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A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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Answer:

B is the answer because if you put in a calculation that what you get

Answer:

cos30=12/x

√3/2=12/x

x=12×2/√3=24√3/3=8√3

sin30=y/x

1/2=y/8√3

1/2×8√3=y

y=4√3

Answer:

3+2=5

5u =12

1u=2.4

2u=4.8

3u=7.2

7.2 hour = 7 hours 12 min

4.8 hour = 4 hours 48 min

assuming first person work longer than the other

so first person worked 7 hours 12 min and second person worked 4 hours 48 min

The answer after rounding is 36

The dependent variable in this case would be the total number of hot dogs needed for the cookout.

In mathematics, a variable is a symbol, usually a letter, used to represent a quantity in an equation or in a mathematical expression. It can be thought of as a placeholder that can take on different values in a given equation or expression. Variables are essential for mathematics because they allow us to explore different scenarios and solve problems.

This is dependent on the number of guests attending, which is the independent variable. Depending on how many people show up, the individual will need to adjust the amount of hot dogs to accommodate the guests.

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Angle-Angle (AA) similarity postulate,  if two angles of one triangle are congruent to two angles of another, then the triangles are similar.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.

As per the diagram,

Triangles RPQ & RST are similar since

∠P = ∠S & ∠Q = ∠T

Side - side - side (SSS) similarity theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Triangles RPQ & RST are similar since

RP/RS = RQ/RT = ST/PQ

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Answer:

Area of the plot of the land is 4840 square units.

Step-by-step explanation:

Let's draw the rectangle approximately on an x y plane. That would help us to find the length and width of the rectangle.

Answer: 4,480yd^2

Step-by-step explanation:

You have the x and y coordinates of the vertices (10, 10), (10,90), (70.5,90),  and (70.5, 10) you have the coordinates: x and y as the first two which are the ones in bold. From that you do 70.5-10= 60.5.

Then you subtract the x and y coordinates again, which are underlined. From that do 90-10=80

Last you do 60.5x80=4,840 yards squared

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The side lengths of the real object will be 50 inches and 60 inches.

The scale factor is the ratio of the actual size of the image to the new size of the image. It is used to Map the objects like if you want to increase or decrease the size without changing the original shape of the image it is done by the scale factor.

The given scale factor is 5:1, which means that the dimensions of the scale drawing are 1/5 of the dimensions of the real object.

To find the side lengths of the real object, we can use the ratio of the dimensions in the scale drawing and the real object.

For example, the length of the real object can be found by multiplying the length of the scale drawing by the scale factor:

Real object length = Scale drawing length x Scale factor

Real object length = 10 in x 5

Real object length = 50 in

Similarly, the width of the real object can be found using the same method:

Real object width = Scale drawing width x Scale factor

Real object width = 12 in x 5

Real object width = 60 in

Therefore, the side lengths of the real object are 50 inches and 60 inches.

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Answer:

823.7 m^2

Step-by-step explanation:

The ratio of the side lengths is 6/5.

The ratio of the areas is the square of the ratio of the side lengths, 36/25.

572 m^2 * 36/25 = 823.7 m^2

Answer:

The percentage of alcohol in the resulting mixture is 30%

Step-by-step explanation:

The equation given are;

Volume of added water = 1 gallon = 3.79 litres = 4 quarts

Volume of mixture of alcohol = 6 quarts = 5.68 litres

Concentration of the alcohol in 6 quarts = 50%

Given that the mixture of alcohol and water is 50% alcohol and 50% water, we  have;

Volume of 100% alcohol in 5.68 liters = 0.5× 5.68 = 2.84 litres = 3 quartz

Total volume of the final solution = 5.68 + 3.78 = 9.46 litres = 10 quarts

Percentage by volume of 100% alcohol in total volume of the resultant solution = 3 quarts/((4 + 6) quarts) × 100 = 3/10 × 100 = 30%

The percentage of alcohol in the resulting mixture = 30%.

Answer:

To put the expression in the standard form for a polynomial we need to multiply the two terms. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

Step-by-step explanation:

Answer:

10 x 3 x 5 = a

Step-by-step explanation:

(12) in base 8

= (1 * 8¹ + 2 * 8⁰) in base 10

= (8 + 2) in base 10

= 10 in base 10.

(117) in base 8

= (1 * 8² + 1 * 8¹ + 7 * 8⁰) in base 10

= (64 + 8 + 7) in base 10

= 79 in base 10.

