A light bulb manufacturer ships large consignments of light bulbs to big industrial users. When the production process is functioning correctly, which is 90% of the time, 25% of all bulbs produced are defective. However, the process is susceptible to an occasional malfunction, leading to a defective rate of 60%. If a defective bulb is found, what is the probability that the process is functioning correctly?
NOTE: This problem is using Bayes Theorem. C(D) = 0.25
Prior probability functioning correctly of no defect P(C) = 0.90
Prior probability it is not working correctly P(NC) = 0.10
Find the conditional probabilities of a defect when the process is working correctly.
Find the conditional probabilities of a defect when it is not working correctly. (the branches of tree diagram)
Because there are only 2 events, you can also use a bivariate table to solve.
I know this is Bayes because I am given evidence (defective bulb) and am asked to update the prior probabilities with this new information.
A. 0.211
B. 0.789
C. 0.944
D. 0.056
The problem involves using Bayes' Theorem to calculate the probability that the manufacturing process is functioning correctly given that a defective bulb is found.
To solve the problem, we can use Bayes' Theorem, which states that the conditional probability of an event A given event B can be calculated using the formula P(A|B) = (P(B|A) * P(A)) / P(B).
In this case, we want to find the probability that the process is functioning correctly (C) given that a defective bulb is found (D). The prior probability of the process functioning correctly is P(C) = 0.90, and the prior probability of a defective bulb is P(D) = 0.25.
We are also given the conditional probabilities: P(D|C) = 0.25 (defective rate when the process is functioning correctly) and P(D|NC) = 0.60 (defective rate when the process is not functioning correctly).
Using Bayes' Theorem, we can calculate P(C|D) as follows:
P(C|D) = (P(D|C) * P(C)) / P(D)
P(D) can be calculated using the law of total probability:
P(D) = P(D|C) * P(C) + P(D|NC) * P(NC)
Substituting the values, we can compute P(D) and then substitute it back into the equation for P(C|D) to find the probability that the process is functioning correctly given a defective bulb.
The correct answer, in this case, is A. 0.211.
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In the coordinate plane, the points X (3, 6), Y (−7, 8), and Z (−11, 2) are reflected over the y-axis to the points X′, Y′, and Z′, respectively. What are the coordinates of X′, Y′, and Z′?
Answer:
X'= (-3,6)
Y'=(7,8)
Z'=(11,2)
Step-by-step explanation:
when a point is reflected over the y axis, (x,y) becomes (-x,y). so the x value is just multiplied by -1
Answer:
X′(−3, 6), Y′(7, 8), Z′(11, 2)
Step-by-step explanation:
Imagine you are a spy who needs to infiltrate a secret base located at the origin of the coordinate plane. You have three accomplices, X, Y, and Z, who are waiting for you at different points on the plane. X is at (3, 6), Y is at (-7, 8), and Z is at (-11, 2). You have a device that can reflect any point over the y-axis, which you plan to use to confuse the enemy guards. You decide to reflect X, Y, and Z over the y-axis to create X', Y', and Z', respectively. What are the coordinates of these new points?
To find the coordinates of X', you simply change the sign of the x-coordinate of X. So, X' is at (-3, 6). Similarly, to find the coordinates of Y' and Z', you change the sign of the x-coordinates of Y and Z. So Y' is at (7, 8) and Z' is at (11, 2). Now you have three new points that are symmetric to the original ones over the y-axis.
But wait! There's a problem. The enemy guards have noticed that something is wrong. They see four points on their radar: one at the origin (you) and three on the right side of the y-axis (X', Y', and Z'). They realize that these points are reflections of some other points on the left side of the y-axis. They quickly deduce that there must be a spy among them. They start searching for you.
You need to act fast. You use your device again to reflect yourself over the y-axis. This creates a new point at (-0, 0), which is exactly the same as (0, 0). You have effectively disappeared from their radar. You sneak into the base while they are busy looking for you on the wrong side of the plane.
You have successfully completed your mission. Congratulations! You are a master of reflections.
✧☆*: .。. That's all folks, have fun with math! (✧ω✧) .。.:*☆✧
Point Z is equidistant from the sides of ARST. C R Z A B S Which must be true? A. SZ&TZ
B. RZ =R BZ
C. CTZ = ASZ
D. ASZ=ZSB
Answer:
B. RZ =R BZ
Step-by-step explanation:
Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.
Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.
Answer: vv
Step-by-step explanation:
Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.
Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.
Now, let's examine the options:
A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.
B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.
C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.
D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.
Therefore, the only statement that must be true is option B: RZ = RB.
12/22 + 1/11 in the lowest terms
Answer: 7/11
Step-by-step explanation:
12/22 +1/11 = 12/22 + 2/22 (make the denominator the same number, in this case the lowest common multiple of 11 and 22, which is 22)
12/22 + 2/22 = 14/22
14/22 = 7/11 (divide both the numerator and denominator by 2)
How many times larger is the volume of a square pyramid if the base edge is tripled?
Answer:
Well first you would just have to look at the equation for the volume of a pyramid. This is:
V = (length * width * height) / 3
and so we can just say all pyramids have a volume of V.
So now we want the base to be 3 times bigger which means we would have to multiple the length and width by 3 and the new volume equation would be
V = (3*length * 3 * width * height) / 3
we can factor the two 3's from the parenthesis and get
V = 9(l * w * h) /3
if we are looking at a ratio of how much the volume increases we can say
aV = b(l * w * h) /3
since:
V = (l * w * h) / 3
then:
aV = bV, divide both sides by V and:
a = b
using this we can see that the volume increases by a factor of 9 for 3 times bigger
now for 6 times
V = (6 * l * 6 * w * h) / 3, pull 6 * 6 out
V = 36(l * w * h) /3
and this one increases by factor of 36
if we see a pattern it always increases by the square of the factor of the growoth of the base
so for 9 times bigger it would be 9^2 = 81
and for 27 times bigger it would be 27^2 = 729
Step-by-step explanation:
Assume that women's weights are normally distributed with a mean given by μ=143 lb and a standard deviation given by σ =29 lb.
b) If 4 women are randomly selected, find the probability that they have a mean weight above 176
c) If 57 women are randomly selected, find the probability that they have a mean weight above 176
Answer:
b) P(mean weight > 176) = 1 - P(mean weight ≤ 176) = 1 - 0.9332 = 0.0668
c) P(mean weight > 176) = 1 - P(mean weight ≤ 176) = 1 - 0.9997 = 0.0003
You and your friends went to dinner and you decided to pay for everyone's meal. The total bill came to $65.00. You decided to give the waiter a 20% tip before tax. You also had to pay 6.8% sales tax. How much did you have to pay in all?
Answer:
82.236
Step-by-step explanation:
20% of 65 is 12
65+12=77 before tax
6.8% of 77=5.236
77+5.236=82.236
Mitosis is a process by which 1 cell divides and becomes 2 cells, those 2 cells divide and become 4 cells, and so on. Write an equation for the nth term of the geometric sequence giving the numbers of cells at each stage of this process, where a1=1. Then find a10.
Answer:
An equation for the nth term is aₙ = 2ⁿ⁻¹
and a₁₀ = 512
Step-by-step explanation:
From the question, 1 cell divides and becomes 2 cells, those 2 cells divide and become 4 cells, and so on
∴The sequence will be
1,2,4, ..., n
From the formula
aₙ = a₁rⁿ⁻¹
Where aₙ is the nth term
a₁ is the first term
n is the number of terms
and r is the common ratio
From the sequence,
a₁ = 1,
r = a₂/a₁ = 2/1 = 2
∴ The nth term (aₙ) will be
aₙ = (1)(2)ⁿ⁻¹
aₙ = 2ⁿ⁻¹
Hence, an equation for the nth term is aₙ = 2ⁿ⁻¹
To find a₁₀, substitute n= 10 into the equation
aₙ = 2ⁿ⁻¹
Then
a₁₀ = 2¹⁰ ⁻ ¹
a₁₀ = 2⁹
a₁₀ = 512
∴ a₁₀ = 512
We consider the measurable space (Ω,F) where Ω={ω1,ω2,ω3,ω4,ω5,ω6} and F=P(Ω). We define the probability measure P on Ω by P(ωi)=21i. We then define the random variables X and Y by Y(ωi)=(−1)i, and X(ωi)={1−1 if i≤3 if i>3 We also define Z=X+Y. (4.1) List all the sets in σ(X) (4.2) Determine E[Y∣X] and E[Z∣X] by specifying the value of each random variable for each ωi. (6) (4.3) Compute E[Z∣X]−E[Y∣X]
(4.1) The sets in σ(X), the sigma-algebra generated by random variable X, can be determined by considering the pre-images of X. Since X can take two possible values, 1 and -1/2, the sets in σ(X) will be all possible combinations of these values. Therefore, the sets in σ(X) are:
{∅, Ω, {ω1, ω2, ω3}, {ω4, ω5, ω6}, {ω1, ω2, ω3, ω4, ω5, ω6}}.
