Let V be the Euclidean space R^2 = {x = (x1,x2) x1 ER, x2 E R}. (a) Construct a subspace of V containing all vectors that are parallel to the vector (1, 2). (b) Construct a subspace of V containing all vectors that are perpendicular to the vector (1, 1).

Answers

Answer 1

(a) To construct a subspace of V containing all vectors that are parallel to (1, 2), we need to find a basis for this subspace. We can choose the vector (1, 2) as a basis vector since every vector parallel to (1, 2) can be written as a scalar multiple of (1, 2). Therefore, the subspace containing all vectors parallel to (1, 2) is spanned by the vector (1, 2), i.e., the set {k(1, 2) : k E R}.

(b) To construct a subspace of V containing all vectors that are perpendicular to (1, 1), we need to find a basis for the orthogonal complement of (1, 1). This subspace is denoted by (1, 1)^⊥ and is defined as follows:

(1, 1)^⊥ = {v E V : (v, w) = 0 for all w E (1, 1)}

where (v, w) is the dot product of vectors v and w. In this case, we have:

(v, (1, 1)) = v1 + v2

Therefore, (v, (1, 1)) = 0 if and only if v1 = -v2. This means that the orthogonal complement of (1, 1) consists of all vectors of the form (x, -x) where x E R. Hence, a basis for (1, 1)^⊥ is given by the vector (1, -1). Therefore, the subspace containing all vectors perpendicular to (1, 1) is spanned by the vector (1, -1), i.e., the set {k(1, -1) : k E R}.

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Related Questions

The table represents a Linear function, what is the slope of the function?

Answers

Answer:

m = 3

Step-by-step explanation:

Pick two points from the table.

(-1, 1) and (1, 7)

Apply the slope formula.

$m=\frac{7-1}{1+1}=\frac{6}{2}=\boxed{3}$

Hope this helps.

Karls pet lizard walked 2/5 mile in 1/3 hour. Use this information to complete the steps to find the unit rate.

1. Write The ratio of distance in time Option 1)
2
—
5
______
1
—
3

Option 2)

1
—
3
_______
2
—
5

Option 3)

5
—
3

Answers

The unit rate represented by the information is 6/5 mile per hour

How to use the information to complete the steps to find the unit rate?

The given parameters are

Distance = 2/5 mile

Time = 1/3 hour

The ratio of distance in time is calculated as

Ratio = Distance : Time

This gives

Ratio = 2/5 mile : 1/3 hour

Divide both ratio by 1/3

So, we have

Ratio = 6/5 mile : 1 hour

Express as fraction

Ratio = 6/5 mile/1 hour

This gives

Ratio = 6/5 mile per hour

Hence, the unit rate represented by the information is 6/5 mile per hour

Answers

Answer:

Is A

Step-by-step explanation:

(2-4)/(-2--6) = -1/2

And the only answer that has -1/2 as the slope is A

-2+ 3(1-4)-2 what to do ???

Answers

Answer:

-13

Step-by-step explanation:

−2+3(1−4)−2

=−2+(3)(−3)−2

=−2+−9−2

=−11−2

=−13

Step-by-step explanation:

Is this ok

If its correct, please don't forget to like and mark me

(X-2)(x+1)

Expand and siplify

Answers

$\\ \sf\longmapsto (x-2)(x+1)$

$\\ \sf\longmapsto x(x+1)-2(x+1)$

$\\ \sf\longmapsto x^2+x-2x-2$

$\\ \sf\longmapsto x^2-x-2$

Is the sum of any two whole numbers always a whole number answer it with at least 3 example?

Answers

Yes, the sum of 2 whole numbers is always a whole number.

Any number that ranges from 0 to infinity with 1 as the denominator in its smallest form is called a whole number.

For example- 0, 3, 78, 9363, etc.

Now if we take up two numbers say 34 and 78.

34 + 78

= 112

According to the definition of the whole number, we can say that this is a whole number.

Another example can be 0 + 237

The sum is 237

which again is a whole number.

The last example can be 2365 + 930

= 3295

This too is a whole number.

Hence the sum of two whole numbers will always be a whole number.

