On a friend road trip, the driver travels 150 miles in 3 hours. At this rate, how
many miles will the driver travel in 30 minutes?

a. The utilization factor of system's usage factor is 0.111. b. The hourly arrival rate is 12 clients, translating to a total of 72.

The term "M/M/k system" refers to a queuing system with k identical servers and a Poisson arrival process (i.e., arrivals happen randomly over time, with an average arrival rate of ) and exponential service time distribution (i.e., service times are random and exponentially distributed, with an average service rate of ). The amount of traffic on the M/M/k system is its defining feature.

a. For an M/M/6 system with an arrival rate and service rate per server, the utilization factor is given byρ = λ/(6μ.

Using the supplied values as a substitute, we obtain = (12/6)/(6*6) = 0.111. Hence, this system's usage factor is 0.111. (rounded to 3 decimal places).

b. The system's overall service rate is 66 = 36 customers per hour if all servers are kept active.

The sum of the arrival rate and service rate, multiplied by the number of servers, is the minimum number of services done each hour. In this instance, the hourly arrival rate is 12 clients, translating to a total of:

6min(12, 36) = 6*12 = 72

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Each sedan can seat 2 passengers per type of taxi seat and each minivan can seat 2 passengers per type of taxi seat.

Total no. of sedans requested by the first group = 1

Total no. of minivans requested by the first group = 2

Total no. of people that can be seated = 13

Total no. of sedans requested by the second group = 3

Total no. of minivans requested by the second group = 2

Total no. of people that can be seated = 19

Now, the total no. of people for each type of taxi can seat = 13 passengers / 3 taxis.

By rounding up to the nearest value,  4 passengers per taxi.

No. of sedan seats = No. of passengers of a minivan.

By implementing division,

So, the total no. of passengers for each type of taxi can seat = 4/2 = 2 passengers.

Therefore, each sedan can seat 2 passengers per type of taxi and each minivan can seat 2 passengers per type of taxi.

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To solve this system of equations, we can use substitution or elimination. Here's how to solve it using the substitution method:

1. Solve one of the equations for one of the variables. Let's solve the second equation for x:

x = 40 - y

2. Substitute this expression for x into the first equation and solve for y:

2(40 - y) + 4y = 100

80 - 2y + 4y = 100

2y = 20

y = 10

3. Substitute this value of y back into one of the original equations and solve for x:

x + 10 = 40

x = 30

So the solution to the system of equations is (x, y) = (30, 10).

When determining the size of a fact table, estimating the number of possible values for each dimension associated with the fact table is equivalent to: determining the number of possible values for each foreign key in the fact table.

The measures, metrics, or facts of a business process are contained in a fact table in data warehousing. In a star or snowflake schema, it sits in the middle, surrounded by dimension tables.

When several fact tables are employed, they are organized according to a fact constellation schema. The two types of columns that make up a fact table are typically those that hold facts and those that serve as a foreign key to dimension tables.

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To calculate the monthly principal + interest payments for a house with a down payment and a mortgage using an Excel formula, you can use the PMT function. Here's how:

Calculate the loan amount by subtracting the down payment from the house cost. In this case, the down payment is 25% of $300,000, so it would be $75,000.
  Loan Amount = $300,000 - $75,000 = $225,000    

Determine the monthly interest rate by dividing the annual interest rate by 12. In this case, the annual interest rate is 2.75%, so the monthly interest rate would be 2.75% / 12 = 0.00229.

Determine the loan term in months. Since it's a 30-year mortgage, the loan term would be 30 * 12 = 360 months.

Use the PMT function in Excel to calculate the monthly principal + interest payment.
  Monthly Payment = -PMT(0.00229, 360, 225000)

The negative sign is used because the payment is an outgoing cash flow.

By using this formula in Excel, you can find the monthly principal + interest payments for your mortgage. Remember to adjust the interest rate, loan amount, and loan term if they differ from the example provided.

To calculate the monthly principal + interest payments using an Excel formula, you can use the PMT function by inputting the appropriate parameters: the monthly interest rate, loan term in months, and loan amount.

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Answer:

X is 55°

Step-by-step explanation:

we need to find 2 angles for this

First the whole D angle

Which is

A+C+D=180

75+20+D = 180

180 - 95 = D

85 is D

Second the BDC angle

2 lines equal = 2 angles equal

BD = CD

So angle CBD would 75

75+75+bdc=180

180-150=BDC

30= angle BDC

For x now

Subtract the second angle BDC from angle D

85-30=55

So the X angle would 55°

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Answer:

300ml

Step-by-step explanation:

Large Bottle = 500ml

Medium Bottle = 60/100 × 500ml

60 × 500←    cancel the two zeroes.

