Solve the systems of equations by substituting
8) -3x+3y=4
-x+y=3

The double integral of 9xsin(x+y) over the region R=[0, π/3]×[0, π/6] is equal to -3π/2 + π^2/2.

To calculate the double integral ∬R 9xsin(x+y) dA over the region R = [0, π/3] × [0, π/6], we need to evaluate the integral in two stages.

First, let's integrate with respect to y, treating x as a constant:

∫[0, π/3] ∫[0, π/6] 9xsin(x+y) dy dx

Integrating with respect to y, we have:

∫[0, π/3] [ -9x cos(x+y) ]|[0, π/6] dx

Now, substitute the limits of integration and simplify:

∫[0, π/3] ( -9x cos(x + π/6) + 9x cos(x) ) dx

Next, integrate with respect to x:

[ -9x sin(x + π/6)/2 + 9x^2/2 ]|[0, π/3]

Now, substitute the limits of integration and simplify further:

[ -9(π/3) sin(π/3 + π/6)/2 + 9(π/3)^2/2 ] - [ -9(0) sin(0 + π/6)/2 + 9(0)^2/2 ]

Simplifying the expression:

[ -3π sin(π/2)/2 + 9(π^2)/18 ] - [ 0 - 0 ]

[ -3π(1)/2 + 9(π^2)/18 ]

-3π/2 + π^2/2

So, the value of the double integral ∬R 9xsin(x+y) dA over the region R = [0, π/3] × [0, π/6] is -3π/2 + π^2/2.

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To minimize the penalty cost, the linear programming problem is formulated as a goal programming problem by introducing deviation variables (d₁, d₂, d₃) and surplus variables (s₁, s₂), with the objective function Z = 100d₁ + 50d₂ + 10d₃ and the corresponding constraints.

To formulate the given linear programming problem as a goal programming problem to minimize the penalty cost, we can introduce deviation variables on each constraint and assign penalty weights to these variables. The goal is to minimize the total penalty cost:

d₁: Deviation variable for the first constraint (3x₁ + 2x₂ ≥ 30)

d₂: Deviation variable for the second constraint (2x₁ + x₂ ≥ 40)

d₃: Deviation variable for the third constraint (5x₁ + 3x₂ ≤ 50)

We also need to introduce positive surplus variables to ensure the original constraints are not violated:

s₁: Surplus variable for the first constraint (3x₁ + 2x₂ ≥ 30)

s₂: Surplus variable for the second constraint (2x₁ + x₂ ≥ 40)

Now, let's formulate the linear programming model with penalty costs and deviation variables:

Minimize:

Z = 100d₁ + 50d₂ + 10d₃

Subject to:

3x₁ + 2x₂ - d₁ + s₁ = 30

2x₁ + x₂ - d₂ + s₂ = 40

5x₁ + 3x₂ + d₃ ≤ 50

x₁, x₂, d₁, d₂, d₃, s₁, s₂ ≥ 0

The objective function minimizes the penalty cost by summing the products of deviation variables and their respective penalty weights.

The first constraint includes the deviation variable d₁ to measure the deviation from the minimum requirement of 30. The surplus variable s₁ ensures that the original constraint is not violated.

Similarly, the second constraint includes the deviation variable d₂ and the surplus variable s₂.

The third constraint includes the deviation variable d₃ to penalize any excess beyond the upper limit of 50.

All decision variables (x₁, x₂, d₁, d₂, d₃, s₁, s₂) are non-negative.

Solving this goal programming problem will minimize the penalty cost associated with failing to satisfy the original constraints.

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Answer:

A  54°

Step-by-step explanation:

Sorry if its wrong <3

Answer:

C

Step-by-step explanation:

You know it is an acute angle, meaning that it has to be below 90 degrees.

~theLocoCoco

Answer:

Answer would be C

Step-by-step explanation:

Answer:

102 beads will be used for each necklace.

Step-by-step explanation:

3,264/32=102

Answer:

PQ = 29

Step-by-step explanation:

Lengths of the two tangents from a external point to the circle is equal

14x - 13 = 8x + 5  {add 13 to both sides}

    14x = 8x + 5 + 13

   14x  = 8x + 18

14x - 8x = 18

      6x =  18

       x = 18/6

x = 3

PQ = 14*3 - 13

      = 42 - 13

     =  29

Answer:

PQ = 29

Step-by-step explanation:

As we know that,

\(\star\) Lengths of two tangents from a external point to the circle is equal.

We've been asked to find out PQ;

Thus,

Answer:

B

Step-by-step explanation:

So a reflection over the x is a change in the y value.

