Answer:
The probability is 0.357
Step-by-step explanation:
Given that,
The system has at least one type of defect,
Suppose, A certain system can experience three different types of defects.
Let [tex]A_{i}[/tex] (i = 1,2,3) denote the event that the system has a defect of type i.
Suppose that the following probabilities are,
[tex]P(A_{1})=0.11[/tex]
[tex]P(A_{2})=0.08[/tex]
[tex]P(A_{3})=0.05[/tex]
[tex]P(A_{1}\cup A_{2})=0.13[/tex]
[tex]P(A_{1}\cup A_{3})=0.13[/tex]
[tex]P(A_{2}\cup A_{3})=0.11[/tex]
[tex]P(A_{1}\cap A_{2}\cap A_{3})=0.01[/tex]
[tex]P(A_{1}\cap A_{2})=0.06[/tex]
[tex]P(A_{1}\cap A_{3})=0.03[/tex]
[tex]P(A_{2}\cap A_{3})=0.02[/tex]
[tex]P(A_{1}\cup A_{2}\cup A_{3})=0.14[/tex]
We need to calculate the probability that it has exactly one type of defect
Using given data
[tex]P=\dfrac{P(A_{1}\cap A_{2}'\cap A_{3}')}{P(A_{1}\cup A_{2}\cup A_{3})}+\dfrac{P(A_{1}'\cap A_{2}\cap A_{3}')}{P(A_{1}\cup A_{2}\cup A_{3})}+\dfrac{P(A_{1}'\cap A_{2}'\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]
[tex]P=\dfrac{P(A_{1})-P(A_{1}\cap A_{2})-P(A_{1}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex] + [tex]\dfrac{P(A_{2})-P(A_{1}\cap A_{2})-P(A_{2}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]+ [tex]\dfrac{P(A_{3})-P(A_{1}\cap A_{3})-P(A_{2}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]
P = [tex]\dfrac{P(A_{1})+P(A_{2})+P(A_{3})-2P(A_{1}\cap A_{2})-2P(A_{1}\cap A_{3})-2P(A_{2}\cap A_{3})+3P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]
Put the value into the formula
[tex]P=\dfrac{0.11+0.08+0.05-2(0.06)-2(0.03)-2(0.02)+3(0.01)}{0.14}[/tex]
[tex]P=0.357[/tex]
Hence, The probability is 0.357
F(x)=-2x -3 and g(x)=x^2 +5x,find g(2)-f(3)
Answer:
f(3)= -9, g(2)=4
Step-by-step explanation:
F(3)= -2(3) -3
F(3)= -6 -3
F(3)= -9
G(2)= 2^2
G(2)= 2×2
G(2)= 4
If you run a 10 km race in 43 minutes 30 seconds, what is your average time per mile? What is your average speed in mph? Hint: there are 1.61 km in a mile.
Answer:
Your Average Speed was 8.57057285 mph.
Step-by-step explanation:
Gabriel surveyed 1000 of the students in his school about their favorite color. 55% said their favorite color was purple. How many students' favorite color was purple?
Answer:
550 students
Step-by-step explanation:
Answer:
550 students
Step-by-step explanation:
The Perez family is researching the cost of keeping their dog at a kennel during an upcoming vacation. The local kennel allows “Silver” families to pay a rate of $36 per day. For a fee, families can buy a “Gold” membership and will be allowed to board their dogs at a discounted rate as shown in the table. Total Cost, Including Membership Fee, to Board a Dog Type of membership 1 Day 2 Days 7 Days Silver $36 $72 $252 Gold $70 $90 $190 What is the cost of a Gold membership? $20 $34 $50 $70
Answer:
it is 50 dollars
Step-by-step explanation:
Answer:
the answer is c.50
Step-by-step explanation:
i just did the assignment
What's 2|–9| – |–2|? Question 10 options: A) 20 B) –18 C) 16 D) –20
Answer:
Step-by-step explanation:
7
What is 6 times 6? #ifyouknowitquestion!
