Is the relationship a function yes or no?
​

(a) The economic loading of unit 4 and B are 11.54 MW and 138.46 MW, respectively.

To find the economic loading of the two units when the total load to be supplied by the power station is 150 MW, we need to minimize the total fuel cost. Let x be the power generated by unit 4 and y be the power generated by unit B. Then, we have:

x + y = 150 (total load)

The total fuel cost C is given by:

C = F4(x) + Fb(y)

where F4(x) and Fb(y) are the fuel costs for units 4 and B, respectively. Using the given relations, we have:

F4(x) = 0.06x^2 + 11.4x

Fb(y) = 0.07y^2 + 10y

Substituting x = 150 - y, we get:

C(y) = 0.06(150-y)^2 + 11.4(150-y) + 0.07y^2 + 10y

Expanding and simplifying, we get:

C(y) = 0.013y^2 - 3.6y + 1710

To minimize C(y), we take its derivative with respect to y and set it equal to zero:

dC/dy = 0.026y - 3.6 = 0

y = 138.46 MW

Substituting y back into x = 150 - y, we get:

x = 11.54 MW

(b) The negative value that is  -1297.5 indicates that there is a net decrease in fuel cost per hour if the load is equally shared by the two units.

To find the net increase in fuel cost per hour if the load is equally shared by the two units, we need to calculate the fuel cost for each unit when they generate half of the total load (i.e., 75 MW). Using the given relations, we have:

F4(75) = 0.06(75)^2 + 11.4(75) = 1282.5

Fb(75) = 0.07(75)^2 + 10(75) = 1312.5

Therefore, the total fuel cost is:

C = F4(75) + Fb(75) = 2595

If the load is equally shared by the two units, each unit generates 75/2 = 37.5 MW. The fuel cost for each unit is:

F4(37.5) = 0.06(37.5)^2 + 11.4(37.5) = 641.25

Fb(37.5) = 0.07(37.5)^2 + 10(37.5) = 656.25

Therefore, the total fuel cost is:

C' = F4(37.5) + Fb(37.5) = 1297.5

The net increase in fuel cost per hour is:

ΔC = C' - C = 1297.5 - 2595 = -1297.5

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Answer: \(\frac{1}{2}\)

Step-by-step explanation:

Find the common denominator:

3, 6, 9, 12

6, 12, 18

- 6 is your common denominator.

Multiply your fraction by 1 \((\frac{2}{2})\)

\(\frac{1}{3} * \frac{2}{2} = \frac{2}{6}\\\)

Add:

\(\frac{2}{6} + \frac{1}{6} = \frac{3}{6}\)

Reduce:

\(\frac{3}{6} = \frac{1}{2}\)

The simplest form is 1/2.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

1/3 + 1/6

Now, we have to add the fraction by focusing the numerator as

=1/3 + 1/6

Now, LCM(3, 6)= 6

= 1/3 x 2/2 + 1/6

=2/6 + 1/6

=(2+1)/6

=3/6

=1/2

Hence, the simplest form is 1/2.

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it would take approximately 1,192,850 joules of energy to heat 0.5 kg of water from 70°C to steam at 100°C.

To calculate the energy required to heat 0.5 kg of water from 70°C to 100°C and then to convert it to steam at 100°C, we need to consider two separate processes: heating the water and then vaporizing it. The energy required for each process can be calculated using the specific heat capacity and latent heat of vaporization of water.