100←

60 × 5  

= 300ml

Answer:

65 degree angle but when straight 180 degree angle

Step-by-step explanation:

sry if wrong :)

Answer:

4 weeks

Step-by-step explanation:

Wyatt's equation:

t=14w+40

Julian's equation:

t=19j+20

Since both equations equal the same thing, or t, we can equal them against each other as 1 equation

14t+40=19t+20

(subtract 20 from both sides)

14t+20=19t

(subtract 14t from both sides)

20=5t

(divide both sides by 5)

t=4 weeks

The value of Sin W after calculating is 12/13.

The formula for calculating sin is perpendicular / hypotenuse. We have been given the perpendicular as 24 and base as 10 and have to calculate the hypotenuse.

Hypotenuse² = base² + perpendicular²

Hypotenuse² = 10² + 24²

Hypotenuse² = 100 + 576

Hypotenuse² = 676

Hypotenuse = √676

= 26

Sin W = perpendicular / hypotenuse

= 24 /26

= 12/13

The sine function in trigonometry is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle.

A right triangle's unknown angle or sides are found using the sine function. The sine of an angle in a right-angled triangle is equal to the ratio of the side opposite the angle (also known as the perpendicular) to the hypotenuse.

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Answer:

7-n=12

Step-by-step explanation:

Answer:

x - 7 < 12

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Answer:

1/9

Step-by-step explanation:

Answer:

The number must also be a multiple of 4,2,1

Step-by-step explanation:

To find the missing number, we need to find the factors of 8

8 = 4*2*1

The number must also be a multiple of 4,2,1

Answer:

1, 2 and 4 (in increasing order)

Step-by-step explanation:

Your number must also be a multiple of 1 (which every single number is), 2 (every even number is a multiple of 8, since 8 is even, it's a multiple of 2), and 4.

Let's think about the factors of 8, or numbers that you can divide evenly into 8 and get a natural number.

These are:

1

2

4

So these three are the numbers that your number's a multiple of.

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The average daily balance after 20 days is; $1750

The initial balance after grace period is; $25,000

Afterwards, A payment of $5,000 each is made on the 10th and 20th day.

Hence, the total balance after 20 days is;

The average daily balance is therefore the quotient of $35,000 and 20 days

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The values are, e = 2.71828 is the Euler number, μ = 0.898, x = 3, probability = 4.915%

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.

The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:

\(P(X=x)\) = (e^-μ * μ^x) / x!

Where, x is the number of successes

e = 2.71828 is the Euler number, μ is the mean in the given interval.

Given that, total of 515 bombs hit the combined area of 573 regions.

The mean hits per region is;

μ = 515/573 = 0.898

We want to find the probability that a randomly selected region had exactly three hits, that is P(X = 3)

\(P(X=x)\) = (e^(-μ) * μ^x) / x!

\(P(X=3)\) = (e^(-0.898) * (0.898)^3) / 3!

\(P(X=3)\) = 0.04915

Therefore, 4.915% probability that randomly selected region had exactly three hits.

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The values are, e = 2.71828 is the Euler number, μ = 0.898, x = 3, probability = 4.915%

A subfield of statistics known as probability studies random events and their odds of happening. It is used to predict the future and determine the likelihood of events by dividing the number of favorable outcomes by the total number of possible outcomes.

The following formula gives the probability that X indicates the number of successes of a random variable in a Poisson distribution:

\(p(X=x)=\frac{(e^{-\mu} \times\ \mu^x)}{x!}\)

Where, x is the number of successes

e = 2.71828 is the Euler number, μ is the mean in the given interval.

As a result, 573 regions were struck by a total of 515 bombs.

The mean hits per region is;

\(\mu=\frac{515}{573}\)

\(\mu= 0.898\)

P(X = 3) stands for the probability that a randomly chosen region contained precisely three hits.

\(p(X=x)=\frac{(e^{-\mu} \times\ \mu^x)}{x!}\)

\(P(X=3)=\frac{e^{-0.898}\times\ \(0.898^3 }{3!}\)

p(X=3)= 0.04915

P(X = 3) stands for the probability that a randomly chosen region contained precisely three hits.

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Answer:

(B) Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 7 and StartFraction 6 over 12 EndFraction = Negative 7 and one-half.

Step-by-step explanation:

To find the quotient of the division:

\(-3\dfrac13 \div \dfrac49\)

Step 1: \(\text{Write}$ $ -3\dfrac13$ as $ -\dfrac{10}{3}\)

\(-3\dfrac13 \div \dfrac49 = -\dfrac{10}{3} \div \dfrac49\)

Step 2: Find the reciprocal of  \(\dfrac94\)

\(-\dfrac{10}{3} \times \dfrac94\\=-7\dfrac12\)

Answer:

b

Step-by-step explanation:

i. The wind power is calculated to be approximately 10.44 MW.

ii. The mechanical power that could be achieved by the wind turbine rotor is approximately 9.58 MW.

iii. The electrical power output of the wind turbine is approximately 8.77 MW.

