Using the binomial distribution, it is found that there is a:
a) 0.3526 = 35.26% probability of rejecting a lot that is 3% defective.
b) 0.4295 = 42.95% probability of accepting a lot that is 4% defective.
For each device, there are only two possible outcomes, either it is defective, or it is not. The probability of a device being defective is independent of any other device, hence the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem, the sample has 100 units, hence [tex]n = 100[/tex].
Item a:
3% of the pieces are defective, hence [tex]p = 0.03[/tex].
The probability is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.03)^{0}.(0.97)^{100} = 0.0476[/tex]
[tex]P(X = 1) = C_{100,1}.(0.03)^{1}.(0.97)^{99} = 0.1471[/tex]
[tex]P(X = 2) = C_{100,2}.(0.03)^{2}.(0.97)^{98} = 0.2252[/tex]
[tex]P(X = 3) = C_{100,3}.(0.03)^{3}.(0.97)^{97} = 0.2275[/tex]
Then:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0476 + 0.1471 + 0.2252 + 0.2275 = 0.6474[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6474 = 0.3526[/tex]
0.3526 = 35.26% probability of rejecting a lot that is 3% defective.
Item b:
4% of the pieces are defective, hence [tex]p = 0.04[/tex].
Lot is accepted if less than 4 units are defective, hence:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = 0) = C_{100,0}.(0.04)^{0}.(0.96)^{100} = 0.0169[/tex]
[tex]P(X = 1) = C_{100,1}.(0.04)^{1}.(0.96)^{99} = 0.0703[/tex]
[tex]P(X = 2) = C_{100,2}.(0.04)^{2}.(0.96)^{98} = 0.1450[/tex]
[tex]P(X = 3) = C_{100,3}.(0.04)^{3}.(0.96)^{97} = 0.1973[/tex]
Then:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0169 + 0.0703 + 0.1450 + 0.1973 = 0.4295[/tex]
0.4295 = 42.95% probability of accepting a lot that is 4% defective.
A similar problem is given at https://brainly.com/question/24863377
Solve for x. SHOW ALL WORK
5(3x+4)−2x=7x−3(−2x+11
Answer:
x = -47/6
Step-by-step explanation:
Simplify both sides of the equation : 13x + 20 = 7x - 27
Subtract 7x from both sides : 6x + 20 = -27
Subtract 20 from both sides : 6x = -47
Divide both sides by 6 : 6x/6 = -47/6
Answer : x = -47/6
Set Question involving real and natural numbers
Only two real numbers satisfy x² = 23, so A is the set {-√23, √23}. B is the set of all non-negative real numbers. Then you can write the intersection in various ways, like
(i) A ∩ B = {√23} = {x ∈ R | x = √23} = {x ∈ R | x² = 23 and x > 0}
√23 is positive and so is already contained in B, so the union with A adds -√23 to the set B. Then
(ii) A U B = {-√23} U B = {x ∈ R | (x² = 23 and x < 0) or x ≥ 0}
A - B is the complement of B in A; that is, all elements of A not belonging to B. This means we remove √23 from A, so that
(iii) A - B = {-√23} = {x ∈ R | x² = 23 and x < 0}
I'm not entirely sure what you mean by "for µ = R" - possibly µ is used to mean "universal set"? If so, then
(iv.a) Aᶜ = {x ∈ R | x² ≠ 23} and Bᶜ = {x ∈ R | x < 0}.
N is a subset of B, so
(iv.b) N - B = N = {1, 2, 3, ...}
Select the correct answer. What is the solution to the equation? 2(x+7)^2/3 = 8 A. -15 and 1 B. -15 C. 1 D. no solution
Answer:
The answer has no solution because it is infinite and that's your vairiable
Answer:
-15 and 1
Step-by-step explanation:
Based on the table below, find the input and output values of the function.
Answer:
the inputs are: 0,1,2,8,12
the outputs are: 19,9,7,16,17
(Put them in order if needed)
**inputs are x values and outputs are the y values**
Find x: 8^2^x=4
pls help!