First, we need to calculate the energy required to heat the water from 70°C to 100°C. This can be done using the formula:

Q = m * c * ΔT

where Q is the energy required, m is the mass of water, c is the specific heat capacity of water (which is 4186 J/(kg°C)), and ΔT is the change in temperature. So:

Q1 = 0.5 * 4186 * (100 - 70) = 62850 J

Next, we need to calculate the energy required to vaporize the water at 100°C. This can be done using the formula:

Q = m * L

where Q is the energy required, m is the mass of water, and L is the latent heat of vaporization of water (which is 2260 kJ/kg). So:

Q2 = 0.5 * 2260 * 1000 = 1130000 J

The total energy required to heat 0.5 kg of water from 70°C to steam at 100°C is the sum of Q1 and Q2: Qtotal = Q1 + Q2 = 1130000 + 62850 = 1192850 J

Therefore, it would take approximately 1,192,850 joules of energy to heat 0.5 kg of water from 70°C to steam at 100°C.

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Answer:

Sqrt 245

Step-by-step explanation:

That's the answer

According to Pythagoras' Theorem

\(h^{2} = a^2 + b^2\)

\(h^{2}\)  \(= 7^{2} + 14^2\)

\(h^{2}\) = 49 + 196

h = \(\sqrt{245}\)

According to diagram x = sqrt 245

Pythagorean hypothesis, the notable mathematical hypothesis that the amount of the squares on the legs of a right triangle is equivalent to the square on the hypotenuse (the side inverse the right point) — or, in recognizable logarithmic documentation, a2 + b2 = c2.

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Answer: y=x+2

Step-by-step explanation:

ok, so the points from the graph in the picture that i used were (0, 2) and (-2, 0).

(0, 2) is the y-intercept, which will replace b.

y=mx+2

the slope of the line is 1.

y=1x+2

y=x+2

An MIS differs from a TPS in that it creates databases is True.

An MIS (Management Information System) does indeed differ from a TPS (Transaction Processing System) in that it creates databases. The main purpose of an MIS is to collect, process, store, and disseminate information to support managerial decision-making within an organization. It involves the use of technology and various information systems to manage and analyze data for strategic planning, monitoring, and control.

One of the key components of an MIS is the creation and management of databases. Databases are structured collections of data that are organized, stored, and accessed in a systematic way. They serve as a central repository for storing relevant information that can be utilized by the MIS. These databases can contain data from various sources within the organization, such as sales records, customer information, inventory data, financial data, and more.

On the other hand, a TPS focuses primarily on the processing of transactions. It is designed to capture, process, and record day-to-day operational transactions, such as sales transactions, inventory updates, customer orders, and so on. While a TPS may store and retrieve data related to these transactions, its main focus is on efficiently processing and ensuring the accuracy and integrity of transactional data.

In summary, an MIS goes beyond the functionalities of a TPS by not only processing transactions but also creating and managing databases to support the informational needs of managers.

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The probability that their first child will have kidney disease is 1/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we have

Both parents must be heterozygous to have a 1/4 chance of having an

affected child. Parent 2 is heterozygous (her father was homozygous recessive, but she has unaffected).

For the child to have the disease, both Parent 1 and Parent 2 would need to be heterozygous

There is a 50% chance of this for Parent 1 and a 100% chance of this for Parent 2 and then, there is a 25% chance that their first child will be affected:

50%× 100% × 25% = 12.5%

1/2 × 1/4 = 1/8

Hence, the probability that their first child will have kidney disease is 1/8.

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-Answer:Option B: Increase the amount of money they save each month by $80 from what they've been saving.

Step-by-step explanation: Only option B will allow them to meet their goal.

Answer:

d

Step-by-step explanation:

Answer:

y = 4x - 1

Step-by-step explanation:

equation of a line in slope-intercept form: y = mx + b

m is the slope and b is the y-intercept

y = 4x - 1

Answer:

Step-by-step explanation:

As per diagram, y = -9 for any value of x, so it is the line with equation:

To fcalculate the magnitude of the average force exerted on the ball by the club, we can use the equation:

F_av = Δp/Δt

where F_av is the average force, Δp is the change in momentum, and Δt is the time of contact.

