Answer:
The probability is [tex]P(A \ge 50 ) = 0.14321[/tex]
Step-by-step explanation:
The average life span is [tex]\pi = 8[/tex]
The sample size is n = 200
Generally we are told that average lifespan for a certain type of vehicle follows an exponential distribution
i.e
[tex]X \~ \ \ \ exp(8)[/tex]
Gnerally the probability distribution function for exponential distribution is
[tex]f(x) = \left \{ {{\lambda * e^{-\lambda * x }\ \ \ x\ge 0 } \atop {0 \ \ \ \ \ \ \ \ \ \ x < 0}} \right.[/tex]
Now [tex]\lambda[/tex] is the constant which is evaluated as
[tex]\lambda = \frac{1}{\pi}[/tex]
=> [tex]\lambda = \frac{1}{8}[/tex]
=> [tex]\lambda = 0.125[/tex]
Generally the that the vehicles will fail in less than 2 years is mathematically represented as
[tex]P(X \le 2 )= p= \int\limits^2_0 {\lambda e^{- \lambda * x} } \, dx[/tex]
[tex]P(X \le 2 )= p= [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * x} } ]|\left 2 } \atop {0}} \right.[/tex]
[tex]P(X \le 2 )= p= [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * 2} } ] - [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * 0} } ][/tex]
[tex]P(X \le 2 )= p= -0.77880 + 1[/tex]
[tex]P(X \le 2 )= p= 0.2212[/tex]
Generally the probability that the vehicle will fail in the first 2 years follows a binomial distribution with the mean evaluated as
[tex]\mu = n * p[/tex]
=> [tex]\mu = 200 * 0.2212[/tex]
=> [tex]\mu = 44.24[/tex]
The standard deviation is
[tex]\sigma = \sqrt{np(1 - p)}[/tex]
[tex]\sigma = \sqrt{200 * 0.2212 (1 - 0.2212)}[/tex]
[tex]\sigma = 5.86[/tex]
Using normal approximation of binomial distribution the probability that 50 or more of them fail in the first 2 years is mathematically represented as
[tex]P(A \ge 50 ) = 1 - P(A < 50 )[/tex]
Applying continuity correction
[tex]P(A \ge 50.5 ) = 1 - P(A < 50.5 )[/tex]
Here
[tex]P(A < 50.5 ) = P(\frac{A - \mu }{\sigma} < \frac{50 - 44.24}{5.87} )[/tex]
Generally
[tex]\frac{A - \mu }{\sigma} = Z (The \ standardized \ value \ of A )[/tex]
=> [tex]P(A < 50.5 ) = P( Z < 1.0664 )[/tex]
From the z-table the probability value of ( Z < 1.0664 ) is
[tex]P( Z < 1.0664 ) = 0.85679[/tex]
So
[tex]P(A \ge 50 ) = 1 - 0.85679[/tex]
=> [tex]P(A \ge 50 ) = 0.14321[/tex]
48 on shelves how many on 12 shelves
Answer: 96 books
If 6 shelves have 48 books on them, this is one half of 12 shelves, because 6 is one half of 12 shelves.
There are 12 shelves. So, multiply 48 by 2.
48 x 2 = 96.
Answer to the question = 96
help quick!! please i have 10 minutes!!
Sorry it's been longer than 10 min I hope this is accurate.
How do you do this question?
Exact value: [tex]c = \frac{-11+\sqrt{165}}{22}[/tex]
Approximate value: c = 0.08387
Round the approximate value however you need to
==============================================
Work Shown:
Let x = 1+c
[tex]\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\[/tex]
We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.
Each new term is found by multiplying the previous term by 1/x.
Assuming -1 < r < 1 is true, the infinite geometric sum is
[tex]S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\[/tex]
Plug in S = 11 and solve for x
[tex]S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\[/tex]
Use the quadratic formula to find the two solutions
[tex]x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\[/tex]
Using these x values, we find that the corresponding r values are
r = 1/x = 1/(1.08387) = 0.92262
r = 1/x = 1/(-0.08387) = -11.92321
The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387
----------------------------------------------
Using the solution that corresponds to x = 1.08387, we find the value of c is
[tex]x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\[/tex]
If g(x) =5-9x and f(x) = 5+ 3x
Find g(2)
Find f(g(2))
Answer:
Step-by-step explanation:
g(2)= 5-9(2)
= -13
f(g(2))= 5+3(-13)
= -34
Answer:
g(2) = -13
f(g(2)) = -34
Explanation:
For g(2), just substitute 2 in for the x, multiply, and simplify.
g(x) = 5-9(x)
g(2) = 5-9(2) = 5-18 = -13
For f(g(2)), substitute this output in for x, multiply, and simplify.
f(x) = 5 + 3(x)
f(g(2)) = 5 + 3(g(2)) = 5 + 3(-13) = 5-39 = -34
Which expression is equivalent to the expression
(2x + 4)(x - 6)?
