Find the distance from the vector (1, 2, 3, 4) to the
subspace of R^4 spanned by the vectors (1, −1, 1, 0) and (3, 2, 2,
1).
Answers
The distance from the vector (1, 2, 3, 4) to the subspace of R^4 spanned by the vectors (1, -1, 1, 0) and (3, 2, 2, 1) can be calculated as the length of the orthogonal projection of (1, 2, 3, 4) onto the subspace.
To find the distance, we first need to determine the orthogonal projection of the vector (1, 2, 3, 4) onto the subspace spanned by (1, -1, 1, 0) and (3, 2, 2, 1).
The orthogonal projection of (1, 2, 3, 4) onto the subspace can be obtained by projecting (1, 2, 3, 4) onto each of the spanning vectors and then summing those projections. Using the projection formula, we find that the projection of (1, 2, 3, 4) onto the first spanning vector (1, -1, 1, 0) is (5/3, -5/3, 5/3, 0), and the projection onto the second spanning vector (3, 2, 2, 1) is (3/2, 1, 1, 1/2).
Next, we calculate the difference vector between (1, 2, 3, 4) and the sum of the two projections: (1, 2, 3, 4) - [(5/3, -5/3, 5/3, 0) + (3/2, 1, 1, 1/2)] = (2/6, 13/6, 7/6, 7/2).
Finally, we find the length of the difference vector, which represents the distance between (1, 2, 3, 4) and the subspace: √[(2/6)^2 + (13/6)^2 + (7/6)^2 + (7/2)^2] = √(242/9).
Therefore, the distance from the vector (1, 2, 3, 4) to the subspace of R^4 spanned by (1, -1, 1, 0) and (3, 2, 2, 1) is √(242/9).
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Related Questions
can someone please help me with this
Answers
Answer:
the answer to the first one is \(20\sqrt7\) and the answer to the second one is i think the first one??
hope this helped...
Amara took geometry in high school but did not use this knowledge for years. During an internship in college, she needed geometry to solve a problem and found that she remembered how to apply the various formulas. In this situational Amara was relying on:.
Answers
Amara relied on her retained knowledge of geometry formulas from high school to solve a problem during her college internship.
In this situation, Amara was relying on her "long-term memory" or "retained knowledge" of geometry formulas. Even though she hadn't actively used this knowledge for years, it was stored in her memory and she was able to access and apply the formulas when needed during her college internship. This demonstrates the concept of long-term memory, where information and skills learned in the past can be retrieved and utilized when appropriate.
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Da los resultados de las siguientes multiplicaciones de expresiones algebraicas:
1) 2a^2 por 3a=
2) -5x^2 por 2xy=
3) 2m (4m - 3)=
4) (3xy - 2) por ( 5x^2 + 4)=
5) 2a^2 por 3a^3=
6) - xy^2 por -5mx^4y^3=
7) 3a^2b por -4b^2x
Porfa ame urge
Answers
Answer:
no se tu dime xd jajajaajajajajajajajsjaa ahahahahahahahahsidigfue
Consider the variable x = time required for a college student to complete a stan- dardized exam. Suppose that for the population of students at a particular university, the distribution of x is well approximated by a normal curve with mean 55 minutes and standard deviation 5 minutes. (You may need to use a table. Round your answers to four decimal places.) (a) If 60 minutes is allowed for the exam, what proportion of students at this university would be unable to finish in the allotted time? (b) How much time (in minutes) should be allowed for the exam if you wanted 90% of the students taking the test to be able to finish in the allotted time? (c) How much time (in minutes) is required for the fastest 20% of all students to complete the exam?
Answers
a) The proportion is 1 - 0.8413 = 0.1587, or approximately 0.1587 when rounded to four decimal places.
b) Approximately 61.408 minutes should be allowed for the exam if we want 90% of the students to be able to finish in the allotted time.
c) Approximately 50.792 minutes are required for the fastest 20% of all students to complete the exam.
(a) The proportion of students at this university who would be unable to finish the exam in 60 minutes can be calculated by finding the area under the normal curve to the right of 60 minutes.
Using the z-score formula, we can convert the given time into a z-score:
z = (x - μ) / σ,
where x is the given time, μ is the mean, and σ is the standard deviation. In this case, x = 60 minutes, μ = 55 minutes, and σ = 5 minutes. Plugging in these values, we get z = (60 - 55) / 5 = 1.
