A summary of two stocks is shown.


Name of Stock Symbol Closing Price Day 1 Closing Price Day 2 Closing Price Day 3
Metroplis, Ltd MTP 17.95 18.28 18.25
Suburbia, Inc SBR 5.63 5.88 4.98


Suppose you purchase 30 shares of Metropolis stock and 55 shares of Suburbia stock on Day 1 at the closing price. Which day, during the following two days, would be the best to sell both stocks?
Day 2 is the best by $26.75.
Day 3 is the best by $26.75.
Day 2 is the best by $23.65.
Day 3 is the best by $23.65.

Total 2.25 Gallons of Paint is required to cover each walls of Given sizes.

We have given,

l = The Length of Wall = 18 feet

h = The Height of Wall = 10 feet

Calculating the area of Single Wall,

A=l*h

A=18*10 sqft

A=180 sqft ______________(1)

(1) shows the area of a single wall. Therefore The Total area of Four walls will be,

A'=4A

A'=180*4

A'=720 sqft

Now, it is given that 1 Gallon of Paint covers 320 feet. From this data, we can calculate the total Volume of paint required by dividing the total area of walls by 320 sqft

Therefore,

V = 720/320 Gallons              ; V= Gallons of Paint Required

V=2.25 Gallons

Therefore, total 2.25 Gallons of Paint is required to cover each walls of Given sizes.

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The ratio problem of a manufacturing plant produces 917 units in 7 hours so it would take approximately 11 hours to produce 1,441 units at the same consistent production rate.

We can use a proportion to solve this problem.

Let's call the number of hours it takes to produce 1,441 units "x". We know that the plant produces 917 units in 7 hours, so we can set up the following proportion:

917 units / 7 hours = 1441 units / x hours

To solve for x, we can cross-multiply and simplify:

917 units × x hours = 7 hours × 1441 units

x = (7 hours × 1441 units) / 917 units

x ≈ 11 hours

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The probability of getting a sample mean grand prize of exactly 84 thousand dollars is 2/6, which reduces to 1/3.

The mean of the four grand prizes is (34+54+74+94)/4 = 64. Therefore, the probability of selecting two envelopes and receiving an average of exactly 84 thousand dollars is the same as the probability of selecting two envelopes and getting a sum of 168 thousand dollars (since the sum of two values divided by two is equal to their average).

There are six possible combinations of two envelopes, as stated in the question. To find the probability of getting a sum of 168 thousand dollars, we need to find the number of combinations that add up to 168. These combinations are (74,94) and (94,74). Therefore, the probability of getting a sample mean grand prize of exactly 84 thousand dollars is 2/6, which reduces to 1/3.

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Answer:

P' (5, 2 )

Step-by-step explanation:

under a translation

([tex]\frac{1}{2}[/tex] x + 3, [tex]\frac{1}{2}[/tex] y - 4 )

means half the original x- coordinate and add 3

half the original y- coordinate and subtract 4

P (4, 12 ) → ([tex]\frac{1}{2}[/tex] (4) + 3, [tex]\frac{1}{2}[/tex] (12 - 4 ) → P' (2 + 3, 6 - 4 ) → P' (5, 2 )

The standard form is y= 3x² - 16x + 132.

We have Equation,

f(x) = 3(x-8)² - 160

We know the standard form is

y= ax² + bx + c

Now, converting vertex form to standard form

y = 3(x-8)² - 160

y = 3 (x² + 64 - 16x )-60

y= 3x² + 192 - 16x -60

y= 3x² - 16x + 132

Thus, the standard form is y= 3x² - 16x + 132.

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The general solution for the second differential equation is y = [tex]e^[(1/2)x^2 + C2] - 4[/tex]

1. [tex]dy/dx = 2x/y[/tex]

Step 1: Separate variables. To do this, multiply both sides by y and divide both sides by dx:
[tex]y dy = 2x dx[/tex]

Step 2: Integrate both sides:
[tex]∫y dy = ∫2x dx[/tex]

Step 3: Evaluate the integrals:
[tex](1/2)y^2 = x^2 + C1[/tex], where C1 is the constant of integration.

Step 4: Solve for y to obtain the general solution:
[tex]y^2 = 2x^2 + 2C1\\y = ±√(2x^2 + 2C1)[/tex]

So, the general solution for the first differential equation is [tex]y = ±√(2x^2 + 2C1[/tex]).

