A car loses its value at a rate of 27% each year. How long will it take for its value to halve?

The minimum amount of green paint he has to throw away so he can use  rest to add blue or yellow paint in order to get exactly 5 liters of correct shade of green is 5/3 liter.

We know that "original-shade" of green color requires "2-liters" of blue paint and "3-liters" of yellow paint.

So, the original-ratio of "yellow-paint" to "total-paint" is = 3 : 5,

He mixes 3-litres of "blue" and 2-litres of "yellow" for 5 liters of paint,

So, he has more blue-paint in mixture than it is required to make green color,

He needs to throw some of green-paint and add yellow-paint to get required shade-of-green.

Let the painter throw away "x-liters" of paint from his mixture and adds "x-liters" of yellow-paint into mixture.

So, New mixture will have same ratio as 3:5,

So, the equation in x is,

⇒ (2/5)×(5 - x) + x = (3/5)×5,

⇒ 2 - (2/5)x + x = 3,

⇒ (3/5)x = 1,

⇒ x = 5/3.

Therefore, the painter needs to throw away 5/3 liters of paint.

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The probability that the sample proportion of households spending more than $125 a week is less than 0.35 is 0.9884.

Using the given information, the population proportion of households spending more than $125 a week is 0.34. The sample size is 196 households.

Population proportion (p) = 0.34

Sample size (n) = 196

Sample proportion (p') = 0.35

Standard error of proportion (p') = √[p*(1-p)/n] = √[(0.34*0.66)/196] = 0.044

To find the probability that the sample proportion is less than 0.35, we need to find the z-score and then find the area to the left of that z-score using a standard normal distribution table.

z-score = (p' - p) / σp' = (0.35 - 0.34) / 0.044 = 2.27 (approx)

Using a standard normal distribution table, the area to the left of the z-score 2.27 is 0.9884.

Therefore, there is a roughly 0.9884 percent chance that the sample proportion of households paying more than $125 per week is less than 0.35.

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The dimensions that will minimize the cost of the metal to manufacture the can are,

Radius = 4.08 cm

Height = 10.84 cm

To minimize the cost of the metal to manufacture the can, we need to minimize the surface area of the can. The surface area of a cylinder is given by

A = 2πrh + 2πr^2

where r is the radius of the cylinder, h is the height of the cylinder, and π is a constant equal to approximately 3.14159.

We are given that the can needs to hold 1.4 liters of oil. We can use this information to find the relationship between the radius and height of the cylinder. The volume of a cylinder is given by

V = πr^2h

Substituting the given volume of 1.4 liters (1400 cubic centimeters) and the constant π, we get

1400 = 3.14159r^2h

Solving for h, we get

h = 1400/(3.14159r^2)

Now we can substitute this expression for h in the formula for the surface area of the cylinder to get

A = 2πr(1400/(3.14159r^2)) + 2πr^2

Simplifying this expression, we get

A = (2800/πr) + 2πr^2

To minimize the surface area, we need to find the value of r that makes the derivative of A with respect to r equal to zero. Taking the derivative, we get

dA/dr = -2800/πr^2 + 4πr

Setting this equal to zero and solving for r, we get:

-2800/πr^2 + 4πr = 0

2800/πr^2 = 4πr

r^3 = 700/π

r ≈ 4.08 cm

Now we can use the formula for h in terms of r to find the corresponding value of h

h = 1400/(3.14159(4.08)^2) ≈ 10.84 cm

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The lifecycle cost of the clothes washer is $1,032.68.

The lifecycle cost of the clothes washer is $1,104.20. Here's how to compute it:Given:Energy consumed by the clothes washer = 198 kWhPrice of the washer = $389Lifetime of the washer = 14 yearsEnergy price in the city = 8 cents per kWhMaintenance cost = $17 per yearFormula: Lifecycle cost = (purchase price + (energy price x energy consumed) + (maintenance cost x lifetime)) / lifetimeLet's substitute the given values in the formula:Lifecycle cost = ($389 + ($0.08 x 198 kWh) + ($17 x 14)) / 14Lifecycle cost = ($389 + $15.84 + $238) / 14Lifecycle cost = $642.84 / 14Lifecycle cost = $45.92 (rounded to two decimal places).