Next, we need to find the cumulative probability associated with a z-score of 1 in the standard normal distribution table (Z-table). The Z-table tells us that the cumulative probability associated with a z-score of 1 is approximately 0.8413.
Since we want the proportion of students who would be unable to finish the exam, we subtract the cumulative probability from 1 (total area under the curve). Therefore, the proportion is 1 - 0.8413 = 0.1587, or approximately 0.1587 when rounded to four decimal places.
(b) To find the amount of time needed for 90% of the students to finish in the allotted time, we need to find the corresponding z-score that gives a cumulative probability of 0.90.
Using the Z-table, we can find the z-score associated with a cumulative probability of 0.90, which is approximately 1.2816.
We can then rearrange the z-score formula to solve for x (the time needed):
x = z * σ + μ.
Plugging in the values, we have x = 1.2816 * 5 + 55 = 61.408.
Therefore, approximately 61.408 minutes should be allowed for the exam if we want 90% of the students to be able to finish in the allotted time.
(c) To find the time required for the fastest 20% of all students to complete the exam, we need to find the z-score associated with a cumulative probability of 0.20.
Using the Z-table, we find that the z-score associated with a cumulative probability of 0.20 is approximately -0.8416.
Using the z-score formula, we can rearrange it to solve for x:
x = z * σ + μ.
Plugging in the values, we have x = -0.8416 * 5 + 55 = 50.792.
Therefore, approximately 50.792 minutes are required for the fastest 20% of all students to complete the exam.
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I need help please. I don’t know the answer to the question
Answers
The angle 1 can be named as follows:
∠RST
∠TSR
∠S
How to name angles?There are various ways to name an angles. You can name an angle by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.
Therefore, let's name the angle 1 indicated on the diagram as follows:
Hence, the different ways to name the angle 1 is as follows:
∠RST or ∠TSR
Or
∠S
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Write a story starting with the following lines. ( no romance included)
The hospital is stuffy and the air has an undertone of bleach. the walls are magnolia and are scraped in places from the hundreds of trolleys. that have bumped into them. The picture in the wall are cheap benign prints of uplifting scenes and above the double doors are large blue plastic signs with the areas of hospital lie ahead.
Answers
Answer:
The hospital is stuffy and the air has an undertone of bleach. the walls are magnolia and are scraped in places from the hundreds of trolleys. that have bumped into them. The picture in the wall are cheap benign prints of uplifting scenes and above the double doors are large blue plastic signs with the areas of hospital lie ahead.I was comig through the two doors to see my grandpa and he was bareley alive then I walked with him back through the blue doors with the sam stuffy feeling after I walked through then as we approached the surgery room he miraculously recovered and walked away and no knows how it happened. Too this day the hospital employees wonder how this had happened
Let y = 5x^2
Find the change in y, ∆y when x = 4 and ∆x = 0.1 ________________
Find the differential dy when x = 4 and dx = 0.1 _______________
Answers
The formula for differential dy is given as: dy = 2xydx Substituting the given values in the above formula, we have:dy = 2(5)(4)(0.1)dy = 4Thus, the differential dy when x = 4 and dx = 0.1 is 4.
Let y = 5x^2 Find the change in y, ∆y when x
= 4 and ∆x
= 0.1We are given a quadratic function as: y
= 5x²Now, we have to find the change in y when x
= 4 and Δx
= 0.1.Using the formula of change in y or Δy, we can determine the answer. The formula for change in y is given as: Δy = 2xyΔx + Δx²Substituting the given values in the above formula, we have:Δy
= 2(5)(4)(0.1) + (0.1)²Δy
= 4 + 0.01Δy
= 4.01Thus, the change in y when x
= 4 and Δx
= 0.1 is 4.01. Find the differential dy when x
= 4 and dx
= 0.1We are given a quadratic function as: y
= 5x²Now, we have to find the differential dy when x
= 4 and dx
= 0.1.Using the formula of differential dy, we can determine the answer. The formula for differential dy is given as: dy
= 2xydx Substituting the given values in the above formula, we have:dy
= 2(5)(4)(0.1)dy
= 4 Thus, the differential dy when x
= 4 and dx
= 0.1 is 4.
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Given m || n, find the value of x and y.
