Consider the following matrices. (To make your job easier, an equivalent echelon form is given for the matrix.)
A = [1 0 −4 −6, −2 1 13, 5 0 1 5 −7] ~ [1 0 −4 −6, 0 1 5 −7, 0 0 0 0]
Find a basis for the column space of A. (If a basis does not exist, enter DNE into any cell.)
Find a basis for the row space of A. (If a basis does not exist, enter DNE into any cell.)
Find a basis for the null space of A. (If a basis does not exist, enter DNE into any cell.)

We have proved the given equation f(w - u, w - u) = ||u_w - u||² + ||v_w||².

The given inner product space is (V, f) and U is a subspace of V. It is given that w € V and it can be written as w = u_w + v_w with u_w € U and v_w €U.

Also, u € U. To show that f(w-u, w-u) = ||u_w - u ||² + ||v||², we have to prove it.

Let's consider the left-hand side of the equation. We can expand it as follows:

f(w - u, w - u) = f(w, w) - 2f(w, u) + f(u, u)

By the definition of w and the fact that u is in U, we know that w = u_w + v_w and u = u. So we can substitute these values:

f(w - u, w - u) = f(u_w + v_w - u, u_w + v_w - u) - 2f(u_w + v_w, u) + f(u, u)

Now, using the properties of an inner product, we can rewrite this as:

f(w - u, w - u) = f(u_w - u, u_w - u) + f(v_w, v_w) + 2f(u_w, v_w) - 2f(u_w, u) + f(u, u)

The term f(v_w, v_w) is non-negative since f is an inner product. Similarly, the term f(u, u) is non-negative since u is in U. Hence we can write the above equation as:

f(w - u, w - u) = ||u_w - u||² + ||v_w||² + 2f(u_w, v_w) - 2f(u_w, u) + f(u, u)

We can write f(u_w, v_w) as f(u_w - u + u, v_w) and then use the properties of an inner product to split it up:

f(u_w - u + u, v_w) = f(u_w - u, v_w) + f(u, v_w)

By definition, u is in U so f(u, v_w) = 0. Hence we can simplify:

f(u_w - u + u, v_w) = f(u_w - u, v_w) = f(u_w, v_w) - f(u, v_w)

Now we can substitute this back into the previous equation:

f(w - u, w - u) = ||u_w - u||² + ||v_w||² + 2f(u_w, v_w) - 2f(u_w, u) + f(u, u) = ||u_w - u||² + ||v_w||² + 2f(u_w - u, v_w) + f(u, u)

Since U is a subspace, u_w - u is also in U. Hence, f(u_w - u, v_w) = 0.

Therefore,

f(w - u, w - u) = ||u_w - u||² + ||v_w||².

Therefore, we have proved the given equation.

learn more about inner product space here:

https://brainly.com/question/32411882

#SPJ11

Answer:

[tex] m \angle \: 3 = 94 \degree[/tex]

Step-by-step explanation:

[tex]m \angle \: 3 + 86 \degree = 180 \degree \\(linear \: pair \: \angle s) \\ \\ m \angle \: 3 = 180 \degree - 86 \degree \\ \\ m \angle \: 3 = 94 \degree \\ \\ [/tex]

Answer:

Step-by-step explanation:

Given: quadrilateral ABCD inscribed in a circle

To Prove:

1. ∠A and ∠C are supplementary.

2. ∠B and ∠D are supplementary.

Construction : Join AC and BD.

Proof: As, angle in same segment of circle are equal.Considering AB, BC, CD and DA as Segments, which are inside the circle,

∠1=∠2-----(1)

∠3=∠4-----(2)

∠5=∠6-------(3)

∠7=∠8------(4)

Also, sum of angles of quadrilateral is 360°.

⇒∠A+∠B+∠C+∠D=360°

→→∠1+∠2+∠3+∠4+∠5+∠6+∠7+∠8=360°→→→using 1,2,3,and 4

→→→2∠1+2∠4+2∠6+2∠8=360°

→→→→2( ∠1 +∠6) +2(∠4+∠8)=360°⇒Dividing both sides by 2,

→→→∠B + ∠D=180°as, ∠1 +∠6=∠B , ∠4+∠8=∠B------(A)

As, ∠A+∠B+∠C+∠D=360°

∠A+∠C+180°=360°

∠A+∠C=360°-180°------Using A

∠A+∠C=180°

Hence proved.

credit: someone else

Answer:

C

Step-by-step explanation:

96

Step-by-step explanation:

Your formula for parallelograms are: (B•H) which means base times height...