The lifecycle cost of the clothes washer is $45.92 per year. To find the total lifecycle cost, multiply it by the lifetime of the washer:Total lifecycle cost = $45.92 x 14Total lifecycle cost = $643.68Add the initial cost of the washer to get the final answer:Final answer = $643.68 + $389Final answer = $1,032.68 (rounded to two decimal places)

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Therefore , the solution of the given problem of expressions comes out to be  the picture of a point P(x,y) on FG will be P'(-x,y), which is P'reflected across the y-axis.

Instead of using approximations produced at random, it is better to use shifting integers that may prove increasing, reducing, or blocking. They could only help one another by sharing materials, information, or solutions to issues. The justifications, components, or mathematical remarks for techniques like additional disapproval, production, and mixture may be included in a statement of truth equation.

Here,

The x-coordinates of all the locations on FG are transformed when FG is reflected across the y-axis, but the y-coordinates stay the same. As a result, the algebraic formula that characterizes this reflection is as follows:

(-x, y)

As a result, the picture of a point P(x,y) on FG will be P'(-x,y), which is P'reflected across the y-axis.

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Answer:

Annie jumps 34.56 cm (approximately)

Step-by-step explanation:

Since we know that Annie jumps 8% higher than Rosie, we can add the 8% increase to the height that Rosie jumped.

32 cm + 2.56 cm = 34.56 cm

Therefore, Annie jumped approximately 34.56 cm in the air, which is 8% higher than the height that Rosie jumped.

Step-by-step explanation:

To find out how high Annie jumped, you first need to calculate what 8% of Rosie's jump height is, and then add this amount to Rosie's jump height.

To calculate 8% of Rosie's jump height, you can multiply 32cm by 8% expressed as a decimal, which is 0.08:

8% of 32cm = 0.08 x 32cm = 2.56cm

So Annie jumped 2.56cm higher than Rosie's jump of 32cm.

To find out how high Annie jumped, you can add 2.56cm to Rosie's jump height:

Annie's jump height = Rosie's jump height + 2.56cm

= 32cm + 2.56cm

= 34.56cm

Therefore, Annie jumped 34.56cm in the air.

Answer:

The shaded plants set has greater variability because more data is clustered around the median. "NC"The sets are equally variable because the ranges of the data sets are equal.The full sun plants set has greater variability because the IQR for full sun plants is greater. The full sun plants set has greater variability because the median for full sun plants is greater.

Step-by-step explanation:

The shaded plants can always get a greater variability because remember more data around the median. The sets would eventually equal the variable.

Sun plans can get greater variability because the median can always be used for sun plants and which is being called greater.

To determine whether there is a statistical difference in the proportion of students in the two groups who have used a performance-enhancing drug at the 5% level, we need to perform a hypothesis test.

are the null and alternative hypotheses: Null Hypothesis: There is no significant difference in the proportion of students in the two groups that have used a performance-enhancing drug. (p1=p2)Alternative Hypothesis: There is a significant difference in the proportion of students in the two groups that have used a performance-enhancing drug. (p1≠p2)Level of Significance: α=0.05In this scenario, we have two different samples of sizes 1679 and 1366, where 34 freshman athletes and 24 senior athletes used performance-enhancing drugs.

Using the two-proportion z-test formula, we get z = (p1 - p2) / sqrt[pq (1/n1 + 1/n2)]wherep1 = number of freshman athletes who have used a performance-enhancing drug / total number of freshman athletes = 34/1679p2 = number of senior athletes who have used a performance-enhancing drug / total number of senior athletes = 24/1366p = (p1 * n1 + p2 * n2) / (n1 + n2)q = 1 - p Now let's plug in the values to get z = (-0.00394) / 0.01267 = -0.311where we round the absolute value of the test statistic to two decimal places.

According to the standard normal distribution table, the critical values are ± 1.96 at a 5% level of significance. Since our test statistic, -0.311, does not fall outside this range, we fail to reject the null hypothesis. Hence, we conclude that there is no significant difference in the proportion of students in the two groups that have used a performance-enhancing drug at the 5% level.

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The equation that can be used to find the nth term in the sequence is:

aₙ= 6n - 24

What is sequence ?

In mathematics, a sequence is a list of numbers, arranged in a specific order. Each number in the sequence is called a term, and the position of the term in the sequence is called its index. A sequence can be either finite or infinite.

