Answer:
a) 0.011
b) 0.0032
Step-by-step explanation:
first lets say A₁ denotes the event that first inspector detects a flaw and A₂ is event that the law will be detected by the second inspector,
also let B denote the event that an item has a flaw.
a)
Given that;
P(B) = 0.1
so
P(A₁ / B ) = 0.9, P(A₂ / B ) = 0.7
using Baye's rule, the probability that an item has a flaw if it was passed by the first inspector is;
P(B / A₁ⁿ ) = [P(A₁ⁿ / B ) P(B)] / [ P(A₁ⁿ / B ) P(B) + P(A₁ⁿ / Bⁿ ) P(Bⁿ) ]
the probability that the first inspector will not detect the flaw if it actually exist is;
P(A₁ⁿ / B ) = 1 - P(A₁ / B )
= 1 - 0.9
= 0.1
Since there are no false detections, the probability that the first inspector will not detect the flaw, given that item does not have flaws is;
P(A₁ⁿ / Bⁿ ) = 1.0
so the probability that the item has flaw if it was passed by the first inspector is;
P(B / A₁ⁿ ) = [(0.1) (0.1)] / [ (0.1 ) (0.1) + (1.0) (1 - 0.1) ]
= 0.01 / ( 0.01 + 0.9)
= 0.01 / 0.91
= 0.011
b)
Also by Bayes rule, the probability that the item has a flaw if it was passed by both inspectors is;
P(B / A₁ⁿ ∩ A₂ⁿ) = [ P(A₁ⁿ ∩ A₂ⁿ / B) P(B)] / [ P(A₁ⁿ ∩ A₂ⁿ / B) P(B) + P(A₁ⁿ ∩ A₂ⁿ / Bⁿ) P(Bⁿ)]
Now since inspectors function independently, the probability that both inspectors will not detect the flaw if it actually exists is;
P(A₁ⁿ ∩ A₂ⁿ / B) = P(A₁ⁿ / B) P(A₂ⁿ / B)
= ( 1 - 0.9 ) ( 1 - 0.7)
= 0.1 * 0.3
= 0.03
since there are no false detections, the probability that both inspectors will not detect the flaw, given that item does not have a flaw is;
P(A₁ⁿ ∩ A₂ⁿ / Bⁿ) = 1.0
therefore
the probability that the item has a flaw if it was passed by both inspectors is;
P(B / A₁ⁿ ∩ A₂ⁿ) = [(0.03)(0.1)] / [(0.03)(0.1) + (1.0)(1-0.1)
= 0.003 / 0.93
= 0.0032
How many different 2-letter passwords can be formed from the letters O, P, Q, R, S, T, and U if no repetition of letters is allowed?
The problem involves a__
because the__
of letters selected
___matter
Answer:
Below.
Step-by-step-explanation:
This is the number of permutations of 2 from 7.
= 7! / (7-2)!
= 7*6*5*4*3*2*1 / 5*4*3*2*1
= 7 * 6
= 42.
Its a permutation because the order of letters do matter,.
Serena paid $194.99 for a game system and then bought two equally-priced games. She spent a total of $284.97.
If p represents the price of one game, which equation represents the situation?
What is the price, p, of one game?
Answer:
The price of each game is $44.99, so P = 44.99
Equation: 2p + 194.99 = 284.97
Step-by-step explanation:
284.97 - 194.99 = 89.98
89.98 divided by 2 = 44.99
A 7 1/4 inch candle burns down its height decreases 3/4 every hour. How many hours does it take to burn down the candle
Answer:
x=9 2/3 hours (or) x=9hours and 40 minutes
Step-by-step explanation:
7.25-.75x=0
-.75x=-7.25
x=9.66666...
-or-
x=9 2/3 hours (or) x=9hours and 40 minutes
How are exponents related to taking the root of a number?
Answer:
with exponents, you take a number and multiply it by itself.
Step-by-step explanation:
the root of a number is the number that can be multiplied a certain amount of times to get us that number.
therefore roots get you to the root of a number.
Hope it helps!
(even if its two weeks late.....)
Hot dogs come packed 10 in a package. Hot dog buns come packed 8 in a package. If we want one hot dog for each bun for a picnic with none left over, what is the least amount of each we need to buy? How many
packages of each item would we have to buy?
