You roll a six-sided number cube and flip a coin. What is the probability of rolling a number greater than 1 and flipping heads?

It is not possible for the graph of a height function of a car on a roller coaster to be a step function. Hence Amy is wrong.

A sort of function called a step function is one that only varies at discrete, isolated places in its domain and is constant everywhere else. A step function is one that "steps" down to the next integer at each integer input while remaining constant in between. An example of this is the floor function, which rounds down any input to the nearest integer.

On the other hand, it is doubtful that the height of a roller coaster car as a function of time is a step function because it is anticipated to fluctuate continually as opposed to hopping from one value to another at certain moments. Instead of abrupt increases in height that would be consistent with a step function, roller coasters often entail smooth, continuous curves and elevation changes.

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The simplified ratios are:  1:6  &  3:25

To simplify the first ratio, we need to convert the units so they are the same. We can either convert 500g to kilograms or 3kg to grams. Let's convert 3kg to grams since it will be easier to compare with 500g.

3 kg = 3000g

Now the ratio becomes:

500g : 3000g

We can simplify this ratio by dividing both sides by 500:

500g/500 = 1 and 3000g/500 = 6

So the simplified ratio is:

1 : 6

For the second ratio, we need to convert either 12cm to meters or 1m to centimeters. Let's convert 1m to centimeters since it will be easier to compare with 12cm.

1m = 100cm

Now the ratio becomes:

12cm : 100cm

We can simplify this ratio by dividing both sides by 4:

12cm/4 = 3 and 100cm/4 = 25

So the simplified ratio is:

3 : 25

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The expression to represent the number of circles at stage 20, assuming a starting circle, is 2²⁰.

To calculate the exponential growth of number of circles at stage 20, we need to consider the number of circles that appear at each stage of a process. Assuming that we start with one circle and that each subsequent stage doubles the number of circles from the previous stage, we can use the expression 2²⁰ to represent the number of circles at stage 20.

This expression is derived from the fact that at each stage, the number of circles is doubled from the previous stage. So, if we start with one circle, the number of circles at each stage is:

Stage 1: 1

Stage 2: 2 (doubled from stage 1)

Stage 3: 4 (doubled from stage 2)

Stage 4: 8 (doubled from stage 3)

...

Stage 20: 2²⁰

This expression gives us the number of circles at stage 20, which is an extremely large number. This shows how exponential growth can lead to very large numbers in a short period.

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The number of circles at stage 20 is 1141

The pattern of circles at each stage is as follows:

We can observe that the number of circles at each stage is equal to the sum of the number of circles in the previous stage, plus the number of circles in a new layer surrounding the previous layer.

Using this pattern, we can write a recursive expression to represent the number of circles at each stage:

C(n) = C(n-1) + 6(n-1)

where C(n) represents the number of circles at stage n.

Using this expression, we can find the number of circles at stage 20 as follows:

C(20) = C(19) + 6(19)

= C(18) + 6(18) + 6(19)

= C(17) + 6(17) + 6(18) + 6(19)

= ...

= C(1) + 6(1) + 6(2) + ... + 6(19)

Using the formula for the sum of an arithmetic series, we can simplify this expression to:

C(20) = C(1) + 6(1+2+...+19)

= 1 + 6(190)

= 1141

Therefore, the number of circles at stage 20 is 1141.

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The balloon is rising at a rate of approximately 3.532 km/h at this moment.

We will use the tangent function in trigonometry and the concept of related rates.

Let x be the horizontal distance from the observer to the lift-off point (5 km) and y be the vertical distance from the ground to the balloon. The angle between the observer's line of sight and the horizontal is given as π/5.

We can use the tangent function:
tan(θ) = y/x

At the given moment, x = 5 km and θ = π/5, so:
tan(π/5) = y/5

Now, let's differentiate both sides with respect to time (t):
d(tan(θ))/dt = d(y)/dt / 5

We know that d(θ)/dt = 0.4 rad/h, so we can find d(tan(θ))/dt using the chain rule:
d(tan(θ))/dt = (sec^2(θ)) * d(θ)/dt
d(tan(θ))/dt = (sec^2(π/5)) * 0.4

Now, substitute this back into the first equation and solve for d(y)/dt:
(sec^2(π/5)) * 0.4 = d(y)/dt / 5
d(y)/dt = 5 * (sec^2(π/5)) * 0.4

After calculating the expression, you'll find that d(y)/dt ≈ 3.532 km/h. Thus, the balloon is rising at a rate of approximately 3.532 km/h at this moment.

