If 10% of a bill is deducted, still rupees 27,000 is left to be paid. How much was the bill?

Answer:

40 and 45

Step-by-step explanation:

let the 2 numbers be x and y with y the larger of the two, then

x + y = 85 → (1)

x = y + 5 → (2)

substitute x = y + 5 into (1)

y + 5 + y = 85

2y + 5 = 85 ( subtract 5 from both sides )

2y = 80 ( divide both sides by 2 )

y = 40

substitute y = 40 into (2)

x = 40 + 5 = 45

the two numbers are 40 and 45

The most suitable data type for storing annual employee salaries ranging from $25,000 to $700,000 would be option (c) decimal(10,4).

Next, we can consider float and double data types, which can store decimal values with a higher range and precision than integers. However, they can be imprecise and cause rounding errors when used to store currency values, which can be a significant issue in financial calculations.

The most appropriate data type for storing currency values is the decimal data type, which is designed to handle decimal values with high precision and accuracy. The decimal data type can store exact numeric values up to 38 digits, with a user-defined scale (the number of digits to the right of the decimal point).

Therefore, option (c) decimal(10,4) would be the best data type for storing annual employee salaries ranging from $25,000 to $700,000.

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Complete Question:

Annual salary of each employee has to be stored in dollars and cents. The salaries vary from minimum of $25,000 to maximum of $700,000. Which of the following would be the most suitable data type?

a) decimal(8.2)

b) decimal

c) decimal(10.4)

d) Small money

e) money

To find the dimensions of the largest room that can be built with a fixed perimeter of 600 feet.

We need to divide the perimeter by 2 and use that as the sum of two adjacent sides. Let's call the length of the rectangle "l" and the width "w".
So we have:  2l + 2w = 600
Simplifying:  l + w = 300
We want to maximize the area of the rectangle, which is given by:  A = lw
We can solve for one variable in terms of the other:  l = 300 - w
Substituting into the area equation:
A = (300 - w)w
A = 300w - w^2
To maximize the area, we need to find the value of w that makes the derivative of A with respect to w equal to 0:  dA/dw = 300 - 2w = 0
w = 150
So the width of the rectangle is 150 feet. Substituting back into the perimeter equation: l + 150 = 300
l = 150
So the length of the rectangle is also 150 feet.
Therefore, the largest room that can be built has dimensions 150 ft by 150 ft, and its area is:  A = lw = 150 * 150 = 22,500 ft^2
The dimensions of the largest rectangular room a carpenter can build with a fixed perimeter of 600 feet are 150 ft by 150 ft. The area of this room is 22,500 ft². This is because when the length and width are equal, the area of the rectangle is maximized.

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The true statements about the given circle's equation are:

(B) The circle's center is on the x-axis.

(A) The circle has a radius of three units.

(E) This circle's radius matches that of the circle whose equation is x2 + y2 = 9.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, the circle's standard equation is written as:

x² + y² + 2gx + 2fy + C = 0

An equation for a circle is:

x² + y² – 2x – 8 = 0

Find the circle's center:

2gx = -2x

2g = -2

g = -1

Similarly:

2fy = 0

f = 0

Centre = (-(-1), 0) = (1, 0)

This demonstrates that the circle's center is on the x-axis.

r = radius = √g²+f²-C

radius = √1²+0²-(-8)

radius =√9 = 3 units

The circle has a radius of three units.

The radius of the circle where x2 + y2 = 9 is written as:

r² = 9

r = 3 units

As a result, this circle's radius matches that of the circle whose equation is x2 + y2 = 9.

Therefore, the true statements about the given circle's equation are:

(B) The circle's center is on the x-axis.

(A) The circle has a radius of three units.

(E) This circle's radius matches that of the circle whose equation is x2 + y2 = 9.

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Complete question:
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.

a. The radius of the circle is 3 units.

b. The center of the circle lies on the x-axis.

c. The center of the circle lies on the y-axis.

d. The standard form of the equation is (x – 1)² + y² = 3.

e. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

To make $3000 selling game tickets, the boys football team needs to sell a combination of adult and student tickets. Solving the system of equations gives the number of adult and student tickets that must be sold 150 adult tickets and 300 student tickets.

