The probability of finding four or more tanks in the system at any time is approximately 0.95. The probability of having 6 or more tanks in the system is approximately 0.77.
A. The utilization of the test station is calculated by dividing the average service rate (1 tank per 8 minutes) by the arrival rate (1 tank every 16 minutes). Utilization = Service rate / Arrival rate = 1/2 = 0.5 or 50%.
B. The probability that a tank has to wait in the queue prior to testing can be calculated using the queuing theory formula for the M/M/1 queue. In this case, the utilization (ρ) is 0.5. The formula for the probability of waiting in the queue (Pw) is Pw = ρ^2 / (1 - ρ) = 0.5^2 / (1 - 0.5) = 0.25 / 0.5 = 0.5 or 50%.
C. The mean time a tank spends in the queue can be calculated using Little's Law, which states that the mean number of customers in a stable system (L) is equal to the arrival rate (λ) multiplied by the mean time spent in the system (W). In this case, L = λ * W. The mean number of tanks in the queue (Lq) can be calculated using Lq = λ * Wq, where Wq is the mean time spent in the queue. Given λ = 1/16 tanks per minute and Lq = 8 tanks, we can rearrange the equation to solve for Wq: Wq = Lq / λ = 8 / (1/16) = 128 minutes / 16 = 8 minutes.
D. The mean time a tank spends in the system (queue + test) is equal to the mean time spent in the queue (Wq) plus the mean service time (1/8 tanks per minute). Therefore, the mean time in the system (Ws) is Ws = Wq + 1/μ = 8 + 1/8 = 8.125 minutes.
E. The mean number of tanks expected to be in the queue at any time can be calculated using Little's Law: Lq = λ * Wq. Given λ = 1/16 tanks per minute and Wq = 8 minutes, we can calculate Lq: Lq = (1/16) * 8 = 0.5 tanks.
F. The mean number of tanks expected to be in the system at any time can be calculated using Little's Law: L = λ * Ws. Given λ = 1/16 tanks per minute and Ws = 8.125 minutes, we can calculate L: L = (1/16) * 8.125 = 0.507 tanks.
G. The probability of finding four or more tanks in the system at any time can be calculated using the Poisson distribution formula. By summing the probabilities for four, five, and more tanks, we get 0.043.
H. The probability of having 6 or more tanks in the system can also be calculated using the Poisson distribution formula, which results in a probability of 0.002.
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What is the difference between a leg and a hypotenuse?
Answer:
Legs - the sides that form the right angle of a right triangle.
Hypotenuse - the side opposite the right angle of a right triangle.
Step-by-step explanation:
Every triangle has 3 sides.
Certain special triangle have specific names assigned to their sides.
A right triangle has one right angle and two acute angles. The two sides that form the right angle of a right triangle are called legs. The third side of the right triangle is called hypotenuse. The hypotenuse is opposite the right angle and does not help form the right angle.
Use the standard normal distribution to find P(Z < -2.33 or z > 2.33). Select one: O 9809 .7888 .0198 O 0606
The probability P(Z < -2.33 or Z > 2.33) is approximately 0.0198.
How to find the probabilitiesTo find the probability P(Z < -2.33 or Z > 2.33) using the standard normal distribution, we can calculate the individual probabilities and then add them together.
Using a standard normal distribution calculator
The value for P(Z < -2.33) is approximately 0.0099.
P(Z < -2.33), which is approximately 0.0099.
we can add the two probabilities together
P(Z < -2.33 or Z > 2.33) = P(Z < -2.33) + P(Z > 2.33)
= 0.0099 + 0.0099
= 0.0198
Therefore, the probability P(Z < -2.33 or Z > 2.33) is approximately 0.0198
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The population of a city is 100,000 and the annual growth rate is of 4.2%. Write an equation to model the population y after x years.
Answer:
y= 100,000*(1.042^x)
Step-by-step explanation:
Giving the following information:
Present Value= 100,000 people
Growth rate (g)= 4.2% per year
To calculate the future value (y) of the in any given year (x), we need to use the following formula:
y= PV*(1 + g)^x
y= 100,000*(1.042^x)
For example, for 5 years:
y= 100,000*1.042^5
y= 122,839.66 = 122,839
Solve 5/4=x/12.
x=
Please help!
Answer: x=15
Step-by-step explanation:Step 1: Cross-multiply.
5
4
=
x
12
(5)*(12)=x*(4)
60=4x
Step 2: Flip the equation.
4x=60
Step 3: Divide both sides by 4.
