Please help as soon as possible!!

Pₙ(F) satisfies the subspace criteria and is a subspace of P(F).

To show that P(F) is a vector space over F, we need to verify that it satisfies the vector space axioms: closure under addition and scalar multiplication, associativity, commutativity, existence of additive and multiplicative identities, and existence of additive and multiplicative inverses.

Closure under addition and scalar multiplication: For any two polynomials p, q ∈ P(F) and any scalar c ∈ F, their sum p + q and scalar multiple cp also belong to P(F) because the coefficients of the resulting polynomial are obtained by performing addition and scalar multiplication on elements from F, which is closed under these operations.

Associativity and commutativity of addition: The addition of polynomials is associative and commutative, as it follows the properties of addition in F.

Existence of additive identity: The zero polynomial, denoted as 0, with all coefficients equal to 0, serves as the additive identity. For any polynomial p ∈ P(F), p + 0 = 0 + p = p.

Existence of additive inverses: For any polynomial p ∈ P(F), there exists a polynomial -p in P(F) such that p + (-p) = (-p) + p = 0, where (-p) is obtained by negating each coefficient of p.

Existence of multiplicative identity: The polynomial 1 serves as the multiplicative identity. For any polynomial p ∈ P(F), p * 1 = 1 * p = p.

Closure under scalar multiplication: Scalar multiplication of a polynomial with a scalar c ∈ F yields a polynomial in P(F) since multiplying each coefficient of the polynomial by c preserves closure.

Since P(F) satisfies all the vector space axioms, it is a vector space over F.

To show that Pₙ(F) is a subspace of P(F), we need to demonstrate that it is closed under addition and scalar multiplication and that it contains the additive and multiplicative identities.

Closure under addition and scalar multiplication: For any two polynomials p, q ∈ Pₙ(F) and any scalar c ∈ F, their sum p + q and scalar multiple cp also belong to Pₙ(F) because the resulting polynomials have degree less than or equal to n, as the highest degree term in p + q or cp is the sum or scalar multiple of the highest degree terms in p and q.

Additive and multiplicative identities: The zero polynomial, denoted as 0, is the additive identity in Pₙ(F) since it has degree less than or equal to n and its coefficients are all zero. The polynomial 1 serves as the multiplicative identity in Pₙ(F) because it has degree 0.

Therefore, Pₙ(F) satisfies the subspace criteria and is a subspace of P(F).

Learn more about subspace

https://brainly.in/question/24467319

#SPJ11

Answer:

The closest answer is B:  1023/4

Step-by-step explanation:

My calculation shows the answer to be 256 exactly.  The term (1023/4) is equal to 255.8, but it is closer than the others.

Answer:

x-intercept = 6.2 , y-intercept = 3.1

Step-by-step explanation:

First turn 2x + 4y = 12.4 to slope-intercept form (y = mx + b) where m is slope and b is y-intercept.

Subtract 2x on both sides to move it to the other side, and get 4y by its self. Now it looks like 4y = -2x + 12.4 (since 2x and 12.4 aren't like terms, you wouldn't combine them).

Next, divide 4 on both side to get rid of it, and to get y by its self. Now you'll have

y = -2/4 x + 3.1 (since 12.4 can be divided by 4, that's how you get 3.1). You can already tell, just by looking at

y = -2/4 x + 3.1 , that the y-intercept is 3.1

Now we graph, to find out what the x-intercept is. I did it for you above.⤴⤴⤴

Answer:

C, A and B

Step-by-step explanation:

Tank A holds 40 Liters and 5 fish.

Tank B holds 100 Liters and 12 fish.

Tank C holds 180 Liters and 23 fish.

Therefore, the volume per fish from least to greatest is:

7.83, 8 and 8.33

These correspond to the tanks: C, A and B respectively.

Answer:

CAB

Step-by-step explanation:

Got it right in Khan!

Answer:

Step-by-step explanation:43.97

Answer: The formula is

A=p (1+rt)

A account balance?

P initial investment 3425

R interest rate 0.03

T time 15 years

A=3,425×(1+0.03×15)

A=4,966.25

Hope it helps!

Step-by-step explanation:

Answer:

It will take them 7.89 days

Answer:

on writing in expanded form we get

9167.364 = 9000 + 100 + 60 + 7 + 0.3 + 0.06 + 0.004

brainliest :)

The total pressure of a mixture of two gases is the finalized value of the summation of the total pressure of each of the gases.

The total pressure of a mixture of two gases can be expressed in the form of an equation, as below,

Total Pressure = Pressure of Gas 1 + Pressure of Gas 2

It is noteworthy to be mentioned that the partial pressure of an individual gas is completely in contrast to that of the individual pressure of a gas. It can be expressed in the form of an equation, as below,

Partial Pressure = Total Pressure of Gas x Mole Fraction of Gas

Learn more about the total pressure here:

https://brainly.com/question/24054667

#SPJ4

The lac curve, also known as the envelope curve, is a curve that shows the maximum amount of work that can be done in a given period of time.

