Your description of the surface is incomplete. But it looks like you're considering some subset of the paraboloid z = 1 - x ² - y ², so I'll go ahead and assume it's the part of said paraboloid above the x,y-plane, so that the boundary is a circle centered at the origin with radius 1.
By Stokes' theorem, the line integral of F along this boundary (∂S) is equal to the surface integral of curl(F ) over the surface itself (S). We have
F(x, y, z) = z ² i + 2x j + y ² k
which has curl
curl(F ) = (∂(y ²)/∂y - ∂(2x)/∂z) i - (∂(y ²)/∂x - ∂(z ²)/∂z) j + (∂(2x)/∂x - ∂(z ²)/∂y) k
curl(F ) = 2y i + 2z j + 2k
Parameterize S by the vector function,
r(u, v) = u cos(v) i + u sin(v) j + (1 - u ²) k
with 0 ≤ u ≤ 1 and 0 ≤ v ≤ 2π.
Take the upward-pointing normal vector to S to be
n = ∂r/∂v × ∂r/∂u
n = (-u sin(v) i + u cos(v) j ) × (cos(v) i + sin(v) j - 2u k)
n = 2u ² cos(v) i + 2u ² sin(v) j + u k
Then the integral of curl(F ) over S - and hence the line integral of F over ∂S - is
[tex]\displaystyle \iint_S \mathrm{curl}(\mathbf F(x,y,z))\cdot\mathbf S \\\\ = \iint_S \mathrm{curl}(\mathbf F(\mathbf r(u,v)))\cdot\mathbf n\,\mathrm du\,\mathrm dv \\\\ = \int_0^{2\pi}\int_0^1 \left(2u\sin(v)\,\mathbf i + 2(1-u^2)\,\mathbf j + 2\,\mathbf k\right)\cdot\left(2u^2\cos(v)\,\mathbf i+2u^2\sin(v)\,\mathbf j+u\,\mathbf k\right)\,\mathrm du\,\mathrm dv \\\\ = \int_0^{2\pi}\int_0^1 \left(4u^3\sin(v)\cos(v)+4(1-u^2)u^2\sin(v)+2u\right)\,\mathrm du\,\mathrm dv \\\\ = \int_0^{2\pi}\left(\sin(v)\cos(v)+\frac8{15}\sin(v)+1\right)\,\mathrm dv \\\\ = \boxed{2\pi}[/tex]
Just to confirm this result, we can compute the line integral directly, since it's not so difficult to deal with. Parameterize ∂S by the vector function
r(t) = cos(t ) i + sin(t ) j
with 0 ≤ t ≤ 2π. (Note that there is a k component, but its coefficient is 0.) Then
dr/dt = -sin(t ) i + cos(t ) j
and the line integral is again
[tex]\displaystyle \int_{\partial S}\mathbf F(x,y,z)\cdot\mathrm d\mathbf r \\\\ = \int_{\partial S} \mathbf F(\mathbf r(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt \\\\= \int_0^{2\pi} (\cos(t)\,\mathbf i+\sin(t)\,\mathbf j)\cdot(-\sin(t)\,\mathbf i+\cos(t)\,\mathbf j)\,\mathrm dt \\\\ = \int_0^{2\pi}2\cos^2(t)\,\mathrm dt \\\\ = \boxed{2\pi}[/tex]
What is the slope of the line that goes through the points (1,-5) and (4,1)?
Answer:
The slope is 2
Step-by-step explanation:
The Slope formula is y2-y1/x2-y1.
1. Plug the numbers into the slope equation which is 1-(-5)/4-1=2
write your answer in simplest radical form
Answer:
[tex] a = 3\sqrt{6} [/tex]
Step-by-step explanation:
θ = 30°
Opposite side length to θ = 3√2 in.
Adjacent side length = a
Apply the trigonometric ratio, TOA:
[tex] tan(\theta) = \frac{Opp}{Adj} [/tex]
Plug in the known values
[tex] tan(30) = \frac{3\sqrt{2}}{a} [/tex]
Multiply both sides by a
[tex] a*tan(30) = 3\sqrt{2} [/tex]
[tex] a*\frac{1}{\sqrt{3}} = 3\sqrt{2} [/tex] (tan 30 = 1/√3)
Multiply both sides by the inverse of 1/√3 which is √3
[tex] a = 3\sqrt{2}*\sqrt{3} [/tex]
[tex] a = 3\sqrt{2*3} [/tex]
[tex] a = 3\sqrt{6} [/tex]
Geometria ayuda por favor
Answer:
72°
Step-by-step explanation:
Para el pentagono ABCDE,
m<C = (n - 2)(180)/n = (3)(180)/5 = 108
m<D = m<C = 108
Para el quadrilatero BCDE,
m<CBE + m<C + m<D + m<DEB = (n - 2)180 = 2(180) = 360
m<C = m<D = 108
m<CBE = m<DEB = x
m<CBE + m<C + m<D + m<DEB = 360
x + 108 + 108 + x = 360
2x + 216 = 360
x + 108 = 180
x = 72
Statement: If there is a swine flu epidemic, then infected people are quarantined and the public will panic; and if the latter occurs, then parents do not send children to school and employees do not go to work.