Answer:
36
Step-by-step explanation:
Find the perimeter of a regular octagon if one of its sides is x + 6 and another side is 14 – x.
Answer:
80 units
Step-by-step explanation:
The sides of a regular octagon are all the same length.
x +6 = 14 -x
2x = 8 . . . . . . add x-6
x = 4
x+6 = 10 . . . . the length of each of the 8 sides
P = 8s = 8(10) = 80
The perimeter of the octagon is 80 units.
Construct a line through P that is
perpendicular to the line.
Answer:
The construct a line through P that is perpendicular to the line.
Step-by-step explanation:
Given that,
Construct a line through P that is perpendicular to the line.
We need to construct a perpendicular line P
Using given data
We draw an arc across the line on each side of the point P.
Now, from each arc on the line, draw another arc on the opposite side of the line from the point P.
The point P to the point where the arcs intersect Q.
Hence, The construct a line through P that is perpendicular to the line.
The equation of the perpendicular line through point 'P' is [tex](y-y_1)=-\dfrac{1}{m'}(x-x_1)[/tex] and this can be determined by using the point-slope form of the line.
The following steps can be used in order to construct a line through P that is perpendicular to the line:
Step 1 - The equation of a line that passes through point 'P' is given below:
[tex](x-x_1)=m(y-y_1)[/tex]
where m is the slope and [tex](x_1,y_1)[/tex] is the point 'P' on the line.
Step 2 - So, the slope of the perpendicular line through point 'P' is:
[tex]mm' = -1[/tex]
[tex]m'=-\dfrac{1}{m}[/tex]
Step 3 - So, the equation of the perpendicular line through point 'P' is:
[tex](y-y_1)=-\dfrac{1}{m'}(x-x_1)[/tex]
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4.5 = m +2.75
what is the answer?
Answer:
m=1.75
Step-by-step explanation:
4.5 = m+2.75Subtract 2.75 on both sides of the equationm = 1.753. If 7 large pizzas are purchased for a party, the amount of pizza each person can have is
inversely proportional to the number of people who come to the party. If 14 people come to
the party, each person can have 6 slices. How many slices can each person have if 21 people
come to the party.
Answer:
9 slices
Step-by-step explanation:
Set up a proportion:
[tex]\frac{14}{6}[/tex] = [tex]\frac{21}{x}[/tex]
Cross multiply and solve for x, the amount of slices if 21 people come:
14x = 126
x = 9
So, each person can have 9 slices
The admission fee at an amusement park is 20$ for children and 35$ adults. On a certain, day 264 people entered the park, and the admission fees collected totaled $6780. How many children and how many adults were admitted?
Answer:
100 Adults and 164 Children
Step-by-step explanation:
To solve this we will need to write two equations to solve for the two unknowns. Firstly, we know that tickets are 20 for children and 35 for adults, and that the total price was 6780. We can write an expression to represent this. 6780 is the total price, this also means it is the price of all the adults + the price of all the children. The total price of the adults tickets is the price of each ticket multiplied by the number of adults, so the total price of adult tickets can be represented by: 35A, 35 being the ticket price per adult, and A being the number of adults. Similarly the total children's price can be expressed as such: 20C, 20 being the price per child, and C being the number of children. Since we know that these two values total to 6780, we can now form an equation:
35A (total adult price) + 20C (total children price) = 6780
35A+20C=6780
Now we need another expression so we can substitute for one of the values. The other piece of information we are given, is that a total of 264 people entered the park. This means that the total number of adults + the total number of children = 264. Since we already have variables for the numbers of adults and children we now have our second equation:
A (number of adults) + C (number of children) = 264
A+C=264
Now we can use this second equation to substitute for one of the values in the first equation. Let's substitute for children:
If we rearrange the second expression we will get:
A+C-A=264-A
C=264-A
So now we substitute this expression into our first formula:
35A+20C=6780
C=264-A
35A+20(264-A)=6780
Now since we only have one unknown, we can simplify, expand and solve!