The first equation relates the number of adults and students: since there are twice as many students as adults, we can write

b = 2a

where b is the number of students and a is the number of adults.

The second equation relates the revenue from ticket sales to the number of adults and students

8a + 6b = 3000

where 8a is the revenue from adult tickets and 6b is the revenue from student tickets.

Now we can substitute the first equation into the second equation to get

8a + 6(2a) = 3000

Simplifying, we get

20a = 3000

Dividing by 20, we get

a = 150

This means we need to sell 150 adult tickets. Using the first equation, we can find the number of student tickets

b = 2a = 2(150) = 300

So we need to sell 300 student tickets.

Therefore, the boys football team must sell 150 adult tickets and 300 student tickets to reach their goal of making $3000.

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Using operations of fractions, the answer obtained is

There are 5  \(1\frac{1}{6}\) in \(5\frac{5}{6}\)

What is fraction?

Suppose there is a collection of objects and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.

The upper part of the fraction is the numerator and the lower part of the fraction is the denominator,

Let there are x  \(1\frac{1}{6}\) in \(5\frac{5}{6}\)

\(1\frac{1}{6} x = 5\frac{5}{6}\\\frac{7}{6}x = \frac{35}{6}\\x = \frac{35}{6} \times \frac{6}{7}\\x = 5\)

There are 5  \(1\frac{1}{6}\) in \(5\frac{5}{6}\)

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Answer:

SORRY HAVING BAD DAY WISH I COULD HELP

Step-by-step explanation:

The future value of $7,790 at the end of 7 periods with 8% compounded interest is approximately $13,350.69.

The future value formula is expressed as:

\(FV = P( 1 + r )^n\)

Given that:

Principal amount (initial investment) P =  $7,790

Interest rate per period r = 8%

Number of periods n = 7

The future value FV =?

First, convert R as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08

Plug these values into the future value formula above:

\(FV = P( 1 + r )^n\\\\FV = 7790( 1 + 0.08 )^7\\\\FV = 7790( 1 .08 )^7\\\\FV = \$ 13,350.69\)

Therefore, the accrued amount is $13,350.69.

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Answer:

7

Step-by-step explanation:

22=6x+1-3x

21=6x-3x

21=3x

7=x

Prove that AC=BC,

Explanation:

To prove AC = BC, we will use the properties of a perpendicular bisector. step-by-step explanation:
1. Given that C is a point on the perpendicular bisector of segment AB, we know that the bisector divides segment AB into two equal parts and is perpendicular to AB.

2. Let's label the midpoint of segment AB as M. Since C is on the perpendicular bisector, CM is perpendicular to AB. This means that angle ACM and angle BCM are both right angles (90 degrees).
3. According to the definition of a bisector, M is the midpoint of AB, so AM = MB.

4. Now, let's consider triangles ACM and BCM. We have the following congruent components:
- Angle ACM = Angle BCM (both are right angles)
- AM = MB (by definition of a bisector)
- CM = CM (common side)

5. By the Hypotenuse-Leg (HL) Congruence Theorem, which states that if the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. So, we have triangle ACM congruent to triangle BCM.
6. As the triangles are congruent, corresponding sides are congruent. Therefore, AC = BC.

So, we have proved that AC = BC when C is a point on the perpendicular bisector of segment AB.

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The derivative of f(z) is  found to be f'(z) = [z⁵+i(z²-3z²sin(1/z) - 2z cos(1/z))]/(z³+i)².

Given function:

f(z)=z⋅sin(1/z )/ z^3+i 1)

Domain of the function:

Here, we see that the denominator of the function is `z^3 + i`,

where i is the imaginary unit, and therefore never equals zero.

Hence, the domain of f(z) is all complex numbers, i.e. f(z) is defined for all z ∈ C.

2) Cauchy-Riemann equations:

Let us consider f(z) = u(x,y) + iv(x,y),

where u(x,y) is the real part and v(x,y) is the imaginary part of f(z).

