Answer:
a)0.976
b)0.00926
c)0.2402
d)0.35
Step-by-step explanation:
Let [tex]X_i[/tex] be an item passed by inspector i
Let Y be the event that there is a fault in an item
The probability that an item has a flaw is 0.1 i.e. P(Y)=0.1
If a flaw is present ,it will be detected by the first inspector with probability 0.92 i.e.[tex]P(\bar{X_1}|Y)=0.92[/tex]
So, [tex]P(X_1|Y)=1-0.92=0.08[/tex]
If a flaw is present ,it will be detected by the second inspector with probability 0.7 i.e.[tex]P(\bar{X_2}|Y)=0.7[/tex]
So,[tex]P(X_2|Y)=1-0.7=0.3[/tex]
If an item does not have a flaw, it will be passed by the first inspector with probability 0.95 i.e. [tex]P(X_1|\bar{Y}) = 0.95[/tex]
So, [tex]P(\bar{X_1}|\bar{Y}) = 1-0.95=0.05[/tex]
If an item does not have a flaw, it will be passed by the second inspector with probability 0.8 i.e. [tex]P(X_2|\bar{Y}) = 0.8[/tex]
So, [tex]P(\bar{X_2}|\bar{Y}) = 1-0.8=0.2[/tex]
a)P(found by atleast one inspector | It has flaw )=1-P(found by none inspector | It has flow )
P(found by atleast one inspector | It has flaw )=[tex]1-P(X_1|Y) P(X_2|Y)[/tex]
P(found by atleast one inspector | It has flaw )=[tex]1-0.08 \times 0.3[/tex]
P(found by atleast one inspector | It has flaw )=0.976
Hence the probability that it will be found by at least one of the two inspectors if it has flaw is 0.976
b)[tex]P(Y|X_1)=\frac{P(X_1|Y) P(Y)}{P(X_1|Y) P(Y)+P(X_1|\bar{Y}) P(\bar{Y})}[/tex]
[tex]P(Y|X_1)=\frac{0.08 \times 0.1}{0.08 \times 0.1+0.95 \times 0.9}=0.00926[/tex]
C)P( two inspectors draw different conclusions on the same item)=[tex]P(X_1 \cap \bar{X_2} \cap Y)+P(\bar{X_1} \cap X_2 \cap Y)+P(X_1 \cap \bar{X_2} \cap \bar{Y})+P(\bar{X_1} \cap X_2 \cap \bar{Y})[/tex]
P( two inspectors draw different conclusions on the same item)=0.2402
D)
[tex]P(Y|(X_1 \cap X_2))=\frac{P(Y \cap X_1 \cap X_2)}{P(X_1 \cap X_2)}\\P(Y|(X_1 \cap X_2))=\frac{P(Y \cap X_1 \cap X_2)}{P(X_1 \cap X_2 \cap Y)+P(X_1 \cap X_2 \cap \bar{Y})}\\P(Y|(X_1 \cap X_2))=0.35[/tex]
Is 0.2x = 100- 0.4/y linear or non linear function?
so i will not give you the answer i will teach you how to do it.
In Mathematics, you must have learned about different types of equations. Here, we are going to discuss the difference between linear and nonlinear equations. The difference between them described here with the help of definitions and examples.
We come across a lot of equations while solving maths problems. Some equations include only numbers and some consist of only variables and some consists of both numbers and variables. Linear and nonlinear equations usually consist of numbers and variables.
Definition of Linear and Non-Linear Equation
Linear means something related to a line. All the linear equations are used to construct a line. A non-linear equation is such which does not form a straight line. It looks like a curve in a graph and has a variable slope value.
The major difference between linear and nonlinear equations is given here for the students to understand it in a more natural way. The differences are provided in a tabular form with examples.
What is the difference between Linear and Nonlinear Equations?
To find the difference between the two equations, i.e. linear and nonlinear, one should know the definitions for them. So, let us define and see the difference between them.
Linear Equations
Non-Linear Equations
It forms a straight line or represents the equation for the straight line It does not form a straight line but forms a curve.
It has only one degree. Or we can also define it as an equation having the maximum degree 1. A nonlinear equation has the degree as 2 or more than 2, but not less than 2.
All these equations form a straight line in XY plane. These lines can be extended to any direction but in a straight form. It forms a curve and if we increase the value of the degree, the curvature of the graph increases.