35A+20*264-20*A=6780
35A+5280-20A=6780
35A-20A+5280-5280=6780-5280
15A=1500
15A/15=1500/15
A= 100
A total of 100 adults were admitted.
Now we can use the number of adults to find the number of children using our second formula:
C=264-A
C=264-100
C=164
And there we are! A total of 100 adults and 164 children were admitted.
Hope this helped!
The standard unit for length is the ____. yard meter foot milliter please help its due in 6 mins!!!
Answer:
Meter
Step-by-step explanation:
The standard unit of length based on the metric system is a meter (m). According to the length that needs to be measured, we can convert a meter into various units like millimeters (mm), centimeter (cm), and kilometer (km).
Find the coordinates of n if n is exactly halfway between m (-10,-13) and d (-7,-7)
X=4 y=0 z=4 x-9y/-z algebraic expression
Hope this helps!
djddc8y8fys9yv9uvsgosoyggysoyd
By how much does the outlier in the following data set increase the range of the data set?
{59, 70, 63, 46, 60, 38, 60, 51, 48, 85, 66, 55, 236}
To find the range, subtract the smallest from the biggest number.
The outlier is most commonly the biggest or smallest number. Obviously it is 236 in this situation.
To find how much the outlier increases the range, you need to find out the range WITH and WITHOUT the outlier.
Without the outlier: 39
With the outlier: 190
Then you subtract 190 - 39 because you are trying to find out how much MORE RANGE the outlier makes.
The answer is 151.
THEREFORE, The outlier increases the range by 151.
Simplify the ratio 24/36
Answer:
2:3
Step-by-step explanation:
24:36
24÷12=2
36÷12=3
Answer=2:3
Answer:
2 : 3
Step-by-step explanation:
24/36 ?
[tex] \frac{24}{36} \div \frac{12}{12} \\ = \frac{24 \div 12}{36 \div 12} \\ = \frac{2}{3} [/tex]
2/3 = 2 : 3
factorise completely.
21a²+28ab
The complete factorization of 21a² + 28ab is 7a(3a + 4b)
Factorization is an arithmetic operation used in resolving an expression into factors in which when the factors are being multiplied together, the original expression can be derived. They produce factors that can be divided into the original expression.
Given that:
= 21a² + 28ab
here, we will look for a factor that if divide in both 21 and 28, there won't be any remainder. The factor is 7;
So, we have:
= 7(3a² + 4ab)
= 7a(3a + 4b)
Therefore, the complete factorization of 21a² + 28ab is 7a(3a + 4b)
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A manufacturer of bulbs for movie projectors finds that the lives of the bulbs are normally distributed with a mean of 61 hours and a standard deviation of 6.3 hours. The manufacturer will guarantee the bulbs so that only 3% will be replaced because of failure before the guaranteed number of hours. For how many hours should the bulbs be guaranteed?
Answer:
49.2 hours
Step-by-step explanation:
Use a chart or calculator to find the z-score associated with the probability.
P(Z < z) = 0.03
z = -1.88
Now find the x value.
z = (x − μ) / σ
-1.88 = (x − 61) / 6.3
x = 49.2
pls help math 15 points
3 x's at 1
4 x's at 1 1/4
3 x's at 1 1/2
1 x at 1 3/4
No x's at 2.
Now, let's combine all the recipes with 1 1/4
5/4 * 4 = 20 / 4 = 5 teaspoons
A _______________________ is a conclusion after you have observed the patterns.
Answer:
Inductive Reasoning is the process of arriving at a general conclusion based on observations of specific examples. When you try to find the pattern for a list of numbers or visuals, you are using inductive reasoning.
urgent answer fast"""""""
Answer:
the fifth number is 11
Step-by-step explanation:
8,11,13 and 17, x
the mean is =12 ( which means the sum of the terms divided by the numbers of terms )
to find the mean :
(8+11+13+17+x)/5 =12
5*12=49+x
60-49=x
x=11
Find B on AC such that the ratio of AB to BC is 3:2. A (4, 2) and C (-6, - 13).