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Which of the following correctly names an angle of the triangle below? A. AB B. AABC C. C D. B

Answers

Answer:

Based on the information provided, none of the given options correctly names an angle of the triangle. The options provided do not correspond to the standard way of naming angles in a triangle.

In triangle ABC, the angles are typically named using capital letters at the vertices of the triangle. For example:

Angle A refers to the angle formed at vertex A.

Angle B refers to the angle formed at vertex B.

Angle C refers to the angle formed at vertex C.

Therefore, none of the given options (A, AABC, C, B) correctly name an angle of the triangle.

Step-by-step explanation:

Based on the information provided, none of the given options correctly names an angle of the triangle. The options provided do not correspond to the standard way of naming angles in a triangle.

In triangle ABC, the angles are typically named using capital letters at the vertices of the triangle. For example:

Angle A refers to the angle formed at vertex A.

Angle B refers to the angle formed at vertex B.

Angle C refers to the angle formed at vertex C.

Therefore, none of the given options (A, AABC, C, B) correctly name an angle of the triangle.

If you cat in at a fist-food restaurant, most of the soda machines are self-serving. If you finish your drink, you can go back and fill up your cup as many times as you want. A loenl fast-food restaurant manager is concemed that people are taking advantage of filling up their drink and that the restaurant is losing money as a result. He selected a random sample of 90 customers who got a drink and are eating in the restaurant. He found that 19 of those customers are filling up more than 3 times. (a) Construct and interpret a 95 percent confidence interval for the proportion of all customers who, when ondering a drink and cating in the restaurant, will fill up their cup more than 3 times. (b) The manger measured if a customer filled up more than 3 times because that is when the restaurant will start to lose money on the drink. It will cost the restaurant

Answers

(a) To construct a 95% confidence interval for the proportion of all customers who fill up their cup more than 3 times, we can use the formula:

CI = p ± z*√((p(1-p))/n)

where pis the sample proportion, z is the z-score corresponding to the confidence level (95% corresponds to a z-score of 1.96), and n is the sample size.

In this case, we have p= 19/90 = 0.2111. Plugging in the values, we get:

CI = 0.2111 ± 1.96*√((0.2111(1-0.2111))/90)

CI = (0.1084, 0.3138)

Interpreting this interval, we can say that we are 95% confident that the true proportion of all customers who fill up their cup more than 3 times when ordering a drink and eating in the restaurant falls between 10.84% and 31.38%.

(b) To calculate the minimum number of times a customer must fill up their cup for the restaurant to start losing money on the drink, we need to know the cost per drink and the profit margin on each drink. Let's assume that the cost per drink is $0.25 and the profit margin is 75% (i.e., the restaurant makes $0.75 for every $1.00 in sales).

If a customer fills up their cup more than 3 times, they are essentially getting more than 4 drinks for the price of one. So, if the cost per drink is $0.25 and the customer pays $1.00 for the drink, the restaurant is losing $0.75 for every extra drink that the customer gets. Therefore, the minimum number of times a customer must fill up their cup for the restaurant to start losing money is:

$1.00 ÷ $0.75 = 1.33

In other words, if a customer fills up their cup more than 1.33 times, the restaurant is losing money on the drink.

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consider following recurrence relation. what will be the number next in series in place of question mark? 0, 3, 8, 15, 24, 35, 48, ?

Answers

The number that will be next in the series will be 63 .

In the question ,

a recurrence relation is given that is 0, 3, 8, 15, 24, 35, 48, ? .

we have to find the number that will come in place of question mark .

On carefully examining the series , we can see that

3 - 0 = 3

8 - 3 = 5

15 - 8 = 7

24 - 15 = 9

35 - 24 = 11

48 - 35 = 13

we can se that increments 3,5,7,9,11,13,... form an Arithmetic Progression

with first term as 3 and common difference as 2 ,

So ,the next increment will be 13+2 = 15

let the next term be "x" .

x - 48 = 15

x = 15 + 48 = 63

the number in place of ? is 63 .

Therefore , The number that will be next in the series will be 63 .