The Cauchy-Riemann equations are as follows:

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

Differentiability: Now, we'll show that the function f(z) is differentiable by verifying that it satisfies the Cauchy-Riemann equations.

We have,

`f(z) = z⋅sin(1/z )/ z^3+i`.

Let us express this in terms of its real and imaginary parts, i.e.

`f(z) = u(x,y) + iv(x,y)`.

We have:

u(x,y) = x sin(1/x² + y²)/(x³ + y³)i

(x,y) = y sin(1/x² + y²)/(x³ + y³)

Using the Cauchy-Riemann equations, we get:

∂u/∂x = sin(1/x² + y²)/(x²(x³ + y³)) - 3x²y²sin(1/x² + y²)/(x⁴ + 2x²y² + y⁴)

∂v/∂y = sin(1/x² + y²)/(y²(x³ + y³)) - 3x²y²sin(1/x² + y²)/(x⁴ + 2x²y² + y⁴)

∂u/∂y = (2xy)/(x³ + y³)cos(1/x² + y²) - 3xy²sin(1/x² + y²)/(x⁴ + 2x²y² + y⁴)

∂v/∂x = (2xy)/(x³ + y³)cos(1/x² + y²) - 3x²y sin(1/x² + y²)/(x⁴ + 2x²y² + y⁴)

It can be shown that ∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x for all z ≠ 0.

Therefore, f(z) satisfies the Cauchy-Riemann equations and is differentiable at all points in its domain.

Analyticity: Since f(z) is differentiable at all points in its domain, it is analytic.

Derivative of the function: Using the quotient rule of differentiation, we get:

f'(z) = [z³+i(3z²) - (z⋅sin(1/z)(3z²-2z))]/(z³+i)²

= [z⁵+i(z²-3z²sin(1/z) - 2z cos(1/z))]/(z³+i)²

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In conclusion, the function f(x) = x^(1/lnx) is always positive and approaches 0 as x approaches 0+ and approaches 1 as x approaches ∞. The equation x^(1/lnx) = 2 has no solution.

To show that the equation x^(1/lnx) = 2 has no solution, we can analyze the properties of the function f(x) = x^(1/lnx) and examine its behavior.

Let's consider the domain of the function f(x). Since we have a logarithm in the denominator, we need to ensure that x is positive and not equal to 1, so x > 0 and x ≠ 1.

Now, let's investigate the behavior of f(x) as x approaches 0 from the positive side (x → 0+). In this case, ln(x) approaches negative infinity, and the exponent 1/ln(x) approaches 0. Therefore, f(x) approaches 0 as x approaches 0+.

Next, let's examine the behavior of f(x) as x approaches positive infinity (x → ∞). In this case, ln(x) approaches infinity, and the exponent 1/ln(x) approaches 0. Therefore, f(x) approaches 1 as x approaches ∞.

Considering the behavior of the function, we see that it is always positive (since x^(1/lnx) is positive for positive x) and approaches 0 as x approaches 0+ and approaches 1 as x approaches ∞.

Now, let's consider the equation x^(1/lnx) = 2. If such an x exists as a solution, it would mean that there is a point where the function f(x) equals 2. However, based on the behavior of the function described above, we can see that f(x) can never equal 2. Therefore, the equation x^(1/lnx) = 2 has no solution.

In conclusion, the function f(x) = x^(1/lnx) is always positive and approaches 0 as x approaches 0+ and approaches 1 as x approaches ∞. The equation x^(1/lnx) = 2 has no solution.

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Answer:19,500

Step-by-step explanation: Yw.

By Pythagorean formula and proportion formula, the length of side VW is equal to 6 units. (Right choice: C)

Herein we find a geometric system formed by two right triangles, in which two side lengths are known (WX, XY) and we need to determine the length of side VW.

