Which of the following is true if the given tree diagram represents
independent events?

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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Answer:

Simple interest:

Compound interest:

Sum of the balances:

\(\sqrt{(24-0)^{2}+(10-0)^{2}}=\boxed{26}\)

Answer:

26

Step-by-step explanation:

√(24 - 0)2 + (10 - 0)2

= √(24)2 + (10)2

= √676 and that would equal

26

The final temperature is calculated to be 41.8 degrees Celcius if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa

The final temperature can be calculated by using the combined gas law as follows;

\(\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }\)

Here \(P_{1}\) and \(P_{2}\) represent the initial and final pressure respectively,

\(V_{1}\) and \(V_{2}\) represent the initial and final volume respectively

\(T_{1}\) and \(T_{2}\) represent the initial and final temperature respectively

Converting \(T_{1}\) to kelvin as follows;

\(T_{1}\) = 27 degrees Celcius = 27 + 273 = 300 K

Now the final temperature can be determined by substituting the values in this equation of the combined gas law as follows;

(0.50×10^5)(1.25) / 300 = (0.82×10^5)(0.80) / \(T_{2}\)

208.333333333 = (0.82×10^5)(0.80) / \(T_{2}\)

208.333333333 (\(T_{2}\)) = (0.82×10^5)(0.80)

\(T_{2}\) = (0.82×10^5)(0.80) ÷ 208.333333333

\(T_{2}\) = 314.8 K

Converting K to degree Celcius as follows;

\(T_{2}\) = 314.8 - 273 = 41.8 degree Celcius

Hence 41.8 degrees Celcius is calculated to be the final temperature.

Although a part of your question is incorrect, you might be referring to this question:

A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m^3. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?

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Answer:

19 cubic centimeters

Step-by-step explanation:

The equation for the volume of a sphere is \((4/3)\pi r^3\).

We can setup the equation as \(29307 = \frac{4}{3}\pi r^3\).

Now we need to isolate the r^3.  Divide both sides by 4/3 and pi, which leaves \(\frac{29307}{(4/3) \pi } =r^3\)

Now we take the cube root of both sides to have a single r on the right side.  This comes out to equal 19 cm^3

Answer:

1+1=2

2+2=4

4+3=7

7+4=11

so the patter is number + natural numbers (serially)

Step-by-step explanation:

(a)To solve the system of equations, x^2 - y^2 = 16 and x^2 - y = 7, we can use substitution or elimination method to find the values of x and y.

(b) To graph the solution set of the system of inequalities, x^2 - y^2 > 7 and x^2 - y < 0, we need to plot the boundaries and shade the appropriate regions based on the given inequalities.

(a)Let's use the substitution method to solve the system of equations:

From the second equation, we can rewrite it as x^2 = y + 7.

Substituting this value of x^2 in the first equation, we get (y + 7) - y^2 = 16.

Rearranging the equation, we have -y^2 + y + 7 - 16 = 0.

Simplifying further, we get -y^2 + y - 9 = 0.

Now, we can solve this quadratic equation for y by factoring or using the quadratic formula.

After finding the values of y, we can substitute them back into the second equation to find the corresponding values of x.

(b)To graph the solution set, we first graph the boundaries of the inequalities. For x^2 - y^2 > 7, we draw the curve of the equation x^2 - y^2 = 7, which represents a hyperbola. For x^2 - y < 0, we graph the curve of the equation x^2 - y = 0, which represents a parabola opening upwards.

Next, we need to determine which regions satisfy the given inequalities. For x^2 - y^2 > 7, the shaded region lies outside the hyperbola. For x^2 - y < 0, the shaded region lies below the parabola.

By combining the shaded regions of both inequalities, we find the solution set of the system of inequalities. It includes the regions outside the hyperbola and below the parabola. We label the corners of the shaded region to indicate the solution set accurately.

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Answer:

\(\boxed {x = \sqrt{3} - 3}\)

\(\boxed {x = -\sqrt{3} - 3}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(x^2 + 6x + 6 = 0\)

-When you use the quadratic formula ( \(\frac{-b\pm \sqrt{b^{2} - 4ac}}{2a}\) ), it would give you two solutions. So, use the quadratic formula:

\(x = \frac{-6\pm \sqrt{6^{2} - 4 \times 6}}{2}\)

-Simplify \(6\) by the exponent \(2\):

\(x = \frac{-6\pm \sqrt{6^{2} - 4 \times 6}}{2}\)

\(x = \frac{-6\pm \sqrt{36 - 4 \times 6}}{2}\)

-Multiply both \(-4\) and \(6\):

\(x = \frac{-6\pm \sqrt{36 - 4 \times 6}}{2}\)

\(x = \frac{-6\pm \sqrt{36 - 24}}{2}\)

-Add \(34\) and \(-24\):

\(x = \frac{-6\pm \sqrt{36 - 24}}{2}\)

\(x = \frac{-6\pm \sqrt{12}}{2}\)