It is defined by the equation: W = min {W1 + W2, W3, W4, ..., Wn}, where W1, W2, W3, W4, ..., and Wn are the individual work tasks. The envelope curve is called such because it forms an envelope that encompasses all of the individual tasks on the graph, visually representing the maximum amount of work that can be done within the given timeline. This curve can be used to assess the efficiency of a task or project, as well as to analyze the impact of changes in the workload, deadlines, and resources.

Learn more about curve here:

https://brainly.com/question/17330676

#SPJ4

Answer:

-3 =m

Step-by-step explanation:

-27/m = 117/13

Solve for m

We can use cross products

-27 * 13 = 117 * m

Divide each side by 117

-27 * 13 /117 = 117*m/117

-351/117 = m

-3 =m

Answer:

m = 3

Step-by-step explanation:

\(\frac{27}{m} =\frac{117}{13}\)

To solve for m, first, use cross multiplication.

\(27*13=117*m\)

\(351=117m\)

And now, divide both sides by 117.

m = 3

Answer:

He would have a total of 90 yards, and I would count by tens on a number line.

Answer) The endoplasmic reticulum takes the proteins that are made by the ribosomes and folds them into sacs that are called cisternae. It then transports these folded proteins to the Golgi apparatus. The Golgi apparatus is a series of membranes that look like flattened pancakes

I hope it is helpful

Answer:

C 174

Step-by-step explanation:

Add 548 + 200 = 748

748 ÷ 2 = 374

548 - 374 = 174

374 - 200 = 174

Hopes this helps :)

The hot air balloons be the same number of feet above the ground after 174 seconds.

Putting numbers in ascending order simply means to do it from smallest to largest.

Given, Keith is in a hot air balloon that is 200 feet above the ground and is ascending 1-feet per second. Erica is in a hot air balloon that is 548 feet  above the ground and is descending 1 feet per second.

To find the same point above the ground;

the average = (200 + 548) / 2

                    = 374 feet

That means Keith at 200+174 = 374 feet above the ground same as Erica 548 - 174 = 374 feet.

Therefore, after 174 seconds, the hot air balloons be the same number of feet above the ground.

To learn more about the ascending order;

https://brainly.com/question/20681445

#SPJ2

Answer:

ED + EF < DF

Step-by-step explanation:

shorter side lengths added together > larger side length

however, smaller side lengths are < larger

So ED + ED < DF means that this cannot be a triangle

Answer:

ED + EF < DF

(second option listed)

Step-by-step explanation:

for a triangle, the sum of the two shorter side lengths must be greater than the larger side length

so we know that the two smaller lengths (DE and FE) would have to add up to be greater than the larger side length (DF)

because this is not the case, we know that we cannot construct a triangle

[to construct a triangle:]

smaller + smaller > bigger

DE + FE > DF; which is false/not the case

so because DE + FE < DF, we cannot form a triangle

so, ED + EF < DF explains why these three segments cannot construct a triangle

For the given Rayleigh distribution with \(f(x)= 2axe^{-ax^{2} }\) , the expected value is E[X] = sqrt(pi/(4a)), and the variance is Var[X] = (2 - π/(2a²)).

the Rayleigh distribution is characterized by a probability density function (PDF) of the form \(f(x)= 2axe^{-ax^{2} }\), where a > 0. This distribution is used to model the magnitude of a two-dimensional vector whose components are independently and identically distributed Gaussian random variables.

For the Rayleigh distribution with the PDF \(f(x)= 2axe^{-ax^{2} }\) , the expected value (mean) is E[X] = sqrt(pi/(4a)), and the variance is :

Var[X] = (2 - pi/2a²).

Now, let's explain the answer in detail. To find the expected value, we integrate the product of the random variable X and its PDF over the range of possible values:

\(E[x] = \int\limits {(0 to a)x* 2axe^{-ax^{2} }} \, dx\)

By substituting u = -ax², du = -2ax dx, the integral becomes:

E[X] = ∫(0 to ∞) -ueⁿ du

Using integration by parts, we have:

E[X] = [-ueⁿ] - ∫(-eⁿ du)

= \([-xe^{-ax^{2}](0 to a) - \int\limits {0 to a}e^{-ax^{2} }\, dx }\)

The first term evaluates to 0 at both limits. The second term can be rewritten as:

E[X] = ∫(0 to ∞) e⁻ᵃˣ² dx

= √(π/4a) (by evaluating the Gaussian integral)

Thus, the expected value of X is E[X] = sqrt(pi/(4a)).