Both triangles XVW and XYW are similar, where they share the same internal angles and proportional corresponding pair of sides. Then, the system is represented by following proportion formula:

XV / WX = XY / XV

XV² = XY · WX

XV = √(XY · WX)

If we know that XY = 9 and WX = 3, then the value of XV is:

XV = √27

XV = 3√3

Then, the side VW is found by Pythagorean theorem:

VW = √(WX² + XV²)

VW = √(3² + 27)

VW = 6

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The limit of the given function as x approaches negative infinity is -2/9.

To find the limit of the given function as x approaches negative infinity, we will first analyze the function:
lim (x → -[infinity]) [(1 - x - x^2) / (9x^2 - 8)]

To analyze the limit at infinity for such functions, we can consider the highest degree terms of both the numerator and the denominator. The highest degree term in the numerator is -x^2, and the highest degree term in the denominator is 9x^2.

Now, we can divide both the numerator and the denominator by 9x^2:
lim (x → -[infinity]) [(1/9x^2) - (x/9x^2) - (x^2/9x^2)] / [(9x^2/9x^2) - (8/9x^2)]
lim (x → -[infinity]) [(-1/9) + (1/x) - (1/9)] / [(1) - (8/9x^2)]

Now, as x approaches negative infinity, the terms (1/x) and (8/9x^2) will approach zero:
lim (x → -[infinity]) [(-1/9) - (1/9)] / [1]
lim (x → -[infinity]) (-2/9) / [1]
The limit of the given function as x approaches negative infinity is -2/9.

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Answer:

18

Step-by-step explanation:

Just took the test

Note that the missing probability P(A | B) =  12/25. this was solved using Bayes Theorem.

By adding new knowledge, you may revise the expected odds of an occurrence using Bayes' Theorem. Bayes' Theorem was called after the 18th-century mathematician Thomas Bayes. It is frequently used in finance to calculate or update risk evaluation.

Bayes Theorem is given as

P(A |B ) = P( A and B) / P(B)

We are given that

P(B) = 1/4 and P(A and B) = 3/25,

so substituting, we have

P(A |B ) = (3/25) / (1/4)

To divide by a fraction, we can multiply by its reciprocal we can say

P(A|B) = (3/25) x (4/1)

 = 12/25

Therefore, P(A | B) = 12/25.

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The most appropriate inference procedure for this investigation is a simple linear regression analysis.

The scientist wants to estimate the mean change in the density for each increase of 1 percent concentration of apple juice, which can be modeled by a linear equation with percent concentration as the independent variable and density as the dependent variable. By fitting a regression line to the data, the scientist can estimate the slope of the line, which represents the change in density per unit change in percent concentration. The slope will provide an estimate of the mean change in density for each increase of 1 percent concentration of apple juice, along with a measure of uncertainty in the form of a confidence interval and a p-value to test the null hypothesis that the slope is zero.

Before conducting the regression analysis, the scientist should check the assumptions of linearity, independence, normality, and constant variance. If these assumptions are not met, the scientist may need to use a different type of regression analysis or transform the data to meet the assumptions. Additionally, the scientist should check for outliers and influential observations that may affect the results of the analysis.

Overall, a simple linear regression analysis is the most appropriate inference procedure for this investigation as it allows the scientist to estimate the relationship between percent concentration and density and make predictions about the density of apple juice based on its percent concentration.

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The square foot price obtained using the national average data should be adjusted for the b) location of the project, c) the size of the facility and design fees, and d) the time of the project.

When using the national average data to calculate the square foot price for a project, it is important to consider certain factors for adjustment. Firstly, the location of the project plays a significant role in determining costs. Different regions or cities may have varying construction costs due to factors such as labour rates, material availability, and local regulations. Therefore, adjusting the square foot price based on the specific location is necessary to reflect the local market conditions accurately.

Secondly, the size of the facility and design fees can affect the overall cost per square foot. Larger facilities often benefit from economies of scale, resulting in a lower square foot price. Additionally, design fees, which include architectural and engineering costs, can vary based on the complexity and customization of the project. Adjusting the price to account for the size of the facility and design fees ensures a more accurate estimation. Lastly, the time of the project can influence construction costs. Factors such as inflation, changes in material prices, and fluctuations in labour rates can occur over time. Adjusting the square foot price to reflect the time of the project helps account for these potential cost changes. In summary, the square foot price obtained using national average data should be adjusted for the location of the project, size of the facility and design fees, and time of the project to provide a more accurate estimation of construction costs.

