QUESTION 6 Determine whether the set {P₁, P2, P3} is linearly independent in P2, where p₁ = 2 + x + 3x² + 4x³, p₂ = 4+3x+2x² + x³ and p3 = 1 + 2x + 3x² + 4x³. Show all working. [7 marks]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following:

X: _1_____2_____3_____4_____5

Y: 480__441____310___248___167

Using the linear regression calculator :

ŷ = -81.9X + 574.9

Where ;

y = predicted variable

x = independent variable

-81.9 = gradient or slope (m)

574.9 = intercept

Average retail price of fame at age 77

ŷ = -81.9X + 574.9

ŷ = -81.9(77) + 574.9

y = - 6306.3 + 574.9

y = −5731.4

At what age is the game system worthless :

Retail Price = y = $0

ŷ = -81.9X + 574.9

0 = - 81.9X + 574.9

81.9X = 574.9

X = 574.9 / 81.9

X = 7.019

X = 7

Hence, game system is worthless at age 7

Answer:

-25

Step-by-step explanation:

-5 * -5= -25

Answer:

-25

Step-by-step explanation:

-5

*

15

=

-25

your welcome please consider brainiest thank you

x + 2x + 8 − x + 6 = 2x + 14

5.1 w = (-3, 2, -5) can be written as a linear combination of u and v,

5.2 The set {u, v} is linearly independent, and

5.3 (u, v) forms a basis for R³.

5.1 To write the vector w = (-3, 2, -5) as a linear combination of u and v, we need to find scalars x and y such that w = xu + yv. By solving the system of equations xu + yv = w, we can find the values of x and y. Substituting the given values,

we get (-3, 2, -5) = x*(1, 2, -1) + y*(6, 4, 2).

Solving this system, we find x = -1 and y = 1.

Therefore, w = (-3, 2, -5) can be written as a linear combination of u and v as w = -u + v.

5.2 To determine if the set {u, v} is linearly independent, we need to check if the only solution to the equation xu + yv = 0 is x = y = 0.

In this case, we need to solve the system of equations x*(1, 2, -1) + y*(6, 4, 2) = (0, 0, 0). By solving this system, we find that x = 0 and y = 0 are the only solution, which means the set {u, v} is linearly independent.

5.3 To check if (u, v) forms a basis for R³, we need to verify if the set {u, v} spans R³ and is linearly independent. Since we have already established that {u, v} is linearly independent, we only need to check if it spans R³. Any vector in R³ can be expressed as a linear combination of u and v, so (u, v) is indeed a basis for R³.

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Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

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Answer:

20

Step-by-step explanation:

26

Answer:

139.9

is what u get if u add all of them

Step-by-step explanation:

Answer:

$5.95

if 20 oz= 7$

then 17 oz= 5.95

Answer:

x = -4

Step-by-step explanation:

Step 1: Define

j(x) = 3x + 1

j(x) = -11

Step 2: Substitute and solve for x

-11 = 3x + 1

-12 = 3x

x = -4

Answer:

it's wrong because he put a closed circle on the nine when he was supposed to put an open circle because nine is not less than itself but the thing that he did right wad that he went to the left if it was a greater than or equal symbol then it would be correct

Happy :) have a good day lol

Step-by-step explanation:

(a) To find the differential of the function y = tan(√3t), we can differentiate it with respect to t and then multiply by dt.

dy = d(tan(√3t))

  = sec²(√3t) * d(√3t)

  = √3 * sec²(√3t) * dt

Therefore, dy = √3 * sec²(√3t) * dt.

(b) To find the differential of the function y = (5 - v²) / (5 + v²), we can differentiate it with respect to v and then multiply by dv.

dy = d((5 - v²) / (5 + v²))

  = [(d(5 + v²) * (5 - v²) - (5 - v²) * d(5 + v²))] / (5 + v²)²

  = [2v * (5 - v²) - (5 - v²) * 2v] / (5 + v²)²

  = [-4v³] / (5 + v²)²

Therefore, dy = -4v³ / (5 + v²)².

These are the differentials for the given functions.

