Answer:
1.20, 10.8
Step-by-step explanation:
d = n^2 - 12n + 43
d = 30
30 = n^2 - 12n + 43
0 = n^2 - 12n + 13
now solve for n using quadratic formula:
a=1, b=-12, c=13
n = (-b +- sqrt( b^2 -4ac))/2a
two answers ( one for + the square root, one for - the square root)
n = 1.20, n = 10.8
Automobiles arrive at the drive-through window at a post office at the rate of 7 every 10 minutes. The average service time is 7 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. (Note: the given equations are NOT necessarily in the correct order.) What is the average time a car is in the system?Formulas for 13.17 What is the average number of cars in the system? What is the average time cars spend waiting to receive service? What is the average number of cars in line behind the customer receiving service? What is the probability that there are no cars at the window? What percentage of the time is the postal clerk busy? What is the probability that there are exactly two cars in the system?
Answer:
1) the average time a car is in the system is 0.1587 min
2) the average number of cars in the system 0.1111
3) the average time cars spend waiting to receive service is 0.01587 min
4) the average number of cars in line behind the customer receiving service is 0.01111
5) the probability that there are no cars at the window is 0.9
6) the percentage of time that the postal clerk is busy is 10%
7) the probability that there are exactly two cars in the system is 0.1217
Step-by-step explanation:
Given that;
Arrival rate λ = the rate of 7 every 10 minutes = 7/10 = 0.7
Average service time μ = 7 minutes
The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.
1) What is the average time a car is in the system?
Average in the system W = 1 / (μ - λ)
= 1 / (7 - 0.7) = 1 / 6.3 = 0.1587 min
therefore the average time a car is in the system is 0.1587 min
2) What is the average number of cars in the system?
Average number of cars L = λ / (μ - λ)
= 0.7 / (7 - 0.7) = 0.7/6.3 = 0.1111
Therefore the average number of cars in the system 0.1111
3) What is the average time cars spend waiting to receive service?
Average time spend waiting for services Wq = λ / μ(μ - λ)
= 0.7 / 7(7 - 0.7) = 0.7/44.1 = 0.01587 min
Therefore the average time cars spend waiting to receive service is 0.01587 min
4) What is the average number of cars in line behind the customer receiving service?
average number of cars in line behind the customer receiving service
Lq = λ² / μ(μ - λ) = (0.7)² / 7(7 - 0.7) = 0.49 / 44.1 = 0.01111
Therefore the average number of cars in line behind the customer receiving service is 0.01111
5) What is the probability that there are no cars at the window?
probability that there are no cars at the window = 1 - (λ / μ)
= 1 - (0.7 / 7) = 1 - 0.1 = 0.9
Therefore the probability that there are no cars at the window is 0.9
6) What percentage of the time is the postal clerk busy?
percentage of the time is the postal clerk busy = (λ / μ)
= (0.7 / 7) = 0.1 ≈ 10%
Therefore the percentage of time that the postal clerk is busy is 10%
7) What is the probability that there are exactly two cars in the system?
the probability that there are exactly two cars in the system = (λ²e^-λ) / 2!
= (0.7²e^-0.7) / 2! = 0.2433 / 2 = 0.1217
Therefore the probability that there are exactly two cars in the system is 0.1217
evaluate this expression c^2 + d^3
Answer:
The expression is not factorable.
Step-by-step explanation:
Mr. Chen is buying cookies for the teachers and staff at Liberty Middle School. Each box contains 10 chocolate chip, 6 peanut butter, and 4 oatmeal raisin cookies. If there were 30 total peanut butter cookies, how many chocolate chip cookies did he buy? chocolate chip cookles
Answer:
50 chocolate chip cookies
Step-by-step explanation:
30÷6=5
(5x+3) - (2x-6) i need help ? ToT
Answer:
3x + 9
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
(5x + 3) - (2x - 6)
Step 2: Simplify
Distribute negative: 5x + 3 - 2x + 6Combine like terms (x): 3x + 3 + 6Combine like terms (Z): 3x + 9please help. as soon as possible would be great thank you
Which equation represents the line whose slope is 2 and y-intercept is 6? a. 2y + 6x = 0 b. y = 6x + 2 c. y = 2x + 6 d. y + 2x = 6
Answer:
c. y=2x+6
Step-by-step explanation:
In slope intercept for (y=mx+b) m is the slope and b is the y-intercept.
