Determine if the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. Select true or false for each statement. This set is closed under scalar multiplications This set is a subspace This set is closed under vector addition The set contains the zero vector

Answers

Answer 1

This set is closed under scalar multiplications. Statement 1 is false.

This set is a subspace. This statement is also false because this set does not contain a zero vector so it is not a subspace.

This set is closed under vector addition. This is false. Because let v and w be two vectors such that v=(v1,v2); w=(w1,w2).

The set contains the zero vector. Statement 4 is false because the sum of two zero vectors cannot be equal to 1.

Since v and w are vectors satisfying the condition of space so v1+v2=1;w1+w2=1

Now we check whether v+w also belongs to the same space or not.

v+w=(v1,v2)+(w1,w2)=(v1+w1, v2+w2)

We shall check whether components of v+w also add up to 1.

v1+w1+v2+w2=v1+v2+w1+w2=1+1=2

So it means that this space is not closed under addition too.

Consider a vector v=(v1,v2) from the space.

Obviously v1+v2=1

Now let us take a constant 'c'  and consider the behavior of

cv=c(v1,v2)=(cv1,cv2)

Now we check whether components of this vector add up to 1.

cv1+cv2=c(v1+v2)=c\neq 1

which clearly indicates that vectors of this space are not closed under scalar multiplication.

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Related Questions

the sample space contains 5 as and 7 bs. what is the probability that a randomly selected set of 2 will in- clude 1 a and 1 b?

Answers

the probability that a randomly selected set of 2 will include 1 a and 1 b is 35/66

What is probability?

The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2. Writing P(heads) = 12

What are the 4 types of probability?

Classical

Empirical

Subjective.

Axiomatic

There are 66 equally likely outcomes, or C(5+7,2) =C(12,2)=66 possible outcomes. Only C(5,1)*C(7,1)=35 of these contain 1A and 1B. thus, the likelihood is 35/66.

The value of the solution is 35/66

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Hassan knows how to sing 6 vocal pieces, thanks to his choir class. Now he's about to start private lessons. His teacher says he will learn 2 new pieces each month.
Write an equation that shows the relationship between the number of months Hassan takes voice lessons, x, and the number of pieces he knows, y.
y=

Answers

Answer:

2x + 6

Step-by-step explanation:

If the number of months Hassan takes voice lessons is x, and he learns two pieces every month, you would multiply the number of months, x, together with the number of pieces he will learn each month, 2, making 2x.

Hassan already knows how to sing 6 vocal pieces, which you would add to 2x.

That makes 2x + 6.

Find the sum of 3x^2 + 2x - 4 and 2x^2 -3x+1

Answers

Answer:

5x^2-1x-3

Step-by-step explanation:

First bring the like terms together:

= 3x^2+2x^2+2x-3x-4+1

then solve it

Ans =5x^2-1x-3

I hope its useful

A leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. At that rate, how many buckets will the leaky faucet fill after 3 days?

Answers

The number of gallons that can be filled is 18 gallons.

What is a rate?

Rate demonstrates how many times one number can fit into another number. It contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, the number of hours in 3 days will be:

= 24 × 3

= 72 hours.

Since the leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. The gallon filled in 72 hours will be represented by x.

5/20 = x/72

Cross multiply

20x = 72 × 5

20x = 360

x = 360/20

x = 18

There'll be 18 gallons

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Given that (-2,3) is on the graph of y=f(x), find a point that must be on the graph of y=f(2x+1)+3. Express your answer as an ordered pair (a,b) where a and b are real numbers.

Answers

The point that must be on the graph of y=f(2x+1)+3 is (-6, 0)

What is ordered pair?

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.

Given that, (-2,3) is on the graph of y=f(x), we need to find a point that must be graphed of y=f(2x+1)+3

3 = f(2X(-3)+1) + 3

0 = f(-6)

Hence, the point on the graph is (-6, 0)

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consider an arbitrary n × n matrix a. what is the relationship between the characteristic polynomials of a and at ? what does your answer tell you about the eigenvalues of a and at ?