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Answer:

-11/2

Step-by-step explanation:

plug in the coordinate for the correct variables, plug in -3 for x and 2 for y

-3 =  m2 + 8, next move the 8 to the left side of the equation which becomes -11 and then -11=m2 and then divide -11/2 and thats what m equals

8.1 The 4x4 checkerboard matrix can be written as:

A = [ 1 0 1 0 ]

     [ 0 1 0 1 ]

     [ 1 0 1 0 ]

     [ 0 1 0 1 ]

8.2 The basis for the nullspace consists of two vectors, and the matrix has a rank of 2 and a nullity of 2.

8.3 For a 17x17 checkerboard matrix, the rank is 17 and the nullity is 0.

For a 4x4 checkerboard matrix, the elements (aij) will be 1 if the sum of the row index i and column index j is even, and 0 if the sum is odd.

The 4x4 checkerboard matrix can be written as:

A = [ 1 0 1 0 ]

     [ 0 1 0 1 ]

     [ 1 0 1 0 ]

     [ 0 1 0 1 ]

To find the basis for the nullspace of A, we need to solve the homogeneous equation Ax = 0, where x is a column vector of unknowns. By row-reducing A, we find that the reduced row-echelon form of A is:

[ 1 0 1 0 ]

[ 0 1 0 1 ]

[ 0 0 0 0 ]

[ 0 0 0 0 ]

From the reduced form, we can see that the columns corresponding to the pivot variables (the first two columns) form a basis for the nullspace. Therefore, the basis for the nullspace of A is:

[tex][ 1 0 0 0 ]^T[/tex]

[tex][ 0 1 0 0 ]^T[/tex]

The nullity of A, denoted as nullity(A), is the dimension of the nullspace. In this case, nullity(A) = 2.

The rank of A, denoted as rank(A), is the number of linearly independent columns in A. Since the first two columns are linearly independent, the rank(A) = 2.

For a 17x17 checkerboard matrix, we can observe that the pattern will continue to alternate along rows and columns. Therefore, all columns will be linearly independent, and the rank of the 17x17 checkerboard matrix will be 17. Since there are no non-zero solutions to Ax = 0, the nullity of the 17x17 checkerboard matrix is 0.

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Coordinate (0, 1) and (π/2, π/2) represent the same mathematical concept of the sine and cosine values at different angles

To show that (0, 1) and (π/2, π/2) are numerically equivalent, we need to demonstrate that they represent the same mathematical concept despite having different numerical values.

By examining the trigonometric functions sine and cosine, we can establish their equivalence.

The points (0, 1) and (π/2, π/2) correspond to the values of the trigonometric functions at those angles. Specifically, (0, 1) represents the point on the unit circle where the angle is 0 radians, while (π/2, π/2) represents the point where the angle is π/2 radians.

The sine function (sin(x)) represents the y-coordinate on the unit circle at a given angle, and the cosine function (cos(x)) represents the x-coordinate. The sine of 0 radians is 0, and the cosine of 0 radians is 1, which matches the coordinates of (0, 1).

Similarly, the sine of π/2 radians is 1, and the cosine of π/2 radians is 0, which matches the coordinates of (π/2, π/2).

Thus, we can see that (0, 1) and (π/2, π/2) represent the same mathematical concept of the sine and cosine values at different angles. Despite having different numerical values, they are numerically equivalent because they represent the same underlying trigonometric relationship.

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Answer:20-5t+=

Step-by-step explanation:

a. The probability that the teller is busy, P(0), is 0.1667

b. The Probability (teller is idle) is 0.8333

c. The Probability of 3 customers in the system 0.1019

d. The average number of customers waiting for service 4.1667

e. The average number of customers in the system is 5

f. The average time a customer spends in the system is 0.25 hour or 15 minutes.

g. The Average time a customer spends in the waiting line is 0.2083 hour or 12.5 minutes

The given M|M|1 system at BBA Bank, the probability that the teller is busy is 0.1667, the probability that the teller is idle is 0.8333, the probability of having 3 customers in the system is 0.1019, the average number of customers waiting for service is 4.1667, the average number of customers in the system is 5, the average time a customer spends in the system is 15 minutes, and the average time a customer spends in the waiting line is 12.5 minutes. These measures provide insights into the performance and efficiency of the bank's drive-through teller window.