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When using the means national average data, it is important to adjust the square foot price for the location of the project and the size of the facility and design fees. These adjustments account for regional variations in construction costs and the specific requirements of the project, resulting in a more accurate estimate.

The square foot price obtained using the means national average data should be adjusted for the following factors: location of the project and size of the facility and design fees. The location of the project is an important factor to consider when adjusting the square foot price. Construction costs can vary significantly based on the regional differences in labour, material costs, and local regulations. For example, construction expenses are generally higher in metropolitan areas compared to rural locations due to higher wages and increased competition. Therefore, adjusting the square foot price based on the project's location helps account for these regional variations.

The size of the facility and design fees are also crucial factors to consider for adjusting the square foot price. Larger facilities often benefit from economies of scale, resulting in lower square foot costs. Additionally, the complexity of the design and the required professional fees can significantly impact the overall project cost. Adjusting the square foot price to reflect the size of the facility and design fees ensures a more accurate estimate that accounts for the specific requirements and complexity of the project.

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Answer: 240ft

Step-by-step explanation:

Width:

10(15) + 10

= 150 + 10

= 160

Length:

4(15) + 20

= 60 + 20

= 80

L x W

= 160 + 80

= 240

Answer:

X= 0 and -4

Step-by-step explanation:

disclaimer: I'm not 100% sure if this is correct

9.66, or 10 if you rounded it up

I THINK that you add 280, 800, and 80 together to get -$1160, then divide 1160 and 30 maybe. then divide your answer with 4 to get 9.66, or 10.0

I hope this helps! if not, i am deeply sorry, friend.

,SivethTheDragon

The Average Daily Balance for Julia's credit card in April is approximately $846.33.

Here, we have,

To calculate the Average Daily Balance for Julia's credit card in April, we will divide the month into four sets of days based on her purchase dates. Here's the breakdown:

Set 1: April 1 to April 9 (9 days)

The balance remains at $300 because no purchases were made during this period.

Set 2: April 10 to April 17 (8 days)

Julia makes a purchase of $250 for groceries on April 10.

Therefore, the balance for these 8 days is $300 + $250 = $550.

Set 3: April 18 to April 22 (5 days)

Julia makes a purchase of $800 for a new phone on April 18.

Therefore, the balance for these 5 days is $550 + $800 = $1350.

Set 4: April 23 to April 30 (8 days)

Julia makes a purchase of $80 for a birthday present on April 23. Therefore, the balance for these 8 days is $1350 + $80 = $1430.

To calculate the Average Daily Balance, we sum up the balances for each set of days and divide by the total number of days in April:

(9 days * $300 + 8 days * $550 + 5 days * $1350 + 8 days * $1430) / 30 days

= ($2700 + $4400 + $6750 + $11440) / 30

= $25390 / 30

= $846.33 (rounded to the nearest cent)

Therefore, the Average Daily Balance for Julia's credit card in April is approximately $846.33.

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Answer:

Substitute respective values of x into the equation.

a) When x = 0,

   (0)² + 2(0) - 1 = -1

    Ans: -1

b) When x = -2,

   (-2)² + 2(-2) -1 = 4 + (-4) - 1

                          = - 1

   Ans: -1

c) When x = 4,

   (4)² + 2(4) - 1 = 16 + 8 - 1

                        = 23

  Ans: 23

The series ∑((-1)⁽ⁿ⁻¹⁾ * 5n)/(6n) from n = 1 to infinity converges based on the alternating series test.

To test the series for convergence or divergence using the alternating series test, we need to check if the terms of the series alternate in sign and if their absolute values decrease as n increases.

The series is given by:

∑((-1)⁽ⁿ⁻¹⁾  * 5n)/(6n) from n = 1 to infinity

Let's analyze the terms of the series:

Alternating sign: The terms alternate between positive and negative because of the (-1)⁽ⁿ⁻¹⁾ factor.