Only point (2,0) is on the x-axis, so it will not move.

Answer:

1.73

Step-by-step explanation:

A situation can have more than one sample space when there are multiple possible outcomes or events that can occur. A sample space is a set of all possible outcomes of an experiment or situation.

For example, let's consider the situation of flipping a coin. The sample space for this situation can be defined as {heads, tails}. In this case, there are two possible outcomes: either the coin lands on heads or it lands on tails.

However, we can also consider a situation where we are interested in the number of times the coin lands on heads in three consecutive flips. In this case, the sample space would be {0, 1, 2, 3}. Each outcome represents the number of times the coin lands on heads in three flips. So, we can have zero heads, one head, two heads, or three heads.

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Answer:

G 13

Step-by-step explanation:

X/125 = 9.6%/100%

125*(9.6) / 100 = 12;

BEST estimate 13

Answer:

-7 or just 7

Step-by-step explanation:

Answer:

Bank A charges 10.4 a month. Bank B charges 27.00 a month

Step-by-step explanation:

Bank A step by step-

0.20 x 52 = 10.4

Bank B step by step=

52-25 = 27

27 x 1.00 = 27.00

the EIR from this transaction is 16.25% (Option B, None of the above).

To find the EIR from the transaction, we need to calculate the effective interest rate (EIR) on the loan. The formula for EIR is:

EIR = [(1 + r/n)ⁿ - 1] x 100

where r is the nominal interest rate, and n is the number of compounding periods per year.

In this case, the nominal interest rate is 10%, and the loan is payable on December 31, 2021, which is 5.5 years from June 30, 2016. Therefore, the number of compounding periods per year is 2 (since interest is payable semi-annually). Substituting these values into the formula, we get:

EIR = [(1 + 0.10/2)₂ - 1] x 100 = 10.25%

However, the bank requires a maintaining balance of 6% for any amount borrowed. Therefore, the effective interest rate is increased by this amount. Adding 6% to the EIR, we get:

EIR = 10.25% + 6% = 16.25%

Therefore, the EIR from this transaction is 16.25% (Option B, None of the above).

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I did not get Your Question Probably But the way I see it the answer is:

The equation of a circle with center (h, k) and radius r can be written as:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (0, -6). To find the radius, we can use the distance formula between the center and the given point (-√28, 3):

r = √((x₂ - x₁)^2 + (y₂ - y₁)^2)

Plugging in the values:

r = √((-√28 - 0)^2 + (3 - (-6))^2)

Simplifying:

r = √(28 + 81)

r = √109

Therefore, the equation of the circle with center (0, -6) and containing the point (-√28, 3) is:

(x - 0)^2 + (y + 6)^2 = (√109)^2

Simplifying further:

x^2 + (y + 6)^2 = 109

Answer:

The equation of the circle with center (0, -6) containing the point (-√28, 3) is x^2 + (y + 6)^2 = 109.

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is given by the formula:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (0, -6), which means that h = 0 and k = -6. We also know that the circle contains the point (-√28, 3), which means that this point is on the circle and satisfies the equation above.

To find the radius r, we can use the distance formula between the center of the circle and the given point:

r = sqrt((0 - (-√28))^2 + (-6 - 3)^2) = sqrt(28 + 81) = sqrt(109)

Substituting h, k, and r into the equation of the circle, we get:

x^2 + (y + 6)^2 = 109

Therefore, the equation of the circle is x^2 + (y + 6)^2 = 109.

Answer:

1/3 x  + 1/2

Step-by-step explanation:

combine like terms   the two opposites cancel out  2/3 and -2/3

1/3x + 3/4 -1/4            3/4 -14 = 12

13x + 1/2  (answer)

Answer:

-17

Step-by-step explanation:

Answer:

8/3

Step-by-step explanation:

Answer:

y= -6/5x - 8

Step-by-step explanation:

I just used desmos easy to use and you understand how graphs work more.

Yes, the business did better on the second campaign. Since a higher ROI or ROAS value indicates better performance, the business did better on the second campaign.

ROI stands for Return on Investment, which is a measure of profitability. It is calculated by dividing the net profit by the total investment and expressing it as a percentage.

In this case, the ROI for the first campaign was 3, indicating that the business generated three times the profit compared to the investment.

ROAS stands for Return on Advertising Spend, which is a measure of the effectiveness of advertising campaigns. It is calculated by dividing the revenue generated by the advertising campaign by the cost of that campaign.

In this case, the ROAS for the second campaign was 4, indicating that the business generated four times the revenue compared to the advertising cost.