To determine the performance measures of the M|M|1 system for BBA Bank, we can use the properties of the exponential distribution and the formulas for queuing theory. Given that the arrival rate is 20 customers per hour and the average service time is 2.5 minutes, we can calculate the following:

(a) Probability (teller is busy):

The utilization factor, ρ, can be calculated as the ratio of the arrival rate to the service rate:

ρ = λ/μ

where λ is the arrival rate and μ is the service rate. In this case, λ = 20 customers/hour and μ = 60 minutes/hour divided by the average service time of 2.5 minutes:

ρ = 20/((60/2.5)) = 20/24 = 0.8333

The probability that the teller is busy, P(0), is given by:

P(0) = 1 - ρ

P(0) = 1 - 0.8333 = 0.1667

(b) Probability (teller is idle):

The probability that the teller is idle, P(∞), can be calculated as the complement of the probability that the teller is busy:

P(∞) = ρ

P(∞) = 0.8333

(c) Probability of 3 customers in the system:

The probability of having n customers in the system, P(n), can be calculated using the formula:

P(n) = (1 - ρ) * ρ^n

P(3) = (1 - 0.8333) * (0.8333)^3 = 0.1019

(d) Average number of customers waiting for service:

The average number of customers waiting in the system, Lq, can be calculated using the formula:

Lq = ρ^2 / (1 - ρ)

Lq = (0.8333)^2 / (1 - 0.8333) = 4.1667

(e) Average number of customers in the system:

The average number of customers in the system, L, can be calculated as the sum of the average number of customers waiting and the customer being served:

L = Lq + ρ = 4.1667 + 0.8333 = 5

(f) Average time a customer spends in the system:

The average time a customer spends in the system, W, can be calculated using the formula:

W = L / λ

W = 5 / 20 = 0.25 hour or 15 minutes

(g) Average time a customer spends in the waiting line:

The average time a customer spends in the waiting line, Wq, can be calculated using the formula:

Wq = Lq / λ

Wq = 4.1667 / 20 = 0.2083 hour or 12.5 minutes

In summary, for the given M|M|1 system at BBA Bank, the probability that the teller is busy is 0.1667, the probability that the teller is idle is 0.8333, the probability of having 3 customers in the system is 0.1019, the average number of customers waiting for service is 4.1667, the average number of customers in the system is 5, the average time a customer spends in the system is 15 minutes, and the average time a customer spends in the waiting line is 12.5 minutes. These measures provide insights into the performance and efficiency of the bank's drive-through teller window.

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Answer:

52.5

Step-by-step explanation:

52.5 times 2 is 105 and 100 less than this is 5.

It can also be set out in the equation 2x-100=5

Answer:

its y=30

Step-by-step explanation:

The maximum price that buyers would be willing to pay for a car is $4900.

The maximum price that buyers would be willing to pay for a car can be determined by considering the expected value of the car. Since one third of all used cars are lemons, buyers would expect that there is a one-third chance of purchasing a lemon and a two-thirds chance of purchasing a plum.

Based on this information, we can calculate the expected value by considering the prices of lemons and plums and their respective probabilities.

The expected value is calculated as follows:

Expected value = (Probability of getting a lemon * Maximum price for a lemon) + (Probability of getting a plum * Maximum price for a plum)

In this case, the probability of getting a lemon is 1/3 and the probability of getting a plum is 2/3. The maximum price for a lemon is $2700 and the maximum price for a plum is $6000. Substituting these values into the formula, we can calculate the expected value:

Expected value = (1/3 * $2700) + (2/3 * $6000)

Simplifying the equation, we get:

Expected value = $900 + $4000

Expected value = $4900

Therefore, the maximum price that buyers would be willing to pay for a car is $4900. This price takes into account the probabilities of getting a lemon or a plum and the respective maximum prices buyers are willing to pay for each type of car. Buyers would consider this price as the maximum they are willing to pay, as it represents the expected value of the car considering the lemon-plum distribution and their respective preferences and valuations.

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Answer:

2,950 pilots and ground crew members all together

Step-by-step explanation:

First, find how many ground crew members there were.

Since the number of ground crew members is 1,560 more than the number of pilots, we can find the number of crew members by adding 1,560 to 695.

695 + 1,560

= 2255

So, there are 2,255 ground crew members.

Add this to the number of pilots to find how many there are altogether:

2255 + 695

= 2950

So, there were 2,950 pilots and ground crew members all together

Answer:

80-62=18

Step-by-step explanation:

plug in the y, which is 80, then subtract 60 from 80, which is 18, not 28.

