The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose α = 2.6 and β = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to four decimal places.) at most 250 less than 250 more than 300 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) (c) What value is such that exactly 50% of all specimens
Answer:
a
P(X \le 250 ) = 0.7564 [/tex] , [tex]P(X < 250 ) = 0.7564 [/tex] ,
[tex]P(X < 300 ) = 0.09922 [/tex]
b
[tex]P(100 < X < 250 ) =0.644 [/tex]
c
[tex] x = 192.1 [/tex]
Step-by-step explanation:
From the question we are told that
The value for [tex]\alpha = 2.6[/tex]
The value for [tex]\beta = 220[/tex]
Generally the Weibull distribution function is mathematically represented as
[tex]F( x , \alpha , \beta ) = \left \{ 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x < 0} \atop { 1- e^{-(\frac{x}{\beta } )^{\alpha } }}\ \ \ \ \ \ x \ge 0} \right[/tex]
Generally the probability that a specimen's lifetime is at most 250 is mathematically represented as
[tex]P(X \le 250 ) = F(250, 2.7 , 220 )[/tex]
[tex]P(X \le 250 )=1 - e^{- (\frac{250}{220} )^{2.7}}[/tex]
[tex]P(X \le 250 ) = 1 - 0.2436[/tex]
[tex]P(X \le 250 ) = 0.7564 [/tex]
Generally the probability that a specimen's lifetime is less than 250
[tex]P(X < 250 ) = F(250, 2.7 , 220 )[/tex]
[texP(X < 250 ) =1 - e^{- (\frac{250}{220} )^{2.7}}[/tex]
[tex]P(X < 250 ) = 1 - 0.2436[/tex]
[tex]P(X < 250 ) = 0.7564 [/tex]
Generally the probability that a specimen's lifetime is more than 300
[tex]P(X > 300 ) = 1- p(X \le 300 )[/tex]
[tex]P(X > 300 ) = 1- F(300, 2.7 , 220 )[/tex]
[texP(X < 300) =1- [1 - e^{- (\frac{300}{220} )^{2.7}}][/tex]
[tex]P(X < 300 ) = 0.09922 [/tex]
Generally the probability that a specimen's lifetime is between 100 and 250 is
[tex]P(100 < X < 250 ) = P(X < 250) - P(X < 100)[/tex]
=> [tex]P(100 < X < 250 ) =F(250 , 2.7 , 220 ) - F(100 , 2.7 , 220 ) [/tex]
=> [tex]P(100 < X < 250 ) =(1 - e^{-(\frac{250}{220})^{2.7}}) - (1 - e^{-(\frac{100}{220})^{2.7}}) [/tex]
=> [tex]P(100 < X < 250 ) = (1 - 0.244 ) - (1- 0.888)[/tex]
=> [tex]P(100 < X < 250 ) =0.644 [/tex]
Generally the value such that exactly 50% of all specimens
[tex]P(X > x) = 1-P(X < x) = 0.50[/tex]
=> [tex]P(X > x) = 1- (1 - e^{- (\frac{x}{220}) ^{2.7}}) = 0.50[/tex]
=> [tex] P(X> x ) = e^(- \frac{x}{20})^{2.7} = 0.50 [/tex]
=> [tex] P(X> x ) = (- \frac{x}{20})^{2.7} = ln0.50 [/tex]
=> [tex] P(X> x ) = \frac{x}{20} =[ -ln0.50 ] ^{frac{1}{2.7}}[/tex]
=> [tex] x = 220[ -ln0.50 ] ^{frac{1}{2.7}}[/tex]
=> [tex] x = 192.1 [/tex]
At the gym, Garson always completes 3 pull-ups for every 8 sit-ups he does. Last night, Garson completed 24 sit-ups. Which ratio represents the relationship between the number of pull-ups and the number of sit-ups Garson completed last night?
Answer:
9:24 simplifies to 3:8
Step-by-step explanation:
3:8
24/8=3
3*3=9
last night he did 9 pull ups and 24 situps
Find the missing side using the pythagorean theorem.
9 in
12 in
x =
Answer:
225 in
Step-by-step explanation:
which number line represents the solutions to absolute value of -2x=4
Answer:
poop
Step-by-step explanation:
-2(39% + **)+(855 + 2K)
Answer:
42711 /50
Step-by-step explanation:
Lana uses factoring by grouping to factor the polynomial 8x2y−10xy2+12x−15y. Her work follows, but the last two lines of work are missing.
Which answers correctly fill in the blanks?
Select two answers: one for blank 1 and one for blank 2.
Answer:
Blank 1: 2xy(4x-5)=3(4x-5)
Blank 2: (2xy+3)(4x-5)
Step-by-step explanation:
The first step in factoring this polynomial is to find the biggest common factor in both numbers inside the parenthesis, and the second step is to find the biggest common factor of the 2 addents.
The other steps are invalid, either because they don't respect positive or negative signs, or that they just factor it wrong completely.