Answers

When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The scaling factor for the eigenvector is the appropriate eigenvalue, frequently represented as lambda.

When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by.

Hence, characteristic polynomial of A and A^T are the same, therefore their eigenvalues are also same.

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In a one-way ANOVA situation, if the overall F value is statistically significant, then you know that all of the means are significantly different from one another (T/F)?

Answers

It is true that in a one-way ANOVA situation, if the overall F value is statistically significant, then you know that all of the means are significantly different from one another.

ANOVA, which represents the analysis of variance, is a statistical test used to examine the distinction between the means of more than two groups.

One independent variable is used in a one-way ANOVA, while two independent variables are used in a two-way ANOVA.

In a one-way ANOVA scenario, the overall F value must be statistically significant for more than two of the means to be significantly different.

thus we can say that the given statement is true.

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Josh is 6 years older than 5 times Kim's age. The sum of their ages is less than 54.
What is the oldest Kim could be? Show all your work.
I

Answers

Answer:

8

Step-by-step explanation:

Josh is 6 years older than 5 times Kim's age. The sum of their ages is less than 54. What is the oldest Kim could be?

J + k < 54 when  J = 5k + 6 so:

5k + 6  + k < 54

6k + 6 < 54

subtract 6 from both sides:

6k + 6 - 6 < 54 - 6

6k < 48

divide both sides by 6:

6k/6 < 48/6

k < 8

Kim could be 8 at maximum.

4x+16=-12
What’s the answer?

Answers

Answer:

x = -7

Step-by-step explanation:

4x + 16 = -12   Subtract 16 from both sides

4x = -28  Divide both sides by 4

x = -7

Answer:

x = -7

Step-by-step explanation:

1. Subtract 16 from both sides

4x + 16 = -12

4x + 16 - 16 = -12 -16

2. Simplify

Subtract the numbers:

4x + 16 - 16 = -12 - 16

4x = -12 - 16

Subtract the numbers:

4x = -12 - 16

4x = -28

3. Divide both sides by the same factor

4x = -28

[tex]\frac{4x}{4}[/tex] = [tex]\frac{-28}{4}[/tex]

4. Simplify

Cancel terms that are in both the numerator and denominator:

[tex]\frac{4x}{4}[/tex] = [tex]\frac{-28}{4}[/tex]

x = [tex]\frac{-28}{4}[/tex]

Divide the numbers:

x = [tex]\frac{-28}{4}[/tex]

x = -7

Solution:

x = -7

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A normal distribution is observed from the number of points per game for a certain basketball player. if the mean (μ) is 15 points and the standard deviation (σ) is 3 points, what is the probability that in a randomly selected game, the player scored greater than 24 points? use the empirical rule

Answers

The likelihood that a player will score more than 24 points in a randomly chosen game is 0.0013 or 0.13%.

Explain the term normal distribution?The majority of the observations are centered around the middle peak of the normal distribution, which is a cumulative distribution function which is symmetrical around its mean. The probabilities for values that are farther from the mean taper away equally in both directions.

To compute the probability for the a data point, we must first get the value's z-score.

Mean = μ = 15 points

SD = σ = 3 points

When calculating the likelihood that a score will be higher than 24, the z-score for 24 is:

z-score = (x-μ)/σ

z = (24-15)/3

z = 9/3

z = 3

The chance of z3 must now be determined using the z-score table, and it will be deducted from 1 to determine the likelihood of z>3.

P(z < 3) = 0.9987

P(z > 3) = 1 - P(z < 3)

P(z > 3) = 1 - 0.9987

P(z > 3) = 0.0013 = 13%

Thus, the probability that a player will score more than 24 points in a randomly chosen game is 0.0013 or 0.13%.

