It is advised that lower pressure test should be administered.
Probability of survival of pressure vessel the pressure vessel is tested under the lower pressure test at 58 bar, the probability of survival is given by the sum of the probability of survival if the vessel is one of the 60% that will survive 70 bar and the probability of survival if the vessel is one of the 40% that will fail at 70 bar but will survive 58 bar or less. If P1 represents the probability of survival of the vessel if it is one of the 60% that will survive 70 bar, and P2 represents the probability of survival if it is one of the 40% that will fail at 70 bar but will survive 58 bar or less, then the probability of survival of the vessel, if it is tested under the lower pressure test at 58 bar, is given by:
P = 0.60 x 1 + 0.40 x (1 - 0.60) = 0.76
If the pressure vessel is tested under the higher pressure test at 65 bar, the probability of survival is given by the sum of the probability of survival if the vessel is one of the 60% that will survive 70 bar, and the probability of survival if the vessel is one of the 40% that will fail at 70 bar but will survive 65 bar or less. If P3 represents the probability of survival of the vessel if it is one of the 40% that will fail at 70 bar but will survive 65 bar or less, then the probability of survival of the vessel, if it is tested under the higher pressure test at 65 bar, is given by:
P = 0.60 x 1 + 0.40 x (1 - 0.80 x P3)
The condition that the probability of survival of the vessel, if it is tested under the higher pressure test at 65 bar, is at least 0.95 is therefore:
0.60 + 0.40 x (1 - 0.80 x P3) ≥ 0.95
This simplifies to: P3 ≤ 0.625
Using the above values for P1, P2, and P3, it is clear that the probability of the vessel surviving if tested at the lower pressure of 58 bar is greater than 0.95. Therefore, the lower pressure test should be carried out.
To learn more about probability: https://brainly.com/question/13604758
#SPJ11
What is the value of the output when the
input is 18?
Answer:
Any number less than greater than or equal to 18
Step-by-step explanation:
Suppose you place a $35 bet on a horse with a 2:7 odds against winnning. Determine the winning payout for this horse.
The winning payout for the horse is $45
To determine the winning payout for the horse, you need to use the following formula:
Odds against winning: B / (A + B)
Betting amount: X Payout: X + (X * B / A)where A is the denominator of the odds and B is the numerator of the odds.
Here, the odds against winning are 2:7.
So, the denominator (A) is 7 and the numerator (B) is 2.
The betting amount is $35.
Plugging these values into the formula:
Payout = 35 + (35 * 2 / 7)
Payout = $45.
#SPJ11
Let us know more about winning payouts: https://brainly.com/question/31119881
Write an equivalent expression for 5+2+2x+2
please help me
Answer:
2x+9
Step-by-step explanation:
You have to combine like terms. 2x stays the same because there are no other like terms, but 5, 2, and 2 can be added together to make 9
Lacey opened a savings account and deposited $100.00. The
account earns 6% interest, compounded monthly. If she wants
to use the money to buy a new bicycle in 2 years, how much
will she be able to spend on the bike?
Round your answer to the nearest cent.
Answer:
$244.00
Step-by-step explanation:
- gave bank $100
- +6% of $100 per month
- 6% of $100 = $6 (earns $6 per month)
- twelve months in a year, so 12 x $6 = $72 per year
- $100 + $72 + $72 = $244
If Lacey wants to utilize her money to purchase a new bicycle in two years, she will spend $244 on the bike.
Let z = (a + ai)(b + b/3i) where a and b are positive real numbers. Without using a calculator, determine arg z.
The argument (arg) of the complex number z = (a + ai)(b + b/3i), where a and b are positive real numbers, is π/6 radians or 30 degrees.
To determine the argument (arg) of the complex number z = (a + ai)(b + b/3i), where a and b are positive real numbers, we can simplify the expression and find the argument without using a calculator.
First, expand the product (a + ai)(b + b/3i):
z = (a + ai)(b + b/3i)
= ab + ab/3i + abi - ab/3
Combining like terms, we get:
z = (ab - ab/3) + (ab/3 + ab)i
= (2ab/3) + (ab/3)i
Now, we have the complex number z in the form z = x + yi, where x = 2ab/3 and y = ab/3.
To compute the argument (arg) of z, we can use the definition of the argument as the angle θ between the positive real axis and the line connecting the origin to the complex number z in the complex plane.
Since a and b are positive real numbers, both x and y are positive.
The argument (arg) of z can be determined as:
arg z = arctan(y/x)
= arctan((ab/3) / (2ab/3))
= arctan(1/2)
= π/6
Therefore, without using a calculator, the argument (arg) of the complex number z = (a + ai)(b + b/3i) is π/6 radians or 30 degrees.