The only correct answer are:
Blank 1: 2xy(4x-5)=3(4x-5)
Blank 2: (2xy+3)(4x-5)
if 75 pumpkins cost 20,000 dollars how many pumpkins will it take to get 200,000
Answer:
750 pumpkins
Step-by-step explanation:
if 75 = 20,000
what about 200,000
Enter the value of the underlined digit.
6.53
The value of the underlined digit is
Cual es el dígito del 3
Answer:
hundredths
Step-by-step explanation:
WILL GIVE BRAINLIEST
Which descriptions can describe more than one triangle? Select two option:
side lengths of 6 ft, 8 ft, and 10 ft
angle measurements of 350, 350, and 110°
angle measurements of 30°, 409, and 50°
angle measurements of 40°, 60°, and 80°
side lengths of 4 cm, 6 cm, and 9 cm
Answer:
angle measurements of 40°, 60°, and 80°
side lengths of 4 cm, 6 cm, and 9 cm
Step-by-step explanation:
help please and tysm to whoever does!!
Answer:
6
1/6
1/360
1/1800
Hope this helps! =)
Lionel Messi, who is running 20 feet per second is 15 feet behind Cristiano Ronaldo who is running at 17 feet per second. How long will it take Messi to catch up with Ronaldo?
Answer:
15 feet
Step-by-step explanation:
Answer:
15 feet
Step-by-step explanation:
PLEASE HELP!!! How many solutions does each polynomial have?
Answer:
answer in picture
Step-by-step explanation:
What is the displacement of the red ball between 0 s and 24 s
Answer:
12s
Step-by-step explanation:
Because 24 divided by 2 is 12
Answer:
Step-by-step explanation:
Find the GCF of the terms of the polynomial.
35Z^4 - 70z3 + 14z2
Answer:
7z^2
Step-by-step explanation:
please help me with this!!!!!
All you have to do is add up all of the numbers and then yo uwill have your answer
∆ABC is translated 2 units down and 1 unit to the left. Then it is rotated 90° clockwise about the origin to form ∆A′B′C′. The coordinates of vertex A′ of ∆A′B′C′ are . The coordinates of vertex B′ of ∆A′B′C′ are . The coordinates of vertex C′ of ∆A′B′C′ are .
Answer:
A'(-2, 1), B'(1, 0), C'(-1, 0)
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and translation.
If a point X(x, y) is translated a units right and b units down, the new location is X'(x + a, y + b) whereas if a point X(x, y) is translated a units left and b units up, the new location is X'(x - a, y - b).
If a point X(x, y) is rotated 90° clockwise about the origin, the new location is X'(y, -x)
From the image attached, ∆ABC is at A(0, 0), B(1,3) C(1, 1)
If ∆ABC is translated 2 units down and 1 unit to the left (x - 1, y - 2), the vertices would be A*(-1, -2), B*(0, 1), C*(0, -1)
If it is then rotated 90° clockwise about the origin, the new location is A'(-2, 1), B'(1, 0), C'(-1, 0)
Answer:
The coordinates of vertex A′ of ∆A′B′C′ are (-2, 1) .
The coordinates of vertex B′ of ∆A′B′C′ are (1, 0) .
The coordinates of vertex C′ of ∆A′B′C′ are (-1, 0) .
Step-by-step explanation:
You read 9.75 pages in your science book and 24.5 pages of a play for English class
It takes you 1.2 minutes to read each page of science and 0.8 of a minute to read each page of the play. How much time do you spend reading?
Answer: 1. You have to multiply 9.75x1.2= 11.7
2.You have to multiply 24.5x0.8= 20.4
3. Add the to products 11.7+20.4= 32.1
4. Answer is- 31.3 minutes
Step-by-step explanation: Hopefully this helped a lot ;D
7. During the Middle Ages, people often used grains, scruples, and drahms to measure the weights of different medicines. If 120 grains are equivalent to 6 scruples and 6 scruples are equivalent to 2 drahms,
how many drahms are equivalent to 300 grains? Explain your reasoning. If you get stuck, try creating a table.
Answer:
5 drahms.
Step-by-step explanation:
From the question given above, the following data were obtained:
120 grains = 6 scruples
6 scruples = 2 drahms
300 grains (in drahms) =..?
From the above data,
120 grains = 6 scruples
6 scruples = 2 drahms
Therefore,
120 grains = 2 drahms
Thus, we can obtain 300 grains in drahms as follow:
120 grains = 2 drahms
Therefore,
300 grains = 300 grains × 2 drahms /120 grains
300 grains = (300 × 2)/120 drahms
300 grains = 5 drahms
Therefore, 300 grains is equivalent to 5 drahms.
is 42% bigger than 0.44
Answer: No
0.44 is equal to 44%.
42% is equal to 0.42.
0.44 is greater than 0.44.
44% is greater than 42%.