X =
y =
(6x-2)(3x+2)
m
n
Answers
Answer:
x = 20
y = 62
Step-by-step explanation:
Angles on a straight line sum to 180°:
⇒ (6x - 2)° + (3x + 2)° = 180°
⇒ 6x - 2 + 3x + 2 = 180
⇒ 6x + 3x - 2 + 2 = 180
⇒ 9x = 180
⇒ 9x ÷ 9 = 180 ÷ 9
⇒ x = 20
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
⇒ y° = (3x + 2)°
⇒ y = 3x + 2
⇒ y = 3(20) + 2
⇒ y = 60 + 2
⇒ y = 62
If we focus upon the historical data, or past values of the variable to be forecast, we refer to this as a time series method of forecasting.True or False?
Answers
Answer:T
Step-by-step explanation:
design a statistical process for finding how satisfied the students are in the cafeteria of the school with the quality of food
Answers
The design of the experiment above will center around:
The administration of questionnaire based on subject's gender, the place of eating, type of school and level satisfaction of meal service. The questionnaires to be used will have 5 point of Likert type scale (where 5 stands for very much agree and 1 is totally disagreed) in regards to the level of satisfaction on the quality of food in school cafeteria.Statistical tests will be done and data analyzed by using SPSS (ver.12.0).What will be the aim of the experiment?The aim of this study is to know and compare student's level of satisfaction with school cafeteria food services so as to improve the quality of food served at school meal service.
Hence The design of the experiment above will center around:
The administration of questionnaire based on subject's gender, the place of eating, type of school and level satisfaction of meal service. The questionnaires to be used will have 5 point of Likert type scale (where 5 stands for very much agree and 1 is totally disagreed) in regards to the level of satisfaction on the quality of food in school cafeteria.Statistical tests will be done and data analyzed by using SPSS (ver.12.0).Learn more about statistical test from
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3. Layla has a coin that has a 60% percent chance of showing heads each time it is flipped (realize that this is an unfair or biased coin). She is going to flip the coin 5 times. Let X represent the number of heads she gets. What is the probability that she gets more than 3 heads? You may round your answer to the nearest hundredth. P(X>3)=? 4. A surgical intervention results in increased quality of life in 60% of patients. If 20 patients undergo surgery, what is the probability that it is effective on 12 patients? 4. A surgical intervention results in increased quality of life in 60% of patients. If 20 patients undergo surgery, what is the probability that it is effective on 12 patients?
Answers
1. The probability that Layla gets more than 3 heads is 0.40 (rounded to the nearest hundredth).
P(X>3) = 0.40.Let X represent the number of heads Layla gets on flipping a coin that has a 60% chance of showing heads. She is going to flip the coin five times and we are supposed to find the probability that she gets more than 3 heads. The probability that Layla gets more than 3 heads is P(X>3).
Solution :We are given that the coin has a 60% chance of showing heads each time it is flipped. The probability of getting a head (success) is p = 0.6 and the probability of getting a tail (failure) is q = 0.4. As Layla is going to flip the coin five times, we have n = 5.On each flip, X can either be a head or a tail. Thus, X is a binomial random variable with parameters n = 5 and p = 0.6.P(X>3) can be calculated as:P(X > 3) = P(X = 4) + P(X = 5)P(X = 4) = nCx × p^x × q^(n-x) = 5C4 × 0.6^4 × 0.4^1 = 0.2592P(X = 5) = nCx × p^x × q^(n-x) = 5C5 × 0.6^5 × 0.4^0 = 0.07776P(X > 3) = P(X = 4) + P(X = 5) = 0.2592 + 0.07776 = 0.33696 ≈ 0.40
2. Probability of surgery being effective on 12 patients = 0.00000078643 and the probability that surgery is effective on at least 12 patients out of 20 is 0.1985502502.
Let p be the probability that a surgical intervention results in an increased quality of life in a patient, which is given as 60%. Let X be the number of patients out of 20 who have an increased quality of life after undergoing the surgery. We are supposed to find the probability that surgery is effective on 12 patients out of 20.