For example, a sequence of even numbers can be written as:

2, 4, 6, 8, 10, ...

where each term in the sequence is obtained by adding 2 to the previous term. The first term of the sequence is 2, the second term is 4, and so on.

Sequences are used in various mathematical applications such as in number theory, calculus, statistics, and computer science. They are also used in real-world applications such as modeling the behavior of stocks in the stock market, modeling the spread of disease in a population, and so on.

We can notice that the given sequence is an arithmetic sequence with a common difference of 6.

So, to find the nth term of the sequence, we can use the formula:

aₙ= a₁+ (n-1)d

where a₁is the first term of the sequence, d is the common difference, and n is the term number we want to find.

Using the information given in the problem, we can find the value of a_1 by working backward from a₄

a₄= a₁ + 3d = 0

a₁= -3d

Substituting the values of a₁ and d, we get:

aₙ = -3d + (n-1)d

aₙ= (n-4)d

Since d = 6, we have:

aₙ= 6n - 24

So, out of the given options, the equation that can be used to find the nth term in the sequence is:

aₙ= 6n - 24

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The matching of the system of equations with the diagrams is:

1 → Diagram A

2 → Diagram B

3 → Diagram D

4 → Diagram C

In the given answered pairs, the systems of equations 1 – 4 have been numbered from left to right, and the diagrams A – D from top to bottom.

The attached the row-reduction of the first three systems (1 – 3). The last system (4) is obviously three repetitions of the same equation, so is the same plane 3 times, as in diagram C.

1. The last row of the given reduced matrix has a non-zero element in the rightmost column, which tells us that there is no solution. The two non-zero rows indicates that the system specifies planes that intersect in parallel lines. In a local area, the solution matches diagram A in that specific one plane intersects the two others in parallel lines. Despite the fact that the lines are parallel, the planes are not parallel.

The last attachment indicates a rendering of the particular first system of equations. Though the colors leave some doubts, but it is clear that they intersect in a way that provides a triangular tunnel. No (x, y, z) value is found on all three planes.

2. The reduced matrix shows there is a single solution, corresponding to the planes all intersecting at one point.

3. The last row of the reduced matrix being all zeros means the solution is a line, as shown in diagram D.

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Raphael bought a 2/3 pound bag of sugar, and he used 3/4 of it for baking.

To find out how much sugar he used, we need to multiply the fraction of the bag that he used (3/4) by the weight of the bag (2/3 pounds):

(3/4) x (2/3) pounds

To simplify this fraction multiplication, we can cancel out the factor of 3 in the numerator and the denominator:

(1/4) x (2/1) pounds

= 2/4 pounds

= 1/2 pound

Therefore, Raphael used 1/2 pound of sugar for baking.

After one rotation of the carousel, after 6.2 more meters has Mei traveled than Anju.

Circumference of Circle:

The circumference of a circle or the circumference of a circle is a measurement of the limit of a circle. Whereas the area of ​​a circle defines the area it occupies. If we open a circle and draw a line through it, its length is the circumference. It is usually measured in units such as centimeters or units of meters.

As we know carousel  is circular

Therefore,

distance covered will be the circumference of a circle

Now,

we know that the circumference of the circle = 2πr where r is the radius

Mei's horse is 3 m away from the carousel  i.e r = 3 m

Distance covered by Mei's =  2π × 3 = 6π m

Anju's horse is 2 m away from the carousel i.e r = 2 m

Distance covered by Anju = 2π × 2 =4π

Mei traveled more = 6π - 4π = 2π m

                                               ≈ 6.2 m

Complete Question:

Mei and Anju are sitting next to each other on different horses on a carousel. Mei’s horse is 3 meters from the center of the carousel. Anju’s horse is 2 meters from the center. After one rotation of the carousel, how many more meters has Mei traveled than Anju?

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The height of the water in cylinder after inversion is h = R(2 - √3) cm.

The curved surface of a liquid in a container is known as a meniscus and is created by the intermolecular interactions between the liquid and the material of the container. The type of the liquid and the container, as well as outside variables like temperature and pressure, all affect the meniscus' form. A concave meniscus has a liquid surface that is lower in the middle than it is at the edges, whereas a convex meniscus has a liquid surface that is higher in the middle than it is at the edges. Many scientific and technical applications, such as figuring out a liquid's surface tension or how fluids behave in microfluidic devices, might benefit from understanding the geometry of the meniscus.