(4.2) To determine E[Y|X] and E[Z|X], we need to find the conditional expectations of Y and Z given X for each ωi.
For Y:
E[Y|X=1] = Σ P(ωi|X=1)Y(ωi) = P(ω1|X=1)Y(ω1) + P(ω2|X=1)Y(ω2) + P(ω3|X=1)Y(ω3) + P(ω4|X=1)Y(ω4) + P(ω5|X=1)Y(ω5) + P(ω6|X=1)Y(ω6)
= 0*(-1) + 0*(-1) + 1*(-1) + 0*(-1) + 0*(-1) + 0*(-1) = -1.
E[Y|X=-1/2] = Σ P(ωi|X=-1/2)Y(ωi) = P(ω1|X=-1/2)Y(ω1) + P(ω2|X=-1/2)Y(ω2) + P(ω3|X=-1/2)Y(ω3) + P(ω4|X=-1/2)Y(ω4) + P(ω5|X=-1/2)Y(ω5) + P(ω6|X=-1/2)Y(ω6)
= 1*(-1) + 1*(-1) + 0*(-1) + 1*(-1) + 1*(-1) + 1*(-1) = -6.
For Z:
E[Z|X=1] = Σ P(ωi|X=1)Z(ωi) = P(ω1|X=1)Z(ω1) + P(ω2|X=1)Z(ω2) + P(ω3|X=1)Z(ω3) + P(ω4|X=1)Z(ω4) + P(ω5|X=1)Z(ω5) + P(ω6|X=1)Z(ω6)
= 0*(1-1) + 0*(1-1) + 1*(1-1) + 0*(1+1) + 0*(1+1) + 0*(1+1) = 0.
E[Z|X=-1/2] = Σ P(ωi|X=-1/2)Z(ωi) = P(ω1|X=-1/2)Z(ω1) + P(ω2|X=-1/2)Z(ω2) + P(ω3|X=-1/2)Z(ω3) + P(ω4|X=-1/2)Z(ω4) + P(ω5|X=-1
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is a number 36 a perfect square and why
Answer:
Yes it is.
Step-by-step explanation:
This is because a perfect square is the product that is given when the multiplier is multiplied by itself
HELP!!! My math is due in 1 hour and I’m confused!
Answer:
welp guess its already due
Step-by-step explanation:
sorry
SOMEONE PLEASE HELP ME
Answer:
27
Step-by-step explanation:
math
surface area of composite figures
Answer:
mark me brainliest hope your day goes wellStep-by-step explanation:
The area of the composite figures is the area of one or more simple polygons and circles combined. We can add the areas of all the basic figures together to calculate the area of the composite figures. Find the area of each shape and add them together to find the area of the composite figure.Answer:
The surface area is the sum of all the faces (or surfaces) of a 3D shape. Composite figures are 2 figures put together. (There is an example of a composite figure below) You find an area of both shapes and then add them together, to find the area of the full figure.
Step-by-step explanation:
please help is this correct
Answer:
yes its correct
Step-by-step explanation:
you dont really need work because its really just substitution.
plEaSe seND HELP
Matt's aquarium is shaped like a rectangular prism. The base of his
tank has sides with lengths of 4.2 feet and 14.1 feet. If the height
of the tank is 9 feet, what is the total surface area of the tank?
A. 283.14 square feet
B. 329.4 square feet
C. 447.84 square feet
D. 532.98 square feet
Answer: C
Explanation:
Formula for SA of a rectangular prism: \(SA = 2(lw + lh + wh)\)
Plug in length, width, and height
\(SA = 2((4.2)(14.1)+(4.2)(9)+(14.1)(9))\)
\(SA = 447.84\) ft
Let g(x) = 2x and h(x) = x2 + 4.