Given:

Mass of the ball, m = 65.0 g = 0.065 kg

Time of contact, Δt = 0.00340 s

Final velocity of the ball, v_f = 56.0 m/s

Initial velocity of the ball, v_i = 0 (assuming the ball is initially at rest)

The change in momentum, Δp, can be calculated using the equation:

Δp = m * (v_f - v_i)

Substituting the given values:

Δp = 0.065 kg * (56.0 m/s - 0)

Now we can calculate the magnitude of the average force:

F_av = Δp/Δt

Substituting the values:

F_av = (0.065 kg * 56.0 m/s) / 0.00340 s

Calculating the result gives us:

F_av ≈ 1070 N

Therefore, the magnitude of the average force exerted on the ball by the club is approximately 1070 N.

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The sociologist would need a sample size of at least 753 students to estimate the proportion of students

Margin error = .03

Confidence Interval = 90%

Proportion size = .44

To estimate the percentage of students, establishing the sample size required -

\(n = (Z^2 x p x q) / E^2\)

Where p is the estimated proportion of students who binge drink during the school year, Z is the Z-score associated with the desired level of confidence, which is 1.645, q is 1 - p which represents the proportion of students who do not engage in binge drinking, and E is the desired margin of error, which is 0.03

Therefore,

\(n = (1.645^2 x 0.44 x 0.56) / 0.03^2\)

= 752.67 or 753.

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Hello, we know that for a and b real numbers

\(a^2-b^2=(a-b)(a+b)\)

So,

\((2a-b)^2-(a-2b)^2=(2a-b-a+2b)(2a-b+a-2b)\\\\=(a+b)(3a-3b)\\\\\boxed{=3(a+b)(a-b)}\)

Thank you.

Answer:

If n > 0, then n= 1

If n < 0, then n=n

If you could word this a bit differently, I might be able to help more, but this is what I'm getting from it. The way you worded it is a bit confusing.

can u search it sweet heart or take a picture on here?

Answer:

x = 2 or x = -4

Step-by-step explanation:

-5|x + 1| + 3 = -12

Add -3 to both sides.

-5|x + 1| = -15

Divide 5 into both sides.

|x+1| = 3

Possibility 1:

x + 1=3

x = 2

Possibility 2:

x + 1 = - 3

x = -4

Answer:

Step-by-step explanation:

This is our absolute value equation for which we want the values of x that make it true:

-5 | x + 1 | + 3 = -12. Subtracting 3 from both sides gives us

-5 | x + 1 | = = -15. Divide both sides by -5 to get

| x + 1 | = 3

This says, in words, "how many units from 3 is -1 on a number line?"

We have the following 2 equations:

x + 1 = 3 and x + 1 = -3

Solving the first one for x:

x = 2

Solving the second one for x:

x = -4

Both 2 and -4 are 3 units from -1 on a number line.

Answer:

Jack took 10 pictures on his bike ride.

Step-by-step explanation:

Given that:

Given measurements of sides are 3 miles and 4 miles

We will find the distance of the new route by using Pythagorean theorem.

\(a^2+b^2=c^2\)

(3)² + (4)² = c²

9 + 16 = c²

25 = c²

c² = 25

Taking square root on both sides

\(\sqrt{c^2}=\sqrt{25}\\c=5\)

The distance of new route = 5 miles

Picture taken per mile = 2

Picture taken on bike ride = 2*5 = 10 pictures

Hence,

Jack took 10 pictures on his bike ride.

Answer: are you asking us to answer it or is that the answer?

Step-by-step explanation:

Answer: Um, I don't understand how did you post your question with the ones that are linear relationship to its algebraic model in slope-intercept form.

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

25% is the same as 1/4

8 times 4 is 32 so 8 is 25% of 32

Answer:

25% would be 8

50% would be 16

75% would be 24

100% would be 32

18x+10=100, 3x+6x+5+3x+6x+5=100, 2(3x)+2(6x+5)=100, – this three equatiοns represent the perimeter οf the rectangle.

