Answer:
a) 0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.
b) Capacity of 252.6 cubic feet per second
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).
This means that [tex]m = 100, \mu = \frac{1}{100} = 0.01[/tex]
(a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)
We have that:
[tex]P(X > x) = e^{-\mu x}[/tex]
This is P(X > 190). So
[tex]P(X > 190) = e^{-0.01*190} = 0.1496[/tex]
0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.
(b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.08?
This is x for which:
[tex]P(X > x) = 0.08[/tex]
So
[tex]e^{-0.01x} = 0.08[/tex]
[tex]\ln{e^{-0.01x}} = \ln{0.08}[/tex]
[tex]-0.01x = \ln{0.08}[/tex]
[tex]x = -\frac{\ln{0.08}}{0.01}[/tex]
[tex]x = 252.6[/tex]
Capacity of 252.6 cubic feet per second
27 campers ate 567 pancakes during a week−long trip. If each camper ate the same amount, how many pancakes did each camper eat?
Answer:
23.6
Step-by-step explanation:
solve x + 1 > 3. graph the solution. can someone help me out??
Answer:
x>2
Step-by-step explanation:
x+1>3
x>3-1
x>2
I hope this helps
A population of values has a normal distribution with u = 69.4 and o = 18.9. You intend to draw a random
sample of size n = 185. Please show your answers as numbers accurate to 4 decimal places.
Find the probability that a single randomly selected value is between 65.9 and 68.8.
P(65.9 < X < 68.8) =
Find the probability that a sample of size n = 185 is randomly selected with a mean between 65.9 and 68.8.
P(65.9 < < 68.8) =
Answer:
234
Step-by-step explanation:
The steps to simplify the expression 5÷1 over 100 times-0.7 times -20 oh shown below with one missing step which is the missing step
Answer:
i did it 4 times and the answer is D
Step-by-step explanation:
Answer:
Option D) is Correct
Step-by-step explanation:
I took the test on T4L and got it right.
For whole numbers between 1 and 1001, inclusive, let m be the sum of odd numbers and n be the sum of even numbers. What is the value of m−n?
Answer:
m - n = 501
Step-by-step explanation:
Remark
The first thing you have to do is find the number of odd and even numbers. This is where you have to be careful because there is a danger of being out by one.
equation
l = a + (n - 1)*d
Solution even
l = 1000
a = 2
d = 2
1000 = 2 + (n - 1)*2
998/2 = (n - 1) * 2 / 2
499 = n - 1
n = 500
Solution odd
l = 1001
a = 1
d = 2
1001 = 1 + (n - 1)*2
1000 = (n - 1)*2
1000/2 = (n - 1)2/2
500 = n - 1
501 = n
Sum Even of even numbers from 1 to 1001
Givens
a = 2
n = 500
l = 1000
Equation
Sum = (a + l ) * n / 2
Solution
Sum = (2 + 1000)*500/2
Sum = 1002 * 250
Sum = 250500
Sum of Odd numbers from 1 to 1001
a = 1
l = 1001
n = 501
Equation
sum = (a + l)*n/2
sum = (1 + 1001) * 501
sum = (1002)*501 / 2
Sum = 251001
Answer
m - n = 251001 - 250500 = 501
What is the surface area of the cube shown? 6.5cm 6.5cm
Answer:
SA = 253.5 cm
Step-by-step explanation:
SA = 6a^2
SA = 6(6.5)^2
SA = 6(42.25)
SA = 253.50 cm
Find the difference: (6a + 6) - (3x - 2) - (2a + 4)
Answer:
4 a − 3 x + 4
Step-by-step explanation:
I just simplified everything together to get this answer.
Hope that this helped! :)
Have a great rest of your day/night!
Please thank me on my profile if this answer has helped you!
A train leaves Miami at 4:00 PM. A second train leaves the same city in the same direction at 8:00 PM. The second train travels 124mph faster than the first. If the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains?
find the the ratio write the answer as a fraction and as a decimal rounded to four decimal places.
Answer:
7 degrees
Step-by-step explanation:
It has a right angle and it's a triangle so the angle is a complementary angle so the total for the angle is 90 degrees.
So then you add 39 + 44 and get 83
So, 90 - 83 +7
So your total is 7 degrees
Share R600 amongst Tom, Paul and Anne in the ratio : 3:4:5 respectively.
Step-by-step explanation:
Total Shares = 3 + 4 + 5 = 12 shares
12 Shares = R600
(12÷12) Share = R(600÷12)
1 Share = R50
(1×3) Shares = R(50×3)
3 Shares = R150
4 Shares = R(50×4) = R200
5 Shares = R(50×5) = R250
Tom Gets R150.