Evaluate (h.g)(1).
A. 2
B. 10
C. 4
D. 8
Answer:
10
Step-by-step explanation:
Hello,
(h.g)(1)=h(1)*g(1)
h(1)=1+4=5
g(1)=2
so h(1)*g(1)=5*2=10
the correct answer is 10
Answer:
10
Step-by-step explanation:
g(x) = 2x
h(x) = x^2 + 4
(h*g)(1)
h(1) = 1^2 +4 = 1+4 = 5
g(1) = 2*2 =2
(h*g)(1) = 5*2 = 10
Is the following statement true or false?
A line segment extends forever.
true
false
Answer:
false
Step-by-step explanation:
Please help me, the attachment is below. (If you don't know the answer to the question please don't answer)
Answer:
Step-by-step explanation:
The three angles of a triangle always have to equal 180 in the end, so if you use the method which is the 4 in this instance, it is an obtuse angle that is equal to the top and left angle. You can add 1 and 2 to get 4, and do 4-3 to get 1+2, So, 4=1+2.
In a chemical blending problem, one of the constraints is that the amount of sulfur relative to total output produced of chemical X may not exceed 7%. In a linear programming model, we should express this constraint as
The constraint can then be written as: S ≤ 0.07 × T. This equation represents the constraint for the amount of sulfur in the chemical blend of X and can be incorporated into the linear programming model to ensure that the solution meets the given requirement.
The constraint can then be written as: S ≤ 0.07 × T, This equation represents the constraint for the amount of sulfur in the chemical blend of X and can be incorporated into the linear programming model to ensure that the solution meets the given requirement.
We are given that the amount of sulfur relative to the total output produced of chemical X may not exceed 7%. To express this constraint in a linear programming model, we can use the following equation:
Sulfur Content ≤ 0.07 × Total Output
Here, the "Sulfur Content" represents the total amount of sulfur present in the chemical blend, while "Total Output" refers to the total amount of chemical X produced. By setting the constraint to be less than or equal to 7% (0.07) of the total output, we are ensuring that the sulfur content does not exceed the given limit.
In a linear programming model, we usually use variables to represent quantities. Let S represent the Sulfur Content and T represent the Total Output. The constraint can then be written as:
S ≤ 0.07 × T
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Hazel is saving her allowance to buy a new handbag to match her favorite dress. The handbag is shaped like a trapezoid with one base that is 23 centimeters long and another base that is 17 centimeters long. The trapezoid has an area of 260 square centimeters. What is the height of the trapezoid? Write your answer as a whole number or decimal. Do not round.
The height of the trapezoid is 13cm.
What is the height of the trapezoid?A trapezoid is a convex quadrilateral with at least one pair of parallel sides.
Area of a trapezoid = 0.5 x (sum of the lengths of the parallel sides) x height
Height = area / (0.5 x sum of lengths)
Sum of lengths = 23 + 17 = 40 cm
= 260 / (0.5 x 40) = 13 cm
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In order to determine whether the differences between group means are statistically significant, ANOVA examines the differences between groups within groups between and within groups neither between nor within groups In a linear equation, the value of Y when X is 0 is called the slope.
In a linear equation, the value of Y when X is 0 is called the y-intercept, not the slope.
In order to determine whether the differences between group means are statistically significant, ANOVA examines the differences between groups.
ANOVA, which stands for Analysis of Variance, is a statistical method used to compare the means of two or more groups.
It analyzes the variability between group means and within group variability to assess whether there are significant differences among the groups.
The main idea behind ANOVA is to compare the variation between groups with the variation within groups.
If the variation between groups is significantly larger than the variation within groups, it suggests that there are meaningful differences among the groups.
This implies that the differences between group means are statistically significant, indicating that the groups are not just randomly different.
ANOVA achieves this by calculating an F-statistic, which is the ratio of the variability between groups to the variability within groups.
If the F-statistic is large enough to exceed a critical value based on the chosen significance level, it indicates that the group means are significantly different.
Regarding the statement about a linear equation, it is incorrect.
In a linear equation, the value of Y when X is 0 is called the y-intercept, not the slope.
The slope refers to the rate of change of Y with respect to changes in X.
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translated 7 units right and 2 units up.
