A company produces only one type of light bulbs. The light bulbs are being manufactured two factories: Factory A and Factory B. Factory A produces 10, 000 bulbs every year, while Factory B produces 2, 000. Also 2% of bulbs from Factory A are defective while 1% of bulbs from Factory B are. After production all bulbs are brought to the same facility and shipped to retail stores.
Required:
a. What is the probability that a bulb bought from a store is defective?
b. Given that the bulb is defective, what is the probability that it was produced by Factory A?
c. Given that the bulb is functional, what is the probability that it was produced by Factory A?
Answer:
Follows are the solution to the given points:
Step-by-step explanation:
Given values:
[tex]P(\frac{D}{A})=0.02 \\\\P(\frac{D}{B})=0.01\\\\P(A)=\frac{10,000}{10,000+2000} =\frac{10}{12} =\frac{5}{6} \\\\P(B)=\frac{1}{6}\\\\[/tex]
For point a:
[tex]P(D) =p(D\cap A) +P(D \cap B)\\\\[/tex]
[tex]=P(\frac{D}{A}) \times P(A) + P(\frac{D}{B}) \times P(B)\\\\=0.02 \times \frac{5}{6} + 0.01 \times \frac{1}{6}\\\\=\frac{0.1}{6} + \frac{0.01}{6}\\\\=\frac{0.1+0.01}{6} \\\\=\frac{0.11}{6} \\\\=\frac{11}{600} \\\\=0.0183[/tex]
For point b:
[tex]P(\frac{A}{D})= \frac{P(\frac{D}{A}) \times P(A)}{P(D)}\\\\[/tex]
[tex]= \frac{0.02 \times \frac{5}{6}}{\frac{11}{600}}\\\\= \frac{0.02 \times \frac{5}{6}}{0.0183333333}\\\\= \frac{0.02 \times 0.833333333}{0.0183333333}\\\\= \frac{0.0166666667}{0.018}\\\\=0.9090 \approx 0.0991[/tex]
For point c:
[tex]P(\frac{A}{D^C})=\frac{P(\frac{D^c}{A}) \times P(A)}{P(D^c)}\\\\[/tex]
[tex]= \frac{1-0.02 \times \frac{5}{6}}{1- \frac{11}{600}}\\\\= \frac{0.98 \times \frac{5}{6}}{0.98}\\\\=\frac{5}{6}\\\\=0.833[/tex]
The width of a rectangle is 4n - 4.5 feet and the length is 4.5n + 9 feet. Find the perimeter of the
rectangle.
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Answer:
17n+9 feet
Step-by-step explanation:
The perimeter of a rectangle is twice the sum of length and width.
P = 2(L +W)
P = 2((4.5n +9) +(4n -4.5)) = 2(8.5n +4.5)
P = 17n +9
The perimeter of the rectangle is 17n +9 feet.
joe has 4/5 of acre of land and wants to sell 2/3 what fraction of an acre does he want to sell
Answer:
The answer is
If all of the land had 100 acres than Joe would want to sell 28 of an acre.
Which of the following is true about the function below?
Answer:
The answer is D.
Ansel has two family members who travel for work. Ansel’s aunt travels every 12 days. Ansel’s cousin travels every 8 days. Today both of Ansel’s family members are traveling for work. After how many days will both family members travel on the same day again
Which expression is equivalent to 5 (n - 9)?
A) 5n - 45
B) 5n + 45
C) 5n - 9
D) 5n + 9
Answer:
[tex]A= 5n-45[/tex]
Step-by-step explanation:
Can u gimme brain plz!
Help&EXPLAIN
==============
Step-by-step explanation:
hope u understand. Answer is 12.56 inches ^2
If AC = 14, what is the measure of AD? Round your answer to the nearest hundredth.
Part A
Answer: Choice D) [tex]\text{AD} = \sqrt{(2n+5)^2+(4n-3)^2}[/tex]
-----------------------------------------------
Explanation:
Let E be the intersection point of the diagonals. For any parallelogram, the diagonals bisect each other. This means that AE = EC = 2n+5 and it also means EB = DE = 4n-3
Focus on triangle AED. This triangle is a right triangle with angle AED as a 90 degree angle (any rhombus has its diagonals that are perpendicular to one another). The legs of this triangle are AE = 2n+5 and ED = 4n-3
Apply the pythagorean theorem to find hypotenuse AD
[tex](\text{leg1})^2+(\text{leg2})^2 = (\text{hypotenuse})^2\\\\(\text{AE})^2+(\text{ED})^2 = (\text{AD})^2\\\\(\text{AD})^2 = (\text{AE})^2+(\text{ED})^2\\\\\text{AD} = \sqrt{(\text{AE})^2+(\text{ED})^2}\\\\\text{AD} = \sqrt{(2n+5)^2+(4n-3)^2}\\\\[/tex]
This points to choice D as the final answer.