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you have 2,000 feet of fencing to enclose a rectangular pasture. one side of the pasture is up against a river. what is the maximum area you could enclose?

Answers

The maximum area to enclose a rectangular pasture with one side of the pasture up against a river is equal to 500,000 square feet.

As given in the question,

Let 'x' represents the length of the rectangular pasture

And 'y' represents the width of the rectangular pasture

Condition:

One side of the pasture is up against a river

Perimeter of the rectangular pasture with one side up against river

= x + 2y

⇒ 2000 = x + 2y

⇒x= 2000 - 2y

Area of the rectangular pasture

=( 2000 - 2y )( y )

= - 2 ( y² - 1000y)

= -2( y² - 1000y + 250000 - 250000 )

= -2 (y - 500 )² + 500, 000

Maximum area is at y = 500

Maximum area is 500,000

Therefore, the maximum area of the given rectangular pasture is 500,000 square pasture.

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a survey of nonprofit organizations showed that online fundraising increased in the past year. based on a random sample of nonprofit​ organizations, the mean​ one-time gift donation in the past year was ​$​, with a standard deviation of ​$. if you test the null hypothesis at the level of​ significance, is there evidence that the mean​ one-time gift donation is greater than ​$​? interpret the meaning of the​ p-value in this problem.

Answers

A. There is enough data to conclude that the average one-time gift giving exceeds $75. with a 5% loss

B. The probability of receiving a sample mean one-time gift donation of $80 or more is the p-value.

What is a p-value?

The p-value, under the assumption that the null hypothesis is true, is the likelihood of receiving findings from a statistical hypothesis test that are at least as severe as the observed results. The p-value provides the minimal level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by greater evidence when the p-value is lower.

P-value is frequently utilized by government organizations to increase the credibility of their research or reports. The United States Census Bureau, for instance, mandates that any analysis with a p-value higher than 0.10 be accompanied by a statement stating that the difference is not statistically significant from zero.

A)

One wants to determine whether there is any proof that the average one-time gift giving exceeds $75.

The right response is thus E, i.e. E. H0:75 Vs H1:>75

Track down the test statistic.

n=54(sample size) (sample size)

Observed mean: 80

Observed standard deviation: 12

valid value=75

test statistic = (12[tex]\sqrt54[/tex])/(80-75)=3.06

Get the p-value by using the R-command shown below:

Lower. Tail=FALSE, p norm (3.06, 0, 1)

There is a 0.001 p-value.

What is the result of this experiment?

At a 5% threshold of significance, we reject H0 since the p-value is less than 0.05. (Los).

A. Dismiss the null theory. There is enough data to conclude that the average one-time gift giving exceeds $75. with a 5% loss

B)

In this situation, explain what the p-value means.

Take into account that the sample mean (Xbar) has a mean of 75 and a standard deviation of 12[tex]\sqrt54[/tex].

The chance that (Xbar) is larger than 80 is then equal to the p-value that was determined before.

The probability of receiving a sample mean one-time gift donation of $80 or more, given that the population mean one-time gift donation is $75, is represented by the p-value, which is B.

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Which rule best red the following patterns 8,4,10,6,12,8,14

Answers

The rule with describes the expression 8,4,10,6,12,8,14 is the alternating numbers gets increased by 2

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the expression be represented as A

Now , the expression A is

A = 8,4,10,6,12,8,14

Taking out the alternate numbers from the expression A , we get

A₁ = 8 , 10 , 12 , 14

So ,the values of A₁ increases by 2

And ,Taking out the alternate numbers from the expression A , we get

A₂ = 4 , 6 , 8 , 10

So , the values of A₂ also increases by 2

Hence , the alternating numbers in the expression increases by 2

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Trapezoid abcd has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1). Is this trapezoid an isosceles trapezoid? select from the drop-down menu to correctly complete the statement.

Answers

Yes, if Trapezoid abcd has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1) , ABCD is an isosceles trapezoid.