Key: C = Parents send children to school.
E = Employees go to work.
P = The public will panic.
Q = Infected people are quarantined.
S = There is a swine flu epidemic.
Translation:
The translation for the discrete statements are:
If S, then (Q and P); S → (Q ∧ P)
If P, then (not C and not E). P → (¬C ∧ ¬E)
Given data:
The given statement can be translated into symbolic logic as follows:
C: Parents send children to school.
E: Employees go to work.
P: The public will panic.
Q: Infected people are quarantined.
S: There is a swine flu epidemic.
The translation of the statement is as follows:
If S, then (Q and P);
If P, then (not C and not E).
Symbolically, the statement can be written as:
S → (Q ∧ P)
P → (¬C ∧ ¬E)
Here, the arrow (→) represents "if...then," ∧ represents "and," and ¬ represents "not."
This translation represents the logical relationships between the events described in the statement.
To learn more about discrete mathematics, refer:
https://brainly.com/question/30565766
#SPJ4
The complete question is attached below:
Use the symbolic logic to transform the given statements.
Statement: If there is a swine flu epidemic, then infected people are quarantined and the public will panic; and if the latter occurs, then parents do not send children to school and employees do not go to work.
Key:
C = Parents send children to school.
E = Employees go to work.
P = The public will panic.
Q = Infected people are quarantined.
S = There is a swine flu epidemic.
The statement when translated into symbolic logic would be (S -> (Q & P)) & (P -> (~C & ~E)).
How to translate into symbolic logic ?The given statement can be translated into symbolic logic as follows:
"If there is a swine flu epidemic, then infected people are quarantined and the public will panic" can be translated to:
S -> (Q & P)
"and if the latter occurs" refers to "the public will panic". Thus, "then parents do not send children to school and employees do not go to work" can be translated to:
P -> (~C & ~E)
Now, combining both parts of the statement using the "and" operator:
(S -> (Q & P)) & (P -> (~C & ~E))
Find out more on symbolic logic at https://brainly.com/question/917076
#SPJ1
The full question is:
Statement: If there is a swine flu epidemic, then infected people are quarantined and the public will panic; and if the latter occurs, then parents do not send children to school and employees do not go to work.
Key:
C = Parents send children to school.
E = Employees go to work.
P = The public will panic.
Q = Infected people are quarantined.
S = There is a swine flu epidemic.
Add or subtract the following mixed numbers using the first method. (Add the whole numbers; add the fractions; combine the parts of the sum for the answer.) Be sure your answers are in mixed number format and reduced to lowest terms.
2 2/3 +4 1/8 =
6 19/24
Step-by-step explanation:
Find the LCM(lowest common multiple) of 3 and 8 which is 24Multiply the denominator of 2/3 by 8 and 1/8 by 3Whatever you do to the denominator you have to do to the numerator, so you also have to multiply the numerator of 2/3 by 8 and 1/8 by 3 = 2 16/24 + 4 3/24Add the whole numbers (4+2= 6)Add the fractions (16/24 + 3/24= 19)Put them together and the answer is 6 19/24I can't really explain things properly, but I hope it helps
A right prism of height 15 cm has bases that are right triangles with legs 5 cm and 12 cm. Find the total surface area of the prism. Please explain.
a) 315 cm2 squared
b) 480 cm2 squared
c) 510 cm2 squared
d) 570 cm2
Answer:
Option (C)
Step-by-step explanation:
Surface area of a right prism = 2(Area of the triangular base) + Ph
Here, P = Perimeter of the base
h = Height of the prism
Area of the triangular base = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]
= [tex]\frac{1}{2}(5)(12)[/tex]
= 30 cm²
Height of the prism = 15 cm
Perimeter of the base = (5 + 12 + 13)
= 30 cm
Surface area of the right prism = 2(30) + 30(15)
= 60 + 450
= 510 cm²
Therefore, Option (C) will be the correct option.