4x
4
=
60
4
x=15
Answer:
x=15
If the number of bacteria in a colony doubles every 46 minutes and there is currently a
population of 150 bacteria, what will the population be 92 minutes from now?
bacteria
Answer: 608
Step-by-step explanation: multiply by 2
Show, using the Mean Value Theorem, that sin xsin y ≤ x − y| for all real numbers x and y. b) Prove, using a), that sinx is uniformly continuous on R.
Using the Mean Value Theorem, sin xsin y ≤ x − y| for all real numbers x and y, sinx is uniformly continuous on R.
The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) where the derivative of the function is equal to the average rate of change of the function over [a, b].
Applying this theorem to the function f(x) = sin x on the interval [x, y], we can find a point c between x and y where the derivative of f(x) is equal to the average rate of change of f(x) over [x, y].
Since the derivative of sin x is cos x, we have cos c = (sin y - sin x) / (y - x). Rearranging the inequality, we get sin y - sin x ≤ cos c (y - x). Now, using the fact that |cos c| ≤ 1, we can rewrite the inequality as sin y - sin x ≤ |y - x|. Thus, sin xsin y ≤ x - y| for all real numbers x and y.
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The center and a point on a circle are given. Find the circumference to the nearest tenth.
center:(2, 2);
point on the circle: (−6, 5)
The circumference is about ?
Answer:
Circumference ~ 53.4
Step-by-step explanation:
Use the distance formula to get the radius of the circle. The radius is about 8.5. Now put 8.5 into the formula 2(pi)r for the Circumference. Rounding to the nearest tenth the answer is 53.4
PLEASE HELP ASAP!!!
In △PQS, m∠Q=22°, m∠S=65°, and s=176. Identify q rounded to the nearest tenth.
Using the law of sines, the value of q is: D. 72.7.
What is the Law of Sines?The law of sines is given as: sin A/a = sin B/b = sin C/c.
Thus, given △PQS, where:
m∠Q = 22°
m∠S = 65°
s = 176
Applying the law of sines, we have:
sin Q/q = sin S/s
Substitute
sin 22/q = sin 65/176
q = (sin 22 × 176)/sin 65
q = 72.7
Therefore, using the law of sines, the value of q is: D. 72.7.
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4h + 6 = 30
h =___?
Im in 7th grade and I really need help
Answer: h = 6
explanation:
first u get h by itself
4h + 6 = 30
subtract 6 from both sides
4h = 24
divide by 4 on both sides
h = 6
Answer:h=3/13
Step-by-step explanation: Subtract 6 from both sides of the equation 4h+6-6=30h-6 you simplify 4h=30h-6. Subtract 30h from both sides of the equation then you get -26h=-6 then you divide both sides of the equation by the same term -26h/-26=-6/-26 and your answer is 3/13.
PLEASE ANSWER THIS ASAP I WILL GIVE YOU 5 STARS AND BRAINLIEST
Answer:
1. d
2. c
3. b
4. f
5. a
6. e
Step-by-step explanation:
Good Luck
Trucking is considering whether to expand its service. The expansion requires the expenditure of $10,500,000 on new service equipment and would generate annual net cash inflows from reduced costs of operations equal to $3,500,000 per year for each of the next 9 years. In year 9 the firm will also get back a cash flow equal to the salvage value of the equipment, which is valued at $0.9 million. Thus, in year 9 the investment cash inflow totals $4,400,000. Calculate the project's NPV using a discount rate of 7 percent.
If the discount rate is 7 percent, then the project's NPV is
If the discount rate is 7 percent, then the project's NPV is $13,950,300.
Total expenditure = $10,500,000
Cost of operations = $3,500,000
Time = 9 years
Cash inflows = $4,400,000.
Calculating the present value (PV) of the annual net cash inflows -
[tex]PV = Cash inflow / (1 + Discount rate)^n[/tex]
[tex]PV = $3,500,000 / (1 + 0.07)^1 + $3,500,000 / (1 + 0.07)^2 + ... + $3,500,000 / (1 + 0.07)^9[/tex]
[tex]PV = $3,500,000 * [1 - (1 + 0.07)^-9] / 0.07[/tex]
= $24,450,300
Calculating the present value of the investment -
[tex]= $4,400,000 / (1 + 0.07)^9[/tex]
= $2,835,607
Calculating NPV -
NPV = PV of cash inflows - Initial investment cost
= $24,450,300 - $10,500,000
= $13,950,300
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A population of values has a normal distribution with 4 = 31.3 and o random sample of size n = 62. 18.4. You intend to draw a What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means?
The standard deviation of the distribution of sample means is approximately 2.331.
The mean of the distribution of sample means, also known as the sampling distribution mean, is equal to the population mean. In this case, the population mean (μ) is given as 31.3. Therefore, the mean of the distribution of sample means is also 31.3.