To know more about argument refer here:
https://brainly.com/question/28324516#
#SPJ11
please tell me where to plot the points and what the solution will be.
Write a linear function f with given values. F(3)=-4, f(5)= -4
Answer:
y = -4
Step-by-step explanation:
dy/dx gives you slope
(-4)-(-4)/5-3 = 0/2 ----> slope = 0
y = mx+b
m = 0
y = 0x+b
y = b
as it says F(3) and F(5) = -4 b must be -4
so you end up with y = -4
using the equation y=x , what would be the value of y if the value of x is 2
Answer:
y = 2
Step-by-step explanation:
y = x
x = 2
Plug in the given value.
y = (2)
This is already simplified.
Therefore, when x = 2, y = 2.
Hope this helps!
HELP PLEASEEEE IT WOULD HELP ME OUT A LOT
Answer:
Step-by-step explanation:
Solve the system using substitution. Show all work.
( 4х + 5y = 7
у = 3х + 9
Answer:
(4x+5y=7
y=3x+9
4x+5(3x+9)=7
4x+15x+45=7
19x=7-45
19x= -38
19×/19=-38/19
x= -2
whlie y=3x+9
y=3(-2)+9
y= -6+9
y=3 end solution
x= -2,y= 3
This XP set is worth a maximum points 1) As of 5/12/22. 72.7% of the residents of Washington state were fully vaccinated against CV19. Also, the population of our state is about 74 million people. a) Suppose that random samples of size n 50 are selected from this state's population. Let X represent the number people in each sample that are fully vaccinated against CV19 The variable X has an approximately Binomial distribution, with n 50 and D 727 Using the special Binomial formulas, compute the mean and the sigma of Round each value to the nearest tenth b) Refer to part . Which specific values of this variable X are within 3- sigma of its mean value? (OW, what are the common numbers of fully vaccinated people you'd expect to find in samples of this size, given the 72.7% fully vaccinated percentage?) c) Refer to part a. Use your calculator / technology like the "binompat and "binomcd commands on the TI-84) to help answer the following questions Report each probability correct to four decimal places Find the probability that one of these samples has exactly 35 fully vaccinated people in ite find the value of PX - 3571 Is this an unusual event using the 5% probability criterion? 10 Find the probability that one of these samples has 25 or fewer fully vaccinated people in it be find the value of PX $25)) is this an unusual event, using the 5% probability criterion? 30 IP 3: DO %: . $ 4 % 5 . # 3 $ 4 % 5 & 7 6 > 0 00 9 E R T T Y U 0 P D F G H J I KL < < C V B N M 1
Random samples of size 50 are taken from this population, and the number of fully vaccinated individuals in each sample, represented by the variable X, follows an approximately binomial distribution with n = 50 and p = 0.727.
(a) Using the binomial formulas, the mean (μ) of X is calculated as np, which is 50 * 0.727 = 36.4, rounded to the nearest tenth. The standard deviation (σ) is given by the square root of np(1-p), which becomes √(50 * 0.727 * 0.273) ≈ 4.1.(b) To determine the values within 3 sigma of the mean, we calculate 3 times the standard deviation (3σ) and find the range around the mean: 36.4 ± 3 * 4.1, resulting in the range of approximately 24.1 to 48.7. Therefore, the common numbers of fully vaccinated people expected in samples of this size, given the 72.7% vaccination rate, would fall within this range.(c) By using appropriate commands on a calculator or technology, the following probabilities can be determined:
The probability of one sample having exactly 35 fully vaccinated people is obtained from the binomial distribution as P(X = 35), which can be calculated using the binompdf command.
The value of P(X ≤ 25) can be found using the binomcdf command, representing the probability of having 25 or fewer fully vaccinated people in a sample. The probabilities should be reported to four decimal places for accuracy.
Learn more about vaccinated click here:
brainly.com/question/30971624
#SPJ11
Jasmine scored a 85 on the last math test. The class average was a 76 with a standard deviation of 4.5. So, XN(76,4,5) Jasmine's Z-score is This tells you that 85 is standard deviations to the left or right) of the mean, 14. The number of problems on all math exams are normal distributed. What is the probability a randomly selected math exam has fewer than 15 questions if the mean is 20 questions with a standard deviation of 2.5? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary. A city has around 890 thousand people. There are 123 parks in this city. What is the number of parks per capita in this city? Write your answer in scientific notation.
Jasmine's Z-score is 2. The number of parks per capita in the city is [tex]1.38 * 10^-4[/tex] in scientific notation.