Let us suppose the height of the water level after inversion = h.

The volume of the figure 1 is:

V1 = πR²(R-h)

where, (R-h) represents the height of the cylinder filled with water.

When inversion takes place water forms a smaller hemisphere with radius h.

The volume is:

V2 = 2/3 πh³ + πh² (R-h)

Setting the equations:

V2 = 2/3 πh³ + πh² (R-h)

h = R(2 - √3)

Hence, the height of the water after inversion is h = R(2 - √3) cm.

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The equation of a line whose slope is 2 and passes through the point (3,1) is y=2x-5

An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal. Every angle we draw between any two locations along a straight line will always be a 180-degree angle. We will explore the universe of straight lines in this mini-lesson by comprehending the equations of straight lines in various formats and learning how to answer problems based on straight lines.

The equation of a line whose slope is m and passes through the point (h,k),

y-k=m(x-h)

y=m(x-h)+k

We have a line with slope 2 and passes through the point (3,1)

y= 2(x-3)+1

y= 2x-6+1

y=2x-5

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The vertical support cable length that is 60 feet from the towers is 56.5 feet.

The given information:

Towers are 400 ft apart

The supporting cable is 100 ft high

The supporting cable runs 30 ft above the road

The shape of the cable is a parabola.

Find the length of the vertical support cables that are 60 feet from the towers.

First, let’s set up a coordinate system with the origin at the lowest point of the cable and the x-axis along the road. The towers are 400ft apart, so their x-coordinates will be -200 and 200.

The equation of a parabola is y = ax^2 + bx + c. Since the cable is 30ft above the road at its lowest point, c = 30.

The towers are 100ft tall, so when x = -200 and x = 200, y = 100. Substituting these values into the equation of the parabola gives us two equations: 100 = a(-200)^2 + b(-200) + 30 and 100 = a(200)^2 + b(200) + 30.

Solving these equations simultaneously for a and b gives us a = 0.001875 and b = 0.

So the equation of the parabola is y = 0.001875x^2 + 30.

The towers are 400ft apart, so their x-coordinates are -200 and 200. The vertical support cable that we want to find the length of is 60 feet from one of the towers. So if we move 60 feet from one of the towers along the x-axis towards the center of the bridge, we will reach the point where the vertical support cable is attached to the road. This point will have an x-coordinate of -200 + 60 = -140 or 200 - 60 = 140.

Now we can find the length of the vertical support cable that is 60 feet from one of the towers. When x = -140 or x = 140,

y = 0.001875(140)^2 + 30 ≈ 56.5.

So the length of the vertical support cable that is 60 feet from one of the towers is approximately 56.5 feet.

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the aggregate demand curve is downward-sloping because, other things being equal, With average price reductions, more people purchase goods and services.

This is known as the law of demand, which states that there is an inverse relationship between the price of a good or service and the quantity of that good or service demanded by consumers. When the price of a good or service goes up, consumers tend to demand less of it, and when the price goes down, consumers tend to demand more of it. Therefore, if all other factors affecting demand remain constant, an increase in price will lead to a decrease in the quantity demanded, and a decrease in price will lead to an increase in the quantity demanded. This is why the aggregate demand curve is downward-sloping.

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Compete Question

the aggregate demand curve is downward-sloping because, other things being equal, ____. FILL IN THE BLANKS

Answer:

Step-by-step explanation:

No, the expression -x^2 + 6x - 9 cannot be non-negative for all values of x.

The expression -x^2 + 6x - 9 cannot be non-negative for all values of x.

To see this, note that the leading coefficient of the quadratic term is negative, which means that the graph of the function is a downward-facing parabola.

The vertex of the parabola occurs at x = -b/(2a) = -6/(2*(-1)) = 3, and the value of the function at this point is -(-3)^2 + 6*(-3) - 9 = -18.

Since the value of the function at the vertex is negative, and the graph of the function is a downward-facing parabola, the function is negative for all x values to the left and right of the vertex, and thus can never be non-negative for all values of x.

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Answer:

D

Step-by-step explanation:

The probability that a second call will not arrive in the next 20 seconds is approximately 0.2636 or 26.36%.

Poisson probability is a mathematical concept that describes the probability of a certain number of events occurring in a fixed interval of time or space, given a known average rate of occurrence. The Poisson probability distribution is named after French mathematician Siméon Denis Poisson, who introduced it in the early 19th century to model the occurrence of rare events, such as errors in counting or measurement, accidents, or phone calls.

The Poisson probability distribution is a discrete probability distribution that gives the probability of a certain number of events (x) occurring in a fixed interval (t), when the average rate of occurrence (λ) is known. The Poisson probability distribution assumes that the events occur independently and at a constant average rate over time or space. The formula for Poisson probability is:

P(x; λ) = ([tex]e^{-\lambda}[/tex]) * λˣ) / x!

where:

P(x; λ) = the probability of x occurrences in a given interval, when the average rate is λ

e = a mathematical constant e (approximately 2.71828)

λ = it is the average rate of occurrence in the given interval

x = it is number of occurrences in the given interval

Given that calls for dial-in connections arrive at an average rate of four per minute and follow a Poisson distribution, we can use the Poisson probability formula to solve this problem. The Poisson probability formula is:

P(x; λ) =  ([tex]e^{-\lambda}[/tex]) * λˣ) / x!

where:

P(x; λ) = the probability of x occurrences in a given interval, when the average rate is λ

e = a mathematical constant e (approximately 2.71828)

λ = the average rate of occurrence in the given interval

x = it is the number of occurrences in the given interval

In this problem, we are interested in finding the probability that a second call will not arrive in the next 20 seconds, given that a call has already arrived at the beginning of a one-minute interval. Since we are given the average rate of calls per minute, we need to adjust the interval to 20 seconds, which is 1/3 of a minute. Therefore, the average rate of calls per 20 seconds is:

λ = (4 calls/minute) * (1/3 minute) = 4/3 calls/20 seconds

Using the Poisson probability formula, we can calculate the probability of no calls arriving in the next 20 seconds:

P(0; 4/3) = ( [tex]e^{-4/3}[/tex]* (4/3)⁰) / 0! = [tex]e^{-4/3}[/tex] ≈ 0.2636

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Answer:

x= y + 5

Step-by-step explanation:

This is simple linear equations!

y = x - 5  

Add 5 to both sides, and you get

y + 5 = x!

Therefore, the length of each side of the original square is 5 cm.

Area is a measure of the size of a two-dimensional surface or region. It is the amount of space enclosed by a boundary in two dimensions. In simple terms, area is the size of a flat surface, such as the floor, a wall, or a piece of paper. It is usually measured in square units such as square meters (m²), square centimeters (cm²), square feet (ft²), or acres.

Here,

Let x be the length of each side of the original square.

When the length of each side is increased by 10 cm, the new length is x + 10, and the area of the new square is (x + 10)².

According to the problem, the increase in area is 200 cm², so we can set up the equation:

(x + 10)² - x² = 200

Expanding the left side of the equation, we get:

x² + 20x + 100 - x² = 200

Simplifying, we get:

20x + 100 = 200

Subtracting 100 from both sides, we get:

20x = 100

Dividing both sides by 20, we get:

x = 5

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The perimeter of the rectangle is 2(sqrt(82) + 4) units.

what is perimeter?

Perimeter is the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. In other words, if you were to walk along the edge of a shape, the distance you would cover would be the perimeter of the shape. The units used to measure perimeter are the same as those used to measure length, such as inches, centimeters, or meters.

Let's call the two points on the x-axis (a,0) and (b,0), where a and b are both positive.

Since the rectangle has an area of 54 square units, we know that:

length x width = 54

We also know that one point is located at (5,9), so the length of the rectangle must be the distance between (5,9) and (a,0) or (b,0). Similarly, the width must be the distance between (5,9) and (a,0) or (b,0).

Let's first find the length. The distance formula gives us:

length = sqrt((5-a)^2 + 9^2) or sqrt((5-b)^2 + 9^2)

Next, let's find the width. Again, using the distance formula, we have:

width = sqrt((a-b)^2 + 0^2)

Now we can use the fact that the area of the rectangle is 54 to solve for a and b.

54 = length x width

54 = sqrt((5-a)^2 + 9^2) x sqrt((a-b)^2 + 0^2)

54 = sqrt((5-a)^2 x (a-b)^2 + 0^2)

2916 = (5-a)^2 x (a-b)^2

Since a and b are both positive, we know that 5 > a > b. Let's try some values of a and b that satisfy this condition and see which one gives us an equation that works out to 2916.

If a = 4 and b = 2, we get:

2916 = (5-4)^2 x (4-2)^2 = 4

This doesn't work. Let's try a = 3 and b = 2:

2916 = (5-3)^2 x (3-2)^2 = 4

Still doesn't work. Let's try a = 6 and b = 2:

2916 = (5-6)^2 x (6-2)^2 = 16

This works! So the two points on the x-axis are (2,0) and (6,0).

Now we can find the length and width:

length = sqrt((5-6)^2 + 9^2) = sqrt(82)

width = sqrt((6-2)^2 + 0^2) = 4

Finally, we can find the perimeter:

perimeter = 2 x length + 2 x width

perimeter = 2 x sqrt(82) + 2 x 4

perimeter = 2(sqrt(82) + 4)

Therefore, the perimeter of the rectangle is 2(sqrt(82) + 4) units.

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The function is a square root function that has been transformed from the parent function. Three parameters are a = -1, h = -2, and k = 3.

A set that has a geometric structure by itself or another set constitutes the geometric transformation. A shape may change shape, but not appearance. Following then, the form could match or resemble its preimage. A change in something's appearance is what transformations actually signify. Planar transformations and spaces can be distinguished from one another using the dimensions of the operand sets. Their characteristics can also be used to classify them.

The given function is f(x) = -√(x+2) + 3.

The function is a square root function that has been transformed from the parent function.

The three parameters of the function are:

a = -1, which reflects the graph of the function over the x-axis.

h = -2, which shifts the graph of the function 2 units to the left.

k = 3, which shifts the graph of the function 3 units up.

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If in the summation formula n starts at n=n0 the starting index  n0 is 2

The given series can be written as:

∑n=n0[infinity]an = (x-7)³/(x-7)⁶³* 2! + (x-7)⁹⁹/(x-7)¹²²⁷ * 3! + ...

We can simplify this expression by canceling out the common factor of (x-7) in each term of the series. This gives:

∑n=n0[infinity]an = (x-7)⁻⁶⁰ * 2! + (x-7)⁻¹¹²⁸ * 3! + ...

Now, we can see that each term in the series has the form:

an = [tex]k!/[(x-7)^{(3k-60)}][/tex]

where k is the index of the term and k ≥ 2, since the first two terms in the original series were combined into the first term of the simplified series.

Therefore, the starting index of the series is n0 = 2.

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Answer:

4 times

Step-by-step explanation:

Find the perimeter of the rectangular field

P=2(L+W)➡️ L is for length, W is for width

P=2(150+100)=2(250)=500m

After that, you need to convert 2KM into metres

So, 2×1000=2000m

Then divide the number of metres the runner would run by the perimeter of the rectangular field

2000/500=4 times

Therefore, the runner will go around the field 4 times

To find the price that maximizes revenue, we need to find the critical points of the function R(x) and set it equal to zero. We should also check that this critical point is a maximum and not a minimum or inflection point, since the second derivative is negative at x = 70.

The questions on the midterm exam will cover every topic, including created and actual places and also algebraic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

This is true when[tex]x = 0 or x = -70[/tex]. Therefore, the company makes no revenue if it charges $0 or -$70 per unit. Of course, charging a negative price doesn't make sense, so the only answer that makes sense is $0 per unit.

a) The company makes no revenue when the revenue function, R(x), is equal to zero. So we have:

[tex]R'(x) = 26250 + 750x - 475x^2 = 0[/tex]

b) To find the price that maximizes revenue, we need to find the value of x that maximizes the revenue function, R(x). We can do this by taking the derivative of R(x) with respect to x and setting it equal to zero:

Solving for x gives us two solutions: [tex]x = 0 and x = 55.26[/tex]. However, we know that x = 0 gives us zero revenue, so the only solution that makes sense is x = 55.26.

Therefore, the company should charge $55.26 per unit to maximize its revenue.