Solution :Let X be the number of patients out of 20 who have an increased quality of life after undergoing the surgery. Then X is a binomial random variable with parameters n = 20 and p = 0.6.The probability of surgery being effective on exactly 12 patients can be calculated as:P(X = 12) = nCx × p^x × q^(n-x) = 20C12 × 0.6^12 × 0.4^8 = 0.00000078643 (rounded to 11 decimal places)
The probability of surgery being effective on at least 12 patients can be calculated as:P(X ≥ 12) = P(X = 12) + P(X = 13) + ... + P(X = 20)Using a binomial probability distribution table, we can calculate this probability as:P(X ≥ 12) = 0.00000078643 + 0.0000105188 + 0.0000976064 + 0.0007052774 + 0.0038752048 + 0.0163110784 + 0.052553726 + 0.125428942 = 0.1985502502Therefore, the probability that surgery is effective on 12 patients out of 20 is 0.00000078643
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Use the fact that 1.5 is the same as 3/2 to select all
of tile equations below that are equivalent to T=A^1.5
Answers
Answer:
It is all 4
Step-by-step explanation:
Answer:
all 4 , the next one is A
Step-by-step explanation:
what is -3 divied - 1/4th
Answers
Answer:
12
Step-by-step explanation:
use keep change flip
keep -3 change the division sign to multiplication sign then flip -1/4 to -4/1
(-3)(-4)=12
pls mark as brainliest, thank u have a great day.
Reorder the steps of the proof to make sure that steps that are logically dependent on prior steps are in the proper order.
Answers
Answer:
Step-by-step explanation:
Correct order to prove BD bisects ∠ABC is,
Statements Reasons
1). AB ≅ BC 1). Given
D is the midpoint of AC
2). AD ≅ DC 2). A midpoint divides a segment into two
congruent segments.
3). BD ≅ BD 3). Reflexive property
4). ΔABD ≅ ΔCBD 4). SSS property
5). ∠ABD ≅ ∠CBD 5). Corresponding parts of congruent
triangles are congruent (CPCTC)
Which of the following does (square root f^2) simplify to, for any nonnegative real number f?
Answers
Answer:A
Step-by-step explanation:
A real estate agent earns a salary of $20,000 a year and 6% commission on any sales. An agent sold 4 homes worth a total of $980,000 last year. What was the agent's total pay for the year, including salary and commission from the sales?
Answers
Answer:78,800
Step-by-step explanation:
Find the measure (in degrees, not equal to the given measure) of the least positive angle that is coterminal with A.
A=343
Answers
The smallest positive angle that is equivalent to A=343 degrees is 703 degrees.
To find the measure of the least positive angle that is coterminal with A, we need to determine the equivalent angle within one full revolution (360 degrees) of A.
A is given as 343 degrees. To find the coterminal angle within one revolution, we can subtract or add multiples of 360 degrees until we obtain a positive angle.
Let's subtract 360 degrees from A:
343 - 360 = -17
The result is a negative angle, so we need to add 360 degrees instead:
343 + 360 = 703
Now, we have a positive angle of 703 degrees, which is coterminal with 343 degrees.
The measure of the least positive angle that is coterminal with A is 703 degrees.
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help me..............................................................................
Answers
Answer:
$7.50 per box
Step-by-step explanation:
it is a proportional relationship, and one of the points is (4,30) so we can find the slope by doing 30/4
30/4=7.5
$7.50 per box
The length of an arc is 7.54 feet and it’s central angle is 144 find the length of the radius
Answers
Answer:
the length of the radius is 0.914422
Step-by-step explanation:
2 time what makes 19.98?
Answers
Answer:
9.99
Step-by-step explanation:
The predator - prey relationship is based primarily on the quest for:
a. Space b. Symbiosis c. energy d.help
Answers
Answer:
C. Energy
Step-by-step explanation:
The predator is looking for the energy needed in order for it to survive which it finds in its prey.
The predator-prey relationship is primarily based on the quest for energy.
Option C is the correct answer.
We have,
Predators hunt and consume prey in order to obtain energy for their survival.
The prey, on the other hand, tries to evade predation and secure its own energy resources for survival.
The interaction between predators and prey is driven by the need for sustenance and the transfer of energy within an ecosystem.
While factors like space, symbiosis, and even occasional instances of help between species can play a role in the dynamics of ecosystems, the primary driving force behind the predator-prey relationship is the quest for energy.
Therefore,
The predator-prey relationship is primarily based on the quest for energy.
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the length of a rectangle exceeds its width by 12 inches, and the area is 85 square inches. what are the length and width of the rectangle?