The general representation of linear equation is;
y = mx +c
Where x and y are the variables, m is the slope of the line and c is a constant value.
The general representation of nonlinear equations is;
ax2 + by2 = c
Where x and y are the variables and a,b and c are the constant values
Examples:
10x = 1
9y + x + 2 = 0
4y = 3x
99x + 12 = 23 and
Examples:
x2+y2 = 1
x2 + 12xy + y2 = 0
x2+x+2 = 25
Note:
The linear equation has only one variable usually and if any equation has two variables in it, then the equation is defined as a Linear equation in two variables. For example, 5x + 2 = 1 is Linear equation in one variable. But 5x + 2y = 1 is a Linear equation in two variables.
Let us see some examples based on these concepts.
Solved Examples
Example: Solve the linear equation 3x+9 = 2x + 18.
Solution: Given, 3x+9 = 2x + 18
⇒ 3x - 2x = 18 - 9
⇒ x = 9
Example: Solve the nonlinear equation x+2y = 1 and x = y.
Solution: Given, x+2y = 1
x = y
By putting the value of x in the first equation we get,
⇒ y + 2y = 1
⇒ 3y = 1
⇒ y = ⅓
∴ x = y = ⅓
What is the key difference between non-linear and linear equations?
A linear equation is used to represent a straight line in a graph, whereas non-linear equations are used to represent curves.
How does the graph of linear and non-linear equations look?
A linear equation graph is a constant slope whereas the graph of the non-linear equation shows the variation in slope at different points.
How is the linear equation represented? Give an example.
The general representation of linear equation is y = mx+c,
where m = slope of the line
x and y are the variables
c is the intercept (constant value)
Example: 2x+y=1
y=-2x+1
How is the nonlinear equation formed?
A non-linear equation is generally given by ax2+by2 = c
where x and y are variables
a,b and c are constant values.
The average price of a movie ticket in the United States from 1980 to 2000 can be modeled by the expression, 2.75+0.10x, where x is the number of years since 1980. Which part of the expression corresponds to the cost of movie tickets in 1980?
Answer:
2.75
Step-by-step explanation:
Here, we want to find which part of the formula corresponds to the cost of movie tickets in 1980
The expression to find the cost is
2.75 + 0.10x
Now, x is the time since 1980
1980 is thus the starting position. The value of x at this point is 0, we simply thus make a substitution;
2.75 + 0.1(0)
=
2.75
The interpretation of the given model is required.
The cost of a movie ticket in the year 1980 was $2.75.
The given expression is
[tex]y=2.75+0.1x[/tex]
The point slope form of a line is
[tex]y=mx+c[/tex]
where,
m = Slope
c = Y intercept
The cost of movie ticket increases by $0.10 every year after 1980.
Here, [tex]x[/tex] is the number of years that have passed after 1980.
So, when [tex]x=0[/tex] it will correspond to the cost of ticket in 1980.
[tex]y=2.75+0.1\times 0\\\Rightarrow y=2.75[/tex]
The cost of a movie ticket in the year 1980 was $2.75.
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https://brainly.com/question/7590971?referrer=searchResults
HELP PLZ!!!i cant figure this out and dont worry about what else im typin it wont let me continue without having 20 word typed so I’m just typin but can u help plz
Answer:
The length is 42 inches and the width is 14 inches
Step-by-step explanation:
You know the width is 1/3 of the length, and the length is basically the longer side of a rectangle. The width is y-4, so multiply using distributive property to get 3y-12.
You now know that the 2y+6 is equal to 3y-12, so you add 12 to both sides using additive property of addition to get 2y+18=3y.
Then you subtract 2y from both sides to get the unit value of y.
Y is equal to 18.
Then you can plug 18 into the y's to get
2(18)+6 which is 36+6 = 42
18-4 = 14
There you go.
The length is the longer side which is 42 inches and the width is 14 inches
Hope this helps!
How do I simplify expressions? (e.g. 8y+6(3y+7)
Answer:
26y + 42
Step-by-step explanation:
Using your example, you would break down the equation into the simplest form by combining like terms.