Whats the mean of 62,78,59and 89
[tex]\huge {\mathcal{\purple{A}\green{N}\pink{S}\blue{W}\purple{E}\green{R}\pink{!}}}[/tex]
As we know that ,
⠀⠀⠀⠀Mean= sum of all numbers/ total number of numbers[tex] \longrightarrow [/tex] Mean= 62+78+59+89/4
[tex] \implies [/tex] Mean = 288/4
[tex] \implies [/tex] Mean= 72[tex]\huge\boxed{\fcolorbox{purple}{yellow}{Answer\:= \:72}}[/tex]Answer:
72
Step-by-step explanation:
62 + 78 + 59 + 89 = 288
then count how many data you have
288 / 4 = 72
Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) + 4? (1 point)
The graph shifts 4 units up.
The graph shifts 4 units down.
The graph shifts 4 units left.
The graph shifts 4 units right.
Answer:
C The graph shifts 4 units left.
Step-by-step explanation:
Answer: its A
Step-by-step explanation:
i took the test on flvs lol
Round the numbers to the nearest ten thousands.
62 389-
65 405-
51 330-
343 021-
102 779-
Answer:
60,00070,00050,000340,000100,000
Find the value of the missing angles ?
Help please for question
A person standing on a moving walkway travels 90 feet in 30 seconds. What equation represents this relationship? How many feet will the person travel in 10 seconds?
A. y = 3x; 30 feet
B. y = 9x; 90 feet
C. y = 1/3x; 3 feet
D. y = 3x; 3 feet
Answer:
What equation represents this relationship? How many feet will the person travel in 10 seconds? A. y = 3x; 30
Which organelle is marked with an X?
Answer:
cell wall :)
Answer:
Lysosome.
Step-by-step explanation:
If You Saw The Questions Before This One, you can see the Question: Which accurately labels the lysosome? and its X, so the answer is Lysosome
Find the slope (3, 7) (-2, 7)
Answer:
(-5,0)
Step-by-step explanation:
The X coordinates go down by five = -5
The Y coordinates don't change = 0
I'm pretty sure this is right :)
Hope it helped!
Answer:
Answer BelowStep-by-step explanation:
Hope this helps! <3
Name the relationship: complementary, linear pair, vertical, adjacent, alternative interior, corresponding, or alternate exterior.
Answer:
Step-by-step explanation:
9. Alternative exterior
10. Alternate interior
11. Complementary
12. Corresponding
13. Corresponding
14. Alternate exterior
15. Vertical
16. Linear Pair
(1.2/0.375-0.2)/(6.16/15.4+0.8)=(0.016/0.12+0.7)/x
9514 1404 393
Answer:
x = 1/3
Step-by-step explanation:
The solution to ...
a = b/x
is ...
x = b/a
It is convenient to let a calculator do the tedious arithmetic.
x = (0.016/0.12+0.7)/((1.2/0.375-0.2)/(6.16/15.4+0.8))
x = 1/3
At the produce store you can buy 4 bags of bananas for $29.88. How much would it cost if u were to buy 6 bags?
Answer:
44.82
Step-by-step explanation:
29.88 divided by 4 is 7.47 times 6 is 44.82
Answer:
44.82$
Step-by-step explanation:
4:29.88
6:x
4x=179.28
x=44.82$
pls look at the picture attached! i need help
it is 9 aahh it says to short well 3 times 9 is 27 then minus 17 is less than 13
Answer:
v <= 10
(-infinity, 10]
Step-by-step explanation:
3v - 17 <= 13
+17 +17
3v <= 30
3v/3 30/3
v <= 10
(-infinity, 10]
What is the slope of a line perpendicular to the line whose equation is 15x+12y=-108
Answer:
m perpendicular 1/3
Step-by-step explanation:
Have a nice evening.
help i forgot 3(x−4)≥−2x+3
Answer:
The answer is x_> 3
Step-by-step explanation:
Answer:
x≥3
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
3x−12≥−2x+3
Step 2: Add 2x to both sides.
3x−12+2x≥−2x+3+2x
5x−12≥3
Step 3: Add 12 to both sides.
5x−12+12≥3+12
5x≥15
Step 4: Divide both sides by 5.
5x
5
≥
15
5
x≥3
Drawing one card from a standard deck of cards. what is the sample space and outcome?
Answer:
sample space 2 inches outcome 1/52
Step-by-step explanation:
in a mixture a there is 2l of syrup in 3l of water. in a mixture b there is 1.8l of syrup in 2.5 water. in which mixture, concentration syrup is higher?
Answer:
Step-by-step explanation:
In the first mixture the concentration syrup is higher
Concentration syrup is higher in mixture B.
What is Proportion?Two or more ratios made to be equal to each other is termed as proportion.
We have to use the proportional concept here by finding the concentration of syrup in 1 l of water.
Mixture A:
Concentration of syrup in 3 l of water = 2 l
Concentration of syrup in 1 l of water = 2/3 l = 0.67 l
Mixture B :
Concentration of syrup in 2.5 l of water = 1.8 l
Concentration of syrup in 1 l of water = 1.8 / 2.5 = 0.72 l
Concentration of syrup in mixture A in 1 liter of water is less than the concentration of syrup in mixture B in 1 liter of water.
Hence the concentration of syrup in mixture B is higher because concentration of syrup in mixture B in 1 liter of water is higher than the concentration of syrup in mixture A in 1 liter of water.
Learn more about Proportion here :
https://brainly.com/question/26974513
#SPJ2
I really need help with this ?
Answer:
H: 4 3/4
Step-by-step explanation:
You subtract Aaron's and Siri's ages together and you get 4 3/4
Alice and her two sisters, Betty and Carol, are avid tennis players. Betty is the best of the three sisters, and Carol plays at the same level as Alice. Alice defeats Carol 50% of the time but only defeats Betty 40% of the time. Alice’s mother offers to give her $100 if she can win two consecutive games when playing three alternating games against her two sisters. Since the games will alternate, Alice has two possibilities for the sequence of opponents. One possibility is to play the first game against Betty, followed by a game with Carol, and then another game with Betty. We will refer to this sequence as BCB. The other possible sequence is CBC.
Calculate the probability of Alice getting the $100 reward if she chooses the sequence CBC.
Answer:
0.484
Step-by-step explanation:
Given that:
Alice defeats Carol 50% of the time.
This implies that, the probability of defeating Carol = 0.5
Also the probability of losing to Carol = 1 - 0.5 = 0.5
Similarly, Alice defeats Betty 40% of the time.
The probability of Alice defeating Betty = 0.4 and the probability of losing to Betty = 1 - 0.4 = 0.6
However, in as much as Alice needs to win two consecutive games, the sequence which satisfies this condition are as follows:
Let W represent Win and L represent L.
Then the conditions are WWW, WWL and LWW
Since the outcome of each game is independent of the other games.
Then, the probability that Alice wins two games against Carol CBC is:
Pr(2W - CBC) = (0.5 × 0.4 × 0.5) + ( 0.5 × 0.4 × 0.5) + ( 0.5 × 0.4 × 0.5)
Pr(2W - CBC) = 0.1 + 0.1 + 0.1
Pr(2W - CBC) = 0.3
The probability that Alice wins two games against Betty (BCB) is:
Pr(2W - BCB) = (0.4 × 0.5 × 0.4) + (0.6 × 0.5 × 0.4) + ( 0.4 × 0.5 × 0.6)
Pr(2W - BCB) = 0.08 + 0.12 + 0.12
Pr(2W - BCB) = 0.32
However, the Probability of winning two consecutive games is the result of the addition of the probability of winning two consecutive games in the sequence CBC together with the probability of winning two consecutive games in the sequence of BCB.
i.e.
Pr(2W) = Pr(2W- CBC) + Pr(2W - BCB)
Pr(2W) = 0.3+0.32
Pr(2W) = 0.62
Finally, to calculate the probability that Alice will get $100 if she chooses the sequence CBC is:
[tex]\dfrac{Pr(2W -CBC)}{Pr(2W)}= \dfrac{0.3}{0.62}[/tex]
[tex]\mathbf{\dfrac{Pr(2W -CBC)}{Pr(2W)}= 0.484}[/tex]
Solve the system of equations using substitution y = 3-4x y = 3x -11
Given the linear function 2x - y= 5 what is the slope? And As x increase does y increase or decrease and as x decreases does y increase or decrease
Answer:
The slope is 2. As x increase y is increase and as x decrease y decrease
The Cowboys have won 11 out of the 12 games they have
played this season. What is their ratio of Wins to Losses?
eleven wins to one lose 11 to 1
Can someone help me I really need it
Answer:
No, the figures are similar but not congruent as although width is same, length of fig A is 3 blocks while length of fig. B is 4 blocks. For two fig. to be congruent, their l and b should be eql.
Hope u find this ans useful.
Pls mark me brainliest
not sure need help
Answer:
8.2
Step-by-step explanation:
You have been asked to order a three-layer cake for the party. In order to feed 75 people, the bakery gave you the following two options for the size of each layer:
Option 1: Option 2:
Layer 1 - 10-inch diameter Layer 1- 11-inch diameter
Layer 2 - 8-inch diameter Layer 2- 7-inch diameter
Layer 3 - 6-inch diameter Layer 3- 4-inch diameter
Each layer is shaped like a cylinder and will have a height of 4 inches. The bakery charges $0.50 per cubic inch of cake.
What is the total cost of cake Option 1?
What is the total cost of cake Option 2?
Must show work and formulas
Answer:
1-11-2-7-3-4-0.50 =-26.5
Step-by-step explanation:
the decimal 105.7 becomes 1057 when multiplied by 10.
Answer:
yes true correct
Step-by-step explanation:
Brainly crown?
Answer:
True.
Step-by-step explanation:
I don't know if this is a true or false thing but it is true.
what’s the unit rate for 10 1/3 miles per 1/6 hour