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Answer:

  34.8°

Step-by-step explanation:

You want the angle between a tangent and a segment to the center from a point on the tangent that is 6 units from the circle of radius 8 units.

The trig relation useful here is ...

  Sin = Opposite/Hypotenuse

  sin(S) = RQ/SQ

The length QT is the same as QR, so we have ...

  sin(S) = 8/(8 +6)

  S = arcsin(8/(8+6)) ≈ 34.8°

The equations that are TRUE based on the exponential function 2x = 8, are I, III and V.

To convert this equation into log equation, we will apply the general rule of logarithm equation as follows;

2x = 8

log2(2x) = log2(8)

Using the logarithmic rule that;

logb(xy) = ylogb(x),

We can simplify the left side of the equation to;

xlog2(2) = log2(8)

Since log2(2) = 1, we can simplify the equation further to;

x = log2(8)

Also in linear equation, we have

2x = 8

x = 8/2

x = 4

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Answer:47.25

Step-by-step explanation:

Answer:

48.5

Step-by-step explanation:

To find the first quartile (Q1) of the data set, we need to arrange the numbers in ascending order:

42, 46, 51, 53, 66, 70, 79, 90

Q1 is the median of the lower half of the data set. Since we have 8 data points, the lower half will be the first four numbers.

42, 46, 51, 53

To find the median of these numbers, we take the average of the two middle numbers:

(Q1) = (46 + 51) / 2 = 48.5

Therefore, the first quartile (Q1) of the data set is 48.5.

Assuming that the muffins were actually ready at two minutes to five in the afternoon, we can determine that it took Robert approximately 38 minutes to prepare and bake the muffins.

To arrive at this conclusion, we can use the following logic:

Robert got home from school at 3:33 PM (twenty-seven minutes before 4:00 PM).

The muffins were ready at 4:58 PM (two minutes before 5:00 PM).

Therefore, the time between when Robert got home and when the muffins were ready is 85 minutes (58 minutes + 27 minutes).

Since Robert decided to bake the muffins immediately upon arriving home, it took him 85 minutes to prepare and bake them.

Of course, this assumes that Robert did not take any breaks or perform other activities during the time between getting home and the muffins being ready. In reality, the actual time it took to prepare and bake the muffins may have been longer or shorter depending on various factors, such as the recipe, equipment used, and Robert's baking experience.

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The table shows the calculated curved surface area, total surface area, and vertical surface area for various geometric objects, including cylinders, cones, and spheres. The missing values are found for each object, with a given value of t = 3.

Radius is 4 cm

Height is 72 cm

curved surface area of cylinder

2πrt = 2π(4)(72) = 576π cm²

total surface area

2πr(r+h) = 2π(4)(76) = 304π cm²

vertical surface area

2πrh = 2π(4)(72) = 576π cm²

Radius is 4 cm

Height is 60 cm

curved surface area of cylinder of cone

πr√(r²+h²) = π(4)√(4²+60²) = 124π cm²

total surface area

πr(r+√(r²+h²)) = π(4)(4+√(4²+60²)) = 140π cm²

vertical surface area

πr√(r²+h²) = π(4)√(4²+60²) = 124π cm²

total surface area of sphere

0.48 m² = 48000 cm²

curved surface area of cylinder

Radius is 5 cm

Height 2 m = 200 cm

2πrt = 2π(5)(200) = 2000π cm²

total surface area

2πr(r+h) = 2π(5)(205) = 2050π cm²

vertical surface area

2πrh = 2π(5)(200) = 2000π cm²

curved surface area of cylinder

Radius is 6 cm

Height 10 cm

πr√(r²+h²) = π(6)√(6²+10²) = 34π cm²

total surface area

πr(r+√(r²+h²)) = π(6)(6+√(6²+10²)) = 78π cm²

vertical surface area

πr√(r²+h²) = π(6)√(6²+10²) = 34π cm²

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Patrick's method of depositing $300 as the principle amount with an interest rate of 6% compounded quarterly results in more money after two years, with a final amount of $337.95.

To compare the two methods, we need to calculate the total amount of money each person will have after 2 years.

For Patrick:
The formula for compound interest is: A = P (1 + r/n)^(nt)
Where:
A = the total amount of money after t years
P = the principle amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

So for Patrick, we have:
A = 300 (1 + 0.06/4)^(4*2)
A = 300 (1.015)^8
A = 300*1.1265 = 337.95

After 2 years, Patrick will have $337.95.