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calculate averages A-C, thanks.
EX#1 - Calculate the average of the following: a- 10, 20, 30 b- 5, 10, 15, 20 C-1, 5, 10, 15, 20

Answers

Answer:

A = 20

B = 12.5

C = 10.2

Step-by-step explanation:

A = (10 + 20 + 30)/3 = 20

B = (5 + 10 + 15 + 20) = 12.5

C = (1 + 5 + 10 + 15 + 20) = 10.2

the hawaiian alphabet has 12 letters. How many permutations are possible for five of these letters

Answers

Answer: The answer is 50980

Step by Step Explanation:

First, temporarily assume that two letters with I are different, call them i 1 and i 2. Three "a" are also called as a 1, a 2 and a 3, and two h as h 1 and h 2. Then there are 11 * 10 * 9 * 8 * 7 = 55440 possible "words" (one of 11 is the first letter, 10 is the second, and so on). But because equal letters do the same "words," some "words" were counted twice or more. We have to deduct the number of "parasitic" counts although it is fairly small. The words that counted more than once are divided into many disjoint sets: 1) with two I but without repetitions of a and h; 2) with two h but without repetitions of a and I 3) with two a but without repetitions of I and h; 4) with three a but without repetitions of I and h; 5) with two I and two a's; 6) two i's and tree a's; 7) two i's and two h's 8) two h's and two a's; 9) two h's and one tree. The first category includes terms counted twice and its scale is (5 * 4) * (6 * 5 * 4) = 2400 (the first I stays at one of the 5 positions, the second at one of the 4, then 11-2i-1h-2a=6). So we have 2400/2 = 1200 to subtract. Group 2 gives -600 as well, and group 3 also. Group 4 gives * (6 * 5) = 1800 (5 * 4 * 3), and the terms are counted 6 times, -300. Groups 5, 7 , 8: 5 * 4 * 3 * 2 * 6 = 720 and counted four times, therefore -180. Group 6 and 9: 5 * 4 * 3 * 2 * 1 = 120, with 12 counts, -10. Altogether -(1200 * 3 + 300 + 180 * 3 + 10 * 2) = -4460.The answer will be 55440-4460 = 50980.

The number of permutations which are possible with the five letters of HAWAIIAN is 1488.

What is permutations?

It is the number of times a word can be arranged in a defined order. to calculate the number of permutations we often use nPr formula which states n!/(n-r)!

How to calculate the permutations?

We are total 12 letters in the word hawaiian and letters in the alphabet for which permutations need to be calculated are 5. So the number of permutations are:

12P1+12P3+12P2+12P1+12P1

=12!/11!+12!/9!+12!/10!+12!/11!+12!/11!

=3*12*11!/11!+12*11*10*9!/9!+12*11*10!/10!

=36+1320+132

=1488

Hence the number of permutations in the word hawaiian for the 5 letters is 1488.

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A model boat i 15 inche long if the boat i bulit to a cale of 1 : 250 inche how long i the real boat
define a variable
write a porortion
olve the porportion
anwer with word

Answers

If the scale of drawing is 1 inches : 250 inche and the real horse height is 15 inche, then the height of the horse in drawing is 0.06 inches.

What does a scale look like in math?

The ratio that describes the relationship between the true figure itself and model is called the scale. It serves as a representation of the real statistics in smaller units on maps. A scale of 1:5, for instance, indicates that 1 on the map is approximately the size of 5 in the actual world.

Briefing:

The scale of drawing the horse = 1 inch :

Therefore in scale

Horse height in drawing equals one inch

The height of the horse = 250 inche

The original height of the horse = 15 inche

The height in the picture = x inches

To find the height the horse in the picture, we have to use proportion

1 inch : 250 inche = x inches : 15 inche

1 / 250 = x / 15

1 × 15= 250x

250x = 15

x = 15/250

x = 0.06 inches

Therefore, the height of the horse in drawing is 0.06 inches

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which number comes next in this series 5, 7, 11, 19, 35

Answers

Answer: 67

Step-by-step explanation:

We see a pattern where we multiply the number we added by previously by two.

For example, from 5 to 7, it is 2.

From 7 to 11, we add by 4.

From 11 to 19, we add by 8.

From 19 to 35, we add by 16.