Answer:
x = 1/3
Step-by-step explanation:
assuming this is saying (8^2)^x = 4
2^6x = 4
2^6x = 2^2
6x = 2
x = 1/3
Pls help. The question is on the picture
Answer:
23518
Step-by-step explanation:
1) the total volume can be calculated as the sum of two volumes (for more info see the picture): V=V₁+V₂, where V₁ belongs to the prisma and V₂ - to the cylinder;
2) V₁=a*b*h; V₁=20*20*37=14800 (m³);
V₂=3/4*(π*r²*h); V₂=3/4*3.1415*100*37≈8717,6625 (m³), note the full volume of the cylinder cannot be included into the result, but 3/4 of its volume;
3) finally, V=14800+8717.6625=23517,6625≈23518 (m³).
Answer:
V = 23518 m3
Step-by-step explanation:
The volume of the cube part of building
(20)(20)(37)=14800 cm3
Each cylinder:
h=37/12=3.083 m
r=10 m
[tex]v=\pi (10)^{2} (3.083)=968.66m^{3}[/tex]
all the cylinders:
[tex]v=(12)(968.66)=11,623.89cm^{3}[/tex]
Total volume.
[tex]V=14800+\frac{3}{4} (11,623.89)[/tex]
[tex]V=14800+8717.92=23,517.92[/tex]
nearest m3:
[tex]V=23518m^{3}[/tex]
I hope this help you
a ladder 7.5m long rests against a wall . the botton of ladder is 2.1m from the wall . calculate how far the ladder reaches up the wall.
Answer:
h = √(7.5² - 2.1²) = 7.2 m
Step-by-step explanation:
The length of a rectangle is three times its width. if the area of the rectangle is 75 in2, find its perimeter.
Answer:
40 in
Step-by-step explanation:
For a width of w, the length is 3w and the area and perimeter are ...
A = LW = (3w)(w) = 3w^2
P = 2(L+W) = 2(3w +w) = 8w
We are given the area, so we can find w to be ...
75 in^2 = 3w^2
25 in^2 = w^2 . . . . . divide by 3
5 in = w . . . . . . . . . square root
Then the perimeter is ...
P = 8w = 8(5 in) = 40 in
fill in the missing value in each equation:
a)0.25+_____=0
b)-5×_____=-5
c)_____×-6=0
Answer:
a) -0.25
b) 1
c)0
Step-by-step explanation:
a) 0.25 + (-0.25)=0
b) -5*1=-5
c) 0*(-6)=0
A restaurant has an electronic system that randomly selects customers when they pay for their meal to receive a coupon for their next visit. Each customer has a 10\%10%10, percent probability of being selected to receive a coupon, and one customer being selected or not doesn't affect whether or not another customer will be selected.
Suppose that 222 customers pay for their meals, one after the other.
What is the probability that NEITHER customer is selected to receive a coupon?
Round your answer to two decimal places.
Answer:
Step-by-step explanation:
Using the binomial distribution, it is found that there is a 0.81 = 81% probability that NEITHER customer is selected to receive a coupon.
For each customer, there are only two possible outcomes, either they receive the coupon, or they do not. The probability of a customer receiving the coupon is independent of any other customer, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
0.81 = 81% probability that NEITHER customer is selected to receive a coupon.
please help me mathematics = x²+2x-24=0
Answer:
x=4
or
x=-6
Step-by-step explanation:
did you know u can solve that equation on your calculator without much struggle?
Answer:
Factors = > (x - 4) (x + 6)Value = > x = 4, -6Step-by-step explanation:
= > x^2 + 2x - 24
= > x^2 + 6x - 4x - 24
= > x(x + 6) - 4(x + 6)
= > (x - 4) (x + 6)...ans
x = -6 , 4
Hope it helps you!!
Dwayne read 3/8 of a chapter of his history book in 1/5 of an hour. At this rate, how many chapters of his history book can he read in 1 hour?
Answer:
1 7/8 (1, 2)
Step-by-step explanation:
60/5=12 so dwayne reads 3/8 chapter per 12 minutes
12/3=4 so dwayne reads 1/8 chapter per 4 minutes
4x8=32 dwayne reads a chapter per 32 minutes.