Since a higher ROI or ROAS value indicates better performance, the business did better on the second campaign. The ROAS value of 4 is higher than the ROI value of 3, indicating that the second campaign was more effective in terms of generating revenue compared to the investment made.

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The ROI (Return on Investment) measures the profitability of an investment and is calculated by dividing the net profit by the cost of the investment.

The ROAS (Return on Advertising Spend) measures the effectiveness of an advertising campaign and is calculated by dividing the revenue generated by the advertising campaign by the cost of the campaign. Based on the information provided, it can be concluded that the business did better on the second campaign.


In this case, the business had an ROI of 3 for the first campaign and a ROAS of 4 for the second campaign.

To compare the two campaigns, we can look at the ratios.

For the first campaign, the ROI was 3, meaning that for every dollar invested, the business received 3 dollars in profit.

For the second campaign, the ROAS was 4, meaning that for every dollar spent on advertising, the business generated 4 dollars in revenue.

Comparing these two ratios, we can see that the second campaign had a higher return on advertising spend (ROAS) compared to the first campaign's return on investment (ROI). This suggests that the second campaign performed better in terms of generating revenue in relation to the advertising cost.

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Answer:

Step-by-step explanation:

Therefore, the slope of the line passing through the points (0, 3) and (2, 6) is 3/2.

In mathematics, the slope refers to the measure of steepness or inclination of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between those points. In other words, the slope of a line is the change in y divided by the change in x between any two points on that line. The slope can be positive, negative, or zero, and it determines the direction and the steepness of the line. The slope is an important concept in algebra, geometry, and calculus, and it is used to describe many real-world phenomena, such as the velocity of an object, the rate of change of a function, and the growth or decline of a population.

Here,

To find the slope of the line passing through the points (0, 3) and (2, 6), we can use the formula:

slope = (change in y) / (change in x)

So, we have:

slope = (6 - 3) / (2 - 0)

slope = 3 / 2

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Answer:

the SSS similarity theorem

Step-by-step explanation:

⇒ It cannot be the SAA similarity theorem as they only share a single common angle

⇒ It cannot be the HL similarity theorem, as the sides are not equal

⇒ It must be the SSS triangles

===========================================================

It states that :

If the lengths of the corresponding sides of two triangles are proportional, then the two triangles are similar.

============================================================

Let's take the sides in proportion :

⇒ 15/5 = 3 (Hypotenuses)

⇒ 6+3/3 = 9/3 = 3 (Heights)

⇒ 8+4/4 = 12/4 = 3 (Bases)

As the sides are in proportion, the triangles are similar by the SSS similarity theorem.

Answer:

(3,-9)

Step-by-step explanation:

Answer:

A. 41 (it is a prime number)

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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The equation of the regression line for the given data is yhat = 0.175 + 3.025x.

The equation of the regression line is found by performing linear regression analysis on the given data points.

To calculate the equation, we first determine the slope (m) and y-intercept (b) of the line. The slope is calculated using the formula (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2), where n is the number of data points, Σxy is the sum of the products of x and y values, Σx is the sum of x values, and Σx^2 is the sum of squared x values. The y-intercept is calculated using the formula (Σy - mΣx) / n.

Using the given data:

n = 4

Σx = 2 + 4 + 5 + 6 = 17

Σy = 7 + 11 + 13 + 20 = 51

Σxy = (2 * 7) + (4 * 11) + (5 * 13) + (6 * 20) = 74

Σx^2 = (2^2) + (4^2) + (5^2) + (6^2) = 81

Substituting these values into the slope formula, we find m = 3.025. Calculating the y-intercept, we find b = 0.175.

Therefore, the equation of the regression line is yhat = 0.175 + 3.025x.

Rounding the coefficients to three significant digits, we have yhat ≈ 0.175 + 3.03x.

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Answer:

4(3x-2)

Step-by-step explanation:

Have a great day :)

Muscular strength can be measured based on the amount of weight lifted.

Muscular strength can be measured based on the amount of weight lifted. The upper-body and lower-body strength are measured separately. Muscular strength is typically measured which is known as a One Rep Max (1RM).

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Answer:

the answer is x > 2

Step-by-step explanation:

Answer:

The answer is D : 4.

Step-by-step explanation:

=2x-3>11-5x

=2x-3+5x>11

=7x-3>11

=7x>11+3

=7x>14

=7x/7>14/7

=x>2

By simplifying the problem, you can see that "x" must be greater than 2. Therefore, eliminating all other possible answers that are shown, but 4.

I answered the same questions with the same exact wording and explanation so please don't report any answers that are the same as this one, they are all mine and written by me.