Answers
Answer:l=17, w=5
Step-by-step explanation:
Evaluate each using the values given. x+z+y; use x = 4, y = 4, and z = 6
Answers
Answer:
14
Step-by-step explanation:
x + z + y = ?
First, substitute in x for 4, y for 4, and z for 6
4 + 6 + 4
Add 4 and 6
10 + 4
Add 10 and 4 to get your answer:
14
Answer:
X + y + z= 4 + 4 + 6= 14 . The Answer is 14. I hoped this helpful for you . If you like this answer then mark this answer as BRAINLIEST answer....Thank you ☺️☺️
What is the value of (ΣX)2 for the scores 1, 5, 2?(PLEASE EXPLAIN)10163064
Answers
The value of (ΣX)² for the scores 1, 5, 2 is:
64
What is a summation?
It is the representation of the sum of infinite or many values. And it is represented by the following symbol:
∑xi
The value of (ΣX)² for the scores 1, 5, 2 can be found by first finding the summation of the scores and then squaring the result.
Steps to follow:
Step 1: Find the summation of the scores.
ΣX = 1 + 5 + 2 = 8
Step 2: Square the summation.
(ΣX)² = 82 = 64
Therefore, the value of (ΣX)² for the scores 1, 5, 2 is 64.
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Dwayne plans to add a railing parallel to a flight of stairs that goes down to the basement in his house. The stairs have the dimensions shown in the sketch. Landing 7.5 in 9.5 in 7.5 95 9.5 What will be the length of the railing from Point A to Point B? Show or explain how you got your answer.
Answers
Answer:
121 inches
Step-by-step explanation:
See the attached diagram. We can form a right triangle as shown. The base and sides of the right triangle can be computed by adding the 10 steps of horizonal distance 9.5" (95" for the base) and the 10 vertical distances of 7.5" (75" total) for the height. Use the Pythagorean Theorem to calculate the hypotenuse, which will be the same as the railing length.
Patrick worker 5.25 hours on monday 6.75 hours on wensday and 7.75 hours on saturday how many hours did he work for the week? 18 hours 19.75 20.25 21 hours
Answers
Patrick worked for 19.75 hours this week. Option A is correct.
Given that,
Patrick worked 5.25 hours on Monday 6.75 hours on Wednesday and 7.75 hours on Saturday how many hours did he work for the week is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here, In the week,
Patrick worked, 5.25 hours on Monday 6.75 hours on Wednesday, and 7.75 hours on Saturday.
The total hours patrick worked for = 5.25 + 6.75 + 7.75 = 19.75
Thus, Patrick worked 19.75 hours this week. Option A is correct.
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******BRAINLIEST IF ANSWERED****** Which equation can be used to find the measure of angle BAC? * inverse tan(5/12) inverse cos(5/13) inverse sin(12/5) inverse tan(12/13)
Answers
Answer:
\(cos^{-1}(\frac{5}{13} )\)
Step-by-step explanation:
We can see that x is at ∠A.
To find x:
cosx° = 5/13
x = cos^-1(5/13)
sinx° = 12/13
x = sin^-1(12/13)
tanx° = 12/5
x = tan^-1(12/5)
Out of our answer choices, the only one that fits is the inverse cos(5/13).
Answer:
inverse cos 5/13
Step-by-step explanation:
i took the quiz
Question 8 of 9 In a science lab, a number of rock samples are weighed. If the scientist finds one of the rocks to weigh 3 pounds and this is 49.3% of the total weight of all of the rocks, what is the weight of all of the rocks? If necessary, round your answer to the nearest tenth. O 6.1 lb O 1.5 lb O 3.1 lb O 147.9 lb
Answers
If (5^n)^3 = 5^12 then n= ?
6
Answers
Answer: n=4
Step-by-step explanation:
Uh I did some trial and error and it came up with the right answer
The ratio of hotdogs to hamburgers sold at the picnic was 3:4. If 98 dinners were sold, how many were hamburgers?
Answers
Answer:
56 Burgers
Step-by-step explanation:
First, add the 3 + 4 for a total of 7, because the total of the ratio will equal the total amount of "the dinners sold".
Then divide 98/7, which will give you 14.
Then in the ration 3:4, 4 represent burgers so multiply 14 x 4.
Which gives you 56 burgers.
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