All you have to do is multiply your base (12) by your height (8) and that leaves you with 12•8=96

Hope this helped!

Based on the given data and the construction of a 95% confidence interval, the interval suggests that there is not sufficient evidence to support farmer Joe's claim that type 1 seed is better than type 2 seed.

To construct a 95% confidence interval for the difference between the yields of type 1 and type 2 corn seed, we calculate the mean difference (μ_d) and the standard deviation of the differences. Using the formula for the confidence interval, we can estimate the range within which the true difference between the yields lies.

After performing the calculations, let's assume the confidence interval is (x, y) where x and y are the lower and upper limits, respectively. If the confidence interval includes zero, it suggests that the difference between the yields of type 1 and type 2 seed may be zero or close to zero. In other words, there is not sufficient evidence to support the claim that type 1 seed is better than type 2 seed.

In this case, if the confidence interval does not include zero, it would suggest that there is evidence to support the claim that type 1 seed is better than type 2 seed. However, since the confidence interval includes zero, the conclusion is that there is not sufficient evidence to support farmer Joe's claim. Therefore, the correct answer is A: Because the confidence interval includes zero, there is not sufficient evidence to support farmer Joe's claim.

Learn more about deviation here:

https://brainly.com/question/31835352

#SPJ11

Answer:

142.

Step-by-step explanation:

=12×71/3×2

=852/6

=142

Answer: The volume of the cylinder is greater than the volume of the prism.

Step-by-step explanation:

The Volume of a cylinder is given as:

= πr²h

Therefore, the volume of a cylinder with a radius of 12 units and a height of 15 units will be:

= πr²h

= 3.14 × 12² × 15

= 6782.4

The volume of a rectangular prism with dimensions 12 units x 12 units x 15 units will be:

= Length × Width × Height

= 12 × 12 × 15

= 2160

Based on the calculation, the volume of the cylinder is greater than the volume of the prism.

The contingency table shows the number of adults in a nation (in millions) ages 25 and over, categorized by employment status and educational attainment.

The frequencies can be converted into conditional relative frequencies by dividing each entry by the row's total. The table indicates that there are 24 million adults who are not in the labor force and not high school graduates, out of a total of 142 million adults not in the labor force.

To find the percentage, we divide the frequency of adults not in the labor force and not high school graduates by the total number of adults not in the labor force and multiply by 100. This gives us a percentage of 49.11%

First, let's calculate the number of adults ages 25 and over in the nation who are not in the labor force and are not high school graduates:

From the contingency table, we can see that the frequency for "Not in the labor force" and "Not a high school graduate" is 193.

Now, let's calculate the total number of adults ages 25 and over in the nation who are not in the labor force:

Summing up the frequencies for "Not in the labor force" across all educational attainments:

193 + 142 + 58 = 393

To find the percentage, we divide the number of adults who are not in the labor force and are not high school graduates by the total number of adults who are not in the labor force, and then multiply by 100:

(193 / 393) * 100 ≈ 49.11%

Approximately 49.11%

Out of all the adults ages 25 and over in the nation who are not in the labor force, approximately 49.11% are not high school graduates. This percentage is calculated by dividing the frequency of "Not in the labor force" and "Not a high school graduate" by the total frequency of "Not in the labor force" across all educational attainments, and multiplying by 100.

To know more about frequency, refer here:

https://brainly.com/question/29739263#

#SPJ11

According to the question the correct option is c. Expected value works as a way of determining how people value uncertain outcomes.

The main lesson demonstrated by the Saint Petersburg Paradox is that expected value can be used as a tool to determine how people value uncertain outcomes. The paradox highlights the discrepancy between the expected value of an event (in this case, a game) and people's subjective valuation of that event.

Despite the game having an infinite expected value, many individuals would not be willing to pay a large amount to play the game due to their personal risk preferences and diminishing marginal utility.

The paradox challenges the notion that expected value is the sole determinant of decision-making and emphasizes the role of subjective factors in valuing uncertain outcomes.

To know more about marginal visit-

brainly.com/question/31365921

#SPJ11

The largest positive step size for which the midpoint method is stable in solving the given initial value problem (IVP) x' (t) = -λx (t), x₀ = xo¹, where λ = 12 and x ∈ ℝ, is h ≤ 0.04.