Next, to find the variance, we use the formula Var[X] = E[X²] - (E[X])². First, we calculate E[X²]:

E[X²] = ∫(0 to ∞) x² * 2axe⁻ᵃˣ²) dx

= ∫(0 to ∞) -x * d(e^(-ax²))

= [-x * e^(-ax²)](0 to ∞) + ∫(0 to ∞) e⁽⁻ᵃˣ²⁾ dx

The first term evaluates to 0 at both limits. The second term is the same as the integral calculated for E[X]. Hence:

= √(π/4a)

Substituting the values into the variance formula:

Var[X] = E[X^2] - (E[X])^2

= (√(π/4a)) - (sqrt(pi/(4a)))²

= (2 - π/(2a²))

Thus, the variance of X is Var[X] = (2 - π/(2a^2)).

Therefore, for the given Rayleigh distribution with f(x) = 2axe⁽⁻ᵃˣ²⁾,

the expected value is E[X] = sqrt(pi/(4a)), and the variance is Var[X] = (2 - π/(2a²)).

Complete Question:

A random variable X has a Rayleigh distribution if its probability density is given by f(x) = 2oxe or for x > 0, where a > 0. Show that for this distribution 1. Al l vandle has a Rayleigh distribution if its probability density i f(x) = 2axe-ar' for I > 0, where a > 0. Show that for this distribution a) The expected value is b) The variance is o? = (1-5)

Learn more about Variance:

brainly.com/question/32159408

#SPJ11

The required, vertex of the parabola is at approximately (9, -100).

A parabola is a cross-section cut out of the cone and represented by an equation.

Here,
To find the roots and vertex of the quadratic function y = x² - 18x - 19 on a calculator, you can use the following steps:

Enter the function into your calculator, typically by pressing the "y =" button and typing the function.

Use the "2nd" button (or another button designated for second functions) and the "graph" button to view the graph of the function.

Use the "trace" or "zero" function on your calculator to find the roots of the function. The "trace" function allows you to move a cursor along the graph to see where it crosses the x-axis (where y = 0), which gives you the x-coordinates of the roots. The "zero" function specifically finds the x-coordinates where the graph crosses the x-axis.

To find the vertex of the parabola, use the "vertex" or "minimum/maximum" function on your calculator. The "vertex" function should display the x-coordinate and y-coordinate of the vertex directly, while the "minimum/maximum" function should display the minimum or maximum value of the function, which corresponds to the y-coordinate of the vertex.

Using these steps on a calculator, we find that the roots of the function are approximately x = -1.097 and x = 19.097,

Learn more about parabola here:

brainly.com/question/4074088

#SPJ1

The required rate of return is 9.375%.

The value of the perpetuity can be found by dividing the annual cash flow by the discount rate.

The discount rate is the rate at which future cash flows are discounted to find their present value.

We need to calculate the present value of the perpetual cash flow stream. The formula for the present value of a perpetuity is:

PV of a perpetuity = C / r

Where, PV = present value C = annual cash flow r = discount rate PV of the perpetuity

= $12,000/0.05= $240,000

Therefore, the value of this perpetuity today with 5% of annual interest rate is $240,000.

If you are willing to pay $32,000 today to receive $3000 per year forever, then your required rate of return must be 9.375%.

The formula for the required rate of return of a perpetuity is: r = C / PV Putting the values, r = $3000 / $32,000 = 0.09375 or 9.375%

Therefore, the required rate of return is 9.375%.

To learn more about rate follow the given link

https://brainly.com/question/29451175

#SPJ11

We have that:

Paul biked 7 miles on Saturday.

Paul bike 15 miles on Sunday.

The total distance, in miles, the Paul biked during Saturday and Sunday is:

Answer:

Area=7850 cm

Step-by-step explanation:

Since the formula for area is A=c(radius squared), we need to plug in the radius first. 50x50=2500. We can identify 'pi' as 3.14 and use that decimal instead of a longer one. The product of 2500 and 3.14 is 7850. Therefore, your answer is 7850 cm

Answer:

a)

Domain : All Real Numbers

Range : All Real Numbers

b)

Domain : All Real Numbers

Range : y\(\geq\)0

These lines will be parallel to the initial line and will intersect the final velocity line at the corresponding values (122 for the lower estimate and 298 for the upper estimate)

To sketch the velocity against time, you can take the following steps:

First, calculate the acceleration using the given data by using the formula;

acceleration = (final velocity - initial velocity)/time

Where; Initial velocity is the velocity before applying the brakes

Final velocity is the velocity at which the car comes to stop

Time is the time it takes to stop the car (6 seconds in this case)

Now, calculate the lower and upper estimates using the formula;

Lower estimate = initial velocity + (acceleration x time)

Upper estimate = initial velocity + (2 x acceleration x time)

Sketch the graph using the following steps;

On the vertical axis, plot the velocity of the car

On the horizontal axis, plot the time

Start from the initial velocity and draw a straight line with the calculated acceleration until the end of the time (6 seconds)This straight line will give you the final velocity (0 in this case)

Now, draw two more lines, one with the lower estimate and the other with the upper estimate

Finally, label the axes and the lines with their corresponding values.'