Answer:
B(-2, -7)
Step-by-step explanation:
The ratio requirement means ...
(B-A)/(C-B) = 3/2
2(B-A) = 3(C-B) . . . . cross multiply
2B -2A = 3C -3B . . . eliminate parentheses
5B = 2A +3C . . . . . . add 3B+2A
B = (2A +3C)/5 . . . . divide by 5
Now that we have a formula for B, we can fill in the given point values:
B = (2(4, 2) +3(-6, -13))/5 = (8-18, 4-39)/5 = (-10, -35)/5 = (-2, -7)
The coordinates of B are (-2, -7).
Mr. Weston boughtn,new microscopesn for his science classroom. each microscope cost $99.90, and he spent a total of $499.50 how many nicroscopesn,did Mr Weston buy?
Answer:
5
Step-by-step explanation:
Take the total amount spent and divide it by the cost of each microscope.
$499.50 ÷ $99.90 = 5
Answer:
5
Step-by-step explanation:
A hot air balloon descends at a rate of 25 feet per minute. how far will the balloon have descended after 7 minutes
Answer:
175 feet
Step-by-step explanation:
25ft/min so you just multiply 25 by however many minutes so its 7 so you do 25x7 which is 175 so its 175feet
A rectangular lawn has a width of 3 1/2 yards. The length of the lawn is 2 yards. What is the area
Answer:
7 yards
Step-by-step explanation:
Multiply length and width wen finding the area so 3 1/2 time 2
Answer:
7 yards
Step-by-step explanation:
Area= LxW
3 1/2 x 2=7
18/42=X/14 solve the proportion
Answer:
x = 6
Step-by-step explanation:
Answer the question marks, and tell me what sequence number 8 is.
Answer:
f[1] = 60; f[n+1] = f[n] -30f[n] = 60 -30(n-1)Step-by-step explanation:
You observe that each term is 30 less than the previous one. This is the recursive rule. It also means the sequence is arithmetic with a common difference of -30.
Recursive equation
f[1] = 60; f[n+1] = f[n] -30
__
Explicit equation
The general form of the explicit equation is ...
f(n) = f(1) +d(n -1)
Here, we have f(1) = 60 and d = -30, so your equation is ...
f(n) = 60 -30(n -1)
An open box is constructed of 3500 cm2 of cardboard. The box is a cuboid, with height h cm and square base of side x cm. What is the value of x which maximises the volume of the box? Give your answer in cm correct to 3 significant figures.
Answer:
this is confusing and my head hurts
Step-by-step explanation:
PLEASE HELPPP!!!
Which statement translates the equation?
8n + 15 = 3n + 60
A) Jessy and Paul all together have 8n + 3n cookies, Jessy has 15 cookies and Paul has 60 cookies. How many cookies does Jessy have?
B) Jessy and Paul all together have 15 + 60 cookies, Jessy has 8n cookies and Paul has 3n cookies. How many cookies does Jessy have?
C) Jessy and Paul all together have 3n + 60 cookies, Jessy has 8n cookies and Paul has 15 cookies. How many cookies does Jessy have?
D) Jessy and Paul all together have 3n + 60 cookies, Jessy has 8n plus 15 cookies more than and Paul. How many cookies does Jessy have?
Answer:
its c
Step-by-step explanation:
Nathaniel mowed 18 lawns in 3 hours. What was his rate of mowing in hours per lawn?
Answer:
1/6 hours for every 1 lawn:)
Step-by-step explanation:
Nathaniel mow 18 lawns in 3 hours, then the rate of mowing will be 0.16 or 1/6 hours per lawn.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the information given in the question,
Total lawns mowed by Nathaniel = 18
Total time taken by Nathaniel to mow 18 lawns = 3 hours.
Then, the time required to mow each lawn is,
= 18/3
= 1/6 hrs. Or 0.16 hrs.
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