What multiplication expression is equal to 3/4 divided by 2/5
Answer:
3 * 5
4 2
Step-by-step explanation:
To convert division problems with fraction into multiplication problems use the KCF rule
Keep the 1st Fraction the same
Change the division sign to a multiplication sign
Flip the fraction (reciprocal)
The average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. Who is relatively taller based on their comparison to their gender, LeBron James at 81 inches or Candace Parker at 76 inches?
a) Candace is relatively taller because she has a larger z-score.
b) LeBron is relatively taller because he has a larger z-score.
c) LeBron is relatively taller because he has a smaller z-score.
d) Candace is relatively taller because she has a smaller z-score.
Answer:
b) LeBron is relatively taller because he has a larger z-score.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
LeBron James:
Height of 81 inches, while the average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, which means that we have to find Z when [tex]X = 81, \mu = 69.5, \sigma = 2.7[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{81 - 69.5}{2.7}[/tex]
[tex]Z = 4.26[/tex]
Candace Parker:
Height of 76 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. This means that we have to find Z when [tex]X = 76, \mu = 64.2, \sigma = 3.2[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{76 - 64.2}{3.2}[/tex]
[tex]Z = 3.69[/tex]
Who is relatively taller?
Due to the higher z-score, LeBron James, and thus, the correct answer is given by option b.
PLEASE ANSWER!!!!! A car traveled s kilometers in 6 hours with a speed of v kilometers per hour. Express the dependence of s on v. Using the formula, find: v for s=363
In this question, the relations between velocity, distance and time are explored to first express the dependence of s on v, given the data in the exercise, and then to find the value of v for which s = 363.
-------------------------
Relation between velocity, distance, and time:
We have that velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance, and t is the time.
-------------------------
A car traveled s kilometers in 6 hours with a speed of v kilometers per hour.
This means that [tex]d = s, t = 6[/tex]
-------------------------
Express the dependence of s on v.
Taking the above values of d and t, and the formula, we have that:
[tex]v = \frac{d}{t}[/tex]
[tex]v = \frac{s}{6}[/tex]
[tex]s = 6v[/tex]
Thus, the dependence of s on v can be expressed as: [tex]s = 6v[/tex]
-------------------------
Using the formula, find: v for s=363
We have that:
[tex]s = 6v[/tex]
And thus
[tex]v = \frac{s}{6}[/tex]
Considering [tex]s = 363[/tex]:
[tex]v = \frac{363}{6} = 60.5[/tex]
Thus, for s = 363, v = 60.5.
For an example of a problem using this formula, you can check here: https://brainly.com/question/14307500
Answer:
v=s/6 is the formula
and if s=363, v=60.5
hope this helped!
Sally plays $240 per year for $12,000 of life insurance coverage. If bill and sally pay proportional rates for their life insurance, how much does bill pay per year for $19,000 of life insurance coverage?
Answer:
$380
Step-by-step explanation:
* means multiply
240/x = 12000/19000
12000x = 240 * 19000
12000x = 4560000
x= 4560000 ÷ 12000
x= 380
Which is true about the solution to the system of inequalities shown?
Answer:
All values that satisfy y ≤ 1x/3 - 3 are solutions (option 2)
Step-by-step explanation:
the values satisfying y ≤ x/3 - 3 (red area) are a subset of those satisfying
y ≤ x/3 - 1 (blue plus red area) and therefore satisfy both inequalities.
Evaluate the expression when y=6 and x=4. x + 7y X s ?
Answer:
4 + 42s
Step-by-step explanation:
When y = 6 and x = 4,
x + 7y * s4 + (7*6) * s4 + 42 * sSOMEBODY PLEASE HELP ME!!!! I NEED THIS!!!!
Answer:
47.1
Step-by-step explanation:
We know side LM corresponds with side OP with a factor of some number. The value of side LM is 8, and the value of side OP is 29. If we divide the two numbers, we will find the scale factor of which triangle NOP is larger than KLM. 29/8 simplifies to 3.625. Now, to find the value of side PN, we must find the side it corresponds to on triangle KLM. Because K corresponds with N, and M corresponds with P, we know the side that PN corresponds with on triangle KLM is side KM. Side KM has a value of 13, so side PN must be 3.625 times larger than 13.