Since, If in a trapezoid two opposite nonparallel sides are equal then it is called isosceles trapezoid.

In trapezoid ABCD sides are AB, BC, CD and DA.

According to the question,  A≡(2,4) B≡(5,4) C≡(7,1) and D≡(0,1)

After making the diagram of ABCD, we found that DA and BC are nonparallel sides.

And, by the distance formula BC = √((7 - 5)² + (1 - 4)²) =

⇒ BC =√(4 + 9)

⇒BC = √13 unit.

Similarly, DA = √((0 - 2)² + (1 - 4)²)

DA  = √(4 + 9)

⇒ DA  = √13 unit.

Thus, In trapezoid ABCD, two non parallel sides BC and DA are equal.

Therefore, trapezoid ABCD is a isosceles trapezoid.

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**WILL MARK BRAINLIEST AND GIVE 30 POINTS**
Fill in the blanks to solve the system of equations. Enter only 1 term in each blank.

Answers

Answer:

1st blank = 6x

2nd blank = 12

3rd blank = 2

4th blank = 2

5th blank = 8

6th blank = 5

Find the x value of the axis of symmetry for the following function: f(x) = - 3x ^ 2 + 13x + 10

Answers

The axis of symmetry of the equation f(x) = - 3x ^ 2 + 13x + 10 is

x = 13/6

How to find the axis of symmetry

The axis of symmetry is calculated

= -b / 2a

The quadratic equation is an equation of the form

ax^2 + bx + c

Comparing the given equation f(x) = - 3x^2 + 13x + 10 with ax^2 + bx + c the values of the axis of symmetry is

x = -b / 2a

x = -13 / 2(-3)

x = -13 / -6

x = 13/6

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A line passes through (1, 1) and (-3,5).
What is the equation of the line in slope-intercept form?

Answers

Answer:      Y=-x+2

Step-by-step explanation:

Ms.D bought 8 1/2 pounds of ham from Excellente Hambaked Shop. She gave 1 3/4 pounds of ham to Mr.Chavir. How many pounds of ham does she have left?

Answers

The amount of ham Ms.D  has left is [tex]6\frac{3}{4}[/tex] pounds.

How to find the pounds of ham she has left?

Ms.D bought [tex]8\frac{1}{2}[/tex] pounds of ham from Excellente Hambaked Shop.  She gave [tex]1\frac{3}{4}[/tex] pounds of ham to Mr.Chavir. The number of pounds of ham she has left can be calculated as follows:

Hence, the amount of hams in pounds she has left is the difference between what she had and the amount of pounds of hams she gave to Mr Chavir.

Therefore,

Amount bought by Ms.D  = [tex]8\frac{1}{2}[/tex] pounds

Amount given to Mr.Chavir.  = [tex]1\frac{3}{4}[/tex] pounds

Therefore,

Amount of she has left = [tex]8\frac{1}{2}[/tex] - [tex]1\frac{3}{4}[/tex]

Amount of she has left = [tex]\frac{17}{2} - \frac{7}{4}[/tex]

Amount of she has left = [tex]\frac{34-7}{4}[/tex]

Amount of she has left = [tex]\frac{27}{4}[/tex]

Amount of she has left = [tex]6\frac{3}{4}[/tex] pounds

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location is known to affect the number, of a particular item, sold by walmart. two different locations, a and b, are selected on an experimental basis. location a was observed for 18 days and location b was observed for 18 days. the number of the particular items sold per day was recorded for each location. on average, location a sold 39 of these items with a sample standard deviation of 9 and location b sold 55 of these items with a sample standard deviation of 6. select a 99% confidence interval for the difference in the true means of items sold at location a and b.

Answers

The required confidence interval for the difference of means is (-18.52, -13.48).

Explain confidence of interval.