To calculate Jasmine's Z-score, we can use the formula:
Z = (X - μ) / σ
where X is the individual score (85), μ is the mean (76), and σ is the standard deviation (4.5).
Z = (85 - 76) / 4.5
Z = 9 / 4.5
Z = 2
Since Jasmine's Z-score is 2, this tells us that her score of 85 is 2 standard deviations to the right of the mean.
Now let's calculate the probability of randomly selecting a math exam with fewer than 15 questions using the mean of 20 and a standard deviation of 2.5.
To apply the empirical rule, we need to determine how many standard deviations 15 is away from the mean.
Z = (X - μ) / σ
Z = (15 - 20) / 2.5
Z = -5 / 2.5
Z = -2
Since 15 is 2 standard deviations to the left of the mean, we can use the empirical rule to estimate the probability.
According to the empirical rule:
The data is within one standard deviation of the mean for about 68% of the time.
The data is within 2 standard deviations of the mean for about 95% of the time.
99.7% of the data are contained within a 3 standard deviation range around the mean.
Since 15 is beyond 2 standard deviations to the left, the probability of randomly selecting a math exam with fewer than 15 questions would be very close to 0. In this case, we can assume it's effectively 0%.
Now let's calculate the number of parks per capita in the city with 890,000 people and 123 parks.
Number of parks per capita = Number of parks / Population
Number of parks per capita = 123 / 890,000
To write the answer in scientific notation, we can express 890,000 as 8.9 x 10^5:
Number of parks per capita =[tex]123 / (8.9 * 10^5)[/tex]
Calculating the result:
Number of parks per capita =[tex]1.38 * 10^-4[/tex]
Therefore, the number of parks per capita in the city is[tex]1.38 * 10^-4[/tex] in scientific notation.
To learn more about Z-score,
https://brainly.com/question/28000192
#SPJ4
Tuition for one year at Mount Tusk University is $13,400. Elijah has saved
$1,800 for this year's tuition. His parents have agreed to pay $5,000 this
year, and he earned a football scholarship for $3,500. Elijah hopes to earn
the rest of the money through his work-study job tutoring in the math
center. How much money does Elijah need to earn tutoring? (Enter the
quantity only)
Your answer
Answer:
The answer is 3,100
Step-by-step explanation:
If you subtract the 8,500 from his parents and his football scholarship you get 4,900 and then take the 1,800 from his saved money, You get what he still needs, which is 3,100.
(5)
A plane contains the points A(1, 2, 8), B(-2, 3, 6), and C(5,-1, 4).
(a) Determine 2 vectors parallel to the plane.
(b) Determine 2 vectors perpendicular to the plane.
(C) Write a vector equation of the plane.
(d) Write a scalar equation of the plane.
(e) Determine if the point D(-7, 4, 0) is contained in the plane.
(f) Write an equation of the line through the y and z intercepts of the plane.
Answer:
7
Step-by-step explanation:
10. Use the two given poInts and calculate the slope.
(7,2), (6,1)
Answer:
The answer is m=1 , the slope is 1
Step-by-step explanation:
Dani has only 1/2 of a cup of baking mix. She needs 3/4 of a cup for one batch of muffins. Which solution method shows how much of a batch of muffins Dani can make?
Answer:
Step-by-step explanation:
Dani has only 1/2 of a cup of baking mix. She needs 3/4 of a cup for one batch of muffins. Which solution method shows how much of a batch of muffins Dani can make?
"6 less than the quotient of a number and 5"
Answer:
[tex]\frac{n}{5} - 6[/tex]
Step-by-step explanation:
Quotient of a number and 5 means n/5
6 less than n/5 means n/5 - 6
Answer:
the product of a triple a number and 19
Step-by-step explanation:
but i'm not 100% sure so don't quote me
Calculate the mean, median, and range of the data in the dot plot.
Answer:
median = 5
range = 2
mean = 11
Step-by-step explanation:
the functions y=x^2+ (c/x^2) are all solutions of equation: xy′ 2y=4x^2, (x>0). find the constant c which produces a solution which also satisfies the initial condition y(6)=4. c= ______--
The constant c that produces a solution satisfying the initial condition y(6) = 4 is c = 24.
To find the constant c that satisfies the given equation and the initial condition, we need to substitute the function y = x² + (c/x²) into the differential equation and solve for c. The given equation is xy' * 2y = 4x².