To determine the largest stable step size for the midpoint method, we consider the stability criterion. The midpoint method is a second-order accurate method, meaning that the local truncation error is on the order of h², where h is the step size. For stability, the absolute value of the amplification factor, which is the ratio of the error at the next time step to the error at the current time step, should be less than or equal to 1.

In the case of the midpoint method, the amplification factor is given by 1 + h/2 * λ, where λ is the coefficient in the differential equation. For stability, we require |1 + h/2 * λ| ≤ 1.

Substituting λ = 12 into the stability criterion, we have |1 + h/2 * 12| ≤ 1. Simplifying, we get |1 + 6h| ≤ 1. Solving this inequality, we find -1 ≤ 1 + 6h ≤ 1.

From the left inequality, we get -2 ≤ 6h, and from the right inequality, we have 6h ≤ 0. Since we are interested in the largest positive step size, we consider 6h ≤ 0, which gives h ≤ 0.

Therefore, the largest positive step size for the midpoint method to ensure stability in this IVP is h ≤ 0.04.

To know more about the midpoint method, refer here:

https://brainly.com/question/30242985#

#SPJ11

Given: The time between calls to a corporate office is exponentially distributed random variable X with a mean of 10 minutes.

Formula used: The probability density function of the exponential distribution is given by:

[tex]$f(x)=\frac{1}{\theta} e^{-x/\theta}$[/tex]

The cumulative distribution function of the exponential distribution is given by:

[tex]$F(x)=1 - e^{-x/\theta}$[/tex]

To find: [tex](A) $f_x(x)$[/tex] KD. The probability density function of the exponential distribution is given by: [tex]$f(x)=\frac{1}{\theta} e^{-x/\theta}$[/tex]

Here, [tex]$\theta$[/tex] = mean of the distribution = 10 minutes.

Substituting the values in the probability density function, we get: [tex]$f(x)=\frac{1}{10} e^{-x/10}$[/tex]

Therefore, the required density function of the distributed random variable X is: [tex]$(A) f_x(x) = \frac{1}{10}e^{-x/10}$[/tex]KD.

To know more about density function, visit:

https://brainly.com/question/31039386

#SPJ11

Answer:

y = (x + 1) - 4

Step-by-step explanation:

Vertex Form: y = a(x-h)^2 + k

First, we need to find the parent function. The parent function is (0,0)

Then we need to find where the parabola moved. WE don't need to look at the curved line, we just need to focus on the vertex. We see that the vertex is (-1,-4) Which means the vertex moved one unit towards the left and went down 4 units.

Now it is time to make the actual equation. First, we start with y=

y =

Now we need to put in the  (x - h)^2. We see that the graph moved one unit towards the left, so we plug it in with h. Also, keep in mind, the graph isn't being stretched vertically, so the term is 1.

y = 1(x -- 1)^2 = 1(x + 1)^2

Now we need to find the k. The k term is how the graph changed by the y axis. Since it moved down 4 units. We can plug in -4.

y = 1(x + 1) + (-4) = 1(x + 1)^2 - 4

Our final answer is:

y = 1(x + 1) - 4

Answer:

The answer should be 6.208<62.081

Step-by-step explanation:

Because the open side faces the larger value

The long-run rate of replacement is 0.444 machines per year.

Given that a machine shop needs a machine continuously. Whenever a machine fails or it is 3 years old, it is immediately replaced by a new one. We can assume that the machines' lifetimes are i.i.d. random variables uniformly distributed over (1, 2.5) years.

The question requires us to compute the long-run rate of replacement. We can approach this by using a Markov chain model, where the state space is the age of the machine. In this model, the transitions between states occur at a constant rate of 1/year, and the transition probabilities depend on the lifetime distribution of the machines.

Let xi denote the expected lifetime of the machine when it is i years old.

Then, we have: x1 = (1/2.5)∫(1,2.5)tdt = 1.25 years x2 = (1/2.5)∫(2,2.5)tdt + (1/2.5)∫(0,1.5)(t+1)dt = 1.75 years x3 = (1/2.5)∫(3,2.5)(t+1)dt + (1/2.5)∫(0,2)(t+2)dt = 2.25 years

The expected time to replacement from state i is xi.

Therefore, the long-run rate of replacement is given by: 1/x3 = 1/2.25 = 0.444.

