If the matrix A = [a1 a2 a3 a4 a5]
has reduced row echelon form
[ 1 -1 0 0 2 ]
[ 0 0 1 0 3 ]
[ 0 0 0 1 1 ]
[ 0 0 0 0 0 ]
then a basis for Col(A) is [ __ __ __ ].
(Note that a1, a2, a3, a4 and a5 are t

The new price of the notebooks is $2.40.

To find the original price and the new price of the notebooks, we can use a proportion model. Let's call the original price "x" and the new price "y".

The proportion model for this problem would be:

40/100 = 1.60/x

To solve for x, we can cross-multiply:

40x = 100(1.60)

And then divide both sides by 40:

x = 4

So the original price of the notebooks was $4.00. To find the new price, we can subtract the decrease in price from the original price:

y = x - 1.60

y = 4 - 1.60

y = 2.40

So the new price of the notebooks is $2.40.

40/100 = 1.60/4

0.4 = 0.4

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The expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable is 4m, where 4 is the coefficient and m is the variable.

What are algebraic expressions?

An algebraic expression is a mathematical phrase that contains one or more variables, numbers, and arithmetic operations (such as addition, subtraction, multiplication, and division). It can also include exponents, roots, and other mathematical symbols.

Algebraic expressions are used to represent mathematical relationships and to solve problems in various areas of mathematics, science, and engineering. Examples of algebraic expressions include 3x + 5, 2y - 7, and 4x² - 3xy + 2.

A. The expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable is 4m, where 4 is the coefficient and m is the variable.

B. The expression that is equivalent to m + m + m + m that is the sum of two terms is 2m + 2m, where 2m is one term and the other term is also 2m.

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Check the picture below.

slope = -1/5

used slope forumula

The standard deviation of Y is 0.49.

Let's assume that D=20 (the last two digits of your student ID). Therefore, there are 20 defective motherboards in a package of 100 motherboards.

The Probability Mass Function (PMF) of Y is given by:
P(Y=0) = (80/100)*(79/99)

=> 0.64
P(Y=1) = (20/100)*(80/99) + (80/100)*(20/99)

=> 0.32
P(Y=2) = (20/100)*(19/99)

=> 0.04

The Cumulative Distribution Function (CDF) of Y is given by:
P(Y<=0) = P(Y=0)

=> 0.64
P(Y<=1) = P(Y=0) + P(Y=1)

=> 0.64 + 0.32

=> 0.96
P(Y<=2) = P(Y=0) + P(Y=1) + P(Y=2)

=> 0.64 + 0.32 + 0.04

=> 1

The mean of Y is given by:
E(Y) = 0*P(Y=0) + 1*P(Y=1) + 2*P(Y=2)

=> 0 x 0.64 + 1 x 0.32 + 2 x 0.04

= 0.4

The standard deviation of Y is given by:
Var(Y) = SD(Y)

=> [tex]\sqrt{(Var(Y))[/tex]

=>[tex]\sqrt{(0.24)[/tex]

=> 0.49

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1. Completing the conversion of 12 feet 8 inches to inches, Stella who stated that 12 feet 8 inches = 152 inches is correct unlike Vladimir who got 9 inches.

2. Stella and Vladimir need to convert the given measurement into inches.

3. No conversion factor is given for the problem.  However, the conversion factor could be found online or using the mathematical table.

4. Stella's and Vladimir's answers differ because Vladimir failed to convert the feet into inches.

5. Stella's answer is more reasonable, and it is correct because 12 feet equal 144 inches plus 8 inches, giving 152 inches.

6. The final answer should not just be a number without indicating the unit of measurement.

A unit conversion is the mathematical expression of the same property in a different unit of measurement.

For instance, instead of stating distance in kilometers, it can be depicted in miles.  Similarly, instead of reporting time in hours, it can be reported in minutes or seconds.

1 foot = 12 inches

12 feet = 144 inches

12 feet 8 inches = 152 inches (12 x 12 + 8)

Thus, in this situation, the measurement to be converted is feet to inches.

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Answer:

-8=x

Step-by-step explanation:

-6=x+2

take away 2 from each side

-8= x

Answer:

x = -8

Step-by-step explanation:

To solve for x in equation 3(x - 2) = 4x + 2, we need to simplify the expression on the left side of the equation by using the distributive property. This gives:

3x - 6 = 4x + 2

Next, we need to isolate the variable x on one side of the equation. We can do this by adding 6 to both sides of the equation:

3x - 6 + 6 = 4x + 2 + 6

Simplifying this expression, we get:

3x = 4x + 8

Now, we need to isolate x again by subtracting 4x from both sides:

3x - 4x = 4x + 8 - 4x

Simplifying this expression gives:

-x = 8

Finally, we solve for x by multiplying both sides of the equation by -1:

x = -8

Therefore, the solution to the equation 3(x-2) = 4x + 2 is x = -8.

not completely sure

3x25=75

answer 75

i think so bye

The equation of the line that passes through the point (14,3) and is perpendicular to the given equation is y = x - 11.