-Take the square root of \(12\):

\(x = \frac{-6\pm \sqrt{12}}{2}\)

\(x = \frac{-6\pm 2\sqrt{3}}{2}\)

-Now solve the equation when \(\pm\) is plus, So, add \(-6\) to \(2\sqrt{3}\):

\(x = \frac{-6\pm 2\sqrt{3}}{2}\)

\(x = \frac{2\sqrt{3} - 6}{2}\)

-Divide  \(-6 + 2\sqrt{3}\) both sides by \(2\):

\(x = \frac{2\sqrt{3} - 6}{2}\)

\(\boxed {x = \sqrt{3} - 3}\) (Answer 1)

-Now solve the equation when \(\pm\) is minus. So, Subtract \(2\sqrt{3}\) from \(-6\):

\(x = \frac{-2\sqrt{3} - 6}{2}\)

-Divide \(-2\sqrt{3} - 6\) by \(2\):

\(x = \frac{-2\sqrt{3} - 6}{2}\)

\(\boxed {x = -\sqrt{3} - 3}\) (Answer 2)

Answer:

Step-by-step explanation:

 8     6     9      5    10     4     11

 1st = 3rd - 1

  3rd = 5th - 1 and so on

2nd = 4th + 1

4th = 6th + 1

6th = 8th + 1

 8th = 6th - 1

         =  4 - 1

         = 3

The probability that the life span of a randomly selected TSI Electronics monitor is more than 19,800 hours is 0.2119 (or 21.19%), given a normal distribution with a mean of 19,000 hours and a variance of 1,000,000.

We are given that the life spans of monitors manufactured by TSI Electronics follow a normal distribution with a mean of 19,000 hours and a variance of 1,000,000.

To find the probability that the life span of a monitor is more than 19,800 hours, we need to standardize the value using the standard normal distribution. The standardized value (z-score) can be calculated as follows:

z = (x - μ) / σ

where x is the value we want to standardize (19,800 hours), μ is the mean (19,000 hours), and σ is the standard deviation (square root of the variance = square root of 1,000,000 = 1000).

Substituting the given values, we get:

z = (19,800 - 19,000) / 1000 = 0.8

Using a standard normal distribution table or calculator, we can find the probability that a randomly selected monitor will have a life span more than 19,800 hours as:

P(Z > 0.8) = 0.2119 (rounded to four decimal places)

Therefore, the probability that the life span of a monitor will be more than 19,800 hours is 0.2119 (or 21.19%).

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Answer: nope there both 3

Step-by-step explanation:

National income increases, causing interest rates to increase - A) demand for loanable funds shifts outward.

Expansionary fiscal policy does not increase output, it only increases interest rates - E) the IS curve shifts outwards while the LM curve is vertical.

Nominal wages grow faster than the price level - B) real wages increase.

Firms become more confident about the future - D) the demand for money decreases and interest rates decrease.

Credit cards are introduced into the economy - C) the demand for money increases.

When national income increases, it leads to an outward shift in the demand for loanable funds, resulting in increased interest rates. This is because higher national income implies a greater demand for borrowing and investment, leading to increased demand for loanable funds.

Expansionary fiscal policy, which involves increasing government spending or reducing taxes, can lead to an outward shift in the IS curve. However, if the LM curve is vertical, it indicates that the central bank is controlling the money supply to maintain a fixed interest rate. In this case, expansionary fiscal policy will only result in increased interest rates and not increase output.

When nominal wages grow faster than the price level, it leads to an increase in real wages. Real wages refer to wages adjusted for inflation. If nominal wages increase at a faster rate than prices, it means workers have increased purchasing power, resulting in an increase in real wages.

When firms become more confident about the future, it leads to a decrease in the demand for money. Increased confidence encourages investment and spending, reducing the demand for holding money as firms are more willing to invest their funds rather than hold them.

The introduction of credit cards into the economy increases the convenience of transactions and allows individuals to easily access credit. This leads to an increase in the demand for money, as individuals require more money for transactions and credit card payments.

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Answer:

1) 8 4/5                         4) 6 2/6

2) 8 3/4                        5) 7 2/5

3) 10 1/ 3                      6) 9 2/6

Step-by-step explanation:

Here is one sampel to understand how to do it

\( 44 \div 5 \\ \frac{44}{5} \\ 8 \frac{4}{5} \)

_________________________________________

\(35 \div 4 \\ \frac{35}{4} \\ 8 \frac{3}{4} \)

_________________________________________

\(31 \div 3 \\ \frac{31}{3} \\ 10 \frac{1}{3} \)

_________________________________________

\(38 \div 6 \\ \frac{38}{6} \\ 6 \frac{2 }{6} \)

_________________________________________

\( 37 \div 5 \\ \frac{37}{5} \\ 7 \frac{2}{5} \)

_________________________________________

\( 56 \div 6 \\ \frac{56}{6} \\ 9 \frac{2}{6} \)

y equals x times 5 is the answer because 2 times 5 is 10 and so on and so forth hope this helps :D

Answer:

Step-by-step explanation:

As you move from left to right along the graph, each y-value gets larger and larger.  Therefore the y value is always increasing.  The correct answer is D.