13 times 3.625 = 47.125. The question says to round to the nearest tenth, so the answer would be 47.1
what is a 6 digit number that is divisible by 3 but not 2,4,5
Answer:
375681
Step-by-step explanation:
this number consists of 6 digits, which are divided by 3 in total. for example, 372-3+7+2=12..12:3=4 so 372 is divisible by 3
next, it's odd number
it doesn't end with 5 and it doesn't end with 0
and the last thing, it doesn't end with 2 numbers, which is divided by 4. for example, 524...24 is divided by 4, so 524 is divided too
so it may be number like
375681...3+7+5+6+8+1=30 so it's divided by 3
it isn't divided by 2 because it's odd number
isn't divided by 5, because it doesn't end with 5 or 0
and isn't divided by 4, because we can't divide 81 by 4
it can be another number, as you wish. you can create it by yourself
What is the solution set of the inequality ?
18<4x+2<24
Answer:
4<x<5.5
Step-by-step explanation:
18<4x+2 and 4x+2<24
16<4x and 4x<22
4<x and x< 5.5
4<x<5.5
Answer:
4 < x < 11/2
Step-by-step explanation:
hey there!!
separate this inequality in to 2 inequalities as
below
18 < 4x+2
4x+2 < 24
solve these 2 inequalities separately
18 < 4x+2
18 -2 < 4x
16 <4x
4 < x
4x+2 < 24
4x < 22
x < 11/2
so x should be greater than 4 and less than 11/2
4 < x < 11/ 2
Plz help
I will be giving extra 50 points
it isn't possible to just give extra points in a simple and reliableway. anyways, let's starts.
a. is simple, just put the terms in order
r² +6r -5
because:
[tex] {r}^{2} + {6r}^{1} + {5r}^{0} [/tex]
anything to the power of 0 equals 1,
because it's the same as r/r, and 5 * r/r = 5*1
b. same logic as above
a²b² -5ab +33
c.
-c³ +ab +d +9
d.
-9y^5 - 2x³y²z +4x² +10x +1
^5 = to the power of five, it's the fastest way to type it without the special math input tool.
hope it helps you
Answer:
I agree with the above one.
Please help! Question in image below:
Answers also below:
Answer:
11, 18, 25, 32, .....
Option D
Step-by-step explanation:
The formula for the nth term of an AP is a+(n-1)d
a+(n-1)d=a+(n-1-1)d+7
a+nd-d=a+nd-2d+7
d=7
As the common difference is 7.
The only option given which is in an AP is the 4th option
Find the range of the following piecewise function.
f(x) =
(3x-2 if -1<(or equal to)x<0
2x+3 if 0<(or equal to)x<5
Answer:
[tex]\huge\boxed{[-5;\ -2)\ \cup\ [3;\ 13)}[/tex]
Step-by-step explanation:
The following piecewise functions are linear functions. The graph of any of them is a line segment.
We just need to calculate the value of the function at each end specified in the brace.
[tex]y=3x-2\ \text{if}\ -1\leq x<0[/tex]
Substitute x =-1 and x = 0:
[tex]x=-1\\y=3(-1)-2=-3-2=-5\\\\x=0\\y=3(0)-2=0-2=-2[/tex]
Range of this piece is [-5; -2)
[tex]y=2x+3\ \text{if}\ 0\leq x<5[/tex]
Substitute x =0and x = 5:
[tex]x=0\\y=2(0)+3=0+3=3\\\\x=5\\y=2(5)+3=10+3=13[/tex]
Range of this piece is [3; 13)
Therefore the range of the following piecewise function is:
[tex][-5;\ -2)\ \cup\ [3;\ 13)[/tex]
Look at the picture.
Write an inequality for the shaded region shown in the figure.
Answer:
y ≥ x^2 - 1
Step-by-step explanation:
First, we can see that the shaded region is above what seems to be a parabola, and we also can see that the lines of the parabola are solid lines (which means that the points on the curve itself are solutions, so the symbol ≥ is used)
Then:
y ≥ a*x^2 + b*x + c
where a*x^2 + b*x + c is the general quadratic equation.
Now let's find the equation for the parabola:
f(x) = a*x^2 + b*x + c
We also can see that the vertex of the parabola is at the point (0, -1)
This means that:
f(0) = -1 = a*0^2 + b*0 + c
= -1 = c
then we have that c = -1
Then:
f(x) = a*x^2 + b*x - 1
Now we can look at the graph again, to see that the zeros of the parabola are at +1 and -1
Which means that:
f(1) = 0 = a*1^2 + b*1 - 1 = a + b - 1
f(-1) = 0 = a*(-1)^2 + b*(-1) - 1 = a - b - 1
Then we got two equations:
a + b - 1 = 0
a - b - 1 = 0
from this we can conclude that b must be zero.
