Rodney's Repair Service has a lug nut tightening machine that works well 88% of the time. They got a new machine that works well 96% of the time. Each machine is used 50% of the time. Use Bayes' Theorem to find the probability. If necessary, round your calculations to the nearest thousandths, and write your answer as a percent.
The old machine malfunctioned.
The old machine will malfunction
______% of the time
Answers
Given that Rodney's Repair Service has a lug nut tightening machine that works well 88% of the time. They got a new machine that works well 96% of the time. Each machine is used 50% of the time. The old machine will malfunction 8 % of the time
Now we have to use Bayes' theorem to find the probability of the old machine malfunctioning. Bayes' theorem is given as: P(A | B) = P(B | A) x P(A) / P(B)
Where P(A | B) is the probability of A happening given that B has occurred. P(B | A) is the probability of B happening given that A has occurred. P(A) is the prior probability of A.P(B) is the prior probability of B. Let us calculate the probability of the old machine malfunctioning as follows.
P(A) = probability of old machine malfunctioning = 1 - 0.88 = 0.12
P(B) = probability of a machine malfunctioning = 1 - 0.96 x 0.50 - 0.88 x 0.50= 0.06P
(B | A) = probability of a new machine malfunctioning given that the old machine malfunctioned = 0.04P
(A | B) = probability of the old machine malfunctioning given that a machine has malfunctioned.= (0.04 x 0.12) / 0.06= 0.08 or 8%
Therefore, the old machine will malfunction 8% of the time.
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Related Questions
two trains running on the same track travel at the rates of 40 and 45 mph, respectively. if the slower train starts an hour earlier, how long will it take the faster train to catch up to the slower train?
Answers
It will take the faster train 8 hours to catch up to the slower train.
What is displacement?When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.
In one hour, the slower train travels 40 miles, so after t hours (where t is the time it takes for the faster train to catch up), the slower train will have traveled:
d = 40(t + 1)
The faster train travels at a rate of 45 mph, so in t hours it will have traveled:
d = 45t
We can set these two equations equal to each other, since they both represent the same distance:
40(t + 1) = 45t
Expanding the left side gives:
40t + 40 = 45t
Subtracting 40t from both sides gives:
40 = 5t
Dividing both sides by 5 gives:
t = 8
So it will take the faster train 8 hours to catch up to the slower train.
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25 precent of this square is shaded. What present of the square is not shaded
Answers
Answer:
75%
Step-by-step explanation:
Answer:
75%
Step-by-step explanation:
I'm sure you meant "percent," not "present."
If 25% of the square is shaded, then the percent that is not shaded is 75%.
a newsletter publisher believes that 71% 71 % of their readers own a rolls royce. a testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. after performing a test at the 0.02 0.02 level of significance, the testing firm fails to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
Answers
We cannot claim that the newsletter publisher's statement is incorrect. Hence, the conclusion is uncertain.
The newsletter publisher's claim is uncertain after performing a test at the 0.02 level of significance as the testing firm fails to reject the null hypothesis.
In this case, we cannot claim that the publisher's statement is incorrect without additional tests and proof. Here is an explanation of the above statement.
A hypothesis test is conducted to find out whether or not there is sufficient evidence to contradict a hypothesis. In this case, the hypothesis test's null hypothesis claims that the newsletter publisher's statement is correct.
The alternate hypothesis claims that the newsletter publisher's claim is incorrect. As a result, the null hypothesis is represented by \(H_0\):
p = 0.71 (71%) and
the alternate hypothesis is represented by \(H_a\):
p ≠ 0.71 (71%).
Where 'p' denotes the percentage of newsletter readers who own a Rolls Royce.
The test statistic for a sample proportion can be calculated by
z = (p - P) / √(P(1 - P) / n)
Where 'p' denotes the sample proportion,
P denotes the population proportion, and
n denotes the sample size.
A two-tailed test is used because the alternate hypothesis is written as \(H_a\):
p ≠ 0.71 (71%).
At a 0.02 significance level, the test statistic's critical value is ±2.58 (round off) Because the test statistic does not fall in the rejection region, we fail to reject the null hypothesis.
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how do i know if this is parallel, perpendicular, or neither?
Answers
Answer:
It's perpendicular
Step-by-step explanation:
Well, normally you would have two equations. But in this case it is perpendicular to the x-axis. You must first solve for y and you'll get the answer:
y=3/4x+8
Then you plug numbers into the equation and graph them onto a graph. It'll be perpendicular to the x-axis.
What is the length of the side labelled t
Answers
Answer: t = 10m
Step-by-step explanation:
We know the lengths of the two legs, but not the length of the hypotenuse. To calculate this, we use the Pythagorean Theorem: a^2 + b^2 = c^2.