===========================================================
Part B
Answer: 7.07-----------------------------------------------
Explanation:
If AC = 14, then half of this is AE = 7. The diagonals bisect each other, so they cut each other in half with E at the midpoint.
Since AE = 2n+5, we can solve for n like so
2n+5 = 7
2n = 7-5
2n = 2
n = 2/2
n = 1
Then we can find the length of AD
[tex]\text{AD} = \sqrt{(2n+5)^2+(4n-3)^2}\\\\\text{AD} = \sqrt{(2*1+5)^2+(4*1-3)^2}\\\\\text{AD} = \sqrt{(2+5)^2+(4-3)^2}\\\\\text{AD} = \sqrt{7^2+1^2}\\\\\text{AD} = \sqrt{49+1}\\\\\text{AD} = \sqrt{50}\\\\\text{AD} \approx 7.0710678\\\\\text{AD} \approx 7.07\\\\[/tex]
Segment AD is roughly 7.07 units long. The other external sides of the rhombus (AB, BC and CD) are also this length because the four sides of any rhombus are the same length.
6x - 5 + 7x = 34 find variable
Answer:
x = 3
Step-by-step explanation:
6x - 5 + 7x = 34
Find x
______________
To solve this, we need to isolate x :
First add like terms :
6x + 7x
13x
13x - 5 = 34
Add 5 to both sides :
13x = 39
Divide 13 from both sides to get x alone :
x = 3
Answer:
x=3
Step-by-step explanation:
Start by moving the 5 over creating 6x+7x=34+5. Then add them together 13x=39. And now simplify x=3
Which shows the dilation with a possible scale factor of One-half?
Triangle A is smaller than triangle A prime.
Triangle A is larger than triangle A prime.
Rectangle A is the same size as rectangle A prime.
Answer:
Option B
Step-by-step explanation:
Answer:
The answer is B
25 + (98-7) x4 PLEASE HELP
Answer: The answer is 464
Step-by-step explanation:
Bc you do 98-7=91, Then you do 25+91*4, Next Do 25+91=116, Last you 116*4= 389 and If this is wrong use a Calaculator Ok
_ Mhart7109
(It’s making me type 20 characters long soooooo.
Answer:
c
Step-by-step explanation:
C is split into thirds which would be 33.333.... B and D are 333.3% and 330% shaded because 1 fully shaded model is 100%.
I need help with this ratio table please!
Answer:
(Down there)
Step-by-step explanation:
ok so, heres what to put in the empty boxes for the dog food:cost
40 : $44
60 : $66
80 : $88
70 : $77
And heres what to put for the 2nd boxes
16 : $20
24 : $30
32 : $40
40 : $50
Find the number that belongs
in the green box.
Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
The unknown angle.
Start by finding the third angle. Call it x.
x + 125 + 32 = 180
x + 157 = 180
x = 180 - 157
x = 23
Now you are set to use the law of sines.
Call ? = x
x/sin(32) = 7/sin(23) Multiply both sides by Sin(32)
x = 7*sin(32)/sin(23)
x = 7*(0.5299) / sin(23)
x = 3.7094/ sin(23)
x = 3.7094 / 0.3097
x = 9.4935
Rounded to the nearest 10th
x = 9.5
Question 1
5 pts
(07.01 LC)
What is the value of x in the equation -6 + x = -2? (5 points)
8
-4
-8
4
Answer:
4
Step-by-step explanation:
Which of the following is true concerning the expression 6x + 3 + x? 6x and 3 are like terms. B 6x and x are like terms. C The simplified form of the expression is 6x + 3. D The simplified form of the expression is 10x.
Answer:
Time is very precious and we should not waste it in any way. Likewise, we can earn the money we spent but we cannot get back the time we have lost. So, this makes the time more valuable than money. Hence, we should utilize the time in the most possible way.
Step-by-step explanation:
Time is very precious and we should not waste it in any way. Likewise, we can earn the money we spent but we cannot get back the time we have lost. So, this makes the time more valuable than money. Hence, we should utilize the time in the most possible way.
Answer:
9 is the answer because it is the answerr
a student earn $16 per day for delivering overnight packages. She is paid $7 per day plus .60 for each package delivered. How many more deliveries mush she must make each day to increase her earnings to $28?
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Answer:
20 more deliveries
Step-by-step explanation:
The student wants to increase her earnings by $28 - 16 = $12 per day. Her earnings increase by $0.60 per package delivered, so she must deliver ...