The standard deviation of the distribution of sample means, also known as the standard error, can be calculated using the formula:
Standard Error = Population Standard Deviation / √(Sample Size)
In this case, the population standard deviation (σ) is given as 18.4, and the sample size (n) is 62. Plugging these values into the formula, we get:
Standard Error = 18.4 / √(62)
Standard Error ≈ 2.331
Therefore, the standard deviation of the distribution of sample means is approximately 2.331.
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NEED HELP!! 50 points!!!
Answer: 3, The initial velocity of the rocket
Answer:
the initial velocity of the rocket
Step-by-step explanation:
Can someone plz help me
Answer:
54 sq ft
Step-by-step explanation:
6ft x 3 ft = 18 sq ft
9 ft x 4 ft = 36 sq ft
18 sq ft + 36 sq ft = 54 sq ft
The choices should be in sq ft, not in sq cm
The value of area in sq cm would be far greater than the value of area in sq ft.
please help me with this question
Simplify 3.(9.).
A. 3x
B. 27x
C. 9x
D. 2 + 7x
i think your answer is B. 27x
A ship sails 9 km due West, then 5 km due South.
Find the bearing of the ship from its initial position.
Give your answer correct to 2 decimal places.
Answer:
10.29 km
Step-by-step explanation:
Given that,
A ship sails 9 km due West, then 5 km due South.
We need to find the distance of the ship from its initial position. Let the distance be d. We can find it as follows :
[tex]d=\sqrt{9^2+5^2} \\\\d=10.29\ km[/tex]
So, the required distance of the ship from its initial position is equal to 10.29 km.
please help ·ω· pppppppllllllllllllllleeeeeeeeeeaaaaaaaassssssssseeeeeeeeee????
Answer:
x=49
Step-by-step explanation:
Is the triangle with leg lengths of 8 mm and 8 mm and a hypotenuse of length 12 mm a right triangle?
Answer:
No
Step-by-step explanation:
Use the Pythagorean Theorem to check on this.
Does 8^2 + 8^2 = 12^2? Does 64 + 64 = 144? NO. So this is not a right triangle.
Please answer correctly! I will mark you as Brainliest!
Multiply the length by width by the height/3
7 x 6 x 8/3 = 112 in^2
The answer is 112 in^2
Answer:
112
Step-by-step explanation:
3x-y=2
x+2y=3
elimination method
Answer:
x=1 and y=1
Step-by-step explanation:
see attachment
HELP ME I NEED HELP!!!
Answer: B
Step-by-step explanation:
4.2 / 0.25 = 21
0.4 · 21 = 8.4
8.4 + 2.5 = 10.9
(2x+1)^2+4x(x-1)-3+3(-4x^2
Answer:
−4x2−2
Step-by-step explanation:
someone byes 24 notebooks they each cost $1.60 what is the total cost? basicly just this: (24x$1.60)
What is the image of (-1, 7) after a reflection over the line y = x?
Answer:
(7, - 1 )
Step-by-step explanation:
Under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
(- 1, 7 ) → (7, - 1 )
Rewrite the equation below in Graphing Form:
2.
y = x2 8x + 31
Answer:
y=x^28x+31
Step-by-step explanation:
Answer: y= x 4 − 6 y = 1 x − 2
Step-by-step explanation:
Yarely ordered a skateboard. There was a discount of 40% and the original price is
$60. What is the sale price?
Does the nature of the data allow you describe the difference of the two medians as a multiple of the interquartile range? If so, what is the multiple?
Answer:
1/3
Step-by-step explanation:
From the figure, we know that the median of Amy is 40 and the median of Megan is 35.
Therefore the difference in their medians is = 40 - 35
= 5
We see that Q1 of Megan is 25 and Q3 is 40. Therefore, her interquartile range is given by Q3 - Q1 = 40 - 25
= 15
So, the difference of the medians is the multiple of the interquartile range.
So the multiple is = 5/15
= 1/3 (IQR of Megan)
Answer:
Yes, I can describe the difference of the two medians as a multiple of the interquartile range as shown below.
Step-by-step explanation:
The difference of the medians for the two data sets is 69 − 60 = 9. The interquartile ranges for the data sets are 9 ounces and 8 ounces.
This shows that the difference of the medians is about 1 times, or nearly equal to, the interquartile range of either data set.
For Genivieve, the multiple is 1:
9 = m(9)
m = 1
For Mindy, the multiple is 1.125:
9 = m(8)
m = 1.125
(This is the answer on edumentum)
help ASAP ill give brainliest
Answer:
9 students is the correct answer :(
please answer asap
i will mark brainliest
Solve for x and find the missing angle measurement.
Answer: x=17 and 98
Step-by-step explanation:
Those two angles are supplementary so just add them together and make it equal to 180.