Paul gets R200.
Anne gets R250.
18. Emma rents a car from a company that rents cars by the hour. She has to pay an initial fee of $75, and then they charge her $9 per hour. Write an equation for the total cost Cif Emma rents the car for h hours. If Emma has budgeted $250 for the rental cars, how many hours can she rent the car? Assume the car cannot be rented for part of an hour.
Step-by-step explanation:
Let h be the number of hours.
Total Cost = Fixed Costs + Variable Cost
= Initial Fee + Hourly Charge
= 75 + 9h
Given,
[tex]75 + 9h = 250 \\ 9h = 250 - 75 \\ 9h = 175 \\ h = 175 \div 9 \\ = 19 \frac{4}{9} hr[/tex]
Since the car cannot be rent part of an hour, the highest possible whole number is 19 hours.
Justin recently drove to visit his parents who live 300 miles away. On his way there his average speed was 11 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 10 hours driving, find the two rates.
Answer:
x=1
Step-by-step explanation:
The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2).
Weekly Gross Revenue Television Advertising Newspaper Advertising
() () ()
97 5.0 2.5
90 2.0 2.0
96 5.0 2.5
93 3.5 2.5
95 3.0 4.3
95 4.5 2.3
94 2.5 5.2
94 3.0 2.5
The estimated regression equation was:_______
Answer:
ŷ = 1.85057X1 + 0.9688X2 + 84.77516
Step-by-step explanation:
Given the data:
Weekly Gross Revenue (Y) :
97
90
96
93
95
95
94
94
Television Advertising (X1) :
5
2
5
3.5
3
4.5
2.5
3
Newspaper Advertising (X2) :
2.5
2
2.5
2.5
4.3
2.3
5.2
2.5
The regression equation obtained using a multiple regression calculator is :
ŷ = 1.85057X1 + 0.9688X2 + 84.77516
x1 and x2 are the predictor variables
y is the predicted variable (Weekly Gross Revenue).
Slope x1 = 1.85057
Slope x2 = 0.9688
Intercept = 84.77516
For the right triangles below, find the exact values of the side lengths b and a. If necessary, write your responses in simplified radical form. 300 Х X 5 ? 459 5 4= 45° 60 3
Answer:
who knows
Step-by-step explanation:
View the work below from a student last year. What was their mistake? Be detailed in their response.
-3(x + 4) = 2x - 5
-3x + 4 = 2x - 5
4 = 5x - 5
9 = 5x
1.8 = x
Can anyone help please???!?!?
Answer:
The third choice 2(a^3+3a^2h+3ah^2+h^3)
Step-by-step explanation:
f(a+h)=2(a+h)^3
How many centimeters does it grow Bamboo grows 91 centimeters per day. per hour? (GIVING BRAINLIEST)
Answer:
3.79 centimetres
Step-by-step explanation:
1 day = 24 hours
91 ÷ 24 = 3.79 centimetres
Answer:
if the question you're asking is how many cm does bamboo grow per hour, then around 3.81 cm per hour.
help please :((( this is the last math problem
Answer:
11.53 degrees.
Step-by-step explanation:
ok so we know the hyp and opp sides. this means that it is sin. according to SOHCAHTOA we do sin^-1(2/10). you should get 11.53
Answer:
11.5396°
Step-by-step explanation:
Please see the attached image
We can do sin(x)=2/10, which simplifies to sin(x)=1/5
To get x by itself do [tex]x=sin^{-1}[/tex](1/5) which ≈11.5396°
HELP PLEASE A total of 29 bills amounts to $73.00. If there are only $1 and $5 bills, how many of each are there?
Answer:
18 $1 bills and 11 $5 bills.
Step-by-step explanation:
First, we use the guess-and-check method.
$5X29=$145
Then, $5-$1=$4.
$145-$73=$72
$72 divided by 4 is 18.
29-11=18
11x$5=$55
$1x18=$18
$55+18=73.
Tom went to a car show over the weekend. he saw 5 blue cars, 2 white trucks, and 10 black cars. what is the ratio of black cars to all motor vehicles.
please help please please please please please.