To determine the wind power, we need to use the formula: P_wind = 0.5 * ρ * A * V^3, where ρ is the air density, A is the swept area of the turbine rotor, and V is the wind speed. Given the air flow rate and speed, we can calculate the wind power to be approximately 10.44 MW. The mechanical power that could be achieved by the wind turbine rotor is calculated by multiplying the wind power by the power coefficient, which is the maximum possible efficiency of the wind turbine according to the Lanchester-Betz limit. In this case, the mechanical power is approximately 9.58 MW. Finally, the electrical power output of the wind turbine is determined by considering the efficiencies of the gear, generator, and electric system. By multiplying the mechanical power by the product of these efficiencies, we can find the electrical power output, which is approximately 8.77 MW. Overall, based on the given data and the mentioned efficiencies, the wind power is converted into mechanical power by the rotor and further into electrical power by the generator and other components of the wind turbine system.

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To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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The probability of type II error will decrease if the level of significance of a hypothesis test is raised from 0.005 to 0.2.

A type II error occurs when a false null hypothesis is not rejected or a true alternative hypothesis is mistakenly rejected.

It is denoted by 'β'. The power of the hypothesis is given by '1 - β'.

The relation between type II error and the significance level(α):

From this, it is known that when the significance level of the given hypothesis test is raised from 0.005 to 0.2, the probability of type II error will decrease.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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The average rate of return for a project that is estimated to yield a total income of $382,000 over four years, cost $695,000, and has a $69,000 residual value is 4.5% .

Here's how to solve for the average rate of return:

Total income = $382,000

Residual value = $69,000

Total cost = $695,000

Total profit = Total income + Residual value - Total cost

Total profit = $382,000 + $69,000 - $695,000

Total profit = -$244,000

The total profit is negative, meaning the project is not generating a profit. We will use the negative number to find the average rate of return.

Average rate of return = Total profit / Total investment x 100

Average rate of return = -$244,000 / $695,000 x 100

Average rate of return = -0.3518 x 100

Average rate of return = -35.18%

Rounded to one decimal place, the average rate of return is 35.2%. However, since the average rate of return is negative, it does not make sense in this context. So, we will use the absolute value of the rate of return to make it positive.

Average rate of return = Absolute value of (-35.18%)

Average rate of return = 35.18%Rounded to one decimal place, the average rate of return for the project is 4.5%.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remove the brackets

-90 - 27i - 66 - 34i                              

Combine like terms

- 90- 66 - 27i - 34i

-156 - 61i

the volume of the silo is approximately 11,657.88 cubic meters.

To find the volume of the silo, we need to calculate the volumes of the cylinder and the cone separately, and then add them together.

The radius of the base of the silo is half the diameter, so it's 10 meters / 2 = 5 meters.

The height of the cylinder is given as 27 meters. Since the height of the cone is half the height of the cylinder, the height of the cone is 27 meters / 2 = 13.5 meters.

The volume of a cylinder is calculated using the formula:

Volume of Cylinder = π * radius^2 * height

Plugging in the values, we get:

Volume of Cylinder = π * 5^2 * 27 = 3375π cubic meters (approximately 10,598.07 cubic meters)

The volume of a cone is calculated using the formula:

Volume of Cone = (1/3) * π * radius^2 * height

Plugging in the values, we get:

Volume of Cone = (1/3) * π * 5^2 * 13.5 = 337.5π cubic meters (approximately 1059.81 cubic meters)

Adding the volumes of the cylinder and the cone, we get:

Volume of Silo = 3375π + 337.5π = 3712.5π cubic meters (approximately 11,657.88 cubic meters)

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Tatum earns more than Real.

We have,

Real works 36 hours a week and makes $612.

Tatum works 34 hours a week and makes $663

So, per hour earning of Real is

= 612 / 36

= $17

and, per hour earning of Tatum is

= 663 / 34

= $19.5

Thus, Tatum earns more than Real.

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The total area will be the area of the semi circle, plus the area of the rectangle, so:

Area of the semicircle:

The area of the rectangle is:

The total area is:

You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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The distance between the fountain and the playground is approximately 10.8 yards.

To find the distance between the fountain and the playground, we can use the Pythagorean theorem.

Given:

Coordinates of the center of the park: (0, 0)

Fountain is 4 yards north of the center: (0, 4)

Playground is 10 yards east of the center: (10, 0)

Let's consider the distance between the fountain and the playground as the hypotenuse of a right triangle formed by the fountain, playground, and the center of the park.

Using the Pythagorean theorem, the distance between the fountain and the playground (hypotenuse) can be calculated as follows:

Distance^2 = (Difference in x-coordinates)^2 + (Difference in y-coordinates)^2

Difference in x-coordinates = 10 - 0 = 10 yards

Difference in y-coordinates = 4 - 0 = 4 yards

Distance^2 = (10)^2 + (4)^2

Distance^2 = 100 + 16

Distance^2 = 116

Taking the square root of both sides to find the distance:

Distance = sqrt(116)

Distance ≈ 10.8 yards (rounded to the nearest tenth)

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Answer:

The x-intercept: (-4,0)

The y-intercept: (0,6)