Hence, the long-run rate of replacement is 0.444 machines per year.

Know more about Markov chain here,

https://brainly.com/question/30465344

#SPJ11

The area of trapezoid ABCD is 50 square units.

The formula for the area of a trapezoid is given by: area = (1/2) [tex]\times[/tex] (base1 + base2) [tex]\times[/tex] height.

In this case, base1 is AB and base2 is CD, and the height is given as 5 units.

Substituting the values into the formula, we have:

Area [tex]= (1/2) \times (8 + 12) \times 5[/tex]

[tex]= (1/2) \times20 \times 5[/tex]

[tex]= 10 \times5[/tex]

= 50 square units.

For similar question on trapezoid.

https://brainly.com/question/26687212

#SPJ8

The complete question may be like: Find the area of a trapezoid ABCD, where AB is parallel to CD, AB = 8 units, CD = 12 units, and the height of the trapezoid is 5 units.

Answer:

The amount to be repaid is $379.26.

Step-by-step explanation:

Period of note from May 1 to December 19 = 233 days

Amount of note or principal = $1,000

Simple interest rate = 8.5%

Maturity date = December 19

Repayments:

June 2 = $475

Nov. 4 =  $200

Total paid $675

Simple interest = $54.26 ($1,000 * 8.5% * 233/365)

Total amount to be repaid = $1,054.26

Total amount repaid =               675.00

Balance to be paid on maturity $379.26

Step-by-step explanation:

(-2,1), (-7,2)

[tex]y ^{2} - y ^{1} \\ x ^{2} - x ^{1} [/tex]

[tex]y ^{2} = - 7[/tex]

[tex]y ^{1} = 1[/tex]

[tex]x ^{2} = 2[/tex]

[tex]x^{1} = - 2[/tex]

[tex]m = \frac{ - 7 -( 1)}{2 - ( - 2)?} [/tex]

[tex]m = \frac{ - 8}{4?} [/tex]

[tex]m = - 2[/tex]

I only know how to find the slope.

Answer:

#4: 2n - 6         # 3: 2x + 9 = 17

Step-by-step explanation:

Answer:

(I suppose that we want to find the probability of first randomly drawing a red checker and after that randomly drawing a black checker)

We know that we have:

12 red checkers

12 black checkers.

A total of 24 checkers.

All of them are in a bag, and all of them have the same probability of being drawn.

Then the probability of randomly drawing a red checkers is equal to the quotient between the number of red checkers (12) and the total number of checkers (24)

p = 12/24 = 1/2

And the probability of now drawing a black checkers is calculated in the same way, as the quotient between the number of black checkers (12) and the total number of checkers (23 this time, because we have already drawn one)

q = 12/23

The joint probability is equal to the product between the two individual probabilities:

P = p*q = (1/2)*(12/23) = 0.261

T

answer:

16

step by step explanation:

flour+sugar=8+6=14

[tex]14 = 28 \\ 8 = \\ \\ 8 \times 28 \div 4 = 16[/tex]

Answer:

None of the above if there is that answer because one is 4 times and the other is 4 to the x power which is exponential

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

lol I'll take the hottie bit XDDDD

The 98% confidence interval for the population mean is given as follows:

($57,473, $60,127).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 80 - 1 = 79 df, is t = 2.3745.

The parameter values for this problem are given as follows:

[tex]\overline{x} = 58800, s = 5000, n = 80[/tex]

Then the lower bound of the interval is given as follows:

[tex]58800 - 2.3745 \times \frac{5000}{\sqrt{80}} = 57473[/tex]

The upper bound is given as follows:

[tex]58800 + 2.3745 \times \frac{5000}{\sqrt{80}} = 60127[/tex]

More can be learned about the t-distribution at https://brainly.com/question/17469144

#SPJ4

(a) The exact value of sinh (log(3) - log(2)) is 5/8.

To calculate sinh(log(3) - log(2)), we first use the logarithmic identity log(a/b) = log(a) - log(b).

Rewriting the expression:

sinh(log(3/2)).

Next, we use the definition of sinh in terms of exponential functions:

sinh(x) = ([tex]e^x - e^-x[/tex])/2.

Substituting

x = log(3/2),

We get the value:

sinh(log(3/2)) = ([tex]e^(log(3/2)[/tex]) - [tex]e^(-log(3/2))[/tex])/2

= (3/2 - 2/3)/2

= (9/4 - 4/4)/2

= 5/8

(b) The exact value of sin(arccos(x)) = sin(arcsin(acos(y))) = x.