To solve the equation 5(y+x)-6(x-y)=-8, we need to use the distributive property and combine like terms.

5(y+x)-6(x-y)=-8

Distribute the 5 and -6:

5y + 5x - 6x + 6y = -8

Combine like terms:

11y - x = -8

Now, we need to find the slope of the line that passes through the point (14,3) and is perpendicular to the given equation.

The slope of the given equation is -1, so the slope of the perpendicular line is the negative reciprocal, which is 1.

Using the point-slope form, we can write the equation of the perpendicular line:

y - 3 = 1(x - 14)

Distribute the 1:

y - 3 = x - 14

Add 3 to both sides:

y = x - 11

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The equation of a horizontal line that passes through (4,2) in slope intercept form is y = 2.

A horizontal line has a slope of 0, which means that the y-value remains constant while the x-value changes. In slope intercept form, the equation of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

Since the slope of a horizontal line is 0, the equation of a horizontal line can be written as y = 0x + b, or simply y = b. The y-intercept is the value of y when x = 0, which is the same as the y-value of any point on the line.

In this case, the line passes through the point (4,2), so the y-value is 2. Therefore, the equation of the line in slope intercept form is y = 2.

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The debt consolidation loan will cost Sheng an additional $1,997.69 in interest charges compared to his credit cards.

From question, we are to calculate how much more in interest the debt consolidation loan will cost Sheng

To calculate the interest charges for Sheng's credit cards, we need to use the following formula:

Interest Charges = Balance x APR x Number of Days in Billing Cycle / 365

Using this formula, we can calculate the interest charges for each of Sheng's credit cards:

For Credit Card A:

Interest Charges = $2,500 x 0.19 x 30 / 365 = $4.94

For Credit Card B:

Interest Charges = $3,000 x 0.22 x 30 / 365 = $6.01

So, the total interest charges for Sheng's credit cards are:

Total Interest Charges = $4.94 + $6.01 = $10.95

Now, let's calculate the total cost of the debt consolidation loan:

Total Cost = Total Monthly Payments x Number of Payments - Loan Amount

Total Monthly Payments = $179.37

Number of Payments = 6 x 12 = 72

Loan Amount = ?

To find the loan amount, we need to solve for it using the interest rate and the total interest charges:

Loan Amount = Total Interest Charges / (APR x Number of Payments / 12)

Loan Amount = $3,414.39 / (0.107 x 72 / 12) = $25,000

So, the total cost of the debt consolidation loan is:

Total Cost = $179.37 x 72 - $25,000 = $2,008.64

Therefore, the additional interest charges for the debt consolidation loan compared to Sheng's credit cards are:

Additional Interest Charges = Total Cost - Total Interest Charges

Additional Interest Charges = $2,008.64 - $10.95 = $1,997.69

Hence, the debt consolidation loan will cost him an additional $1,997.69 in interest charges

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On simplifying ((7)/(8)+(1)/(2))/(2(1)/(4)) the correct answer is 2 3/4.

To solve the problem ((7)/(8)+(1)/(2))/(2(1)/(4)), we can follow these steps:

Step 1: Simplify the expression inside the parentheses in the numerator.
(7/8) + (1/2) = (7/8) + (4/8) = (11/8)

Step 2: Simplify the expression inside the parentheses in the denominator.
2(1/4) = (2/1)(1/4) = (2/4) = (1/2)

Step 3: Divide the simplified numerator by the simplified denominator.
(11/8) ÷ (1/2) = (11/8) × (2/1) = (22/8) = (11/4)

Step 4: Simplifying the final expression, if possible.
(11/4) = 2 3/4

Therefore, the correct answer is 2 3/4.

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A) To graph the constraints of the problem, we need to rearrange each constraint into slope-intercept form (y = mx + b) and plot them on a graph.

For the first constraint, 4x1+6x2 <= 22, we can rearrange it as follows:

6x2 <= -4x1 + 22

x2 <= (-2/3)x1 + (22/6)

For the second constraint, 1x1+5x2 <= 15, we can rearrange it as follows:

5x2 <= -1x1 + 15

x2 <= (-1/5)x1 + (15/5)

For the third constraint, 2x1+1x2 <= 9, we can rearrange it as follows:

1x2 <= -2x1 + 9

x2 <= (-2)x1 + 9

We can now plot these constraints on a graph with x1 on the x-axis and x2 on the y-axis.

B) To solve the LP relaxation of this problem, we can use the simplex method. The objective function is Max 1x1+1x2. The constraints are 4x1+6x2 <= 22, 1x1+5x2 <= 15, 2x1+1x2 <= 9, x1 >= 0, and x2 >= 0.