2. [tex]dy/dx = x(y+4)[/tex]

Step 1: Separate variables. To do this, divide both sides by (y+4) and multiply both sides by dx:
[tex]dy / (y+4) = x dx[/tex]

Step 2: Integrate both sides:
[tex]∫[1 / (y+4)] dy = ∫x dx[/tex]

Step 3: Evaluate the integrals:
[tex]ln|y+4| = (1/2)x^2 + C2[/tex], where C2 is the constant of integration.

Step 4: Solve for y to obtain the general solution:
[tex]y+4 = e^[(1/2)x^2 + C2]\\y = e^[(1/2)x^2 + C2] - 4[/tex]

So, the general solution for the second differential equation is y = [tex]e^[(1/2)x^2 + C2] - 4[/tex]

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The area principle is a fundamental concept in data visualization that states that the size of a graphical element (such as a bar, a pie slice, or a bubble) should be proportional to the quantity it represents.

In other words, the area of the graphical element should accurately reflect the magnitude of the data it is displaying. This principle is particularly important when comparing quantities, as it allows the viewer to quickly and accurately perceive the relative differences between them. For example, if two bars in a bar chart have the same width but different heights, the viewer may be misled into thinking that the two quantities are closer in magnitude than they actually are.

The area principle is often applied in conjunction with other principles of good data visualization, such as using clear and simple designs, avoiding clutter, and choosing appropriate scales and units. The goal is to create visualizations that are not only aesthetically pleasing but also informative and effective in communicating the underlying data.

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There are 213,444,595,200 different ways a bus driver can pay a toll of 45 cents using only nickels and dimes.

To find the number of ways a driver can pay a toll of 45 cents using only nickels and dimes, we can use a combination of counting and multiplication principles.

First, we can list out all the possible combinations of coins that add up to 45 cents:

- 9 nickels
- 4 nickels and 5 dimes
- 3 nickels and 6 dimes
- 2 nickels and 7 dimes
- 1 nickel and 8 dimes
- 18 dimes
- 15 dimes and 1 nickel
- 12 dimes and 2 nickels
- 9 dimes and 3 nickels
- 6 dimes and 4 nickels
- 3 dimes and 5 nickels

This gives us a total of 11 different combinations.

Next, we need to calculate the number of ways each combination can be arranged. For example, the combination of 9 nickels can be arranged in 9!/(9-9)! = 1 way (since there is only one way to arrange 9 objects in a line). Similarly, the combination of 4 nickels and 5 dimes can be arranged in (4+5)!/(4!5!) = 126 ways, using the formula for permutations with repetition.

Using this method, we can calculate the number of ways each combination can be arranged and then multiply them together to get the total number of ways the driver can pay a toll of 45 cents:

- 9 nickels: 1 way
- 4 nickels and 5 dimes: 126 ways
- 3 nickels and 6 dimes: 84 ways
- 2 nickels and 7 dimes: 36 ways
- 1 nickel and 8 dimes: 9 ways
- 18 dimes: 1 way
- 15 dimes and 1 nickel: 16 ways
- 12 dimes and 2 nickels: 66 ways
- 9 dimes and 3 nickels: 84 ways
- 6 dimes and 4 nickels: 126 ways
- 3 dimes and 5 nickels: 84 ways

Total number of ways: 1 x 126 x 84 x 36 x 9 x 1 x 16 x 66 x 84 x 126 x 84 = 213,444,595,200 ways.

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Answer:

5 minutes

Step-by-step explanation:

The speed is the same, So its the ratio assuming that x minutes are required so,

[tex] \frac{640}{4} = \frac{800}{x} [/tex]

(Multiplication cross)

[tex] 640 \times = 800 \times 4[/tex]

[tex]x = \frac{800 \times 4}{640} [/tex]

Answer =

[tex]x = 5[/tex]

Hopefully this helps!! :)

please mark as brainliest! :)

The correct P-value is 0.013 and the appropriate decision is to reject the null hypothesis and conclude that there is a significant difference between treatment A and treatment B.

To determine if there is a difference between treatment A and treatment B, we can conduct a two-sample t-test assuming equal variances.

Using a calculator or software, we find that the calculated t-statistic is 3.079 and the degrees of freedom is 8. With a significance level of 0.05, the critical t-value is 2.306.

The P-value is 0.013, which is less than 0.05, indicating that there is a statistically significant difference between treatment A and treatment B.

Therefore, we reject the null hypothesis that there is no difference between the means of treatment A and treatment B, and conclude that there is a significant difference between the two treatments.

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The fallacy committed by this argument is an informal fallacy, specifically the fallacy of false analogy. The comparison between the ship of state and a ship at sea is not a valid analogy as they are not completely analogous situations.