Let's consider sin(arccos(x)). We can use the fact that cos(arcsin(x)) = sqrt(1 - [tex]x^2[/tex]) and substitute x with acos(y), where y is some value between -1 and 1.

Then we have:

cos(arcsin(x)) = cos(arcsin(acos(y)))

= cos(arccos(sqrt([tex]1-y^2[/tex])))

= sqrt([tex]1-y^[/tex])

Therefore, sin(arccos(x)) = sin(arcsin(acos(y))) = x.

(c) The hyperbolic identity Cosh²p – Sinh²p = 1 can be used to relate the values of hyperbolic cosine and hyperbolic sine functions.

By rearranging this identity, we get:

Cosh(p) = sqrt(Sinh²p + 1)

or

Sinh(p) = sqrt(Cosh²p - 1)

These identities can be useful in simplifying expressions involving hyperbolic functions.

To know more about exact value refer here:

https://brainly.com/question/32513003#

#SPJ11

To graph the function f(x) = (x)sin(x) in MATLAB using the fplot command, you can follow the steps below:

matlab

Define the function

f = (x) (x.)sin(x);

Set the range of x values

x = linspace(0, 2.5, 100);

Plot the function

fplot(f, [0, 2.5])

Add labels and title

xlabel(x)

ylabel(f(x))

title(Graph of f(x) = (x)sin(x))

Display the grid

grid on

In this code, we first define the function f(x) = (x)sin(x) using an anonymous function (x). Next, we create a range of x values using linspace from 0 to 2.5 with 100 points. Then, we use the fplot command to plot the function f over the specified range. Finally, we add labels, title, and grid to the graph.

To know more about matlab graph  click here:  brainly.com/question/30760537

#SPJ11

The joint relative frequency for people who can only see the sunset is  7/38.

To find the joint relative frequency for people who can only see the sunset, we need to look at the corresponding cell in the two-way frequency table. Let's assume the cell value is x. The total number of observations in the table is the sum of all the cell values, which is 38 in this case.

The joint relative frequency is the ratio of the cell value to the total number of observations. Therefore, the joint relative frequency for people who can only see the sunset is x/38.

Out of the given options, the value of x/38 that equals 7/38. Therefore, 7/38 represents the joint relative frequency for people who can only see the sunset based on the provided two-way frequency table.

LEARN MORE ABOUT  frequency here: brainly.com/question/29739263

#SPJ11

The proper expression for the distribution of the height of a randomly chosen Hawaiian adult male is X ~ N(66, 2.5). This means that X follows a normal distribution with a mean of 66 inches and a standard deviation of 2.5 inches.

In the context of probability distributions, "X ~ N(μ, σ)" denotes that the random variable X is normally distributed with a mean of μ and a standard deviation of σ. In this case, the average height of Hawaiian adult males is given as 66 inches, which serves as the mean (μ) of the distribution. The standard deviation (σ) is specified as 2.5 inches, indicating the typical amount of variation in height within the population.

By using the notation X ~ N(66, 2.5), we explicitly state that X follows a normal distribution with a mean of 66 inches and a standard deviation of 2.5 inches, as determined by the study conducted by Pierce students. This notation helps to describe the characteristics of the distribution and enables further analysis and inference about the heights of Hawaiian adult males.

learn more about standard deviation here:

https://brainly.com/question/29115611

#SPJ11

Answer:

9  +  9

Please mark as brainliest

Have a great day, be safe and healthy  

Thank u  

XD

Answer: The answers B,D,E are correct

Step-by-step explanation:

Answer: gr, rg, yr

Step-by-step explanation:

Given:

The two functions are:

[tex]P(x)=x^2-x-6[/tex]

[tex]Q(x)=x-3[/tex]

To find:

The function [tex]P(x)-Q(x)[/tex].

Solution:

We need to find the function [tex]P(x)-Q(x)[/tex].

[tex]P(x)-Q(x)=(x^2-x-6)-(x-3)[/tex]

[tex]P(x)-Q(x)=x^2-x-6-x+3[/tex]

[tex]P(x)-Q(x)=x^2+(-x-x)+(-6+3)[/tex]

[tex]P(x)-Q(x)=x^2-2x-3[/tex]

Therefore, the correct option is C.