For Brooklyn:
Using the same formula, we have:
A = 300 (1 + 0.05/12)^(12*2)
A = 300 (1.004167)^24
A = 300 * 1.10495 = 331.485

After 2 years, Brooklyn will have $331.485.

Therefore, Patrick's method of depositing $300 as the principle amount with an interest rate of 6% compounded quarterly results in more money after two years. Patrick will have $337.95, which is slightly more than Brooklyn with $331.485.

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0.1859 is the relative frequency for male goats, female goats, adult goats, and baby goats

To find the relative frequency of marked mountain goats by gender and age group, we need to divide the number of marked goats in each group by the total number of marked goats.

The total number of marked goats is:

Total = Male + Female + Adult + Baby = 71 + 93 + 103 + 61 = 328

The relative frequency for male goats is:

Male/Total = 71/328 = 0.2165 or 433/2000 (simplified fraction)

The relative frequency for female goats is:

Female/Total = 93/328 = 0.2835 or 567/2000 (simplified fraction)

The relative frequency for adult goats is:

Adult/Total = 103/328 = 0.3140 or 157/500 (simplified fraction)

The relative frequency for baby goats is:

Baby/Total = 61/328 = 0.1859 or 93/500 (simplified fraction)

Therefore, the relative frequency for male goats is 433/2000, for female goats is 567/2000, for adult goats is 157/500, and for baby goats is 93/500, all expressed as simplified fractions.

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Entry debits the Depreciation Expense account for $7,000 and credits the Accumulated Depreciation account for the same amount, reflecting the decrease in the value of the machine over time.

To calculate  deprecation using the straight- line  system, we need to abate the residual value from the  original cost of the machine and  also divide the result by the estimated useful life. Using the given values, we have  

Cost of machine = $ 39,000

Residual value = $ 4,000  

Depreciable cost = $ 35,000($ 39,000-$ 4,000)

Estimated useful life =  5 times  

To calculate the periodic  deprecation  expenditure, we divide the depreciable cost by the estimated useful life  

Periodic  deprecation  expenditure = $ 7,000($ 35,000 ÷ 5)

Depreciation Expense $7,000

Accumulated Depreciation $7,000

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The journal entry is as given in figure:

Starting with a 1-by-1 square, a sequence of squares J1, J2, J3, ... is created by attaching squares half as wide as the previous squares to the outer edges of each successive square. The area of J∞, the limit of this sequence, is 4/3.

To find the area of J1, we simply calculate the area of the original 1-by-1 square, which is 1.

To find the area of J2, we need to attach squares half as wide (and half as tall) to the middle of each side of J1. The area of each attached square is (1/2)² = 1/4, so the total area added to J1 is 4(1/4) = 1. Thus, the area of J2 is 1 + 4(1/4) = 2.

To find the area of J3, we need to attach squares half as wide as the squares added in the previous step to every outer edge of J2. The area of each attached square is (1/4)² = 1/16, so the total area added to J2 is 4(1/16) = 1/4. Thus, the area of J3 is 2 + 4(1/4) = 3.

We can continue this process to find the areas of J4, J5, and so on. In general, the area of Jn is equal to the area of the previous square plus the area added by the attached squares, which is 4(1/2^(n-1))^2 = 1/2^(2n-2). Therefore, the area of Jn is 1 + 1/4 + 1/16 + ... + 1/4^(n-1) = (4/3)(1 - 1/4^n).

As n approaches infinity, the area of Jn approaches the limit of (4/3)(1 - 0) = 4/3. Therefore, the area of J∞, the limit of the sequence, is 4/3.

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The mass of the cylinder of lead with a radius of 1 centimeter and a height of 3 centimeters is  107.388 g

The radius of the cylinder is 1 cm, the height of the cylinder is 3 cm and the density of lead is 11.4 g/cm.

Here, to find mass we will use the density formula

Density = mass/volume

Mass = density × volume

Where, the volume of the cylinder = πr²h

Here, r = radius of the cylinder and h = height of the cylinder

Mass of cylinder = density × πr²h

Mass of cylinder= 11.4×3.14×1×1×3

Mass of cylinder = 107.388 g

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The value of 6x-5y = -31

The given equations are 2x-y=-7 -eq (1)

& 4x=-3y+16 -eq (2)

Multiplying eq (1) with 2 and rearranging to get equation as follows

(2x-y=-7)*2

4x-2y=-14 -eq (3)

Now, subtracting eq (3) from eq (2) to get y.