Using octal numeral system, 12₈ number as 10₁₀ and (117)₈ number as (79)₁₀.

Octal numeral system has "a base of 8 and uses the number from 0 to 7".

According to the question,

a) (12)₈

          = (1 * 8¹ + 2 * 8⁰)₁₀

          = (8 + 2)₁₀

          = 10₁₀.

b) (117)₈

        = (1 * 8² + 1 * 8¹ + 7 * 8⁰)₁₀

        = (64 + 8 + 7)₁₀

        = (79)₁₀

Hence, using octal numeral system, 12₈ number as 10₁₀ and (117)₈ number as (79)₁₀.

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Answer:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

A = the balance after t years

P = the principal amount (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this problem, P = $6,500, r = 0.084, n = 12 (monthly compounding), and t = 12. Plugging in these values, we get:

A = $6,500(1 + 0.084/12)^(12*12)

A = $6,500(1.007)^144

A = $6,500(2.008)

A = $13,052.20

Therefore, the balance after 12 years is $13,052.20 when the interest is compounded monthly.

Answer:

3

Step-by-step explanation:

27=3^3

=3*3*3

27=27

i think it is clear &i hope it helps you

The probability that an irs auditor will catch only 2 income tax returns with illegitimate deduc-tions = 0.24

Let us assume that X be the number of returns containing illegitimate deductions in the sample.

Here, X has a hypergeometric distribution.

We need to find the probability that an IRS auditor will catch only 2 income tax returns with illegitimate deduc-tions.

Here, N = 15, r = 9, n = 5

So, P (X = 2) = (⁹C₂ × ⁶C₃) / (¹⁵C₅)

We know that the combination formula:

⁹C₂ = 9! / (2! × 7!)

     = 36

⁶C₃ = 6! / (3! × 3!)

     = 20

¹⁵C₅ = 15! / (5! 10!)

      = 3003

P (X = 2) = (⁹C₂ × ⁶C₃) / (¹⁵C₅)

              = (36 × 20) / (3003)

              = 0.24

Therefore, the required probability is: 0.24

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Answer:the answer is that if thruster b is going the opposite way it will stay in 1 place as thruster a is firing up to make the rocket fly if thruster b is going the opposite way it will just hover with that being said that's the answer

Step-by-step explanation:

The probability is approximately 0.9772, which means there is a 97.72% chance that a bulb will last for at most 620 hours. The answer is rounded to four decimal places as requested.

To find the probability of a bulb lasting for at most 620 hours, we will use the normal distribution properties. Given that the mean lifetime (μ) is 590 hours and the variance (σ^2) is 225, we can find the standard deviation (σ) by taking the square root of the variance, which is σ = √225 = 15.
Next, we'll calculate the z-score, which standardizes the value we want to find the probability for. The z-score formula is:
z = (X - μ) / σ
Where X is the value we want to find the probability for (in this case, 620 hours). Plugging in the values, we get:
z = (620 - 590) / 15 ≈ 2
Now, we need to find the probability of a bulb lasting for at most 620 hours, which is the area under the standard normal curve to the left of z = 2. You can either use a standard normal table or a calculator to find this probability.

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Answer:

not sure explain it better please

Answer:

10 2/3 or 132/13

AKA D. is the answer

Step-by-step explanation:

Brainlies please

A recent report estimates that four out of every five dentists recommend a brand of toothpaste situation involves Inferential statistics.

Inferential statistics are widely employed to compare the differences between the treatment groups. Inferential statistics compare the treatment groups and make generalizations about the subject population using data from the experiment's sample of subjects. To offer answers for a situation or phenomena, inferential statistics is helpful. It differs fundamentally from descriptive statistics, which do not allow for result extrapolations and merely report the data that has already been measured.

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Answer:

Approximately 2.04 cm in height.

Step-by-step explanation:

h=V/π r^2

H=40/π×2.5^2≈2.03718

^2 means squared

in words its height equals 40 over pi times 2.5cm squared

To find the first derivative of f(x), we need to integrate the second derivative with respect to x once.

f'(x) = ∫ f''(x) dx = ∫ x(x-a)(x-b)^2 dx

f'(x) = ∫ (x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2) dx

f'(x) = 1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C

where C is the constant of integration.