Answer:
40 individual hotdogs and 40 individual hot dog buns
4 hotdog packages and 5 hot dog bun packages
Step-by-step explanation:
multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80
multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Least common multiple (LCM) is 40
10*4=40
8*5=40
Why is the square root of 23 an irrational number
Answer:
When simplified, the square root of 23 is a non-terminating and non-repeating decimal. This, and the fact that it can't be written as a fraction is why it is an irrational number.
hi! i’ll mark brainlest :) i’m dumb so idk the answer
Answer:
its the second one :)
Step-by-step explanation:
Answer:
√17
Step-by-step explanation:
Using the Pythagorean Theorem a² + b² = c², where a is the distance along the y axis from point to point and b is the distance along the x axis from point, 1² + 4² = 17. c²=17. c =√17
The value of the 3 in 23 817 is times the value of the 3 in 1936
Answer:
90000
Step-by-step explanation:
Value of the 3 in 23 817 is 3 thousand
Value of the 3 in 1936 is 30
thus
3000 x 30
= 90000
Which equations are equivalent to 3/4 +m= -7/4 Select three options
I think its B, C and E. Sorry if im wrong
Answer:
B peepee C peepee E pee pee
Step-by-step explanation:
Got 100 percent on exam!
If a full moon occurs on August 10, the next full moon would occur on/around _________.
Question 5 options:
August 17
September 10
September 1
October 10
Answer:
I would say September 10 just because it takes 27 days, 7 hours, and 43 minutes for our Moon to complete one full orbit around Earth.
Step-by-step explanation:
Situation 1. ROCKET RIDE.
The Rocket Coaster has 10 cars, some that
hold 4 people and some that hold 8 people.
There is room for 56 people altogether.
How many 4-passenger cars are there?
How many 8-passenger cars are there?
Let x= number of 4-passenger cars
Let y = number of 8-passenger cars
equation #1:
equation #2:
Solution:
Solve for x
X-9= -33
Answer:
X=-24
Step-by-step explanation:
Let's solve your equation step-by-step.
x−9=−33
Step 1: Add 9 to both sides.
x−9+9=−33+9
x=−24
Answer:
x=-24
136 feet to 150 feet
Answer for every 136 feet their are 150 feet
Step-by-step explanation:
i hope this helped.
whats 1+8............ ...
Answer:
9
Step-by-step explanation:
ez points bruh
Answer:
8
Step-by-step explanation:
Help me
A room is 12 feet long and 10.5 feet wide. A scale model of the room is 3.5 feet wide. What is the area of the scale model?
a: 10.3 square feet
b:14 square feet
C; 36 square feet
d: 122.5 square feet
Answer:
B. 14 square feet
Step-by-step explanation:
just took the test
pls i need help fast i will give you a like flow you in here pls answer
Answer:
sorry i cant see it
step-by-step explanation:
.
Please help! In a _ IRA, the contributions are taxable when deposited, but the money is
_ when withdrawn at retirement.
Answer:
roth, tax exempt
Step-by-step explanation:
Answer:
In a Roth IRA, the contributions are taxable, and withdrawals at retirement are tax exempt. In a traditional IRA, the contributions are tax deductible up to a certain income limit, and earnings are tax deferred. Withdrawals from a traditional IRA are taxed at the individual’s income tax rate at the time of withdrawal.
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION AND ANSWERS
8x + 4y= 12
2x + y= 3
[tex]\tt Step-by-step~explanation:[/tex]
In order to solve for both x and y, we need to use the substitution property, where we replace a variable with what we solved for.
[tex]\tt Step~1:[/tex]
Let's solve for y first. Equation (1st one): 8x + 4y = 12. To isolate y, we can first subtract 8x from both sides, and then divide all terms by 4.
[tex]\tt 8x- (8x)+4y=12-(8x)\\4y=12-8x\\4y/4=y\\12/4=3\\-8x/4=-2x\\y=3-2x[/tex]
[tex]\tt Step~2:[/tex]
Then, we can solve for x. Let's take the second equation: 3x + y = 3. We take what we solved for in the previous step and plug it into this equation.
[tex]\tt 2x+(3-2x)=3\\2x+3-2x=3\\2x-2x=0\\3-3=0\\0=0\\x=x[/tex]
[tex]\large\boxed{\tt Our ~final~answer:(x,3-2x)}[/tex]
Both equations are also the same, so the solution = all real numbers for x.
[tex]\tt y=3-2x\\3-2x=3-2x[/tex]
(6.8*10^4) +(9.24*10^5)
had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
Step-by-step explanation:
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
How did the Muhammad’s death in 632 affect the Muslim state he had established?
Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h2) to estimate the first derivative of the function examined in the previous problem (Q1). Evaluate the derivative at x = 2 using a step size of h = 0:25. Compare your results with the true value of the derivative (note: when someone says `compare' that's almost always an invitation to use a relative or percent metric for comparison). Interpret your results on the basis of the remainder term of the Taylor series expansion.
Answer:
Answer has explained below.