(4x+3y=16) - (4x-2y=-14)

5y=30

y=5

Substituting y=5 in eq (1) to get x.

2x-5=-7

x=-1

Now to determine 6x-5y substitute obtained values of x & y.

6*(-1)-5(5)=-31

Hence the value of 6x-5y=-31.

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The percent increase in Patti's hourly wage is 23%.

Percent​ increase is aimply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.

It is expressed as:

percent increase = ((new value - old value) / old value) × 100%

Given that, the old hourly wage was $10.00 and the new hourly wage is $12.30.

Substituting the values into the formula, we get:

percent increase = ((new value - old value) / old value) × 100%

percent increase = (($12.30 - $10.00) / $10.00) × 100%

percent increase = ($2.30 / $10.00) × 100%

percent increase = 0.23 × 100%

percent increase = 23%

Therefore, the percent increase is 23%.

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The differential for the function y = 5x^3 - 9x^2 + 9x + 10 is dy/dx = 15x^2 - 18x + 9.

Given function,

y = 5x^3 - 9x^2 + 9x + 10.

2. Differentiate the function with respect to x:

dy/dx = d(5x^3)/dx - d(9x^2)/dx + d(9x)/dx + d(10)/dx

3. Apply the power rule for differentiation (d(x^n)/dx = n*x^(n-1)):

dy/dx = 3*(5x^2) - 2*(9x) + 9

4. Simplify the expression:

dy/dx = 15x^2 - 18x + 9

So, the differential for the function y = 5x^3 - 9x^2 + 9x + 10 is dy/dx = 15x^2 - 18x + 9.

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To determine if the 275 fish are the right number for the cylindrical fish tank, we need to calculate the tank's capacity and compare it to the recommended average density of 16 fish per 100 gallons of water.

The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height of the cylinder.

Assuming the tank has a height of h and a radius of r, we can calculate its volume as follows:

[tex]V = πr^2h[/tex]

Since the tank has a vertical tube in the middle, we need to subtract the volume of the tube from the total volume of the tank. Let's assume the tube has a radius of 2 feet and a height of 8 feet. Then the volume of the tube is:

Vtube = π(2)^2(8) = 100.53 cubic feet

Thus, the volume of the tank without the tube is:

Vtank = πr^2h - Vtube

To find the value of r, we need to know the diameter of the tank. Let's assume the tank has a diameter of 10 feet, which means the radius is 5 feet.

Then the volume of the tank without the tube is:

Vtank = π(5)^2h - 100.53

We need to convert the volume of the tank from cubic feet to gallons, so we multiply by 7.48 (1 cubic foot = 7.48 gallons):

Vtank(gallons) = 7.48[π(5)^2h - 100.53]

Now we can calculate the recommended number of fish for the tank:

Recommended number of fish = 16 fish/100 gallons x Vtank(gallons)

Recommended number of fish = 16 fish/100 gallons x 7.48[π(5)^2h - 100.53]

Recommended number of fish = 1.175[π(5)^2h - 100.53]

So, if the number of fish available is 275, we can set up the following equation:

275 = 1.175[π(5)^2h - 100.53]

Solving for h, we get:

h = (275/1.175π(5)^2) + (100.53/π(5)^2)

h ≈ 8.3 feet

Therefore, the cylindrical fish tank with a height of 8.3 feet and a radius of 5 feet can hold 275 fish with an average density of 16 fish per 100 gallons of water. If the aquarium manager wants to add more fish, they should recalculate the volume of the tank and adjust the height accordingly to maintain the recommended density of 16 fish per 100 gallons of water. Conversely, if they want to remove fish, they can do so without changing the height of the tank.

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In the surface area, the amount of tin needed to make a milk can is 87.92 [tex]cm^2[/tex].

What is surface area?

A three-dimensional object's surface area is the space it takes up when viewed from the outside.

Here we know that the tin is in the shape of cylinder.

Now to find the amount we need to determine the surface area of the cylinder.

Now Height h = 5 cm, Diameter = 4 cm then radius r = d/2 = 4/2 = 2 cm.

Now using formula then,

Surface  Area  = 2[tex]\pi\\[/tex]r(h+r) square unit.

=> Surface area = [tex]2\times3.14\times2(5+2)=2\times3.14\times2\times7[/tex] = 87.92 [tex]cm^2[/tex]

Hence the amount of tin needed to make a milk can is 87.92 [tex]cm^2[/tex].

