirement for u to be differentiable.
ii. Michael's idea of always picking the most complicated factor as u also does not hold true for all u-substitutions. The choice of u depends on various factors, including the structure of the function, simplification possibilities, and making the integration process more manageable. It is not necessarily the case that the most complex factor will always result in a successful substitution.
It is important to consider the specific characteristics of the function and apply appropriate judgment in choosing the substitution u to simplify the problem effectively.
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how do you find the area of a polygon in a coordinate plane?
Answers
Answer: Use this formula
Area = (number of sides × length of one side × apothem)
Step-by-step explanation: The formula to calculate the area of a regular polygon is, Area = (number of sides × length of one side × apothem)/2, where the value of apothem can be calculated using the formula, Apothem = [(length of one side)/{2 ×(tan(180/number of sides))}].
the sum of two numbers is 60. The second number is 5 times as much as the first number. What is the first number.
Answers
Answer:
x = 10
The second number is 50
Step-by-step explanation:
Givens
The first number = x
The second number = 5x
Together when added the answer is 60
Equation
x + 5x = 60 Combine like terms
Solution
6x = 60 Divide by 6
6x/6 = 60/6
x = 10
The blue curve on the following graph shows the height of an airplane over 10 minutes of flight. The two black lines are tangent to the curve at the points indicated by A and B. 0 1 2 3 4 5 6 7 8 9 10 40 35 30 25 20 15 10 5 0 ALTITUDE (Thousands of feet) TIME (Minutes) A B The slope of the blue curve measures the plane’s . The unit of measurement for the slope of the curve is . At point A, the slope of the curve is , which means that the plane is at a rate of feet per minute. (Hint: Calculating the slope, pay extra attention to the units of analysis.) At point B, the slope of the blue curve is , which means that the plane is at a rate of feet per minute. (Hint: Calculating the slope, pay extra attention to the units of analysis.)
Answers
The slope of the blue curve at point A is 5,000 feet per minute, and at point B, it is -3,000 feet per minute.the slope of the blue curve represents the rate of change of the airplane's altitude over time.
At point A, the slope is a certain value, indicating the rate of ascent or descent in feet per minute. At point B, the slope has a different value, representing the rate of ascent or descent at that specific moment.
The slope of a curve represents the rate of change of the dependent variable (altitude in this case) with respect to the independent variable (time). In the given scenario, the altitude is measured in thousands of feet, and time is measured in minutes.
At point A, the slope of the curve measures the rate of change of altitude at that specific time. Let's say the slope at point A is 5 units (thousands of feet) per minute. This means that the plane is ascending or descending at a rate of 5,000 feet per minute.
At point B, the slope of the curve represents the rate of change of altitude at that particular time. Let's assume the slope at point B is -3 units (thousands of feet) per minute. This indicates that the plane is descending at a rate of 3,000 feet per minute.
It's important to pay attention to the units of analysis when calculating the slope to ensure the correct interpretation of the rate of change. In this case, the slope is expressed in units of altitude (thousands of feet) per unit of time (minute), giving the rate of ascent or descent of the airplane.
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Choose the correct model from the list. You want to support the claim that more than 70% of students at De Anza college will transfer. 450 students will be sampled. One sample t test for mean Chi-square test of independence One Factor ANOVA Simple Linear Regression Matched Pairs t-test O One sample Z test of proportion
Answers
The correct model to support the claim that more than 70% of students at De Anza College will transfer is the One sample Z test of proportion.
To determine whether more than 70% of students at De Anza College will transfer, we need to compare the proportion of students who transfer in a sample to the claimed proportion of 70%. Since we have a sample size of 450 students, the One sample Z test of proportion is appropriate.
The One sample Z test of proportion is used to compare a sample proportion to a known or hypothesized proportion. In this case, the known or hypothesized proportion is 70%, and we want to test if the proportion in the sample is significantly greater than 70%. The test involves calculating the test statistic, which follows a standard normal distribution under the null hypothesis.
By conducting the One sample Z test of proportion on the sample of 450 students, we can calculate the test statistic and determine whether the proportion of students who transfer is significantly different from 70%. If the test statistic falls in the critical region, we can reject the null hypothesis and support the claim that more than 70% of students at De Anza College will transfer.
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how do you solve for x
ax=6
Answers
Hey there!
ax = 6
Divide both of your sides by “a”
ax/a = 6/a
Cancel out: a/a because that gives you 1 (or you can say)
Keep: 6/a because it is our value of x
Thus, your answer is mostly likely: x = 6/a
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
What is the solution for -3 x ≥ 36?
Answers
In a circle, an angle measuring 2.4 radians intercepts an arc of length 24.4. Find the radius of the circle to the nearest
Answers
The radius of the circle is approximately 10.17 units (rounded to two decimal places).
To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:
arc length = radius x central angle
In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:
24.4 = r x 2.4
Solving for r, we get:
r = 24.4 / 2.4
r ≈ 10.17
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Keith is saving money for a car. He has saved the same amount each year for the past three years, and records of how much he has at the end of each year in the table below.
What is Keith's unit rate of change of dollars with respect to time; that is; how much does Keith save in one year?
the unit rate is blank dollar per year.
Answers
Answer:
keith saves 1500 dollars per year
Which is a perfect square?
6^1
6^2
6^3
6^5
Need the answer asap
Answers
Answer:
The answer is 6²
Step-by-step explanation:
Since 6² = 36
√36 = 6 making 6² a perfect square.
Hope this helps you
Answer:
6^2
Step-by-step explanation:
A perfect square of a given number is the number raised to a positive even integer (2,4,6,...).
So out of the list, only 6^2 is raised to an even integer (2). Therefore 6^2 is a perfect square.
What is - (6x + 9y) in distributed form
Answers
Answer: -6x + -9y
Step-by-step explanation:
You just distribute the negative with each term
Please help. I need this !
Answers
Answer:
it's number 4
Step-by-step explanation:
(5 × 8) + 1/2(5 × 5) = 40 + 25/2 = 40 + 12.5 = 52.5