Step-by-step explanation:
Consider the function is:
F(x) = 25x3 – 6x2 +7x -88
Differentiate with respect to x, we get
F’(x) = 25. 3x2 – 6.2x + 7
= 75x2 – 12x +7
At x = 2, we have
F (2) = 25(2)3 – 6(2)2 + 7(2)-88
=102
And f’(2) = 75(2)2 – 12 (2) +7
=283
Now, calculate forward divided difference as:
xi + 1 = xi + h
=2 + 0.25
=2.25
F (xi + 1) = f (2.25) = 25 (2.25)3 – 6(2.25)2 +7(2.25) -88
=182.21
f’(2) = f(2.25) – f(2) / 0.25 = 182.21 – 102 / 0.25
= 320.84
Єt = 283 – 320.8 / 283 = -13.36%
Now calculate backward divided difference:
Xi-1 = xi –h = 2 – 0.25 = 1.75
F(xi-1)= f(1.8) = 25 . (1.8)3 -6 (1.8)2 + 7 (1.8) – 88
= 50.96
F’(2) = f(2) – f(1.8) / 0.25 = 102 – 50.96 / 0.25 = 204.16
Єt = 283 – 204.16 / 283 = 27.86%
Finally, centered divided difference is obtain by inserting f(xi+1) and f (xi-1):
F’(2) = f(2.25) – f(1.8) /2 x 0.25 = 320.84 -50.96 / 0.5 = 539.68
Єt = 283 – 539.68 / 283 = -90.7%
I put a picture in please help
A car dealership likes to have 4 blue cars on the lot for every 3 white cars. At this rate, how many white cars
will be on the lot when there are 16 blue cars?
Answer:
There will be 12 white cars ^‿^:
A recent study found that 51 children who watched a commercial for Walker Crisps (potato chips) featuring a long-standing sports celebrity endorser ate a mean of 36 grams of Walker Crisps as compared to a mean of 25 g of Walker Crisps for 41 children who watched a commercial for an alternative food snack. Suppose that the sample standard deviation for the children who watched the sports celebrity–endorsed Walker Crisps commercial was 21.4 g and the sample standard deviation for the children who watched the alternative food snack commercial was 12.8 g. Assuming the population variances are not equal and alpha-05, is there any evidence that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial?
1. What is the claim from the question? What are Null and Alternative Hypothesis for this problem?
2. What kind of test do you want to use?
3. Calculate Test Statistics.
4. Find P-value.
5. What is the conclusion that you could make?
Answer:
1
The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial
2
The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population
3
[tex]t = 3.054[/tex]
4
The p-value is [tex]p-value = P(Z > 3.054) = 0.0011291[/tex]
5
The conclusion is
There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial
The test statistics is
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 51[/tex]
The first sample mean is [tex]\mu_1 = 36[/tex]
The second sample size is [tex]n_2 = 41[/tex]
The second sample size is [tex]\mu_2 = 25[/tex]
The first standard deviation is [tex]\sigma _1 = 21.4 \ g[/tex]
The second standard deviation is [tex]\sigma _2 = 12.8 \ g[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_ 2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 > \mu_2[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }[/tex]
=> [tex]t = \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51} + \frac{ 12.8^2}{41} } }[/tex]
=> [tex]t = 3.054[/tex]
The p-value is mathematically represented as
[tex]p-value = P(Z > 3.054)[/tex]
Generally from the z table
[tex]P(Z > 3.054) = 0.0011291[/tex]
=> [tex]p-value = P(Z > 3.054) = 0.0011291[/tex]
From the values obtained we see that [tex]p-value < \alpha[/tex] so the null hypothesis is rejected
Thus the conclusion is
There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial
The value of the difference in the mean number of chips eaten can be used to test the hypothesis.
The correct responses are;
1. The claim is that children that watched the given commercial ate more Walker Crisps potato chips than others. The null hypothesis is [tex]\underline {H_0; \ \overline x_1 = \overline x_2}[/tex] , the alternative hypothesis is, [tex]\underline{H_a; \ \overline x_1 > \overline x_2}[/tex] 2. The kind of test to use is a t-test3. The test statistic is approximately 3.0544. The p-value is; 0.001 < p-value < 0.00255. Reject the null hypothesis, there is significant statistical evidence to suggest that the children that watched the commercial ate more Walter Crisps potato chips than children that watched the commercial for an alternative snack.Reasons:
The given parameters are;
The amount of Walker Crisps potato chips children ate, based on commercial watched.
Celebrity endorsed food snack commercial mean, [tex]\overline x_1[/tex] = 36 g
Sample size that watched the celebrity endorsed commercial, n₁ = 51
Alternative food snack commercial mean, [tex]\overline x_2[/tex] = 25 g
Sample size that watched the other commercial = 41
Standard deviation, SD, of the samples;
Sample that watched the celebrity endorsed commercial, SD₁ = 21.4 g
Sample that watched the other commercial, SD₂ = 12.8 g
Reasons:
1. The claim from the question is; The mean amount of Walker Crisp eaten was significantly higher for the children who watched the sports celebrity - endorsed Walker Crisps commercial.