8y + 6(3y + 7) ← multiple what's in parenthesis by 6
8y + 18y + 42 ← Combine like terms
26y + 42
can someone please identify the slope of 10x + 8y = 40
Answer:
Y=-5/4+5
=5/4
Step-by-step explanation:
First lets put it into proper form
we get Y=-5/4+5
Then lets locate the slope which is -5/4
Thats your slope
please answer these !!! hurry please
Answer:
D, A
Step-by-step explanation:
9. Slope = 2-8/1-(-2)=-6/3=-2 = D
10. Line going left to right so it must be negative and it is going down by 3 every time so it is -3 = A
what operation is this
18 + 3 x 6 / 2
Explanation:
18 + 3 × 6 ÷ 2
First let's solve the multiplication18 + 18 ÷ 2
Following the division18 + 9
Add[tex]\boxed{27}[/tex] ← Result
Att: MusicSubtituladosSolve for x 3(x + 1) = −2(x − 1) − 4
Answer:
x = -1
Step-by-step explanation:
distribute:
3x + 3 = -2 (x -1) -4
distribute:
3x + 3 = -2x + 2 - 4
calculate difference:
3x + 3 = -2x - 2
move variable to left and change sign
3x + 2x + 3 = -2
3x + 2x = 2 - 3
collect like terms
5x = -2 - 3
5x = -5
x = -1
Answer:
x = -1
Step-by-step explanation:
3 ( x + 1 ) = -2 ( x - 1 ) - 4
distibute
3x + 3 = -2x + 2 - 4
simplify
3x + 3 = -2x - 2
inverse operations
3x + 3 = -2x - 2
+2x +2x
5x + 3 = -2
-3 -3
5x = -5
/5 /5
x = -1
What is the average rate of change of the line?
Answer:
- 12
Step-by-step explanation:
The slope of the line is a measure of the average rate of change
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 3 = - 12(x + 4) ← is in point- slope form
with slope m = - 12 ← average rate of change
i really need help on this one
Answer:the one going in a positive direction. so up lIke this /
Answer:
the bottom left choice,
positive graphs show the points going from bottom left of the graph to the upper right of it
negative correlation shows the opposite, points from the upper left to the lower right
Step-by-step explanation:
branon bought eight pounds of hambuger meat that cost 13.60 how much will 14 pounds of it cost
6-3+k=32
Solve equation.
Answer:
k=29
Step-by-step explanation:
what solution does the equation |4x+7|=-3 have
The result of an absolute value function is never negative. This is because absolute value represents distance on a number line, and negative distance is not possible. Negative distance doesn't make sense.
So we don't have solutions to something like |x| = -5 or the given equation. The right hand side must be 0 or a positive number if you want to have at least one solution.
is -14n-7=7 true or false
Type the correct answer in the box.
Consider this expression,
(6 – 4i)(6 – 4i) – 3(7 – 11i)
What is this expression written in the form a + bi, where a and b are rational numbers?
Answer:
-1-15i
Step-by-step explanation:
Plato
From definition ,find derivatives of [tex]a^{x}[/tex]
Answer:
Step-by-step explanation:
d /d x [ a ^x ]
= d/ d x [ e ^ln ( a ) x ]
= e ^ln ( a ) x ⋅ d /d x [ ln ( a ) x ]
= e ^ln ( a ) x ⋅ ln ( a ) ⋅ d /d x [ x]
= e ^ln (a ) x ln ( a ) ⋅ 1
= ln ( a ) e ^ln ( a ) x
Rewrite/simplify:
= a ^x ln ( a )
-f(a) Think of this as “the opposite of f(a).”
-f(a)=
F) does f(3)=f(-3)? (Yes or No)
D) does f(a) = f(-a)? ( Yes or No)
Answer:
F) yes
D)no
no
bfhdfthjfyktyrztjkgtwfhdhdgdrdrdth
Find the value of the expression:
0.01y4
for y=–2; 3; 10
Answer:
make your questions detailed
Josh's chicken soup recipe calls for 212L of chicken stock. Josh makes 314times the recipe for a family reunion. How much chicken stock does Josh use to make soup for the family reunion? Express your answer as a mixed number in the simplest form.
Answer:
[tex]8\dfrac{1}{8}\ L[/tex]
Step-by-step explanation:
Given that,
Amount needed for chicken stock is [tex]2\dfrac{1}{2}\ L[/tex]
Josh makes [tex]3\dfrac{1}{4}[/tex] times the recipe for a family reunion.