Additionally, the premise that sailors should not protest orders from the captain does not necessarily translate to the idea that citizens should not protest presidential policies. The argument you provided commits an informal fallacy called "false analogy." This fallacy occurs when two things are compared based on a superficial similarity, but the comparison doesn't hold up under scrutiny. In this case, the comparison between a ship at sea and the ship of state is used to argue that citizens shouldn't protest presidential policies, but the two situations are not directly comparable in terms of authority and dissent.

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Answer:

The answer is 120 seconds

Step-by-step explanation:

1 minutes---->60 seconds

2 minutes---->x seconds

x×1=2×60

x seconds =120 seconds

Answer:

120 seconds

Step-by-step explanation:

60 seconds per minute

60×2= 120 seconds

Answer: The answer is Does it have same matching sides, is it congruent. This is how we will know if it's a square.

Step-by-step explanation: Please give Brainlist.

Hope this helps!!!!

I can answer more questions.

We can find the probabilities of ever transiting from states 4, 5, and 6 to a transient state by looking at the fourth, fifth, and sixth rows of F, respectively.

To find the mean time spent by the Markov chain in any transient states of the chain which starts at any transient state, we need to first identify the transient states. In this case, we can see that states 1, 3, and 7 are transient states since there is a non-zero probability of reaching an absorbing state (states 4, 5, and 6) from these states.

Next, we need to find the expected time spent in each of the transient states before reaching an absorbing state. We can set up a system of equations to solve for these expected times using the fact that the expected time spent in a state is equal to 1 plus the sum of the expected times spent in each possible next state, weighted by their transition probabilities.

For example, for state 1, we have:

E(T1) = 1 + 0.5E(T2) + 0.25E(T3)

where E(Ti) is the expected time spent in state i before reaching an absorbing state.

Similarly, for state 3, we have:

E(T3) = 1 + 0.4E(T2) + 0.2E(T4)

And for state 7, we have:

E(T7) = 1 + 0.2E(T5) + 0.5E(T6)

Solving these equations, we get:

E(T1) = 5

E(T3) = 5.5

E(T7) = 4

Therefore, the mean time spent by the Markov chain in any transient state is:

(E(T1) + E(T3) + E(T7))/3 = (5 + 5.5 + 4)/3 = 4.83

To find the probability that the Markov chain will ever transit to one of the transient states starting from another transient state, we can use the concept of fundamental matrix. The fundamental matrix F is defined as the matrix (I-Q)^-1, where Q is the submatrix of P consisting of the transition probabilities between transient states.

In this case, we have:

Q = [0 0.25 0.2;

0.4 0 0.2;

0.2 0.2 0]

Using a calculator or software to calculate the inverse of (I-Q), we get:

(I-Q)^-1 = [1.25 0.625 1;

0.625 1.25 1;

1 1 1.5]

The (i,j)-th entry of F represents the expected number of times the Markov chain will visit state j starting from state i before reaching an absorbing state. Therefore, the probability of ever transiting to a transient state starting from another transient state is simply the sum of the corresponding entries in F.

For example, to find the probability of ever transiting from state 2 to a transient state, we look at the second row of F:

[0.625 1.25 1]

The sum of these entries is 0.625 + 1.25 + 1 = 2.875, so the probability of ever transiting from state 2 to a transient state is 2.875.

Similarly, we can find the probabilities of ever transiting from states 4, 5, and 6 to a transient state by looking at the fourth, fifth, and sixth rows of F, respectively.

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NORMDIST calculates the probability of a value being within a certain range of a normal distribution curve using mu and sigma.

The NORMDIST command is a function in Excel that calculates the probability of a value being within a certain range of a normal distribution curve. The command requires four parameters: X, Mu, Sigma, and true. X is the value for which you want to find the probability, Mu is the mean of the distribution, Sigma is the standard deviation of the distribution, and true specifies whether you want to calculate the cumulative distribution (true) or the probability density function (false).

The Sigma parameter is a measure of the variability or spread of the distribution. A higher value of Sigma indicates a wider spread of the distribution, whereas a lower value of Sigma indicates a narrower spread of the distribution. In other words, Sigma represents the average distance of the data points from the mean of the distribution.

Overall, the NORMDIST command can be used to determine the likelihood of an event occurring within a given range of a normal distribution curve, which can be useful in various fields such as finance, statistics, and science.
The NORMDIST command in Excel is a statistical function that calculates the probability density of a given value "X" in a normal distribution with a specified mean "Mu" and standard deviation "Sigma." The syntax for the function is NORMDIST(X, Mu, Sigma, true). Here's a step-by-step explanation:

1. X: This is the value for which you want to find the probability in the normal distribution.
2. Mu: This is the mean (average) of the normal distribution.
3. Sigma: This is the standard deviation of the normal distribution, representing the spread or dispersion of data.
4. true: This parameter indicates that you want to calculate the cumulative probability, which is the probability that a random variable from the distribution is less than or equal to X.

When you input the values for X, Mu, Sigma, and set the last parameter to true, Excel will calculate the cumulative probability of the value X occurring in a normal distribution with the specified mean and standard deviation.

For example, if you want to find the probability of a value (X) being less than or equal to 75 in a normal distribution with a mean (Mu) of 70 and a standard deviation (Sigma) of 10, you would use the formula: =NORMDIST(75, 70, 10, true). Excel will then calculate the cumulative probability and provide the result.

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To calculate real interest rates, you need to take into account inflation. The formula for real interest rate is: Real interest rate = Nominal interest rate - Inflation rate.

To calculate nominal interest rates, you simply divide the interest rate by 100 and multiply it by the principal amount. For example, if the nominal interest rate is 5% and you put $100 in the bank, you would earn $5 in interest ($100 x 0.05).

To calculate real interest rates, you need to take into account inflation. The formula for real interest rate is:

Real interest rate = Nominal interest rate - Inflation rate

For example, if the nominal interest rate is 5% and the inflation rate is 2%, the real interest rate would be 3% (5% - 2%). This means that your $100 in the bank would earn $3 in real terms after accounting for inflation.

In summary, to calculate nominal interest rates, simply multiply the principal by the interest rate, while to calculate real interest rates, subtract the inflation rate from the nominal interest rate.

Nominal interest rate is the rate at which you earn interest on your deposit without accounting for inflation. Let's assume you deposit $100 in a bank that offers a 5% annual nominal interest rate. To calculate the interest earned in one year, you would use the following formula:

Interest earned = Principal amount x Nominal interest rate
Interest earned = $100 x 0.05
Interest earned = $5

Now, to calculate the real interest rate, you need to consider the inflation rate. The real interest rate is the nominal interest rate adjusted for inflation, and it provides a more accurate representation of the true return on your investment. To calculate the real interest rate, use the Fisher equation:

Real interest rate ≈ Nominal interest rate - Inflation rate

Assuming the annual inflation rate is 2%, you would calculate the real interest rate as follows:

Real interest rate ≈ 0.05 - 0.02
Real interest rate ≈ 0.03 (or 3%)

So, in this example, your real interest rate is 3%, which takes into account the effects of inflation on your $100 deposit.

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Answer:250

Step-by-step explanation: A circle is 360 degrees.

1. 60+30+x+20=360

2.60+30=90

3.90+x+20=360

4. 360-90=270

5.x+20=270

6.270-20=250

7.x=250

I'm just an algebra student so I'm not completely reliable.

The Ways to use coordinates to prove quadrilaterals are parallelograms, rectangles, rhombi, or squares are listed below:

Here are some ways to use coordinates to prove quadrilaterals are parallelograms, rectangles, rhombi, or squares:

Parallelogram: To prove that a quadrilateral is a parallelogram using coordinates, you need to show that both pairs of opposite sides are parallel.

Rectangle: To prove that a quadrilateral is a rectangle using coordinates, you need to show that it is both a parallelogram and that it has four right angles.

Rhombus: To prove that a quadrilateral is a rhombus using coordinates, you need to show that it is both a parallelogram and that it has four congruent sides.

Square: To prove that a quadrilateral is a square using coordinates, you need to show that it is both a rectangle and a rhombus.

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The value of angle x is 70⁰.

The value of angle x is calculated by applying intersecting chord theorem.

The intersecting chord theorem states that for two chords intersecting at the center of the circle, the angle formed by the intersection of the two chords is equal to the arc angle subtended at the circumference.

The value of the angle adjacent to angle x is calculated as follows;

∠QON = arc angle QN

∠QON = 110⁰

The value of angle x is calculated as;

x + ∠QON  = 180

x = 180 - ∠QON

x = 180 - 110⁰

x = 70⁰

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Answer:

2/5

Step-by-step explanation:

add 4 + 6 +5

=15

black =6

possible outcomes / total number of outcomes

6 / 15

simplifies to 2/5

To speak to the circumstance depicted, able to type in the taking after imbalance: h ≥ 50 inches, where h speaks to the stature of the individual who needs to ride the rollercoaster. Her companion does not meet the tallness confinement since her tallness is less than 50 inches.

To change over Sarah's stature to inches, we are able to utilize the reality that 1 foot is break even with 12 inches. So, Sarah's stature in inches is:

4 feet × 12 inches/foot + 6 inches = 48 inches + 6 inches = 54 inches Sarah meets the tallness confinement since her tallness is more noteworthy than or breaks even with 50 inches. On the other hand, her friend's tallness in inches is:

4 feet × 12 inches/foot + 2 inches = 48 inches + 2 inches = 50 inches

thus, Her companion does not meet the tallness confinement since her tallness is less than 50 inches. 

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The equations of the graph from the figure are y = 4 and y = -2

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we can see that

We have two horizontal lines that pass through the points y = 4 and y = -2

This means that the equations represented on the graph are y = 4 and y = -2

So, we can conclude that none of the options are true from the options

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The probability that a student is a science major given that they are science student would be = 0.18.

To calculate the probability of the science major graduate student would need the use of the formula given below;

Probability = possible outcome/sample space

The possible outcome = 188

The sample space = 1073

The probability = 188/1073 = 0.18

Therefore, the probability that a student who is a graduate science student would be chosen at random would be = 0.18.

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The mathematical term for raising a number to the power of 2 is called squaring.

When we square a number, we multiply it by itself. For example, if we square the number 4, we get 16 because 4 multiplied by 4 is 16.

We can represent squaring using the exponent notation. The number being squared is the base, and the power, which is always 2, indicates how many times the base is being multiplied by itself. So, 4 squared can be represented as [tex]4^{2}[/tex].

Squaring is a fundamental operation in mathematics and has many applications in different fields, including physics, engineering, and finance. It is commonly used in geometry to calculate the area of a square or rectangle. For instance, if we have a square with a side length of 5 units, we can find its area by squaring the side length: A = [tex]5^{2}[/tex] = 25 square units.

Squaring is also used in statistics to calculate the variance of a data set. The variance measures the spread of the data from the mean, and it is calculated by squaring the difference between each data point and the mean, summing up these squares, and dividing by the number of data points.

In conclusion, squaring is the mathematical term used to describe the operation of raising a number to the power of 2.

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To determine whether the ball clears the fence, we need to find its maximum height and horizontal distance traveled.

First, we can use the given initial velocity and angle to find the vertical and horizontal components of the ball's velocity:

Vertical velocity = 120 sin(30) = 60 ft/sec
Horizontal velocity = 120 cos(30) = 103.9 ft/sec

Next, we can use kinematic equations to find the time it takes for the ball to reach its maximum height:

Vertical displacement = (60t) - (16t^2) = 4
Simplifying this equation, we get:
-16t^2 + 60t - 4 = 0

Solving for t using the quadratic formula, we get:
t = 0.961 sec

We can then use this time to find the maximum height reached by the ball:
Vertical displacement = (60 x 0.961) - (16 x 0.961^2) = 56.5 ft

Now, we can find the horizontal distance traveled by the ball during this time:
Horizontal displacement = 103.9 x 0.961 = 99.8 ft

Adding this horizontal displacement to the distance from home plate to the fence (350 ft), we get:
Total horizontal distance = 350 + 99.8 = 449.8 ft

Therefore, the ball does clear the 30-ft fence, since it travels a total distance of 449.8 ft before landing.

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We know that the double-angle formula for cosine is: cos(2x) = 2cos²(x) - 1. So, we can rewrite the given identity as: (2cos²(x) - 1) - cos

To use a half angle or reduction formula to fill in the blanks in the identity below:

(Cos(2x)) - Cos(x) = -2*(sin((3x)/2))^2

We can use the following reduction formula for cosine:

cos(2x) = 2cos^2(x) - 1

Substituting this into the identity above gives:

2cos^2(x) - 1 - cos(x) = -2*(sin((3x)/2))^2

Next, we can use the half angle formula for sine:

sin((3x)/2) = ±sqrt[(1 - cos(3x))/2]

Substituting this into the equation above gives:

2cos^2(x) - 1 - cos(x) = -2*(1 - cos(3x))/2

Simplifying further gives:

2cos^2(x) - 1 - cos(x) = -1 + cos(3x)

Finally, rearranging the terms gives the desired identity:

cos(2x) - cos(x) = -2*(sin((3x)/2))^2
Hello! I'd be happy to help you with your question. Using the half-angle formula, we can fill in the blanks in the identity:

The given identity is: (cos(2x))? - cos

We know that the double-angle formula for cosine is: cos(2x) = 2cos²(x) - 1

So, we can rewrite the given identity as: (2cos²(x) - 1) - cos

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The probability that the total sick-leave for the next month will be less than 150 hours is approximately 0.0062.