A plant has a height of 8 1/4 inches. What is the height of the plant after it grows 1 7/8 inches?
What fraction best represents 5x2/3
Answer:
Maybe 5 2/3
Step-by-step explanation:
What could be the approximate value of the
correlation coefficient for the accompanying scatter
plor?
-X
1) -0.85
2) -0.16
3) 0.21
4) 0.90
Answer:
Step-by-step explanation:
The expression -25t+1250 represents the volume of liquid of a container after t seconds. The expression 50t+250 represents the volume of liquid of another container after t seconds. What does the equation -25t+1250=50t+250 mean in this situation?
Answer:
t = 13.33 second
Step-by-step explanation:
Given:
Equation first -25t+1250
Equation second 50t+250
Computation:
-25t+1250=50t+250
75 t = 1,000
t = 13.33 second
Means in t (13.33) second both container have same amount of liquid
The lines represented by the equations 2y + 5x = –2 and y
- x + 3 are
parallel
Submit Answer
neither parallel nor perpendicular
perpendicular
the same line
Answer:
you should use desmos graphing. When you get there in the top left corner there are 3 lines. press that and scroll down. when you see sarcastic linear regression press that and put the coordinates points I hope this helped :))
Given the problem below what mistake did Bob make in solving the equation? Bob and his friends paid $30 for 3 sandwiches and and 3 bottles of water.
-Each sandwich cost the same amount.
-The bottles of water cost $1.50 each.
The equation 3(x + 1.50) = 30 can be used to determine x, the cost of each sandwich. Bob solved the equation using these steps: 3(x + 1.50) =30
3x + 1.50 = 30
3x = 28.50
x = 9.50
Answer:
Bob forgot to distribute 3 to 1.50 in the parentheses
Step-by-step explanation:
Bob made the mistake in his first step.
In the equation 3(x + 1.50) = 30, the 3 has to be distributed to both x and 1.50.
But, Bob only distributed it to x, which led him to get the wrong answer.
So, Bob's mistake when solving was that he forgot to distribute the 3 to 1.50
Don't worry gotten it
Answer:
Step-by-step explanation:
Ok :)
Bob is going on a bike ride. He rides for 7 hours for a total of 105 miles. How fast did he ride?Immersive Reader
(1 Point)
15 miles per hour
735 miles per hour
0.066 miles per hour
Answer:
15 miles per hour.
Step-by-step explanation:
105/7=15
PLZ HELP!! ITS ALMOST DUE!! ILL MARK BRAINLIEST!!
Answer: $32.74
Is your answer
Glad I could help!
Step-by-step explanation:
A 13-ounce box of cereal sells for $3.25. An 18-ounce box of cereal sells for $3.60. Which statement describes the difference in the unit prices of the two boxes of cereal?
A. The 13-ounce box is 5 cents cheaper per ounce.
B. The 13-ounce box is 7 cents cheaper per ounce.
C. The 18-ounce box is 5 cents cheaper per ounce.
D. The 18-ounce box is 7 cents cheaper per ounce.
Answer:
its c
Step-by-step explanation:
Reilly, Maria, and Tamara figured out that the ratio of the times they spent painting a deck is 3:5:1. They are going to use this ratio to share the $36.90 they earned. How much will Maria get?
A rental car company charges $68.80 per day to rent a car and $0.08
for every mile driven. Paisley wants to rent a car, knowing that:
• She plans to drive 325 miles.
• She has at most $370 to spend.
Write and solve an inequality which can be used to determine d, the
number of days Paisley can afford to rent while staying within her
budget.
Answer:
5 days maximumStep-by-step explanation:
Given
Daily charge = $68.80Charge per mile = $0.08Target distance = 325 milesMoney limit = $370Required inequality:
68.8d + 325*0.08 ≤ 370Solving for d:
68.8d + 26 ≤ 37068.8d ≤ 344d ≤ 344/68.8d ≤ 5Up to 5 days is the answer
Determine which of the four postulates, if any, can be used to prove that the triangles are congruent.
50 points
The red lines mean the sides with the lines are the same. The red arc means those angles are the same.
Using that information you know the angle where the two same sides connect would also be the same.
So you have one side (S) and 2 angles (A) that are identical.
You can use B. ASA
Answer:
I think it is B.
Step-by-step explanation:
Hope this helped have an amazing day!
Which set of ordered pairs represents y as a function of x ?