Statisticians use  confidence intervals to gauge vulnerability in an example variable. For instance, a scientist chooses various examples haphazardly from a similar populace and registers a certainty span so that each example might be able to perceive how it might address the genuine worth of the populace variable. The subsequent datasets are different where a few stretches incorporate the genuine populace boundary and others don't.

According to question:

[tex]n_{a}[/tex] = 18 represent the sample of A

[tex]n_{b}[/tex] = 18 represent the sample of B

μₐ = 39 represent the mean sample  for A

μᵇ =  represent the mean sample for B  

σ = 9 represent the sample deviation for A

σ = 6 represent the sample deviation for B

α = 0.01 represent the significance level

Confidence =99% or 0.99

confidence interval for the difference of means is given by the following formula,

μₐ - μᵇ± [tex]t_{\frac{α}{2}}[/tex][tex]\sqrt{\frac{S_{a}}{n_{a}} +\frac{S_{b}}{n_{b}} }[/tex]

39 - 55 ± 2.756[tex]\sqrt{\frac{9}{18} +\frac{6}{18} }[/tex]

-16 - 2.756(0.912) =  -18.52

-16 + 2.756(0.912) = -13.48

Thus, required confidence interval is (-18.52, -13.48).

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i need some help plsssssss

Answers

Answer:

Option 3 (Parentheses, division, multiplication, subtraction)

Step-by-step explanation:

Using PEMDAS, we can know that we need to solve the parentheses first. Next, we need to solve the multiplication and division, so we can eliminate the first option and last option. However, we need to solve the operations left to right, meaning we'd solve the division first. Therefore, the answer is option 3.

Answer:

The answer is Parentheses multiplication division subtraction

Step-by-step explanation:

Always remember

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

where do i start with this world problem

Answers

The measure of an angle ∠TQU is 26.6° if  PQ=3 and QR=4

What is meant by an angle?

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.

Given,

Rectangle PQRS has PQ=3 and QR=4

The points T and U are on side PS such that PT=US=1

As PQRS is rectangle so opposite sides of rectangle should be equal.

PS=QR and PQ=RS

QR=4, PS=4

But, PS=PT+TU+US

4=1+TU+1

TU=4-2

TU=2

And PU=PT+TU

1+2=3

PU=3

Consider, ΔQPU, Right angled at P.

We know that,

tan Q=PU/PQ

tan Q=3/3

tan Q=1

Q=tan⁻¹

Q=45°

∠PQU=45°

Now, let us consider ΔQPT is right angled at P

tan Q=PT/PQ

tan Q=1/3

Q= tan⁻¹(1/3)

Q=18.43°

∠PQT=18.43°

∠PQU=∠PQT+∠TQU

45°=18.43°+∠TQU

∠TQU=45°-18.43°

∠TQU=26.57°

∠TQU≈26.6°

Therefore, the measure of ∠TQU is 26.6°.

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3(12-5)+8x4 what is this problem? How do I solve it?

Answers

Parentheses come first! 12-5=6, if theres a number infront of the parentheses, you multiply it. 3 x 6 = 18. 8x4= 32 and added with 18 = 50!
53 would be the answer
PEMDAS

need help on 11 and 12! or you can solve one instead of both if u want

Answers

Answer:

11. (-4, 5)

12. (0, 2)

Step-by-step explanation:

The solution from the graph is to determine the point of intersection of the two rays. And find the x and y values corresponding to that point.

In 11, the point of intersection is at x = -4, y =5

In 12, the point of intersection is at x = 0, y = 2

I am not clear on what they want you to do for checking the solution. You could mathematically solve for the set of equations.

I think what they mean is to check if your reading of the point coordinates from the graph is correct.
In which case just plug in the values of x and y into both equations in each problem and find if they are consistent

Let's take Problem 12 which has a solution of x = 0, y = 2

Plug in these values into each of the equations:

For 2x - y = -2, with x = 0, y = 2
2(0) - 2 = 0 - 2 = -2 so consistent

For 2x + 4y = 8
2(0) + 4(2) = 0 + 8 = 8

So both equations are consistent with the values read off the graph.