The entire length οf a shape's bοrder is referred tο as the perimeter in mathematics. A shape's perimeter is calculated by cοmbining the lengths οf all οf its sides and bοrders. Its dimensiοns are expressed in linear measures like millimeters, meters, inches, and feet.

Given,

The length οf a rectangle is represented by 6x+5.

The width οf the rectangle is represented by 3x

The perimeter is 100 cm

Sο,

2(6x+5+3x)=100

Or, 2(9x+5)=100

Or, 18x+10=100………..(1)

We can write this as

3x+6x+5+3x+6x+5=100…….(2)

Or we can write this equatiοn as

2(3x)+2(6x+5)=100………(3)

18x+10=100, 3x+6x+5+3x+6x+5=100, 2(3x)+2(6x+5)=100, – this three equatiοns represent the perimeter οf the rectangle.

Hence the cοrrect answers are A, C, E

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Answer:

Removing the -6 makes the average go from 4.1 to 5.2

Removing the -6 makes the median go from 4 to 5

Step-by-step explanation:

Average:

-6+3+3+3+3+5+6+6+8+10 = 41

41/10 = 4.1 (This is the mean/average)

If we remove -6, then:

3+3+3+3+5+6+6+8+10 = 47

47/9 = 5.2222 (This would be the new average)

So removing the -6 makes the average go from 4.1 to 5.2

Median:

The median of (-6+3+3+3+3+5+6+6+8+10) is between 3 and 5, so the median is 4.

Without -6, the median of (3+3+3+3+5+6+6+8+10) is 5.

So removing the -6 makes the median go from 4 to 5

To evaluate the limit of (theta/sin(theta)) as theta approaches 0 without using L'Hôpital's rule, we can apply a trigonometric identity that relates sin(theta) and theta.

The given limit is (theta/sin(theta)), where theta approaches 0. We can use the trigonometric identity lim (sin(theta)/theta) = 1 as theta approaches 0. Applying this identity to our expression, we can rewrite it as (1/(sin(theta)/theta)).

Now, let's consider the reciprocal of sin(theta)/theta. As theta approaches 0, sin(theta)/theta approaches 1 according to the trigonometric identity mentioned earlier. Therefore, the reciprocal of 1 is 1/1, which equals 1.

Thus, the limit of (theta/sin(theta)) as theta approaches 0 is equal to 1.

By leveraging the trigonometric identity and understanding the behavior of sin(theta)/theta as theta approaches 0, we can evaluate the limit without relying on L'Hôpital's rule.

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Answer:

b-250

Step-by-step explanation:

Step-by-step explanation:

the answer is 250 B hope this helps

Step-by-step explanation:

m = y2-y1/X2-X1

slope intercept equation is: y=Mx+b

The slope is based on the formula m and from there pick any points then do the forumla m to find the slope. Anything that have 0 as the X is b which is the y intercept.

Your answer would be

Slope: 2

y-intercept: 7

Answer: y=2x+7

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Answer: FIRST ONE IS -1/7

The second one is 1

Step-by-step explanation:

The system of equations from the graph are y= -1/3 x+6 and y= 4x-4.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Equation of green line:

Points on the green line are (-3, 5) and (3, 3)

Here, slope (m)= (3-5)/(3+3)

= -2/6

m= -1/3

Substitute, m= -1/3 and (x, y)=(-3, 5) in y=mx+c, we get

5= -1/3 (3)+c

c=6

Substitute, m= -1/3 and c=6 in y=mx+c, we get

y= -1/3 x+6

Equation of blue line:

Points on the blue line are (1, 0) and (0, -4)

Slope (m)= (-4-0)(0-1)

m= 4

Substitute, m= 4 and (x, y)=(1, 0) in y=mx+c, we get

0=4(1)+c

c= -4

Substitute, m= 4 and c= -4 in y=mx+c, we get

y= 4x-4

Therefore, the system of equations from the graph are y= -1/3 x+6 and y= 4x-4.

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