Answer = no
1-(2x+4)=4x+5 solution
Use properties to rewrite the given equation. Which equations have the same solution as x + + x = – x? Check all that apply.
x + = – x
18x + 20 + 30x = 15 – 6x
18x + 20 + x = 15 – 6x
24x + 30x = –5
12x + 30x = –5
Answer:
options (a), (b), (c), and (e) have the same solution as the solution of 3/5 x + 2/3 + x = 1/2 -1/5x.
Step-by-step explanation:
The given equation is
3/5 x + 2/3 + x = 1/2 -1/5x
First, rearrange the equation to have constant terms and the terms having variable on the separate side.
3/5 x + x +1/5x= 1/2 - 2/3
9/5 x = -1/6
x= -1/6 ÷ 9/5
x= -1/6 x 5/9
x= -5/54 ...(i)
Now, find the solution of all the options in the similar way:
(a) 8/5 x +2/3 = 1/2 -1/5 x
8/5 x + 1/5 x = 1/2 - 2/3
9/5 x = -1/6
x= -1/6 ÷ 9/5
x= -1/6 x 5/9
x= -5/54 which is same as the solution of the mentioned equation. [ from equation (i)]
(b) 18x + 20 + 30x = 15 – 6x
18x+30x+6x = 15 -20
54x=-5
x= -5/54 which is same as the solution of the mentioned equation. [from equation (i)]
(c) 18x + 20 + x = 15 – 6x
18x+x+6x = 15 -20
25x=-5
x= -5/25 which is not the same as the solution of the mentioned equation. [ from equation (i)]
(d) 24x + 30x = –5
54x = -5
54x=-5
x= -5/54 which is same as the solution of the mentioned equation. [ from equation (i)]
(e) 12x + 30x = –5
42x = -5
42x=-5
x= -5/42 which not is same as the solution of the mentioned equation. [ from equation (i)].
Hence, options (a), (b), (c), and (e) have the same solution as the solutions of the given equation.
Help pleaseeeeeeeeee
Reflecting across the y axis followed by rhe x atation 180 degrees clockwise
Rotation 180 counterclowise
You deposited a check for $1,200 into your checking account that had a balance of $625 and it "bounced". You had written checks for $450, $225, $215, and $187. Your bank will pay the largest check that you wrote first. Your account is overdrawn, and the remaining checks written to pay monthly bills did not clear. Your bank charged you a $35 overdraft fee and each of the remaining creditors receiving bounced checks charged you a $25 late payment fee. What did the $1,200 check that "bounced" on you cost you?
Answer:
total cost = $110
Step-by-step explanation:
Your bank will charge you $35 as overdraft fee.
The bank will only pay one check for $450, so that means that 3 more checks will remained unpaid. Since your creditors charge you $25 per bounced check, then they will charge you 3 x $25 = $75.
Total costs = $35 + $75 = $110
Which of the following shows the prime factorization of 50?
A.
5 × 10
B.
2 × 25
C.
2 × 2 × 5
D.
2 × 5 × 5
Answer:
two and five are prime numbers. so it would be B
Step-by-step explanation:
brainliest? if not its cool too :D
Which is an irrational number?
Answer:
[tex]\sqrt{\frac{5}{3} }[/tex]
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal. [tex]\sqrt{\frac{5}{3} }[/tex] is irrational.
Hope this helps! o(〃＾▽＾〃)o
Which set of values is a function?
a.
(6,-5) (7, -3) (8, -1) (9, 1)
b.
(9,5) (10,5) (9,-5) (10,-5)
c.
(3,4) (4,-3) (7,4) (3, 8)
d.
(2, -2) (5, 9) (5, -7) (1, 4)
Answer:
Its A
Step-by-step explanation:
Had it on quizziz
simplify the variable expression by evaluating it’s a numerical part, and enter your answer below. (13-6)•w
Answer:
(13-6)* w =7w
Step-by-step explanation:
Answer:
7*w ...........................
Need help asap
x=4 and y= -9
2xy+15x
Answer:
12
Step-by-step explanation:
2xy+15x
Let x=4 and y= -9
2(-4)(-9) + 15(-4)
Multiply
72 -60
Subtract
12
Answer:
-12
Step-by-step explanation:
2(4)(-9)+15(4) is what it should look like.
Someone give me a helping hand
Answer:
a) vertical angles
b) same side interior angles
c)alternate interior angles
Step-by-step explanation:
vertical angles are angles that are across from each other and they are congruent
interior angles are angles that are in between the parallel lines and when they are on the same side it means that they are on the same side of the transversal
interior angles are angles that are in between the parallel lines and when they are on different sides it means that they are on opposite sides of a transversal, this is called alternate interior angles
1. You pay $25.00 to fill up the 13-gallon gas tank of your internal combustion engine car.
How much are you paying for one gallon of gas?
Answer:
$1.92 a gallon!!
Step-by-step explanation:
Answer:
You will pay $1.92 per gallon.
Step-by-step explanation:
Divide 25.00 by 13 to by how much money per gallon:
[tex]25.00/13=1.923[/tex]
You cannot round up.
You will pay $1.92 per gallon.
-Hope this helps! :)