Let A is the amount neededto make soup for the family reunion. It can be calculated as follows :
[tex]A=2\dfrac{1}{2}\times 3\dfrac{1}{4}\\A=\dfrac{5}{2}\times \dfrac{13}{4}\\\\A=\dfrac{65}{8}\ L\\\\\text{or}\\\\A=8\dfrac{1}{8}\ L[/tex]
So, [tex]8\dfrac{1}{8}\ L[/tex]of chicken stock Josh use to make soup for the family reunion
Please help i’m actually crying rn give step by step
Answer:
X = 70 degrees
Step-by-step explanation:
The way to figure this out is by taking the angle of the 30 degrees and applying it to the opposite side of its self then just add it to the 80 degrees which will equal 110 and since a straight line has 180 degrees just subtract 180 by 110 and that will be the value of x because the lines are parallel and the line that goes through both lines will always have the same angle.
Compare 8 ⋅ 107 to 2 ⋅ 104. Convert 0.00049 to scientific notation.
show work plz in response. I will develop explicit and recursive forms of arithmetic sequences to model a scenario.
The first four terms of a sequence are: 1, 4, 7, 10. What is a formula that can be used to determine the nth term in the sequence?
A theater is designed with 15 seats in the first row, 19 in the second, 23 in the third, and so on. If this seating pattern continues, how many seats are in the 10th row?
I will identify the relationship between input and output of a function and recognize the domain and range values in a function.
This question is multiple choice. Put your answer in this box!
I will be able to calculate the average rate of change for a function represented in a table, on a graph or in an equation.
A function is shown below. What is the average rate of change from -3 < x < 2?
I will evaluate a function for a given value and interpret functions that arise in context.
Suppose f(x) = x2 and g(x) = 2x - 3. What is the value of g(4) + f(-3)?
Rewrite each expression using properties
2(x + 4) - 3(x -5)
2(x + 4) - 3(x -5) = 2x + 8 - 3x + 15 = 23 - x
give a name for the shaded angle below
Answer:
It's probably ∠PNC
27 - 11x = x - 13
Need an answer fast will mark Brainliest!
Answer:
x=.3 or 3/10
Step-by-step explanation:
to solve for x, we need to separate it
so, we add 13 to the left side
40-11x=x
then add 11x to the right side so we have different coefficients on each side to solve for x
40=12x
then we divide 40/12 to get what x equals
we get
x= 0.3 or 3/10
hope this helped!
Answer:
x=10/3
Step-by-step explanation:
27 - 11x = x - 13
27+13=x+11x
40=12x
x=40/12
x=10/3
The ratio of men to women at a basketball game was 4:3. If there were 80 men at the basketball game, how many women were at the game?
Answer:
60
Step-by-step explanation:
braniest please
plz guys help me with that questions plz
plz guys help me
Step-by-step explanation:
Issun Sengeki... Messatsu!
In my opinion, I'd say A and C aren't functions, but B is a function.
The reason being is because every "X" value has a "Y" value. For those that don't have exactly 1 "Y" value aren't functions.
A. has more "Y" values than "X" values, so that proves not to be a function.B. Has "X" values that are exactly appointed to a "Y" value.C. Has one "X" value that's missing, and a "Y" value that doesn't exist.Hope this helps!
Quote:
"The answer lies in the heart of battle."
- Ryu
Please help!!! How many pages can be read in 45 minutes? Answer with a decimal point rounded to the nearest tenth if necessary.
Answer:
157.5 pages
Step-by-step explanation:
First, find your rate. You want to know how many pages you can read per minute. We can use any nuber, but using 2 minutes will be the simplest solution:
2m = 7
--- --- <---- Here we divide both sides of the equal sign by 2
2 2
m = 3.5 <---- we read 3.5 pages per minute
45 x 3.5 = 157.5 (We multiplied 45 because it's the number of minutes we have, by the 3.5 pages we read each minute. This gives us our total of 157.5 pages in 45 minutes.
which is greater, √10 or π?
Answer:
the square root of 10 is the answer becuase that = 3.16 and pi is 3.14
Step-by-step explanation:
In June, Mr. Chen's students read 40 books. In July they read 30 books.
What is the percent increase or decrease of the books they read?
Answer:
25% decrease
Step-by-step explanation:
