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]
Bone-shaped treats are 5 for $3.50 at Shelley’s store and Sarah wants to buy 12. She set up and solved this proportion to find how much they would cost. Describe her error and find the correct solution.
5
3.5
=
12
x
3.5x = 60
x = $17.15
Answer:
Sarah multiplied the denominator by the denominator and the numerator by the numerator instead of finding the cross products. The equation should be 5x = 42, so the cost should be $8.40.
Step-by-step explanation:
I don’t understand this question.
Answer:
-7.89 is the answer
mark me the brainlets
Step-by-step explanation:
When are `x+2` and `3x` equal?
ARE THEY EQUAL?
Answer:
but tbh this equation cannot be equal
Step-by-step explanation:
Answer:
No, they are not equal, because you can not add x to 2, because it does not have an x after the 2, so they are not the same
Step-by-step explanation:
Three consecutive integers have a sum of 48. Find the integers.
Answer:
15, 16, and 17.
Step-by-step explanation:
They are consecutive and they add up to 48.
100 points!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answer:
y=5.8
x=10
Step-by-step explanation:
30\3=10
10-4.2=5.8
Answer:
x = 10 cm
y = 5.8 cm
Step-by-step explanation:
Area of a rectangle
[tex]\large\boxed{A=l\:w}[/tex]
where l is the length and w is the width.
From inspection of the given rectangle:
Width = 3 cmLength = x = y + 4.2 cmArea = 30 cm²Substitute the given values of area, width and length into the formula and solve for x:
[tex]\begin{aligned}A&=l\:w\\\implies 30&=x \cdot 3\\3x&=30\\x&=10\end{aligned}[/tex]
Substitute the found value of x into the expression for length and solve for y:
[tex]\begin{aligned}y+4.2&=x\\y+4.2&=10\\y&=10-4.2\\\implies y&=5.8\end{aligned}[/tex]
The set of all numbers greater than -1 and less than 0.
Answer:
I would just think that it is 0
Step-by-step explanation:
0 is greater then -1 and it is the exact same thing and not less than 0
Answer:
-0.5
Step-by-step explanation:
<________-1_-0.5_0__1_________>
its greater than -1 and less than 0
I don’t understand this question.
Haley makes a total of $400 a part-time job over a two week period. The first week she makes $20 more than her second weeks paycheck. How much money did she make each week
Answer: on the first week she earned 220$ and on the second week she earns 200$
Step-by-step explanation: Haley makes a total of 400$ in a week. divided by 2 would equal 200$ each. but Haley made an extra 20$ in the first week. so, 200$+20$=220$.And the two combined is 420$.
solve for brainliestA keem measured the capacity of a glass as
2 7 0 mL and the capacity of a Th e rm o s® a s
1 L. He said that the ratio 270 :1 compare s
the capacity of the glass with the cap a c i t y
of the Th e rm o s®. Is his reasoning corre c t ?
E x p l a i n .
Answer:
[tex]his \: reasoning \: is \: correct.[/tex]
Step-by-step explanation:
[tex]since \: the \: ratio \: of \: the \: glass \: to \:that \\ \: of \: the \: thermos \: is \: in \: the \: fraction : \\ \frac{2 7 0 mL }{1mL} \: which \: is \:270 mL : 1mL \\ then \: the \: keem \: is \: right.[/tex]
Find the 2nd term in the expansion of (1+3y)5
Step-by-step explanation:
Using pascal's triangle;
Then second term of the expansion (1+3y)5
is given as:
5(1)^4(3y) = 15y
Answer:
15y
Step-by-step explanation:
Which kind of line ( solid or dashed) is used for < or > ?
I think it has to do with inequalities but not sure
QUESTION #2 unless you know how to a different one
Answer:
dashed lines are used for both < and >, solid lines are used for >= or <=
Step-by-step explanation:
Which expression is equivalent to 42 + 63?
Answer: 104-63 maybe?
Step-by-step explanation:
24+26
[tex]25 + 52[/tex]
What is the ratio of 11 inches to 3 feet? (Change the feet to inches.) Group of answer choices
11:36
36:11
3:11
11:3
Answer:
The first option (11:36)
Step-by-step explanation:
When you convert the 3 feet to inches, you multiply by 12. There is 12 inches in each foot, so multiply 3 by 12 will result in 36.
We are comparing the 11 inches to the 3 feet (36 inches), so it would look like this:
11 : 36
(Can also be shown as 11 - 36)
1 Foot = 12 inches
3 feet x 12 = 36 inches.
Ratio = 11:36
What is -9 + m + (-6) in simplest form?
Answer:
m-15
Step-by-step explanation:
Help ? anybody ion know any of these I’m sorry please give me the correct answer .
Which is not a classification for AFGH?
A acute
C isosceles
B scalene D equiangular
/60
H
Answer:
A
Step-by-step explanation:
washewepshepshepshepshep
what is the slope of the line
Answer:
Rise/Run = up 3 over 1 = 3/1 (m = 3)
Step-by-step explanation:
Learn this stuff it is very important for future math
need help again please i’m sorry...
Answer:
The slope is -1/5
Step-by-step explanation:
y = mx +b is in slope intercept form
m is the slope and b is the y intercept
y = -1/5x -1
The slope is -1/5 and the y intercept is -1
Answer:
Step-by-step explanation:
The slope is -1/5
seven children the School bus yo school some more children. walked to school there are 13. children ay. school how many. children. walked to school?
Answer: 6 kids walked to school
Step-by-step explanation:
Since there are 13 kids altogether and 7 rode the bus, it can be solved using subtraction.
13 - 7 = 6
what is 4.8367 rounded to the nearest hundredth
Answer:
4.84
Step-by-step explanation:
4.84 is the nearest hundredth number of 4.8367.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
4.8367 is a decimal number.
Four point eight three six seven is the given decimal number.
We have to round the decimal number to the nearest hundredth.
In the given decimal number the value at hundredth position is 3.
We need to follow the rules when rounding a decimal number.
if the last digit is less than 5, round the previous digit down.
if it's 5 or more than you should round the previous digit up.
In the given decimal number on right of 3 it is 6 which is more than 5. So we need to round the increase the value of 3 by 1 which makes it 4.
Hence 4.84 is the nearest hundredth number of 4.8367.
To learn more on Equation:
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What are the possible degrees for the polynomial function?
degrees of 6 or greater
even degrees of 6 or greater
degrees of 5 or greater
odd degrees of 5 or greater
Answer:b
Step-by-step explanation:on edge2020
Please help ASAP ! Find the expressions for the perimeter of these shapes.
Answer:
Quest 1. P = 3xat2 + 4yat2 + 11xy
Quest 2. P = 7xat2 + 21x + 5y + 5
Step-by-step explanation:
Note: Perimeter, P is the total sum of the distance round about an object. that at symbol cant be used here.so.am.using at2 for squared
Which of these is a set of inputs and outputs for the function f(x) = 2x + 4 ?
Answer:
(1, 6), (2, 8), (3, 10)
2(1) + 4 = 6, 2(2) + 4 = 8 and 2(3) + 4 = 10.
Step-by-step explanation:
The set of inputs for the equation f ( x ) = 2x + 4 is
( 1 , 6 ) , ( 2 , 8 ) , ( 3 , 10 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be f ( x ) = 2x + 4
f ( x ) = y
Now ,
Let the first point be A ( 1 , 6 )
Let the second point be B ( 2 , 8 )
Let the third point be C ( 3 , 10 )
a)
A ( 1 , 6 )
Substitute the value of x and y in the equation , we get
y = 2x + 4
6 = 2 ( 1 ) + 4
6 = 2 + 4
6 = 6
Hence , the input A ( 1 , 6 ) satisfies
b)
B ( 2 , 8 )
Substitute the value of x and y in the equation , we get
y = 2x + 4
8 = 2 ( 2 ) + 4
8 = 4 + 4
8 = 8
Hence , the input B ( 2 , 8 ) satisfies
c)
C ( 3 , 10 )
Substitute the value of x and y in the equation , we get
y = 2x + 4
10 = 2 ( 3 ) + 4
10 = 6 + 4
10 = 10
Hence , the input C ( 3 , 10 ) satisfies
Hence , The set of inputs for the equation f ( x ) = 2x + 4 is
( 1 , 6 ) , ( 2 , 8 ) , ( 3 , 10 )
To learn more about equations click :
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help please its important
Answer:
DBYesStep-by-step explanation:
x: cupcakes
y: cakes
no more than 224 minutes: ≤ 224, average 4 minutes cupcakes: 4x and average 32 minutes cakes: 32ywhen you plug in the 4 cakes as y it becomes x≤24....4x+32(4)≤224...(4x+128≤224)-128....(4x≤96)/4...x≤24when you plug in the given numbers it is a true statement.... 4(32)+32(3)≤224...128+96≤224....224≤2249514 1404 393
Answer:
1. d. 4x +32y ≤ 224
2. b. x ≤ 24
3. yes
Step-by-step explanation:
1. For x number of cupcakes, at 4 minutes each, the time required for their decoration is 4x.
For y number of cakes, at 32 minutes each, the time required for their decoration is 32y.
The total decorating time must be less than or equal to 224 minutes:
4x +32y ≤ 224
__
2. For y=4, the constraint on x is ...
4x +32(4) ≤ 224
4x ≤ 96
x ≤ 24
__
3. We can try the numbers and see if the inequality is true:
4(32) +32(3) ≤ 224
128 +96 ≤ 224 . . . . . . . . true (equal)
Yes, it is possible.
Economists study the way society uses its resources. One important resource studied is agriculture. The recent increase in demand for organic produce has created some interesting economic scenarios for both farmers and consumers. Click the article to learn key facts about the economics of organic produce and answer a few questions.
Which is a reason that organic farming is more expensive than conventional farming?
How many years must a farm be run organically before its produce can be labeled as “organic”?
What is a benefit of crop rotation?
Answer:
Which is a reason that organic farming is more expensive than conventional farming?
Organic farmers must pay for a costly certification process
How many years must a farm be run organically before its produce can be labeled as “organic”?
3
What is a benefit of crop rotation?
Rotating crops can help build healthy soil.
Step-by-step explanation: Hope you pass! :)))
first one is C second one is 3 third one is A
hope i helped
what expression is equivalent to 2
Answer:
4 - 2 = 2
Step-by-step explanation
If n is divisible by 2, 5 and 14, which of the following is also divisible by these numbers?
Answer:
The number 70 is divisible by 2,5 and 14.
Explanation:
Out of all the equations, n+70 ⇒ 70+70 ⇒ 140.
140 is divisible by 2, 5 and 14.
SO the answer is option e: n+70
Carolyn is using the table to find 360% of 15. What values do X and Y represent in her table? Percent Total 100% 100% 100% 20% 20% 20% 360% X X X Y Y Y X = 2.5; Y = 2.5 X = 5; Y = 0.75 X = 15; Y = 3 X = 15; Y = 5
Answer: c
Step-by-step explanation:
Based on the percent breakdown of 360%.
100% 100% 100% 20%20%20%
15. 15. 15. 3. 3. 3.
100% is all of it, so 15. This is x.
20% of it would be calculated as 0.2 x 15 or 3. This is y.
Answer:
c
Step-by-step explanation:
Audrey deposits $27 in her account. Then she makes two withdraws one for $15 and one for 12. What is the total change to the balance of Audrey's account? Explain