Answer:
where was the starting point?
if the starting point was the origin then the translated point is (7, 2)
Answer:
are you talking about a graph? If it's from (0,0) then (7,2)
Step-by-step explanation:
Please help with algebra 2 Possible Answers(-3, 2)(-3, 3)(2, -3)(6, 8)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Re-draw the given circe to show the radius
STEP 2: Explain the radius
A radius is a line drawn from the centre of a given circle to any part on the circumference. This line divides a circle into equal quarters as seen on the image. The radius divides the circle equally both vertically and horizontally.
STEP 3: Show the centre
Since the line of the radius goes from the centre, therefore the part identified below will be the centre
STEP 4: Get the coordinate of the centre
The coordinate of the centre will be the point on the x-axis as agianst the point on the y-axis.
Hence, the center of the given circle is:
\(\lparen-3,2)\)men can do a work in 32 days in how many days will 24 men complete the same work
Answer:
It will take 32/24, or 1 1/3 days, for 24 men to get the job done.
Step-by-step explanation:
I will mark brainliest if u help with 6
Answer: For 6 only 1=45degrees 2=45degrees and 3=135 degreed
Step-by-step explanation:
Corresponding and complimentary angles
a certain statistic dˆ is being used to estimate a population parameter d. the expected value of dˆ is not equal to d. what property does dˆ exhibit?a. The sampling distribution of d hat is normal.b. The sampling distribution of d hat is binomial.c. The sampling distribution of d hat is uniform.d. d hat is unbiased.e. d hat is biased.
The right answer is: E, according to the Central Limit Theorem for proportionality. The statistic is inaccurate.
In probability theory, the central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
The Central Limit Theorem establishes that for a proportion p in a sample of size n:
The expected value is μ=р
The standard error is s=\(\sqrt{\frac{p(1-p)}{n} }\)
In this problem, the expected value is different of the expected of μ=р , hence, the statistic is biased, and the correct option is E.
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Someone pleasee help Find the perimeter of the figure
Answer:
Hello! Your answer is 24 inches!
Step-by-step explanation:
Solve for x.
5x - 6 = 4x + 8
Answer:
x = 14
Step-by-step explanation:
5x - 6 = 4x + 8
+6 +6
5x = 4x + 14
-4x -4x
x = 14
Answer:
5x-6=4x+8
5x=4x+8+6
5x=4x+14
x=14
I hope this is good enough:
please help im failing
Statement
∠1 = ∠2
Reason(1): l║m, Corresponding angles are congruent
Reason(2): Corresponding angles are congruent (Postulate)
Hope this can help
We have to prove how j||k?
As <1=<2 Theya are opposite interior angles .<1 and <4 are corresponding angles so they are equal .Hence
J||K ProvedJordan is starting to save $150 to buy a new cell phone. In December, he saved $5. In January, he plans twice as much as he did in December, for a total savings of $15 ($5 + $10). If Jordan continues to save twice as much he saved from the previous month, in which month will his total savings will be enough to buy the phone.
Answer: At the Month May Jordan as able to get enough money to buy the phone.
Work:
December:$5
January:$10
February:$20
March:$40
April:$80
May:$160 <--Answer
____________________________________________________________In the problem Jordan saves $5 at December, then at January Jordan saved $10 which is twice as December's saved money amount. February, Jordan saved $20, which is twice as January's saved money amount. March is $40, which is twice as February's saved money amount. For April it is $80, which is twice as March's money amount, May is $160 which is twice as April's money amount. Or another way to say this is by starting at $5. Then, keep multiplying by 2 for each month until you get $150 or more. When you do, stop at the month that gets you $150 or more. When i did this exact method, I got $160 on the Month of May. $160 is more than enough for Jordan to buy his phone. So the month May is the correct answer where Jordan can get enough money for his phone.
Answer: The fifth month; By April Jordan would have saved more than enough to buy a new phone.
Step-by-step explanation:
Dec $5
Jan $10
Feb $20
Mar $40
Apr $80
Dec + Jan = $15($5+$10)
Dec+ Jan + feb = $35($5+$10+$20=$35)
Dec+ Jan + feb + mar = $75 ($5+$10+$20+$40=$75)
Dec+ Jan + feb + mar + apr = $155
($5+$10+$20+$40+$80=$155)