Then:
b = 0
and these equations become:
a - 1 = 0
a - 1 = 0
solving for a, we get:
a = 1
Then the quadratic equation is:
f(x) = 1*x^2 + 0*x - 1
f(x) = x^2 - 1
And the inequality is:
y ≥ x^2 - 1
Will give brainliest answer
Answer:
Step-by-step explanation:
2%
Solve, expressing your answer in an exact form involving a natural logarithm and showing your steps: 3*e^1/2t+4=27
Answer:
3 e^t/2 + 4 = 27
e^t/2 = 23 / 3
Taking natural log of both sides
t/2 = ln 23/3 = ln 7.667 = 2.037
t = 4.074
Check:
3 e^4.074/2 + 4 = 27
27 = 27
Find the period of the function y = 3/2 tan(1/3^x).
А) pi
B) pi/3
C) 3pi
D pi/6
==========================================================
Explanation:
I'm assuming you meant to say
y = (3/2)*tan( (1/3)x )
If so, then that equation is in the form
y = A*tan(Bx)
The B coefficient is B = 1/3 and it directly ties together to the period T.
T = pi/B
T = pi/(1/3)
T = pi*(3/1)
T = 3pi .... answer is choice C
Side note: This formula only works for tangent and cotangent functions.
I don't get this question i need some help please!!!
Answer:
2 sqrt(2) = x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 45 = x/4
4 sin 45 = x
4 ( sqrt(2)/2) =x
2 sqrt(2) = x
Answer: D
Use sine to find the x-value:
[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]
Find the slope of the line that passes through (4,2) and (4,5)
and. Write your answer in simplest form.
Select "Undefined" if applicable.
Answer: Undefined
Step-by-step explanation:
(slope = m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{4-4}=\frac{3}{0}[/tex]
(3 divided by 0 is undefined, so the slope is undefined)
ii) The time taken by a train to travel from Colombo to Kandy
You are walking from home to a grocery store you stop for a rest after tofit miles the grocery store is actually 3/4 miles from home how much farther do you have to walk
Answer:
no I don't know I am sorry for this question
Find two numbers that have 2, 5, and 7 as factors.
Step-by-step explanation:
One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.
To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140
A random sample of 50 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.21 per car. The population standard deviation is $5.92.
Round your answers to two decimal places.
(a) State the point estimate for the population mean cost of fast food bills at this restaurant $
(b) Calculate the 95% margin of error. $
(c) State the 95% confidence interval for the population mean cost of fast food bills at this restaurant.
$
≤ µ ≤ $
(d) What sample size is needed if the error must not exceed $1.00?
n =
First, we find the point estimate, given by the sample mean. Then, with this, and the standard deviation of the population given, we can find the margin of error, and then, we can find the confidence interval and the minimum sample size necessary.
Doing this, we get that:
a) The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.
b) The 95% margin of error is $1.64.
c) The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.
d) The sample size needed is 135.
Question a:
The point estimate for the population mean is the sample mean, which is of $18.21.
The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.
Question b:
We have to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of .
That is z with a p-value of , so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{5.92}{\sqrt{50}} = 1.64[/tex]
The 95% margin of error is $1.64.
(c) State the 95% confidence interval for the population mean cost of fast food bills at this restaurant.
The lower end of the interval is the sample mean subtracted by M. So it is 18.21 - 1.64 = 16.57
The upper end of the interval is the sample mean added to M. So it is 18.21 + 1.64 = 19.85
The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.
(d) What sample size is needed if the error must not exceed $1.00?
This is n for which M = 1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 1.96\frac{5.92}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 1.96*5.92[/tex]
[tex](\sqrt{n})^2 = (1.96*5.92)^2[/tex]
[tex]n = 134.6[/tex]
Rounding up:
The sample size needed is 135.
For a question in which you find a confidence interval using the z-distribution, you can check https://brainly.com/question/24175328
To find the minimum sample size for a confidence interval, you can check https://brainly.com/question/22667000
ASAP ! PLSSSQ!!!!!!!
Answer:
16
Step-by-step explanation:
Two shipments of components were received by a factory and stored in two separate bins. Shipment I has4% ofits contents defective, while shipment II has5% of its contents defective. If it is equally likely an employee willgo to either bin and select a component randomly, what is the probability a selected component is defective
Answer:
0.045 = 4.5% probability a selected component is defective
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Probability of a defective component:
4% of 50%(shipment I)
5% of 50%(shipment II). So
[tex]p = 0.04*0.5 + 0.05*0.5 = 0.045[/tex]
0.045 = 4.5% probability a selected component is defective