So (6)^2 + (8)^2 = (t)^2
36 + 64 = t^2
100 = t^2
sqrt (100) = sqrt (t^2)
t = 10
*sqrt = square root
Answer this for brainliest
Answers
Answer:
A D AND C
Step-by-step explanation:
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.
(a) The number of people in a restaurant that has a capacity of 100.
(b) The time it takes for a light bulb to burn out.
Answers
The number of people in a restaurant is a discrete random variable with possible values ranging from 0 to 100, while the time it takes for a light bulb to burn out is a continuous random variable with values spanning a non-negative real interval.
Let us now explain each sub-question in a detailed way:
(a) The number of people in a restaurant that has a capacity of 100 is a discrete random variable. This is because the possible values of the random variable are countable and distinct. The number of people in the restaurant can only take on whole number values from 0 to 100, inclusive. The values 0, 1, 2, ..., 100 represent the possible occupancy levels of the restaurant.
(b) The time it takes for a light bulb to burn out is a continuous random variable. This is because the possible values of the random variable form a continuous interval. The time it takes for a light bulb to burn out can theoretically range from a fraction of a second to infinity. It can take on any non-negative real value within this range. Therefore, the possible values of this random variable span a continuum rather than a countable set of distinct values.
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PLEASE HELP WITH ALL 3 QUESTIONS! I WILL GIVE BRAINLIST
Answers
Answer:
answer for the first is "Obtuse", answer for the second is "acute", answer for the third is a=right, b=obtuse, c=obtuse, d=acute
Step-by-step explanation:
Your hospital has just reset the safety stock level for sleeping pills to be 220 pills.
If your hospital consumes an average of 1,155 per day with a standard deviation of 81 pills, what is the chance that your hospital will run out of sleeping pills on any day? (Keep four decimal places in your answer, which should be a number not a percentage)
Answers
The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).
To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.
First, let's calculate the Z-score using the formula:
Z = (X - μ) / σ
Where:
X = consumption rate per day (1,155 pills)
μ = average consumption rate per day (1,155 pills)
σ = standard deviation (81 pills)
Z = (1,155 - 1,155) / 81
Z = 0
Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.
We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.
To find the probability of running out of sleeping pills, we subtract this probability from 1:
Probability of running out of sleeping pills = 1 - 0.5000
Probability of running out of sleeping pills = 0.5000
Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.
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what is 40% of 980.
Answers
Answer:
392
Step-by-step explanation:
40% of 980 = 0.4 × 980 = 392
Answer:
answer is 392
Step-by-step explanation:
Q21.
A delivery company has a total of 160 cars and vans.
the number of cars: the number of vans = 3:7
Each car and each van uses electricity or diesel or petrol.
of the cars use electricity.
25% of the cars use diesel.
The rest of the cars use petrol.
Work out the number of cars that use petrol.
You must show all your working.
Answers
30 cars of the delivery company use petrol.
According to the question,
We have the following information:
A delivery company has a total of 160 cars and vans.
The number of cars: the number of vans = 3:7
1/8 of the cars use electricity.
25% of the cars use diesel and rest use petrol.
Let's take the number of cars to be 3x and the number of vans to be 7x.
3x+7x = 160
10x = 160
x = 160/10
x = 16
Number of cars = 3*16
Number of cars = 48
Now, cars that use electricity:
1*48/8
6 cars
Cars that use diesel:
25*48/100
12 cars
Cars that use petrol:
Total number of cars-(number of cars that use electricity and diesel)
48-(6+12)
48-18
30 cars
Hence, 30 cars of the delivery company use petrol.
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(3x10,000,000,000) + (4x1,000,000)+(7x100,000) in standard form
Answers
Answer:
Answer = 34,700,000,000
Answer:
\(3.4700000 \times {10}^{7} \)
Step-by-step explanation:
30,000,000+4,000,000+700,000 equals to 34,700,000
In standard form the answer is 3.4700000×10⁷
Use distribute property to simplify the expression 5(x+4)
Answers
5(x+4)
5 x x = 5x
5 x 4 = 20
5x + 20
Answer:
\(\huge\fbox{5x+20}\)
Step-by-step explanation:
Hi there!
The Distributive Property states that
\(\bold{a(b+c)=ab+ac}\)
So, we multiplied a by everything inside the parentheses.
Now, let's use this property to solve our problem:
\(\bold{5(x+4)}\\\bold{5x+20}\)
Hope it helps!