The amount of sick-leave time that must be budgeted for next month to exceed with a probability of 0.1 is approximately 225.6 hours.

a) To find the probability that the total sick-leave for the next month will be less than 150 hours, we need to standardize the value using the formula z = (x - mean) / standard deviation. Here, x = 150, mean = 200 and standard deviation = sqrt(variance) = sqrt(400) = 20.

So, z = (150 - 200) / 20 = -2.5

Using a standard normal distribution table or calculator, we can find the probability that a standard normal variable is less than -2.5 is 0.0062.

b) Let x be the amount of sick-leave time to be budgeted for next month. We need to find the value of x such that the probability of the total sick-leave exceeding x is 0.1 or 10%.

Using the same formula as above, we standardize x as z = (x - mean) / standard deviation. Here, mean = 200 and standard deviation = 20.

We need to find the z-value such that the area to the right of z in the standard normal distribution table is 0.1. From the table, we find that the z-value is approximately 1.28.

So, 1.28 = (x - 200) / 20

Multiplying both sides by 20, we get:

x - 200 = 25.6

x = 225.6

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The height of the pile is increasing at a rate of approximately 0.397 feet per minute when the pile is 20 feet high.

To solve this problem, we need to use related rates. Let's start by drawing a diagram:

```
        /\
       /  \
      /    \
     /      \
    /        \
   /__________\
```

We know that the rate at which gravel is being dumped is 50 cubic feet per minute, so the volume of the pile is increasing at a rate of 50 cubic feet per minute. We also know that the base diameter and height of the cone are always equal, so we can call them both "r".

Let's use the formula for the volume of a cone to relate the rate of change of the volume to the rate of change of the height:

V = (1/3)πr^2h

Taking the derivative with respect to time t, we get:

dV/dt = (1/3)π(2rh)(dh/dt) + (1/3)πr^2(dh/dt)

Simplifying and plugging in the values we know:

50 = (1/3)π(2r*20)(dh/dt) + (1/3)πr^2(dh/dt)

Simplifying further:

50 = (2/3)πr^2(dh/dt)

dh/dt = 50/[(2/3)πr^2]

We still need to find the value of "r" in order to calculate the final answer. We know that the base diameter and height are equal, so the radius is half of the base diameter, which is also equal to the height. Therefore, when the pile is 20 feet high, the radius is also 20 feet.

Plugging in the values:

dh/dt = 50/[(2/3)π(20^2)]

dh/dt ≈ 0.397 feet per minute

Therefore, the height of the pile is increasing at a rate of approximately 0.397 feet per minute when the pile is 20 feet high.

Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute, forming a right circular cone with equal base diameter and height. When the pile is 20 feet high, let's find out how fast the height is increasing.

Since the base diameter and height are always equal, the radius of the cone base (r) is half the height (h). Therefore, r = h/2. The volume (V) of a cone is given by the formula V = (1/3)πr^2h.

Substitute r with h/2: V = (1/3)π(h/2)^2h.

Now differentiate both sides with respect to time (t) to find dV/dt and dh/dt (rate of height increase):

dV/dt = (1/3)π (h^3/4) dh/dt.

We know dV/dt is 50 cubic feet per minute, and we want to find dh/dt when h = 20 feet:

50 = (1/3)π (20^3/4) dh/dt.

Now, solve for dh/dt:

dh/dt = 50 / [(1/3)π(20^3/4)].

dh/dt ≈ 0.424 ft/min.

So, the height of the pile is increasing at approximately 0.424 feet per minute when the pile is 20 feet high.

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Answer:

The total gain is $212.44

Step-by-step explanation:

First, we need to calculate the total cost of purchasing 60 shares of stock:

60 shares * $61.83/share = $3,709.80

Next, we need to calculate the total amount received from selling the 60 shares:

$3,992.10

We need to subtract the brokerage fee, which is 1.75% of the total amount received: 0.0175 * $3,992.10 = $69.81

The total amount received after paying the brokerage fee is:

$3,992.10 - $69.81 = $3,922.29

The gain or loss is the difference between the total amount received and the total cost of purchasing the stock:

$3,922.29 - $3,709.80 = $212.49.