Using the simplex method, we can find that the optimal solution is x1 = 3 and x2 = 2, with an objective function value of 5.

C) To find the optimal integer solution, we can use the branch and bound method. We start with the LP relaxation solution of x1 = 3 and x2 = 2. Since this is already an integer solution, it is the optimal integer solution. The objective function value is 5.

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The correct coordinates for N' after a 180° rotation about the origin are (-3, -4).

Ari's likely error was that they incorrectly flipped the signs of the coordinates independently.

It should be noted that to rotate a point 180° about the origin, we need to flip the sign of both coordinates of the point. Therefore, the correct coordinates for N' after a 180° rotation about the origin are (-3, -4), not (-4, 3) as Ari claimed.

Ari's likely error was that they incorrectly flipped the signs of the coordinates independently, rather than flipping both signs together. This mistake could have arisen from a misunderstanding of the geometric concept of rotation or a simple arithmetic error.

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The matrices A and B are given as:

A = [3/4 0]
[0 3/4]

B = [-4 0]
[0 -4]

2a) Compute AB:

AB = [3/4 0] * [-4 0]
[0 3/4] [0 -4]

= [3/4 * -4 + 0 * 0 3/4 * 0 + 0 * -4]
[0 * -4 + 3/4 * 0 0 * 0 + 3/4 * -4]

= [-3 0]
[0 -3]

2b) Compute BA:

BA = [-4 0] * [3/4 0]
[0 -4] [0 3/4]

= [-4 * 3/4 + 0 * 0 -4 * 0 + 0 * -4]
[0 * 3/4 + -4 * 0 0 * 0 + -4 * 3/4]

= [-3 0]
[0 -3]

2c) How did your answer in part (a) and (b) compare?

The answers in part (a) and (b) are the same. Both AB and BA resulted in the matrix [-3 0] [0 -3].

2d) Will this be true, in general, for any two matrices when you multiply them (assuming their dimensions line up so that they may be multiplied)? If so, explain your reasoning. If not, show an example of two matrices C and D such that CD≠DC.

No, this will not be true in general for any two matrices when you multiply them. The order in which matrices are multiplied matters, and in most cases, AB≠BA. Here is an example of two matrices C and D such that CD≠DC:

C = [1 2]
[3 4]

D = [5 6]
[7 8]

CD = [1 * 5 + 2 * 7 1 * 6 + 2 * 8]
[3 * 5 + 4 * 7 3 * 6 + 4 * 8]

= [19 22]
[43 50]

DC = [5 * 1 + 6 * 3 5 * 2 + 6 * 4]
[7 * 1 + 8 * 3 7 * 2 + 8 * 4]

= [23 34]
[31 50]

As you can see, CD≠DC.

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The points (1, 1) and (2, 2) have been used to graph the inequality as shown in the image attached below.

The boundary line is dashed.

The boundary line is shaded below.

In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:

Additionally, the point (2, 2) and point (1, 1) are not solutions to the given inequality y < 1/4(x) + 1 because the lie below the boundary line

y < 1/4(x) + 1

2 < 1/4(2) + 1

2 < 3/2 (False)

y < 1/4(x) + 1

1 < 1/4(1) + 1

2 < 5/4 (False)

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the height of the cylinder is 12/π inches. This is an exact value, but if you want an approximate decimal value, you can use a calculator and substitute 3.14 or 22/7 for π. For example, if we use π ≈ 3.14, we get:

h ≈ 12/3.14

h ≈ 3.822 inches (rounded to three decimal places)

The solution for each expression is given as follows:

To solve an expression for a variable, we isolate the desired variable applying the inverse operations.

The solution for x of the first expression is obtained as follows:

2x + 5y = 5

2x = 5y - 5

x = 5(y - 1)/2

x = 2.5(y - 1).

The solution for y of the second expression is obtained as follows:

3x - 2y = 9

2y = 3x - 9

2y = 3(x - 3)

y = 3/2(x - 3)

y = 1.5(x - 3).

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The total cost of the dress including sales tax is 95.21.

The amount of discount that Isabella received on the dress is:

35% of 135.00 = 0.35 x 135.00 = 47.25

So, the price she paid for the dress after the discount is:

135.00 - 47.25 = 87.75

To find the total cost including sales tax, we need to add the sales tax to the price of the dress:

Sales tax = 8.5% of 87.75 = 0.085 x 87.75 = 7.46

Total cost = Price of dress after discount + Sales tax

= 87.75 + 7.46

= 95.21

Therefore, the total cost of the dress including sales tax is 95.21.

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Answer:

11

Step-by-step explanation:

There are 23 students taking exactly 2 subjects.