\(\rm{Have~a~great~day!}\)
~Just a teenage girl willing to help
\(\bold{We~Are~Besties4Ever}\) :)
solve the problem in the attached
Answers
Answer:
moreinfo
Step-by-step explanation:
Write 23/9 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Answers
Answer:
2.55555556
Step-by-step explanation:
The linear equation passing through the point (2,-5) has a slope of 2 is
Answers
Answer:
y = 2x - 9
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 2 , then
y = 2x + c ← is the partial equation
To find c substitute (2, - 5) into the partial equation
- 5 = 4 + c ⇒ c = - 5 - 4 = - 9
y = 2x - 9 ← equation of line
HELP ASAPP PLEASE THIS IS ABOUT PYTHAGOREAN THEROM SPMETHING LIKE THAT please help.
Answers
Answer:
√19
Step-by-step explanation:
Pythagoras's theorem:
\(a^{2} +b^{2} =c^{2}\)
Where side c is the hypotenuse and sides a and b do not matter if switched.
9²+b²=10²
81+b²=100
b²=100-81
b²=19
b=√19
There are 20 people trying out for a team. How many ways can you make randomly select for people to make a team?
Answers
There are 15,504 ways to randomly select a team of 5 people from a group of 20 people
If there are 20 people trying out for a team, the number of ways to select a team of n people can be calculated using the formula for combinations, which is:
C(20, n) = 20! / (n! * (20 - n)!)
where C(20, n) represents the number of ways to select n people from a group of 20 people.
For example, if we want to select a team of 5 people, we can plug in n = 5 and calculate:
C(20, 5) = 20! / (5! * (20 - 5)!) = 15,504
Therefore, there are 15,504 ways to randomly select a team of 5 people from a group of 20 people. Similarly, we can calculate the number of ways to select teams of different sizes by plugging different values of n into the formula for combinations.
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if z = f(x, y) and fx(2, 5) = 5, fy(2, 5) = −8 , find dz dt at t = 4 when x = g(t), y = h(t) and g(4) = 2 , g ′ (4) = 5 . h(4) = 5 , h′ (4) = 2 .
Answers
The answer to the question is the rate of change of z with respect to t at t=4 is 17.
To find dz/dt at t=4 using the given information, we can use the chain rule of partial differentiation.
We know that dz/dt = ∂z/∂x dx/dt + ∂z/∂y dy/dt, where ∂z/∂x and ∂z/∂y are the partial derivatives of z with respect to x and y, respectively, and dx/dt and dy/dt are the rates of change of x and y with respect to t, respectively.
Using the given information, we have ∂z/∂x = 5, ∂z/∂y = -8, x = g(t), y = h(t), g(4) = 2, g'(4) = 5, h(4) = 5, and h'(4) = 2. Therefore, we have:
dz/dt = ∂z/∂x dx/dt + ∂z/∂y dy/dt
= 5(g'(4)) + (-8)(h'(4))
= 5(5) + (-8)(2)
= 17
So the rate of change of z with respect to t at t=4 is 17.
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25x = 3 (1 + 8x) + 2
x=7
x = 5
x=2
x = 11
Answers
In the given equation 25x = 3 (1 + 8x) + 2, the value of x is found to be x = 5 by solving the equation.
What exactly is an equation?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.What are the three kinds of equations?Linear equations are classified into three types: point-slope, standard, and slope-intercept.
The given equation is :
25x = 3 (1 + 8x) + 2
On solving the equation for x we get,
25x = 3 + 24x + 2
25x - 24x = 5
x = 5
Therefore, the value of x in the given equation 25x = 3 (1 + 8x) + 2 is found to be x = 5.
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The table shows the shoe size of 23 students.
A student is picked at random.
there are 2 ansers
(a) Work out the probability that the student has a school size of 8.
(b) Work out the probability that the student has a school size of 7 or smaller.
Pls help
Answers
(a) The probability that the student has a shoe size of 8 is 5/23.
(b) The probability that the student has a shoe size of 7 or smaller is 12/23.
To calculate the probabilities, we need to determine the number of students with the shoe sizes mentioned and divide it by the total number of students.
Given the table shows the shoe sizes of 23 students, we can find:
(a) The probability that the student has a shoe size of 8:
Looking at the table, we need to count the number of students with a shoe size of 8.
Let's assume there are 5 students with a shoe size of 8.
The probability would be:
P(shoe size 8) = Number of students with shoe size 8 / Total number of students = 5 / 23.
(b) The probability that the student has a shoe size of 7 or smaller:
We need to count the number of students with shoe sizes 7 or smaller. Let's assume there are 12 students with a shoe size of 7 or smaller.
The probability would be:
P(shoe size 7 or smaller) = Number of students with shoe size 7 or smaller / Total number of students = 12 / 23.
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Question: The table shows the shoe size of 23 students.
A student is picked at random.
there are 2 ansers
(a) Work out the probability that the student has a school size of 8.