To find the second derivative of f(x), we need to differentiate f'(x) with respect to x.

f''(x) = d/dx [1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C]

f''(x) = 1 x^4 - 1(a+b)x^3 + 1(a^2+3ab+b^2)x^2 - 1ab(a+b)x + 1ab^2

f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2

Therefore, the second derivative of f is given by f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2.

The equation of the tangent line at t = 5 is y = -5x + 0. and the equation of the tangent line at t = -5 is y = 5x + 0.

To find the equation for the tangent line to the parametric curve at the points where t=5 and t=-5, we need to calculate the derivatives of x and y with respect to t.

Given the parametric equations:

x = t³ - 25t

y = 25t² - t⁴

We differentiate both equations with respect to t:

dx/dt = 3t² - 25

dy/dt = 50t - 4t³

To find the slope of the tangent line, we evaluate dx/dt and dy/dt at the specific values of t.

For t = 5:

dx/dt = 3(5)² - 25 = 75 - 25 = 50

dy/dt = 50(5) - 4(5)³ = 250 - 500 = -250

The slope of the tangent line at t=5 is m = dy/dt / dx/dt = -250 / 50 = -5.

Using the point-slope form of a linear equation (y - y₁ = m(x - x₁)), where (x₁, y₁) is a point on the line, we substitute the values of (x, y) = (t³ - 25t, 25t² - t⁴) when t = 5:

x = (5)³ - 25(5) = 125 - 125 = 0

y = 25(5)² - (5)⁴ = 625 - 625 = 0

Similarly, for t = -5:

dx/dt = 3(-5)² - 25 = 75 - 25 = 50

dy/dt = 50(-5) - 4(-5)³ = -250 + 500 = 250

The slope of the tangent line at t = -5 is m = dy/dt / dx/dt = 250 / 50 = 5.

Using the point-slope form again, we substitute the values of (x, y) = (t³ - 25t, 25t² - t⁴) when t = -5:

x = (-5)³ - 25(-5) = -125 + 125 = 0

y = 25(-5)² - (-5)⁴ = 625 - 625 = 0

Therefore, the equation of the tangent line at t = -5 is y = 5x + 0.

In both cases, the tangent lines have a slope of 5 and -5 respectively, passing through the origin (0, 0).

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Answer: The first three odd prime numbers are 3, 5, and 7. A number is a multiple of two but not three of these prime numbers if it is divisible by two of them, but not the third.

To find the number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers, we can count the number of multiples of each pair of prime numbers and subtract the number of multiples of all three prime numbers.

There are 200 multiples of 3 and 5 between 1000 and 2000 (200 numbers for each, for a total of 200 * 2 = 400). There are 133 multiples of 3 and 7 between 1000 and 2000 (133 numbers for each, for a total of 133 * 2 = 266). There are 80 multiples of 5 and 7 between 1000 and 2000 (80 numbers for each, for a total of 80 * 2 = 160). There are no multiples of all three prime numbers between 1000 and 2000.

Thus, the total number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers is 400 + 266 + 160 = 826.

Step-by-step explanation:

The length of the arc is  18.85 m.

The area of the sector is 84.82 m².

The length of the arc is calculated as follows;

L = 2πr (θ/360)

where;

The measure of the angle of the arc is calculated as follows;

π -------- 180⁰

2π/3 ------- ?

? = 120⁰

L = 2π(9) x (120/360)

L = 18.85 m

The area of the sector is calculated as follows;

A = πr² x (θ/360)

A =  π(9)² x (120/360)

A = 84.82 m²

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Answer:Evaluate: 12y+9d if y = 5 and d = 7

Step-by-step explanation:

Evaluate: 12y+9d if y = 5 and d = 7

Answer:

espanol si amego kumasta

Step-by-step explanation:

When a person is 3 feet from a street light, the length of the shadow grows at a rate of 4 feet per second.

See the figure that illustrates the in question statement, attached.

making use of the related triangle theorem;

4/y = 12/x+y

Cross multiply

4(x+y)=12y

4x+4y = 12y

4x=8y

x/y =2

x=2y

Divide the two sides of the equation by t, where dx/dt = 2 dy/dt. The speed at which the person is walking away from the street light is expressed as dx/dt 

The growth rate of the shadow's length is measured by the ratio dy/dt.

Given that dx/dt = 8ft/s

by solving,

dy/dt = 4 ft/s

Hence the rate at which the length of the shadow growing when the person is 3 feet from the street light is 4ft/s

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