First, we differentiate y with respect to x to find y',
y = x² + (c/x²)
y' = 2x - (2c/x³)
Now we substitute y and y' into the differential equation,
xy' * 2y = 4x²
x(2x - (2c/x³)) * 2(x² + (c/x²)) = 4x²
Simplifying,
2x³ - 2cx + 4c = 4x²
Rearranging,
2x³ - 4x² - 2cx + 4c = 0
Now we substitute x = 6 and y = 4 (from the initial condition y(6) = 4) into the equation,
2(6)³ - 4(6)² - 2(6)c + 4c = 0
432 - 144 - 12c + 4c = 0
288 - 8c = 0
8c = 288
c = 36
Therefore, the constant c that produces a solution satisfying the initial condition y(6) = 4 is c = 36.
To know more about differential equations, visit,
https://brainly.com/question/1164377
#SPJ4
Shirley is saving money to buy a computer.
• The computer she will buy costs $1,200.00
• She has already saved $300.00
Shirley will save $60.00 per week until she has enough money to buy
the computer.
Answer:
It will take her 15 weeks to have enough money for the computer.
Step-by-step explanation:
$1200 - $300 = $900
900 divided by 60 gives you 15
Therefor, it'll take Shirley 15 weeks to save $1200.
Describe a situation that can be represented by the integer - 6
Answer:
One Chilly Night, Elijah Was Sleeping but Then Woke Up. He Realized It Was 45 Degrees According To the AC Monitor, So He Changed it To 70 Degrees But The Monitor Broke And Changed to -6 DEGREES!!
Step-by-step explanation:
A situation that can be represented by the integer - 6 was envisaged.
What are integers?An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
One day maths teacher decided to take a random test
There were 16 questions each of 4 marks and 1 mark deduction for each wrong answer, with no penalties for non-attempt.
David was so good at guessing. He guessed all the 16 answers out of which 2 were correct and 14 were incorrect.
So, the total marks that David got = 4(2)-1(14) = 8-14 =-6
Thus, a situation that can be represented by the integer - 6 was envisaged.
To get more about integers visit:
https://brainly.com/question/17695139
solve the following question
Answer:
g) [tex]u^{4}\cdot v^{-1}\cdot z^{3}[/tex], h) [tex]\frac{(x+4)\cdot (x+2)}{3\cdot (x-5)}[/tex]
Step-by-step explanation:
We proceed to solve each equation by algebraic means:
g) [tex]\frac{u^{5}\cdot v}{z}\div \frac{u\cdot v^{2}}{z^{4}}[/tex]
1) [tex]\frac{u^{5}\cdot v}{z}\div \frac{u\cdot v^{2}}{z^{4}}[/tex] Given
2) [tex]\frac{\frac{u^{5}\cdot v}{z} }{\frac{u\cdot v^{2}}{z^{4}} }[/tex] Definition of division
3) [tex]\frac{u^{5}\cdot v\cdot z^{4}}{u\cdot v^{2}\cdot z}[/tex] [tex]\frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{b\cdot c}[/tex]
4) [tex]\left(\frac{u^{5}}{u} \right)\cdot \left(\frac{v}{v^{2}} \right)\cdot \left(\frac{z^{4}}{z} \right)[/tex] Associative property
5) [tex]u^{4}\cdot v^{-1}\cdot z^{3}[/tex] [tex]\frac{a^{m}}{a^{n}} = a^{m-n}[/tex]/Result
h) [tex]\frac{x^{2}-16}{x^{2}-10\cdot x + 25} \div \frac{3\cdot x - 12}{x^{2}-3\cdot x -10}[/tex]
1) [tex]\frac{x^{2}-16}{x^{2}-10\cdot x + 25} \div \frac{3\cdot x - 12}{x^{2}-3\cdot x -10}[/tex] Given
2) [tex]\frac{\frac{x^{2}-16}{x^{2}-10\cdot x+25} }{\frac{3\cdot x - 12}{x^{2}-3\cdot x - 10} }[/tex] Definition of division
3) [tex]\frac{(x^{2}-16)\cdot (x^{2}-3\cdot x -10)}{(x^{2}-10\cdot x + 25)\cdot (3\cdot x - 12)}[/tex] [tex]\frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{b\cdot c}[/tex]
4) [tex]\frac{(x+4)\cdot (x-4)\cdot (x-5)\cdot (x+2)}{3\cdot (x-5)^{2}\cdot (x-4) }[/tex] Factorization/Distributive property
5) [tex]\left(\frac{1}{3} \right)\cdot (x+4)\cdot (x+2)\cdot \left(\frac{x-4}{x-4} \right)\cdot \left[\frac{x-5}{(x-5)^{2}} \right][/tex] Modulative and commutative properties/Associative property
6) [tex]\frac{(x+4)\cdot (x+2)}{3\cdot (x-5)}[/tex] [tex]\frac{a^{m}}{a^{n}} = a^{m-n}[/tex]/[tex]\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot c}{b\cdot d}[/tex]/Definition of division/Result
Please help me, I’m struggling.