Use the same technique for the others

Hope that helps

An equation and some of the steps used to solve the equation are shown below. One step is missing: 2(x-3) + 10x = 5(3 + x) ? 2x-5x + 10x = 15 + 6 7x = 21 x=3 Which set of statements is most likely the missing step and the property that justifies the step?

Answers

The missing step was 2x-6+10x= 15+5x, the step where was applied the distributive property.

Applying the distributive property, the given radical expression can be represented by 15.

Properties of Multiplication

The properties of multiplication are:

Distributive:  a(b±c)=  ab±acCommutative:   a . b = b. aAssociative:    a(b+c)=  c(a+b)Identity: b.1=b

For answering the question, you should solve the given expression step by step. After that, you should identify the missing step from the information given for the question.

The question gives:  2(x-3) + 10x = 5(3 + x), from the distributive property. you have

2x-6+10x= 15+5x     (step 1)

2x -5x +10x = 15+6  (step 2)

7x=21                       (step 3)

x=3                          (step 4)

See that step 1 (2x-6+10x= 15+5x ) is not shown in the question.

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Which number did he add?

Answers

x= 7 and x=11 are two solutions of equation  x²+7x-11=0

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The given equation is x²+7x-11=0

x square plus seven times of x minus eleven

Add 11 on both sides

x²+7x=11

x(x+7)=11

x=11

and x+7=11

Now subtract 7 on both sides

x=7

Hence, x= 7 and x=11 are two solutions of equation  x²+7x-11=0.

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an integer from the range 00000 - 99999 is generated uniformly at random. we are interested only in even integers that start with 2 odd digits where all digits are unique. if we randomly generate 8 of these numbers in succession, what is the probability we get exactly 5 numbers that meet our criteria?

Answers

Randomly generating 8 of these numbers in succession, the probability we get exactly 5 numbers that meet our criteria is 0.13875.

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Thus, by Fundamental Principle of Counting, the number of possible even integers that start with 2 odd digits is 13875.

= (5 x 5 x 5) + (5 x 5 x 10 x 5) + (5 x 5 x 10 x 10 x 5)

= 125 + 1250 + 12500

= 13875

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

probability = desired outcome / total outcomes

probability = 13875/100000

probability = 0.13875

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How many sides do 2 decagons and 5 hexagons have in all?

Answers

Answer: 50 sides

Step-by-step explanation:

a decagon has 10 sides and 2 decagons have 20 sides total

a hexagon has 6 sides and 5 hexagons have 30 total

20 + 30 = 50

Therefore the answer is 50 sides

please help me solve this asap

Answers

So for the first part, use the equation (y2-y1)/(x2-x1)
(6+1)/(2+4) it becomes adding as you are subtracting a negative. So then you get
7/6 as your slope.
Since it is a positive slope, the line is rising. That is the second answer.
Sketch the line by plotting the two given points. The slope should be rise 7 over run 6

Answer:

B. Falls

Step-by-step explanation:

can you help me solve this problem (x - 5)(x+2) = 0

Answers

Answer: -2

Step-by-step explanation:

(x - 5) (x + 2) = 0

(x - 5) = 0

(x - 2) = 0

Add 5 to both sides, then simplify. After that, you will subtract 2 from both sides. Simplify again, and the solution is -2.

45 POINTS
i really need help
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Hikers walk 3 miles east and then 2 miles north and take a water break. They continue hiking 4 miles east and a final 2 miles south to their destination. What single
transformation took place from their starting position to their final destination? Use
mathematical language and create a graphic to explain your answer. Be sure to use a
straight edge and grid paper for your graphic to represent this problem.

(please add steps and notes)

Answers

Answer:

they could've walked 4 miles east to make the trip quicker. Would look alot nicer if i had grid paper

Step-by-step explanation:

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