Answer:41
Step-by-step explanation:the week end is three days and he saw 5 blue car and 2 white car and 10 black car multiple 5 times 3 and = 15 now multiple 2 times 3 = 6 then add 15 and 6 and 10
Answer:
I think it is 10:17 the ratio
Find the conjugate and product of
i3 + i7
Answer:
Complex conjugate: 2i Product: -2iSuppose that a random sample of eighteen recently sold houses in a certain city has a mean sales price of , with a standard deviation of . Under the assumption that house prices are normally distributed, find a confidence interval for the mean sales price of all houses in this community. Then find the lower limit and upper limit of the confidence interval.
This question is incomplete, the complete question is;
Suppose that a random sample of eighteen recently sold houses in a certain city has a mean sales price of $280,000, with a standard deviation of $10,000. Under the assumption that house prices are normally distributed, find a 95% confidence interval for the mean sales price of all houses in this community. Then find the lower limit and upper limit of the confidence interval.
Answer:
At 95%, confidence interval is ( 275026.7, 284973.3 )
Hence;
Lower limit = 275026.7
Upper limit = 284973.3
Step-by-step explanation:
Given that;
mean x = $280,000
standard deviation σ = $10,000
sample size n = 18
degree of freedom df = n - 1 = 18 - 1 = 17
∝ = 1 - 95% = 1 - 0.95 = 0.05
so
Critical t value = tinv( 0.05, 17 ) = 2.11
now, at 95% confidence interval for mean will be;
⇒ x ± [ Critical t value × ( σ/√n) ]
so we substitute
⇒ 280,000 ± [ 2.11 × ( 10000/√18) ]
⇒ 280,000 ± [ 2.11 × 2357.0226 ]
⇒ 280,000 ± 4973.3
⇒ 280000 - 4973.3, 280000 + 4973.3
At 95%, confidence interval is ( 275026.7, 284973.3 )
Hence;
Lower limit = 275026.7
Upper limit = 284973.3
What is its potential energy when compressed by 0.25 m?
a. 1.25 Joules b. 33.33 Joules
c. 8.33 Joules d. 5.0 Joules
Help and no links plzz
Answer:
20
Step-by-step explanation:
2 1/2 = 5/2
(5/2)/(1/8) = 20
a motorbike has been marked down by 38% to $130000.what is the original price?
Answer:
49400
Step-by-step explanation:
Answer:
so 38 % of 130000 = 49,400
so now after loss it's original price will be 130000-49400(38%)
=$800600
The seventh-grade class supplied bags of snacks and beverages for the school dance. They supplied 50 more beverages than bags of snacks. The dance was supplied with a total of 400 items. How many of each were supplied.
A) Define the variables.
B) Write a systems of equations for the situation.
C) Graph the system.
Answer:
C
Step-by-step explanation:
Hope this help and have a nice day
sin 0
4. Find tan0 .
A.
B.
C.
D.
Answer:
A
Step-by-step explanation:
Answer:
D. 9/40 would be the answer.
Step-by-step explanation:
formula
sinQ= opp/hyp (9/41)
TanQ= opp/adj (which mean 9 /40)
( 7x + 1/2) + ( 7x - 7 and 1/2) Simplify
Answer:
The answer will be 7(2x - 1)
Step-by-step explanation:
1) Convert 7 and 1/2 to improper fraction. Use this rule: a b/c = ac + b/c
[tex]7x + \frac{1}{2} + 7x - \frac{7 \times 2 + 1}{2} [/tex]
2) Simplify 7 × 2 to 14 .
[tex]7x + \frac{1}{2} + 7x - \frac{14 + 1}{2} [/tex]
3) Simplify 14 + 1 to 15.
[tex]7x + \frac{1}{2} + 7x - \frac{15}{2} [/tex]
4) Collect like terms.
[tex](7x + 7x) + ( \frac{1}{2} - \frac{15}{2} )[/tex]
5) simplify.
[tex]14x - 7[/tex]
6) Factor out the common term 7.
[tex]7(2x - 1)[/tex]
Therefor, the answer is 7( 2x - 1 ).
Can someone help me out pls.
What was done to the previous equation?
A) 2x – 10. <--original equation
B) 11x – 10
C) -8 + 11x – 2
D) -8 – 11x – 2
E) -8 + 6x + 5x – 2
F) -8 – 3x + 5x – 2
Ok ill answer the question but do you want me to evaluate it or find it to the simplest form ?
¿Cual es el diámetro del círculo que se puede trazar con un compás cuyo brazos miden 10 cm y forman un ángulo 34?
Answer:
Sorry that it is in english.
Step-by-step explanation:
The arms of the compass mesure the radius.
[tex]r=10\\2r=diamater (d)\\2*10=d\\20=d[/tex]