F {(0,0), (-1,2), (-1,-2), (-2,4), (-2,-4)}
G {(0,0), (1,1), (2,4), (3,9), (3,16)}
H {(0,0), (0,1),(0,2), (0,-1), (0, -2)}
J {(0,0), (-1,-0.5), (-2,-1), (-3,-1.5), (-4,-2)}
Graph f(x) = 4[x] +5.
Answer:
See image for reference
Step-by-step explanation:
Answer:
Its b
Step-by-step explanation:
1. Place a _____________ on the number line for the number in the expression.
Answer:
the answer is a equation
Step-by-step explanation:
because u supposed to make it a equation in order for it to be a expression.
hope you get it right!!!!!!!!
–5x+4-x-1
10 points I’ll mark brainliesr I need asap
-5x+4-x-1
combine the like terms first
-5x-x+4-1
-5x-x=-6x
+4-1=3
answer:
-6x+3 or 3-6x
Answer:
-6x+3
Step-by-step explanation:
-5x+4-x-1
(-5x-x)+(4-1)
-6x+3
You run around the perimeter of a baseball field at a rate of at most 12 feet per second. Which of the following are possible amounts of time that it takes you to run around the baseball field?
Answer: 79 seconds.
Step-by-step explanation:1) we have to calculate the lenght of the baseball field.
perimeter of the baseball field=2(radius)+lenght of a semicircle.
2(radius)=2(175 ft)=350 ft
lenght of a semicircle=40% of a circumference=(40/100)(2πr)
Perimeter of the baseball field=2(175 ft) + (40/100)(2π175 ft)=
=350 ft + 140π ft=350 ft + 439.82 ft=789.82 ft,
2)Now, we calculate the amounts of time that it takes you to ruan arount the baseball field.
10 ft------------------------1 second
789,82 ft----------------- x
x=(789.82 ft * 1 second) / 10 ft=78.98 s≈79 s
Guys please help me its really important i only have a bit of time
Answer:
B
A
Step-by-step explanation:
Use the graph to find the amplitude and period.
Notice amplitude is the absolute value of the number in front of either sin or cos
please give a heart for thanks :)
WHAT IS 5/6 TIMES 15
Answer:
12.5
Step-by-step explanation:
it's the awnser. I need to explain why
4.
IF AABD
ACBE, find the value of x.
27 cm
12 cm
SE
E
23.4 cm
Answer:
[tex] x = 10.4 [/tex]
Step-by-step explanation:
Since ∆ABD is similar to ∆CBE, therefore, the ratio of their corresponding side lengths would be equal to each other. Thus:
[tex] \frac{BD}{BE} = \frac{AD}{CE} [/tex]
BD = 12 cm
BE = x
AD = 27 cm
CE = 23.4 cm
Plug in the values
[tex] \frac{12}{x} = \frac{27}{23.4} [/tex]
Cross multiply
[tex] x \times 27 = 23.4 \times 12 [/tex]
[tex] 27x = 280.8 [/tex]
Divide both sides by 27
[tex] x = 10.4 [/tex]
Which of the following is equal to 16.4 ?
O A. 32
O B. V16.4
O c.
D. 64
Answer:
b?
Step-by-step explanation:
b= v16.4
A court holds jurisdiction over five counties, and the juries are required to be made up in a representative manner from the eligible populations of these five counties. An investigator notices that the county where she lives has 14% of the total population of the five counties eligible for jury duty, yet records reveal that over the past five years only 122 out of the 1386 jurors used by the court reside in her county. Do you feel that this constitutes reasonable evidence that the jurors are not being randomly selected from the total population
Answer:
Yes.
I feel that since only about 9% of the jurors are being appointed from the county, instead of the more representative 14%, this constitutes reasonable evidence that the jurors are not being randomly selected from the total population.
Step-by-step explanation:
a) Data and Calculations:
County population proportion = 14%
This implies that the country is supposed to have at least 1,386 * 14% = 194 of the jurors used by the court.
Evidence from records show that the county has only 122 of 1,386 = 9% (122/1,386)
This means that about 72 (194 - 122) jurors are not being appointed from the county.
And 72 represents about 5% of 1,386 (72/1,386). This number is more than half of those being appointed from the county or more than 50% or precisely 59%.
Therefore, this constitutes reasonable evidence that the jurors are not being randomly selected from the total population. The selection is not representative of the population characteristics.
Correctly identify the slope and y -intercept of the
slope intercept form equation:
y= mx + b
slope
intercept