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The Surface Area of the sphere is approximately 339.79 square inches.

The surface area of a sphere is given by the formula:

surface area= [tex]4\pi r^{2}[/tex]

where r is the radius of the sphere.

The diameter of the sphere measures 10.4 inches, hence the radius can be calculated as:

r=10.4/2=5.2inches

Hence, the surface area can be calculated as by substituting r=5.2 inches

Therefore, surface area of the sphere is:

Surface Area = [tex]4\pi (5.2)^{2}[/tex]=[tex]4\pi (27.04)[/tex]= 108.16[tex]\pi[/tex] square inches.

So, the Surface Area of the sphere is approximately 339.79 square inches(if we use [tex]\pi[/tex]=3.14 as an approximation)

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Jane is 14 years old, if Sebastian is 12 34 years old. Camden is 1 38 years older than Sebastian and Jane is 1 15 years older than Camden.

To find out how old Jane is, we will first determine the ages of Sebastian and Camden, then add the additional years to find Jane's age.

Sebastian is 12 34 years old, but the correct age should be 12 years old (ignoring the typo).

Camden is 1 38 years older than Sebastian, which should be correctly written as 1 year older. So, Camden's age is 12 (Sebastian's age) + 1 = 13 years old.

Jane is 1 15 years older than Camden, which should be correctly written as 1 year older. Therefore, Jane's age is 13 (Camden's age) + 1 = 14 years old.

So, Jane is 14 years old.

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Answer:

2√6 + 9

Step-by-step explanation:

√24 + √81

= √4√6 + 9

= 2√6 + 9

the height of the pyramid is 99 inches.

(explain)

To solve this problem, we can use the formula for the volume of a square pyramid which is:

Volume = (1/3) x (base area) x (height)

Since the base of our pyramid is a square with a side length of 10 inches, the base area would be:

Base area = (side length)^2 = 10^2 = 100 square inches

Substituting the values given in the problem, we get:

3300 = (1/3) x 100 x height

Multiplying both sides by 3, we get:

9900 = 100 x height

Dividing both sides by 100, we get:

height = 99 inches

Therefore, the height of the pyramid is 99 inches.

The new diet was not effective, the researchers may need to continue searching for other solutions.

In the trial to determine whether a new diet reduces cholesterol, a group of twenty volunteers with high cholesterol were selected. The trial likely involved splitting the volunteers randomly into two groups - a treatment group and a control group.

The treatment group would be given the new diet to follow, while the control group would continue with their normal diet. The participants' cholesterol levels would be measured at the beginning of the trial, and then again at regular intervals throughout the trial to track any changes.

After the trial has ended, the researchers would analyze the results to see if there was a significant difference in cholesterol levels between the treatment and control groups. If the new diet was effective in reducing cholesterol, the researchers may recommend it as a potential treatment option for people with high cholesterol. However, if the new diet was not effective, the researchers may need to continue searching for other solutions.

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The formula for the volume of a cone is:

V = (1/3)πr^2h

where r is the radius of the base of the cone and h is the height of the cone.

We are given that the radius of the cone is 5 cm and the slant height is 13 cm. We can use the Pythagorean theorem to find the height of the cone:

h^2 = l^2 - r^2

where l is the slant height of the cone. Substituting the given values, we get:

h^2 = 13^2 - 5^2

h^2 = 144

h = 12

Now we can substitute the values of r and h into the formula for the volume of the cone:

V = (1/3)πr^2h

V = (1/3)π(5^2)(12)

V = (1/3)π(25)(12)

V = (1/3)π(300)

V = 100π

Therefore, the volume of the cone is 100π cubic centimeters.

The phase of the process cycle for customer relationship management that represents the actual implementation of the customer strategies and programs is the "Execution" phase.

This is where the plans and strategies that were formulated in the earlier phases of the process cycle are put into action to interact with customers and build strong relationships with them.

During the Execution phase, the focus is on carrying out specific tactics to engage with customers and meet their needs, such as targeted marketing campaigns, personalized communication, and efficient service delivery.

The success of this phase relies heavily on the quality of the planning and preparation done in the earlier phases, as well as ongoing monitoring and adaptation to customer feedback and changing market conditions.

Effective execution of customer strategies and programs is crucial for building loyal and satisfied customers, and ultimately driving business growth.