To know more about times visit:

https://brainly.com/question/26941752

#SPJ11

Weighing the available information and assigning a probability.

A sort of probability called subjective probability is one that is based on a person's subjective assessment or personal knowledge of the likelihood of a particular result. It solely represents the subject's thoughts and prior experience and does not include any formal computations. A "gut instinct" used when making a deal is an illustration of subjective probability.

So, as per the definition of subjective probability

Dividing the number of favourable events by the number of possible events and Studying the fraction of times in the past a particular event has happened, both can be determined through calculations mathematically accurate but for Weighing the available information and assigning a probability we might use a "gut instinct". Thus

Weighing the available information and assigning a probability.

To learn more about subjective probability, visit

brainly.com/question/14743062

#SPJ4

Answer:

-88

Step-by-step explanation:

8 x -11 = 88

Sure! A table of values for f(x) = log base 8 of x is shown below:

x) f(x)

1) 0

2) 1/3

3) 0.54

4) 0.67

5)0.79

6)0.89

7) 0.97

8) 1

9) 1.10

10) 1.18

A logarithmic function is a type of mathematical function that involves the use of logarithms. Logarithms are a way of expressing numbers in terms of exponents, and logarithmic functions are functions that involve the logarithm of one or more variables.

The general form of a logarithmic function is:

f(x) = log_b(x)

where b is the base of the logarithm, and x is the argument of the logarithm.

Logarithmic functions have several important properties. One of the main properties is that they can be used to convert between exponential and logarithmic forms of equations. For example, the equation\(2^3\) = 8 can be written in a logarithmic form as log_2(8) = 3.

Logarithmic functions are also used in many applications in science, engineering, and finance. In science, logarithmic functions are used to describe the behavior of phenomena that exhibit exponential growth or decay, such as radioactive decay or population growth. In finance, logarithmic functions are used to calculate compound interest and to model the growth of investments over time.

The graph of a logarithmic function is a curve that approaches but never touches the x-axis as the x approaches zero. The shape of the curve depends on the base of the logarithm, and it becomes steeper as the base gets larger. The inverse function of a logarithmic function is an exponential function.

To know more about the function visit:

brainly.com/question/29120892

#SPJ1

Rounding this to the nearest hundredth, the area of the sector is approximately 28.88 f\(t^2\).

To find the area of a sector, we can use the formula:

Area = (θ/360) × π × \(r^2\)

where θ is the central angle in degrees, π is approximately 3.14, and r is the radius.

Given a central angle of 131° and a radius of 7.2 ft, we can plug in these values into the formula to find the area:

Area = (131/360) × 3.14 × (7.2\()^2\)

Calculating this expression:

Area = (0.3639) × 3.14 × (7.2\()^2\)

Area ≈ 28.879 f\(t^2\)

Rounding this to the nearest hundredth, the area of the sector is approximately 28.88 f\(t^2\).

for such more question on sector

https://brainly.com/question/22972014

#SPJ11

If the sample size is multiplied by 4, the standard deviation of the distribution of sample means will be decreased by a factor of 2 (option D).

If the sample size is multiplied by 4, the standard deviation of the distribution of sample means, also known as the standard error, is affected as follows: The standard error is halved. So, the correct answer is D) The standard error is halved. This is because the standard deviation is inversely proportional to the square root of the sample size, so increasing the sample size by a factor of 4 will result in a square root of 4 (which is 2) decrease in the standard deviation. It's important to note that the standard error (which is the standard deviation of the distribution of sample means) is not the same as the standard deviation of the population.

To know more about standard deviation, visit:

https://brainly.com/question/31516010

#SPJ11

The probability of a home for sale having a garage but no pool is 0.42.

To do this, we need to use some probability rules. One useful rule is the formula for calculating the probability of an event not occurring. This is given by:

P(not A) = 1 - P(A)

where A is the event we are interested in, and not A is the event of A not occurring.

In this case, we are interested in the probability of a home having a garage but no pool. Let's call this event GNP (short for garage no pool). Using the information given, we know that 60% of homes have garages and 18% have both garages and pools. We can use this information to calculate the probability of a home having a garage but no pool as follows:

P(GNP) = P(G) - P(G and P)

where G is the event of a home having a garage and P is the event of a home having a pool.

Substituting the values we have:

P(GNP) = 0.6 - 0.18

P(GNP) = 0.42

To know more about probability here

https://brainly.com/question/11234923

#SPJ4