A: 116 square cm
B: 106 square cm
C: 143 square cm
Answer:
The answer is A. 116 square cm
Step-by-step explanation:
Assume the population is normally distributed. Given a sample size of 225, with a sample mean of 750 and a standard deviation of 30, we perform the following hypothesis test.
H0: μ = 745
Ha: μ ≠ 745
a) Is this test for the population proportion, mean, or standard deviation? What distribution should you apply for the critical value?
b) What is the test statistic?
c) What is the p-value?
d) What is your conclusion of the test at the α = 0.1005 level? Why?
We need to determine whether the test is for the population proportion, mean, or standard deviation, and what distribution should be applied for the critical value.
a) This test is for the population mean since we are comparing the sample mean to a hypothesized population mean. To find the critical value, we apply the t-distribution since the population standard deviation is un known, and we are working with a sample.
b) The test statistic for comparing means is calculated using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size).
Substituting the given values, we have:
t = (750 - 745) / (30 / √225) = 5 / 2 = 2.5.
c) To find the p-value, we compare the absolute value of the test statistic to the critical value associated with the significance level. Since the significance level α is not specified, we cannot directly calculate the p-value without knowing the critical value or α.
d) Without the critical value or the specific significance level, we cannot determine the conclusion of the test. The conclusion is drawn by comparing the p-value to the significance level α. If the p-value is less than α, we reject the null hypothesis, and if the p-value is greater than α, we fail to reject the null hypothesis.
Learn more about distribution here:
https://brainly.com/question/29664127
#SPJ11
Write the difference of 8 and 2 times m
Answer:
Your answer would be A
Step-by-step explanation:
(please help)!!!!!!!!!!!!!!
Answer
use trigonometry to find both the answers.
i have done the working out in the picture hope it helps...
Step-by-step explanation:
Find the slope of the line
Answer:
2/3
Step-by-step explanation:
Answer:
Slope = -6
Step-by-step explanation:
Given: ΔWXY is isosceles with legs WX and WY; ΔWVZ is isosceles with legs WV and WZ. Prove: ΔWXY ~ ΔWVZ. Complete the steps of the proof.
a. ASA (Angle-Side-Angle)
b. SAS (Side-Angle-Side)
c. SSS (Side-Side-Side)
d. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
We have proven that ΔWXY is similar to ΔWVZ using the ASA criterion.
We have,
To prove that ΔWXY is similar to ΔWVZ, we can use the ASA (Angle-Side-Angle) criterion.
Here are the steps of the proof:
Proof:
- Given: ΔWXY is isosceles with legs WX and WY; ΔWVZ is isosceles with legs WV and WZ.
Since ΔWXY is isosceles, we have WX ≅ WY. (Given)
Since ΔWVZ is isosceles, we have WV ≅ WZ. (Given)
We also know that ΔWXY and ΔWVZ share the common side segment WZ. (Common side)
Let's consider the angles: ∠WXY and ∠WVZ. Since ΔWXY is isosceles, we have ∠WXY ≅ ∠WYX. (Isosceles triangle property)
Similarly, since ΔWVZ is isosceles, we have ∠WVZ ≅ ∠WZV. (Isosceles triangle property)
Now, we have two pairs of congruent angles: ∠WXY ≅ ∠WYX and ∠WVZ ≅ ∠WZV.
We already know that WX ≅ WY and WV ≅ WZ.
By the ASA criterion, if two pairs of corresponding angles and the included side are congruent, then the triangles are similar.
Applying the ASA criterion, we conclude that ΔWXY ~ ΔWVZ. (Angle-Side-Angle)
Therefore,
We have proven that ΔWXY is similar to ΔWVZ using the ASA criterion.
Learn more about triangles congruency here:
https://brainly.com/question/12413243
#SPJ4
Will give crown for the RIGHT answer please do not mess around or give me weird links
Answer:
28
Step-by-step explanation:
can you guys help me please as much as you can ^^
Answer:
Step-by-step explanation:
m<1 = 50
m<2 = 22
m<3 = 108
m<4 = 50
m<5 = 65
m<6 = 50
m<7 = 43
m<8 = 65
m<9 = 75
m<10 = 18
m<11 = 25
m<12 = 40
m<13 = 115
m<14 = 65
m15 = 115