To find the number of students taking exactly 2 subjects, we can use the formula:

n(A∩B∩C) = n(A) + n(B) + n(C) - 2n(A∩B) - 2n(B∩C) - 2n(C∩A) + 3n(A∩B∩C)

Since we know that no one takes all three subjects, n(A∩B∩C) = 0. We can plug in the values given in the question and solve for n(A∩B), which represents the number of students taking exactly 2 subjects:

0 = 12 + 16 + 18 - 2n(A∩B) - 2(0) - 2(0) + 3(0)

0 = 46 - 2n(A∩B)

2n(A∩B) = 46

n(A∩B) = 23

Therefore, the number of students taking exactly 2 subjects is 23.

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Answer:

53

Step-by-step explanation:

becuas eyou divide it all togtheir and then subtract 42 from 83 and you ga the anwer

Answer:

To find the shorter route, we need to calculate the distances for both routes and compare them.

Route through Towns P and Q:

The distance between Town A and Town P is 3 units to the right and 5 units up, so it is √(3² + 5²) = √34 km.

The distance between Town P and Town Q is 2 units to the right, so it is 2 km.

The distance between Town Q and Town B is 4 units to the right and 4 units down, so it is √(4² + 4²) = 4√2 km.

Therefore, the total distance for this route is √34 + 2 + 4√2 km.

Route through Town R:

The distance between Town A and Town R is 5 units to the right and 3 units up, so it is √(5² + 3²) = √34 km.

The distance between Town R and Town B is 5 units to the right and 7 units down, so it is √(5² + 7²) = √74 km.

Therefore, the total distance for this route is √34 + √74 km.

Comparing the distances, we can see that:

√34 + 2 + 4√2 km ≈ 10.2 km

√34 + √74 km ≈ 12.6 km

Therefore, the shorter route is the one that goes through Towns P and Q, which is approximately 10.2 km long.

Answer:If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. the intersection points (-3,3) Since the system is infinite it means there is 1 line on the graph-

Step-by-step explanation:

400 children and 600 adults bought tickets to the circus.

Let's call the number of children who bought tickets "C" and the number of adults who bought tickets "A". We can set up two equations to represent the information given in the question:

C + A = 1000 (the total number of people who bought tickets)
15C + 40A = 30000 (the total gate revenue)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for C in terms of A:

C = 1000 - A

Now we can substitute this equation into the second equation to solve for A:

15(1000 - A) + 40A = 30000
15000 - 15A + 40A = 30000
25A = 15000
A = 600

So 600 adults bought tickets. We can use the first equation to find the number of children who bought tickets:

C + 600 = 1000
C = 400

So 400 children bought tickets. Therefore, the answer is that 400 children and 600 adults bought tickets to the circus.

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The value of the length WY is 40√3 mm. Option J

The different types of trigonometric identities are;

From the information given, we have that;

Opposite side = WY

Angle of elevation, θ = 60 degrees

Adjacent side = 40mm

Now, let's use the tangent identity;

tan θ = WY/40

substitute the value

tan 60 = WY/40

cross multiply

WY = 40 × √3

Multiply the values

WY = 40√3 mm

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cosx = cos4x = cos5x.

19. Using the identity sin2x + cos2x = 1, we can rewrite the equation as:

sin2x/2 - sin2x/2 = cosx/sinx

Simplifying both sides: cosx/sinx = 0

Therefore, cosx = 0 and sinx = 0.


20. Using the identities secx = 1/cosx, tanx = sinx/cosx, and sec2x = 1 + tan2x, we can rewrite the equation as:

secx(secx tanx) - sec4x(secx tanx) = sec5x tanx

Simplifying: secx - sec4x = sec5x

Therefore, secx = sec4x = sec5x.

Simplifying further: 1/cosx = 1/cos4x = 1/cos5x

Therefore, cosx = cos4x = cos5x.

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The values of x are 0.732 and -2.732.

Given function:f(x) = g(x)We need to determine the value of x.For, f(x) = g(x), we have the following equation:f(x) = x^2 + 2x + 1 = 2x + 3g(x) = 2x + 3To solve for x, we can substitute the value of g(x) in the first equation:x^2 + 2x + 1 = g(x)Substituting g(x) = 2x + 3 in the above equation:x^2 + 2x + 1 = 2x + 3x^2 + 2x - 2 = 0x^2 + 2x - 2 = 0Applying the quadratic formula, we get:$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$Where, a = 1, b = 2, and c = -2Substituting the values in the formula, we get:$$x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-2)}}{2(1)}$$$$x = \frac{-2 \pm \sqrt{12}}{2}$$$$x = -1 \pm \sqrt{3}$$Therefore, the value of x is x = -1 + √3 or x = -1 - √3.To round off the answer to 3 decimal places, we get:x = -1 + 1.732 = 0.732 or x = -1 - 1.732 = -2.732Hence, the values of x are 0.732 and -2.732.

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