Answer:

$3

Step-by-step explanation:

25 times 3=75

Answer:

x^4  ⋅ (x−5)⋅(3x+4)

Step-by-step explanation:

Answer:

322x

Step-by-step explanation:

if you do 3·3·3·3·3·3 you would get 729

then you would do 11·11·11·11·11 you would get 161051

finally you would do 20·20·20·20 to get 160000

finally you would subtract all those together to get 322 then you would just add the x to get the final answer of 322x

The optimal solution point that returns the maximum Z is (x₁, x₂) = (9, 3).

To find the optimal solution for the given linear programming problem, we need to evaluate the objective function Z = 10x₁ + 20x₂ at each feasible point and choose the combination (x₁, x₂) that maximizes Z.

The feasible region is defined by the following constraints:

x₁ ≤ 9

x₂ ≤ 3

x₁, x₂ ≥ 0

Let's calculate the value of Z at each feasible point:

1. (x₁, x₂) = (0, 0)

Z = 10(0) + 20(0) = 0

2. (x₁, x₂) = (0, 3)

Z = 10(0) + 20(3) = 60

3. (x₁, x₂) = (9, 3)

Z = 10(9) + 20(3) = 90 + 60 = 150

4. (x₁, x₂) = (9, 0)

Z = 10(9) + 20(0) = 90

Comparing the values of Z at each feasible point, we see that the combination (x₁, x₂) = (9, 3) yields the maximum value of Z, which is 150.

Therefore, the optimal solution point that returns the maximum Z is (x₁, x₂) = (9, 3).

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Answer: 66 2/3% decrease because you got less this week and if you do what you got this week over what you got last week then you get the percent dicrease

Step-by-step explanation:

Step-by-step explanation:

The prime factor of the 144 is 24 x 32. The exponents in the prime factorisation are 4 and 2. Add the number 1 with the exponents and multiply it. (4+1)(2+1) = 5 x 3 = 15.

Answer:

My answer is

7+9-18-19+18= -3.

The steps of finding mean and standard deviation of a simple random sample are given below.

What is standard deviation and mean?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.

The steps of finding mean and standard deviation of a simple random sample are:

Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX):  = σ/n.

How to determine sample means

Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...

Sum divided by the quantity of samples.

The outcome is the mean.

To determine the variance, use the mean.

To determine the standard deviation, use the variance.

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The second option shows a pair of triangles which are congruent by the SSS congruence theorem.

The SSS (Side - Side - Side) congruence theorem states that if two triangles have three sides that are congruent to each other, then the two triangles are congruent by the SSS theorem.

The congruent sides for the second option are given as follows:

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By applying algebra, radical and power properties, we find that the simplified form of (√5 + √6) · (√7 - √5) is equal to √35 + √42 - 5 - √30.

How to simplify a product of two binomials with radical numbers

Herein we need to apply algebra and radical and power properties to simplify the expression described in the statement, whose procedure is shown below:

(√5 + √6) · (√7 - √5)     Given

(√5 + √6) · √7 + (√5 + √6) · (- √5)     Distributive property

√7 · √5 + √6 · √7 + √5 · (- √5) + √6 · (- √5)     Distributive property

√35 + √42 - 5 - √30     (- a) · b = - a · b/ √a · √b = √a · b/Result

By applying algebra, radical and power properties, we find that the simplified form of (√5 + √6) · (√7 - √5) is equal to √35 + √42 - 5 - √30.

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Answer:

6.9

Step-by-step explanation:

Answer:

The change is a decrease of $2700.

Step-by-step explanation:

Given

Total Number of people = 27

Amount each person withdrew = $100

The total withdrawn amount by 27 people = 100 × 27

                                                                       = $2700

Let M be the amount of money in the ATM at the beginning.

As $2700 was drawn from the ATM, therefore, the change the amount of money in the machine will be:

It means the change is a decrease of $2700.

Answer: Both Technically, Look Below

Step-by-step explanation:

This is a very interesting problem they are technically both not wrong. You can choose to subtract the 6x first if you want or add 4x. Both technically work and will end up with the same value for x. Which I will show here. Although both work adding 4x can be the easier way as there is less negatives to deal with.

Adding 4x:

6x - 2 = -4x + 2

10x - 2 = 2

10x = 4

x = 4/10

x = 2/5

Subtraction 6x:

6x - 2 = -4x + 2

-2 = -10x +2

-4 = -10x

4/10 = x

2/10 = x

Answer:

Both are correct in their order of steps. In does not matter which you subtract or add as long as you are eliminating something from each side. However, in order to keep the equation positive, the most preferred step would be to add 4x.