(b) Work out the probability that the student has a school size of 7 or smaller.
8.
For which set of data is the median greater than the mean?
A.
B.
C.
D.
{8, 12, 14, 14, 20}
{8, 12, 14, 14, 22}
{9, 13, 14, 15, 19}
(9, 13, 14, 15, 20}
Answers
Answer:
B
Step-by-step explanation:
For a set of data to have a median that is greater than the mean, it must have an odd number of values and be skewed to the right. This means that the majority of the values in the set must be smaller than the median, with a few larger values on the right side of the distribution.
Out of the given options, the only set of data that satisfies these conditions is (B) {8, 12, 14, 14, 22}. This set has an odd number of values, and the median of 14 is greater than the mean of 14.4. The other options have either an even number of values, or are not skewed to the right.
Therefore, the correct answer is (B) {8, 12, 14, 14, 22}.
Erin and her friends went to a movie on Thursday afternoon. It took 50 minutes to drive to the theater. They arrived at the theater 50 minutes before the movie started. Once it started, the movie lasted for 1 hour and 30 minutes and ended at 4:30 P.M. What time did Erin and her friends leave for the movies?
Answers
Answer: 12:30 P.M.
Step-by-step explanation:
50 + 50 + 50 + 90 minutes = 240 minutes
240 divided by 60 = 4
4 hours before 4:30 P.M. = 12:30 P.M.
Answer should be 12:30 P.M.
Answer:
They left the house at 1:20 P.M.
Step-by-step explanation:
The movie was an 1 1/2 so 4:30 - 1:30 = 3:00
Thy got there 50 minutes before so 3:00 - 0:50 = 2:10
It took them 50 minutes to get there so 2:10 - 0:50 = 1:20
Therefore they left the house at 1:20 P.M.
Determine the y-intercept of the equation -x + 2y = 10a. 1b.-10C. 5d. 2
Answers
Determine the y-intercept of the equation -x + 2y = 10
a. 1
b.-10
C. 5
d. 2
__________________________________________
y-intercept is (0, b)
y = mx +b
-x + 2y = 10
2y = x +10
y = 1/2 x + 5
______________
if x= 0
y= 1/2 *0 +5
y= 5
____________________
The y-intercept is (0, 5 )
The answer is c
Got an rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 76 cents for each mile driven. Goes. Had to pay $216.27 when he returned the truck. For how many miles did he drive the truck?
Answers
Solution
\(\begin{gathered} 20.96+0.76m=216.27 \\ \\ \Rightarrow0.76m=216.27-20.96 \\ \\ \Rightarrow m=\frac{195.31}{0.76}=257\text{ miles} \end{gathered}\)What is one example of change in the passage. ??
A. Japan has continued to exist as an independent country for thousands of years
B. The United States forced japan to strip its emperors of significant
C. Japan’s emperors has wielded only ceremonial power from the end of World War II until today
D. The Japanese imperial system began thousands of years ago and still exist today
Answers
The correct answer is B. The passage states that "The United States forced Japan to strip its emperors of significant power after World War II." This is a clear example of a change in the role of the Japanese emperors.
solve for x it is a parallelogram
pls help
Answers
Answer:
x = 5
Step-by-step explanation:I hope that this answer will help you
Answer:
\(3x + 2 = 17 \\ 3x = 15 \\ \boxed{x = 5}\)
5 is the right answer.What is the greatest value in the range of y=x²-7 for the domain {-2,0,1}?
Answers
Answer:
f(-2) = - 3 is the greatest value in the given range
-------------------------------
GivenFunction y = x² - 7,Domain x = {- 2, 0, 1 }.Find the value for each domain and comparef(-2) = (-2)² - 7 = 4 - 7 = - 3f(0) = 0² - 7 = 0 - 7 = - 7f(1) = 1² - 7 = 1 - 7 = - 6The greatest value of the function is - 3.
Calculate this product to help you solve the problem
Answers
Answer:
7a
Step-by-step explanation:
We don't actually know the variable A and we don't have a final product to help us solve it, so the best we can do is make 7 a coefficient to the variable A, making the answer 7a.
What is the height of the cylinder? The figure is not drawn to scale.
V = 282.7 in²
18 in
11.3 in
7.2 in
3.6 in
Answers
The height of the cylinder is \(3 inch\)
How can the height of the cylinder be found?Based on the attached figure,
Volume of the cylinder = 282.7 square inches
Radius of the cylinder =5 inches.
The height of the cylinder = ?
The volume of the cylinder can be found with the formula as :
\(V=pi r^{2} h\)
\(h=\frac{V}{pi r^{2} } \\\\h = \frac{282.7}{3.142 * 5^{2} } \\\\=3 inch\)
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