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Here is the probability distribution table:

|Outcome|Probability|
|-------|-----------|
|$0     |1/10       |
|S100   |4/10       |
|$200   |3/10       |
|$500   |2/10       |

To create the table, you simply list each possible outcome (in this case, the different amounts that could be won on the spinner), and then calculate the probability of each outcome occurring. In this case, there are 10 sectors in total, so the probability of landing on each sector is 1/10. There is 1 sector that says "$0," so the probability of getting that outcome is 1/10.

There are 4 sectors that say "S100," so the probability of getting that outcome is 4/10, or 2/5. Similarly, there are 3 sectors that say "$200," so the probability of getting that outcome is 3/10, or 3/10.

And finally, there are 2 sectors that say "$500," so the probability of getting that outcome is 2/10, or 1/5.

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Answer:

Sure, here is the solution for the equation G/B=M/n:

```

B = Gn/M

```

Here is the step-by-step solution:

1. Multiply both sides of the equation by B.

```

G/B * B = M/n * B

```

2. Simplify both sides of the equation.

```

G = Gn/n

```

3. Divide both sides of the equation by n.

```

G/n = Gn/n * 1/n

```

4. Simplify both sides of the equation.

```

B = Gn/M

```

Therefore, the solution for B is Gn/M.

Step-by-step explanation:

The quantity of heat which must be removed from the system in order to reduce the pressure from 2 bar to 1.6 bar is 4.23 kJ. The change in enthalpy per unit mass of the system is -123 kJ/kg, and the change in entropy per unit mass of the system is 0.134 kJ/kg-K.

To solve this problem, we need to use the steam tables to determine the properties of the steam at the initial and final conditions. We will assume that the system is undergoing a reversible, adiabatic process, so there is no heat transfer into or out of the system.

First, we determine the specific volume and enthalpy of the steam at the initial conditions of 2 bar and 0.9 dryness fraction. From the steam tables, we find that the specific volume is 0.4019 m^3/kg and the specific enthalpy is 2895.5 kJ/kg.

Next, we use the steam tables to find the specific volume and enthalpy of the steam at the final conditions of 1.6 bar. We find that the specific volume is 0.5059 m^3/kg and the specific enthalpy is 2772.5 kJ/kg.

The change in specific enthalpy per unit mass of the system is then given by:

Δh = h2 - h1 = 2772.5 - 2895.5 = -123 kJ/kg

The change in specific entropy per unit mass of the system is given by:

Δs = s2 - s1 = s2 - s1 = s2 - sf - x2*(sg - sf)

where sf and sg are the specific entropy of saturated liquid and saturated vapor at the final pressure of 1.6 bar, and x2 is the final dryness fraction. From the steam tables, we find that sf = 7.4332 kJ/kg-K, sg = 8.1248 kJ/kg-K, and x2 = 0.714.

Thus, we have:

Δs = s2 - s1 = s2 - sf - x2*(sg - sf) = (7.9757 - 7.4332) - 0.714*(8.1248 - 7.4332) = 0.134 kJ/kg-K

Finally, we can calculate the quantity of heat that must be removed from the system using the first law of thermodynamics:

Q = m*(h1 - h2) = m*Δh

where m is the mass of the steam in the system. To determine the mass of the steam, we use the specific volume at the initial conditions:

V = m/v1

where V is the volume of the system and v1 is the specific volume at the initial conditions. Substituting the given values, we have:

V = 85 L = 0.085 [tex]m^3[/tex]

m = Vv1 = 0.0850.4019 = 0.0344 kg

Substituting this value into the equation for Q, we obtain:

Q = mΔh = 0.0344(-123) = -4.23 kJ

Therefore, the quantity of heat which must be removed from the system in order to reduce the pressure from 2 bar to 1.6 bar is 4.23 kJ.

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The length of the sides AB, BC and AC are √13, √13 and √26, hence the triangle is a isosceles triangle.

a. Points (-2, 3), (1, 1), (-1, 2) in the triangle are vertex. The distance formula for any two points is,

AB = √[(d-b)²+(c-a)²]

= √[(1 - (-2))² + (1 - 3)²]

= √[3² + (-2)²]

= √13

BC = √[(d-b)²+(c-a)²]

= √[(-1-1)²+(-2-1)²]

= √[(-2)² + (-3)²]

= √13

AC = √[(d-b)²+(c-a)²]

= √[(-1 - (-2))² + (-2 - 3)²]

= √[1² + (-5)²]

= √26

b. The triangle is an isosceles triangle because AB = BC.

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