Answer:

Ax+5=2*3+2*2x

Ax+5-6-4x=0

x(A-4)-1=0

x=1/(A-4)

Answer:

4 hours

Step-by-step explanation:

185-25=160

160/39=4.10 but we round it to 4

To find the optimal solution to the given linear programming problem, we need to solve the system of inequalities and determine the values of X and Y that minimize the objective function 3X + 3Y, while satisfying the constraints. The constraints of the problem are:

1) 12X + 4Y ≥ 84

2) 10X + 5Y ≥ 80

3) 4X + 8Y ≥ 44

4) X, Y ≥ 0 To solve the problem graphically, we can plot the feasible region determined by the intersection of the three constraint lines and the non-negativity constraints. However, without the inequality signs (≥, ≤) for the first three constraints, it is not possible to determine the feasible region and find the optimal solution. If you provide the correct inequality signs for the constraints (≥ or ≤), I would be able to assist you in finding the optimal solution by either graphical or algebraic methods.

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A. The point estimate of the mean value of y when X1 = 170 and X2 = 320 is 285.829.

B. The number of observations (n) and predictors (k) are not mentioned in the question, we cannot calculate the point estimate for the standard deviation of the error term without this information.

(a) To develop a point estimate of the mean value of y when X1 = 170 and X2 = 320, we can substitute these values into the estimated regression equation:

ŷ = b0 + b1x1 + b2x2

Given:

b0 = 26.1270

b1 = 0.5906

b2 = 0.498

x1 = 170

x2 = 320

Substituting the values into the equation, we get:

ŷ = 26.1270 + 0.5906(170) + 0.498(320)

Calculating the expression, we find:

ŷ = 26.1270 + 100.342 + 159.36

ŷ = 285.829

Therefore, the point estimate of the mean value of y when X1 = 170 and X2 = 320 is 285.829.

(b) To develop a point estimate for the standard deviation of the error term, we can use the residuals from the regression model.

The point estimate for the standard deviation of the error term is given by:

s = sqrt(SSE / (n - k))

Where:

SSE = Sum of Squared Errors (residuals)

n = Number of observations

k = Number of predictors (including the intercept)

Since the number of observations (n) and predictors (k) are not mentioned in the question, we cannot calculate the point estimate for the standard deviation of the error term without this information.

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Answer:

Step-by-step explanation:

In this problem, we are given the characteristic equation of matrix C and asked to determine the size of the matrix, its determinant, eigenvalues, and eigenvectors.

(a) The size of matrix C can be determined from the characteristic equation. The degree of the characteristic equation corresponds to the size of the matrix. Therefore, the size of matrix C is the degree of the characteristic equation.

(b) To determine the determinant of matrix C, we can look at the constant term of the characteristic equation with the appropriate sign.

(c) Given that A = 2 is an eigenvalue of matrix C, we can substitute A = 2 into the characteristic equation and solve for the other two eigenvalues.

(d) With the eigenvector u corresponding to A = 2, we are provided with specific values for u and X. Using this information, we can evaluate the expressions Au and A²v by substituting the respective values and performing the matrix operations.

Furthermore, we are asked to solve the equation AX = v, where v is a given vector. This can be done by substituting the values of A and v into the equation and solving for the matrix X.

In summary, we need to determine the size and determinant of matrix C, find the eigenvalues (including A = 2) and eigenvectors, evaluate expressions involving the matrix, and solve an equation involving the matrix and a given vector.

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A matrix C has characteristic equation: (a) Determine the size of matrix C. (b) Determine the determinant of C. 1 BET ALG ENGINEERING MATHEMATICS 1 TUTORIAL 3 (c) Show that A = 2 is an eigenvalue of C and find the other two eigenvalues. (d) An eigenvector corresponding to A = 2 is u. It is further given that: 0.4 -0.8 u= -4 & X= i. Evaluate each of the following expressions: A. Au. B. A²v. ii. Solve the equation: AX = v. 21³7A²+7A+ 10 = 0

Answer:

1/2

Step-by-step explanation:

You could formalize your answer by setting up a proportion.

3 boxes /6 months = x / 1 month

Cross multiply

3 boxes * 1 month = 6 months * x

the months cancel out.

Divide by 6

x = 3 boxes / 6

x = 1/2

Answer:

-12

Step-by-step explanation:

you do -4 plus 8 but u count downwards from -4 so the answer is -12

Answer:

B. $25,700

Step-by-step explanation:

(sorry it took me so long to answer it was kinda hard)