This means the next number would be 32, adding 35 by 32 gives us 67,

which of the following statements regarding the normal distribution is not true? it is bimodal it is symmetric around the mean the mean, median, and mode are all equal it is asymptotic

Answers

The statement that the normal distribution is bimodal is not true. The normal distribution is a unimodal distribution, meaning it has only one mode. It is symmetric around the mean, and the mean, median, and mode are all equal.

Additionally, the normal distribution is asymptotic, meaning that the tails of the distribution approach but never touch the horizontal axis. The normal distribution is a bell-shaped curve that is widely used in statistics and probability theory to describe real-world phenomena such as the heights of people, test scores, and IQ scores. The properties of the normal distribution make it a useful tool for modeling data, making predictions, and conducting hypothesis tests.

By understanding the normal distribution, statisticians and data analysts can better understand the patterns and trends in their data and make informed decisions based on that understanding.

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a) Calculate the size of angle x in the diagram
below.
b) Work out the bearing of A from B.

Answers

The angle x in the diagram is 98 degrees.

How to find the angles in parallel lines?

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.

A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.

Which statement about probability is true?

The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.

Answers

The probability of landing on yellow is less than the probability of landing on blue

How to determine which statement about probability is true?

Probability is the likelihood of a desired event happening.

Since there are one orange, two purple, two yellow, and three blue and the spinner divided into eight equal colored sections.

Thus, we can write the probabilities as follow:

probability of orange = 1/8

probability of purple = 2/8 = 1/4

probability of yellow = 2/8 = 1/4

probability of blue = 3/8

Therefore, the probability of landing on yellow is less than the probability of landing on blue is the true statement

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Hi does anyone know the answer?

Answers

Answer:

The correct equation is actually: y=10x+10.

Jaiden calculated the slope of the line incorrectly, as the y-axis increases by 10, not 2. The correct slope of the line is 20/2, which is equal to 10.

Hope this helps!

A cylinder has a height of 19 centimeters and a radius of 9 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.

Answers

Answer:

the answer for your question is 4832.46 cm3

math question (2 QUESTIONS!!)

Which expression represents the distance between −14.6 and −5.2 on the number line?
Drag and drop the correct expression into the box.

and

Which expression shows the distance on the number line between −12 and −1?

(IMAGES BELOW AND PLEASE EDIT THE IMAGE INSTEAD AND QUICK! also give brainlist if that is what its called)

Answers

Answer: |-14.6-(-5.2)|

|-12-(-1)| ==> 4th option

Step-by-step explanation:

In order to find the distance between two points, you have to subtract one point from another and take the absolute value of the difference.

|-14.6-(-5.2)|=

|-14.6+5.2|=

|-9.4|=9.4

|-14.6-(-5.2)| ==> |-12-(-1)| ==> 4th option

|-12+1|=

|-11|=11

10 expressions equivalent to 10/10x+.50y
PLS Hurry ima have to present soon

Answers

Is the a I in that one

it is known that for a given mass of gas, the volume varies inversely as the pressure 'P'.Fill in the missing entries in the following table:-

Answers

Given that for a given mass of gas, the volume varies inversely as the pressure 'P'.To fill the missing entries in the given table, we have to apply the formula of inverse variation which is given by, V α 1/PAlso, V1P1 = V2P2, where V1 and P1 are initial volume and pressure and V2 and P2 are final volume and pressure.

Now, we are given the value of P1, V1 and P2. We need to calculate the value of V2 as shown in the table below:Pressures (P)Volumes (V)200 400 ?500 250From the formula of inverse variation,V α 1/PV = k/Pwhere k is the constant of variation.For pressure 200, volume is 400.V1 = 400, P1 = 200

Substituting the values in the above formula, we get,k = PV = 400(200)k = 80,000Now, for pressure 500,V2 = k/P2V2 = (80,000)/(500)V2 = 160 . Hence, the missing volume in the given table is 160.

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help appreciated thanks

Answers

Answer:

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Calculate the cost (omit commission) of buying the 500 shares of Delta Air at $50.61.

Answers

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The cost of 500 shares of Delta Air is $25,305.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The cost of a single share is $50.61, therefore, the cost of 500 shares will be,

Cost of 500 shares = 500 × cost of single share

= 500 × $50.61

= $25,305

Hence, the cost of 500 shares of Delta Air is $25,305.