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Answer: 37

Step-by-step explanation:

STEP 1: Write out the equation; 89 - 4^2 (4) + 12

STEP 2: Determine 4^2 [16]

STEP 3: Rewrite the equation to reflect the above step; 89 - 16 (4) + 12
STEP 4: Determine 16 (4) [64]

STEP 5: Rewrite the equation to reflect the above step; 89 - 64 + 12

STEP 6: Determine 89 - 64 + 12 [37]

Therefore, the answer is 37.

NOTE: Following PEMDAS for these types of problems is very helpful. Feel free to message me if you have any questions.

The steady-state surface temperature of the heater is estimated to be 91.7°C.

To solve this problem, we need to apply the energy balance equation, which states that the heat transferred to the heater must be equal to the heat dissipated by the heater. Assuming steady-state conditions and neglecting radiation, the energy balance equation can be written as

q_conv = q_gen

where q_conv is the heat transferred to the heater by convection, and q_gen is the heat generated by the electrical energy dissipated per unit length of the heater.

The heat transferred to the heater by convection can be calculated using the following equation

q_conv = hA(T_s - T_inf)

where h is the convective heat transfer coefficient, A is the surface area of the heater, T_s is the surface temperature of the heater, and T_inf is the temperature of the air in the duct.

The convective heat transfer coefficient can be estimated using the Dittus-Boelter correlation for cross-flow over cylinders

Nu_D = 0.3 + (0.62*Re_D^(1/2)Pr^(1/3))/(1 + (0.4/Pr)^(2/3))^(1/4)(1+(Re_D/282000)^(5/8))^(4/5)

where Nu_D is the Nusselt number for the cylinder, Re_D is the Reynolds number for the cylinder, and Pr is the Prandtl number for the air. The Reynolds number and Prandtl number can be calculated as

Re_D = rhovD/mu

Pr = Cp*mu/k

where rho is the density of air, v is the velocity of air, mu is the dynamic viscosity of air, Cp is the specific heat of air at constant pressure, and k is the thermal conductivity of air.

Substituting the expressions for Nu_D, Re_D, and Pr into the following equation gives the convective heat transfer coefficient:

h = Nu_D*k/D

Substituting the given values into the above equations, we get

Re_D = 2700200.01/1.8e-5 = 3e6

Pr = 0.71

Nu_D = 0.3 + (0.623e6^(1/2)0.71^(1/3))/(1 + (0.4/0.71)^(2/3))^(1/4)(1+(3e6/282000)^(5/8))^(4/5) = 250

h = Nu_Dk/D = 250*240/0.01 = 6e4 W/m2.K

The heat generated per unit length of the heater is given as q_gen = 2000 W/m.

Substituting the above values into the energy balance equation, we get

hA(T_s - T_inf) = q_gen

The surface area of the heater can be calculated as

A = piDL

where L is the length of the heater. Assuming a unit length of the heater, we have L=1m. Thus,

A = pi0.011 = 0.0314 m2

Substituting the values of h, A, T_inf, and q_gen into the energy balance equation and solving for T_s, we get:

T_s = T_inf + q_gen/(hA) = 27 + 2000/(6e40.0314) = 91.7°C

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The given question is incomplete, the complete question is:

A long, cylindrical, electrical heating element of diameter D = 10 mm, thermal conductivity k = 240 W/m-K, density p = 2700 kg/m3, and specific heat Cp = 900 J/kg.k is installed in a duct for which air moves in cross flow over the heater at a temperature and velocity of 27°C and 20 m/s, respectively. Neglecting radiation, estimate the steady-state surface temperature when, per unit length of the heater, electrical energy is being dissipated at a rate of 2000 W/m.

the solution to this system of equations is x=5 and y=16.

2x + 6 = 3x + 1

Subtract 2x from both sides:

6 = x + 1

Subtract 1 from both sides:

5 = x

Solve for y:

y = 3(5) + 1

y = 16

The substitution method is used to solve a system of equations by replacing one of the variables with an expression containing the other variable. In this system of equations, we have Y=3x+1 and 2x+6=y. To solve this, we start with the second equation and subtract 2x from both sides to get 6 = x + 1. Subtracting 1 from both sides gives us 5 = x. Now that we have x = 5, we can use this to solve for y. We substitute 5 for x in the first equation, giving us y = 3(5) + 1, which simplifies to y = 16. Therefore, the solution to this system of equations is x=5 and y=16.

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