$12/($0.60/pkg) = 20 pkgs
more each day.
because like a population has a standard deviation of 11 what is the approximate standard error of the mean for a sample size of 150
Answer:?
Step-by-step explanation:
Here are the first five terms of a number sequence.
45
40
35
30
25
Write down the next two terms of this sequence.
Answer:
40 is surface the answer of I think about it but I will solve the sum and will give the ans
405\450 = 9/10
process
Answer:
Correct
Step-by-step explanation:
Just divide both the numerator and the denominator by their common factors.
First of all factor both of the numbers.
405=5*3^4
450=5^2*3^2*2
Now line it up.
5*3*3*3*3
---------------
5*5*3*3*2
Now we can cancel out some numbers and get
3*3
-----
5*5
Now we actually multiplies them again and get.
9/10
This is the process of how to get it hope it helped!
A summer picnic is being planned and 96 employees are invited to vote for one of the
following themes: Sun, Surf, or Sand. Seventy-five percent of the employees
participate in the voting.
If there are 19 votes for Sun and 27 votes for Surf, how many employees voted for
Sand?
24
26
Ο Ο Ο Ο Ο
38
42
50
Adam invests £520 into an savings account.
Adam gets 0.5% per year simple interest.
Work out the total interest Adam will get after 5 years.
Answer: 1300 i think
Step-by-step explanation:
Adam invest 250 into account and then he gets 0.5% interest, that means he has to multiply 250 by 0.5% and then multiply again by five because of the five years.
if mary smith and karen white have identical sat scores and quality of letter, but mary smiths high school gpa is 1.5 point higher than karen, how much higher will marys college gpa be than karens
Required table is attached below :
Answer:
0.56
Step-by-step explanation:
Since they both have :
SAT score is the same ; quality of letter is the same ;
High school GPA is 1.5 points higher ;
Therefore, to determine how much Mary's GPA will be higher than Karen's :
Multiply the number of points by the Coefficient of high school GPA Given in the regression table attached below :
High school GPA Coefficient = 0.37635
Number of points = 1.5
= 1.5 * 0.37635
= 0.564525
= 0.56
-4>k-2 solve the inequality
Answer:
k<-2
Step-by-step explanation:
hope this helps :)
I am very confused about this
Answer:
Area of triangle = 1/2 b×h1/2×22×7 = 77cm^2Area of parallelogram = b×hArea = 22×9= 198cm^2Total area of composite figure77cm^2 + 198cm^2= 275cm^2Answer:
Triangle: 77
Parallelogram: 198
Total: 275
Step-by-step explanation:
The area of a triangle is one half the base times the height.
[tex]A_{T}=\frac{1}{2}bh=\frac{1}{2}(22)(7)=77[/tex]
The area of a parallelogram is base times height.
[tex]A_{P}=bh=(22)(9)=198[/tex]
The total area is the sum.
77+198=275
If the numerator of a fraction is increased by 3, the fraction becomes 3/4.If the denominator is decreased by 7,the fraction becomes 1. Determine the original fraction.
Answer:
9/16
Step-by-step explanation:
Let the original fraction be
x/y
Then
x+3/y=3/4
and
x/y-7=1
Look at 2nd fraction, rearrange it such that you multiply by "y-7" on both sides
x=y-7
Substitute this into 1st fraction:
x-7+3/y=3/4
Now we can solve this for y: cross-multiply --> (Note: y-7+3 = y-4)
4(y-4)=3y
y=16
Sub this back into "x = y-7" to get x
x=16-7=9
Therefore the original fraction is:
9/16
Which set of national numbers is arranged from least to greatest?
Answer:
the first one
Step-by-step explanation:
negative . 50 then -.20 1/9 then one
solve problems
5 1/2×3 1/3
Classify the polynomial by Degree and number of Terms
b^3+2b^2-b^2+3b^2+25
A. Quadratic Polynomial
B. None of the answers apply.
C. Cubic Trinomial
D. Polynomial
Answer:
C) Cubic Trinomial
Step-by-step explanation:
First, we combine like terms to simplify the polynomial. Like terms means having the same variable and exponent.
We get this expression: b^3+4b^2+25
There are 3 terms in this polynomial. Thus, it classifies as a trinomial. And its highest degree is 3, so it’s a cubic trinomial
plz help will give brainliest
The number of cans the soup kitchen has is represented by the equation, y = -63x + 825, where x represents the number of days and y represents the number of cans. How many cans will the soup kitchen have left after 10 days?
Answer:
195 cans
Step-by-step explanation:
Start by multiplying -63 by 10, since 10 should be in place of x. You will get -630. Add 825 to -630 and you will get 195.