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Help please wats the correct answer

Answers

Answer: whats the question

Step-by-step explanation:

Answer:

380.13

Step-by-step explanation:

The area of a circle can be found using the formula A= pir^2. If the diameter is 22, then the radius is 11. Plug those numbers in a calculator and you get 380.13

When we conclude that the results we have gathered from our sample are probably also found in the population from which the sample was drawn, we say that the results are:

Answers

When we conclude that the results we have gathered from our sample are probably also found in the population from which the sample was drawn, we say that the results are statistically significant.

In statistical analysis, we use hypothesis testing to determine whether the results of a sample are likely to be representative of the population as a whole. If the results are statistically significant, we can infer that there is a low probability that the observed differences between the sample and the population occurred by chance alone.

This allows us to generalize the findings from the sample to the larger population with a reasonable degree of confidence.

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At Smith Mountain Lake Boat Rentals, it cost $25 per hour to rent a pontoon boat, plus a one-time charge for cleaning. The Bengal family rented a boat from 11 am - 6:30 pm and paid $226.50. If the Jones family rented a boat from 8 am- 1pm, how much did the pay?

Answers

Answer: $164

Step-by-step explanation:

25*7=175

175+12.5

226.50-187.50

5*25=125+39

Jones family payed $164

Making a round trip from Fairview to Cartersville, a distance of 20 miles, a pilot faces 30 mph head wind one way and 30 mph tail wind on the return trip. The return trip takes 45 minutes less than the outbound journey. Find the speed of the plane in still air

Answers

Answer:

50mph

Step-by-step explanation:

Given the following :

Distance (d) of journey = 20 miles

Wind speed = 30mph head wind in one way, 30mph tail wind in the other direction

Return trip = 45 minutes (45/60 = 0.75 hour) less Than the outbound journey

Speed of plane in still air

Outbound trip :

Velocity = Distance / time

Time = distance / velocity

Velocity = (v - 30) due to head wind

Return Velocity (V +30) due to tail wind

Outbound time = return distance

20 / (v - 30) = 20 / (v +30) + 0.75

20v + 600 = 20v + 0.75v^2 + 22.5v - 600-22.5v-675

600 = 0.75v^2 - 1275

0.75v^2 = 1875

v^2 = 1875/ 0.75

v^2 = 2500

v = sqrt(2500)

v = 50mph

suppose there are ten five- and six-year-olds attending a birthday party. when a 30-year-old mother walks into the room with an infant in her arms, what happens to the standard deviation of ages in the room? (changes or stays approximately the same) changes what happens to the median of ages in the room? (gets bigger; gets smaller; stays approximately the same

Answers

The standard deviation of ages in the room increases, while the median of ages stays approximately the same.

Standard deviation is a measure of the variability of a set of data points. The addition of a 30-year-old mother and an infant to the group of ten five- and six-year-olds increases the spread of the ages, thus increasing the standard deviation.

The median, on the other hand, is the middle value in a set of data points. Since the median only depends on the order of the values, not their magnitude, adding a mother and an infant to the group of children does not significantly affect the median age in the room, which would still be close to 5 or 6 years old.

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Help!!! I need help I don't know how to do it

Answers

100% of 42 people=42
50% of 42 people =21
150% of 42 people=63

Hope it helps : )

Which of the following does the Pythagorean Theorem reveal

Answers

According to the Pythagorean theorem, "in a right-angled triangle, the squares of the hypotenuse side is equivalent to the sum of squares of the other two sides," the hypotenuse side is the longest side of the triangle.

This is further explained below.

What is Pythagorean Theorem?

Generally, The Pythagorean theorem is a well-known geometric theorem that states the number of squares just on the legs of a right triangle is equal to the square just on the hypotenuse (the side that is opposite the right angle).

This theorem can also be expressed in the familiar algebraic notation of a2 + b2 = c2, where a and b are the lengths of the legs of the triangle.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is an essential connection in Euclidean geometry that describes the relationships between the three sides of a right triangle.

It indicates that the total of the areas of the squares on the other two sides is equal to the area of the square whose side is the hypotenuse.

In conclusion, This means that the area of the square whose side is the hypotenuse is equal to that amount.