The null hypothesis is, H₀; [tex]\overline x_1 = \overline x_2[/tex] (There is no difference in the mean)
The alternative hypothesis is, Hₐ; [tex]\overline x_1[/tex] > [tex]\overline x_2[/tex] (The mean of the amount of Walker Crisps eaten is significantly higher for the children that watched the sports celebrity-endorsed commercial)
2. Given that the aim of the study is to determine if the mean of the first
sample is higher than the mean of the second sample, the kind of test to
be performed is the test of the difference in the mean of the two samples
based on specified hypothesis, (one sample is higher), which is done using
a t-test, given that the population mean is not specified (unknown).
The kind of test to use is a t-test
3. The test statistic is given by Welch's Test for unequal variance as follows;
[tex]\displaystyle t = \mathbf{\frac{\overline x_1 - \overline x_2}{\sqrt{\dfrac{s_1^2}{n_1} +\dfrac{s_2^2}{n_2} } }}[/tex]
Which gives;
[tex]\displaystyle t = \frac{36- 25}{\sqrt{\dfrac{21.4^2}{51} +\dfrac{12.8^2}{41} } } = \frac{77500}{25379} \approx 3.054[/tex]
The test statistic, t ≈ 3.054
4. From the above test statistic and by finding, degrees of freedom, df as follows, the p-value can be found.
[tex]\displaystyle df = \mathbf{\frac{\left(\dfrac{s_1^2}{n_1} +\dfrac{s_2^2 \righ}{n_2} \right)^2}{\dfrac{1}{n_1 - 1} \cdot \left( \dfrac{s_1^2}{n_1} \right)^2 + \dfrac{1}{n_2 - 1} \cdot \left( \dfrac{s_2^2}{n_2} \right)^2}}[/tex]
Which gives;
[tex]\displaystyle df = \frac{\left(\dfrac{21.4^2}{51} +\dfrac{12.8^2 \righ}{41} \right)^2}{\dfrac{1}{51 - 1} \cdot \left( \dfrac{21.4^2}{51} \right)^2 + \dfrac{1}{41 - 1} \cdot \left( \dfrac{12.8^2}{41} \right)^2} \approx \mathbf{83.69}[/tex]
From the t-test table, we have the p-value of the result as follows;
The p-value is; 0.001 < P(t > 3.054) < 0.0025.
5. The conclusion that can be made is; Given that the p-value of the test
statistic is less than the given alpha value of 0.05, we reject the null
hypothesis, given that there is significant statistical evidence to show that
the mean amount of Walker Crisp eaten was significantly higher for the
children that watch the celebrity-endorsed Walker Crisps commercial.
Learn more here:
https://brainly.com/question/6501190
https://brainly.com/question/22797341
convert 7/8 to a decimal Then determine if the decimal is terminating or repeating
Answer:
0.875 = 7/8 and it is terminating
Step-by-step explanation:
The sales representatives at the geek padd makes a commission $13.13 from the sale of $191. What is the commision rate?
Answer:
about 6.87%
Step-by-step explanation:
First, set up your problem:
$13.13 = x %
$191 100%
Explaining the setup: $191 is the total, so it is equal to 100%. We're trying to find what percent $13.13 is of $191, so we can call that x %. Then, because they are equal to each other, cross multiply.
You should end up with this:
1313 = 191x
Simplify the equation:
x = 6.874 . . .
Then, round to the given value.
(nearest hundredth) 6.87%
Calculate the income tax for a person earning $28,000. Round to the nearest dollar.
Ms. Fitzsimmons wanted to buy two of the same jackets in different colors online. The online store
charged a one-time flat rate of $7.99 for shipping. Her grand total was $62.27. What is the cost of
one jacket?
The cost of one jacket is $
Answer:
the cost of one jacket is $27.14
Simplify |15-26 / 3| + |-8 + 19 / 2|
A). 11/3
B). 11/2
C). 55/6
D). 0
Answer:
55/6
Step-by-step explanation:
55/6 is the answer if you want that simplified.
what do I have when I round 6.385 to the nearest tenth
7. The terms of expression 5x - 3xy are
a. 5xy and 3x b. 5x and 3x c. 5x and -3x d. 5x and
3xy
Answer:
7. The terms of expression 5x - 3xy are
a. 5xy and 3x b. 5x and 3x c. 5x and -3x d. 5x and
3xy
Step-by-step explanation:
Im /gucci.