Decreasing absolute values: We can simplify the terms by canceling out the common factors of 5 and 6:

((-1)⁽ⁿ⁻¹⁾  * 5n)/(6n) = (-5/6)ⁿ

The absolute values of the terms are decreasing because

|(-5/6)ⁿ| < |(-5/6)⁽ⁿ⁻¹⁾ | for all n.

Since the series satisfies the conditions of the alternating series test, namely alternating sign and decreasing absolute values, we can conclude that the series converges.

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Step-by-step explanation:

Hers your answer friend

Answer:

180 and 300

Step-by-step explanation:

We want to divide up the number 480 in a 3:5 ratio.

=> We should turn 480 into 3+5=8 portions, each portion is 480/8 = 60.

=> 480 could be divided into 2 smaller numbers that satisfy 3:5 ratio:

60x3=180 and 60x5 = 300.

Check:

180:300 ratio <=> 3:5 ratio (valid)

Hope this helps!

If a number k, is selected at random from a set of 11 consecutive even integers, the  probability that k = 10 is 1/11

One number, k , is selected at random from a set of 11 consecutive even integers.

So, the sample space is 11

We need to find the  probability that k = 10

The desirable outcome is 1

Probability = desirable outcomes/sample space

P(k = 10) = 1/11

Therefore, if a number k , is selected at random from a set of 11 consecutive even integers, the  probability that k = 10 is 1/11.

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Answer:

give me brainlist please

Step-by-step explanation:

We can use the formula for conditional probability and the formula for the probability of the union of events to find P(C).

Using the formula for conditional probability, we can find P(A|B) = P(A n B) / P(B) = 0.05 / 0.26 = 0.192

Using the formula for conditional probability again, we can find P(A|C) = P(A n C) / P(C) = 0.05 / P(C)

Since A and C are independent events, we know that P(A|C) = P(A), so we can write:

0.05 / P(C) = 0.24

Solving for P(C) we get P(C) = 0.05/0.24 = 0.208

Alternatively, we can use the formula for the probability of the union of events:

P(A u B u C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C)

We know that P(A u B u C) = 1 - P((A u B u C)^/) = 1 - 0.33 = 0.67

and we know the values of P(A), P(B), P(A n B), P(A n C), P(B n C), P(A n B n C)

We can substitute these values into the above equation to find P(C)

P(C) = 0.67 - 0.24 - 0.26 + 0.05 + 0.05 + 0.05 - 0.02 = 0.208

So P(C) = 0.208

The average waiting time in minutes is approximately 0.317 minutes.

To determine the average waiting time in minutes, we can use the queuing theory formula for average waiting time in an\($\mathrm{M} / \mathrm{M} / \mathrm{c}$\) queue:

\($$W_q=\frac{\rho^{c+1}}{c ! \cdot(1-\rho)} \cdot \frac{1}{\mu-\lambda}$$\)

Where:

\($W_q$\) is the average waiting time in the queue.

\($\rho$\) is the traffic intensity, given by $\frac{\lambda}{c \cdot \mu}$.

\($c$\) is the number of service channels (cashiers).

\($\mu$\) is the service rate (customers per hour).

\($\lambda$\)  is the arrival rate (customers per hour).

Given:

\($\lambda=85.5$\)customers per hour.

\($\mu=19$\) customers per hour.

\($c=5$\) cashiers.

First, let's calculate $\rho$ :

\($$\rho=\frac{\lambda}{c \mu}=\frac{85.5}{5 \cdot 19} \approx 0.9011$$\)

Now, let's calculate \($W_q$\) :

\($$W_q=\frac{\rho^{c+1}}{c ! \cdot(1-\rho)} \cdot \frac{1}{\mu-\lambda}\\=\frac{0.9011^{5+1}}{5 ! \cdot(1-0.9011)} \cdot \frac{1}{19-85.5} \\\approx 0.317 \text { (rounded to two decimal places) }$$\)

Therefore,the average waiting time in minutes is approximately 0.317 minutes.

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