2x32=64 and got 4 minute extra which is the time for dwayne to read 1/8 chapter
So Dwayne can read 1 7/8 chapter in 1 hour, if rounding off then 2 chapters, if only an entire chapter counts then 1
3. Consider the system { 9x – 12y = b
3x – 4y = 10
For what value of b will the system have infinitely many solutions?
Answer:
B=30
Step-by-step explanation:
Like and give 5 star rating
Answer:
b = 30
Step-by-step explanation:
all terms in the first equation will be three times the related terms in the second equation.
Then the two equation describe the same infinite line and any x,y pair that fits on one line will also fit on the other.
Kylie has lemon and watermelon in a ratio of 10:71. How many watermelon does she have if she has 20 lemons
Answer:
142 watermelon
Step-by-step explanation:
10/71 = 20 / w
w = 20(71/10) = 142
Can someone answer these questions? Thank you!
Answer:
It's not a function
Because it's not a function, you don't have to answer b and c
what percent equals 44 =33
Answer:
33/44 = 0.75
0.75*44 = 33
Answer:
44% of 75 = 33
Step-by-step explanation:
True or false: An absolute value function is an example of a piecewise function.
Answer:
True
Step-by-step explanation:
An absolute function can be re-written as:
[tex]|x| = \left \{ {{x} \quad \ \ \ \text{if} \ x \geq \ 0\atop {-x} \quad \text{if} \ x < 0} \right.[/tex]
That is the form of a piecewise function.
Solve each proportion 3 = 72 – 7
1. 3/7 = 72/x
By cross multiplication we get :
➟ 3x = 72 × 7
➟ x = 72 × 7/3
➟ x = 24 × 7
➟ x = 168
2. m/8 = 8/20
By cross multiplication we get :
➟ 20m = 8 × 8
➟ 20m = 64
➟ m = 64/20
➟ m = 16/5
1cm +4cm+2cm+1.5cm+2.5cm
find its perimeter
Answer:
11 cm
Step-by-step explanation:
add whole numbers
1 + 4 + 2 = 7
add decimal numbers
1.5 + 2.5 = 4
add the answers
7 + 4 = 11
have a splendid day <3
Answer:
11cm
Step-by-step explanation:
To find perimeter, you simply just add each of the side lengths.
To make this easier to read, lest group some of the terms
1cm + 4cm = 5cm
2cm + 1.5cm = 3.5cm
5cm + 3.5cm = 8.5cm
8.5cm + 2.5cm = 11cm
The five terms are bolded to make sure that we added each term in the sum.
geometry help on 34 please
Answer:
x=112, y=28, z=22
Step-by-step explanation:
68°+4y°=180° (adj angles on a str line)
4y=180-68
=112
y=112÷4
=28
x°+68°=180° (int angles)
x=180-68
=112
(5z+2)°=x° (corr angles)
5z+2=x
5z+2=112
5z=112-2
=110
z=110÷5
=22
What is the equation of the line in slop-intercept form?
Enter your answer in the blank spots
y= __x + __
Answer: i think its 4 -4 or 4 and 8
Step-by-step explanation: sorry if imma wrong
What is the value of x?
Answer:
Step-by-step explanation:
45
Answer:
x=44°
Step-by-step explanation:
It's an Isosceles triangle, it has two equal sides (DC=CE) so also its two equal angles of 44 degrees
Hope this helps
5. 3 out of 750 light bulbs is what percent?
Answer:
0.00706666666
Step-by-step explanation:
Write 5 • 5 • 5 • 5 • 5 • 5 • 5 using an exponent.
Answer:
5^6
Step-by-step explanation:
5 was multiplied repeatedly 6 times, so it's 5 to the power of 6
Answer:
5 to the power of 6 or 5^6
Step-by-step explanation:
Write the equation (y=mx+b) that represents the relationship show on the graph.
Answer:
y= 3x + 4
Step-by-step explanation:
yeah-ya....... right?
find the perimeter of a trapezium whose side is 3cm,4cm,5cm,6cm
Answer:
18 cm
Step-by-step explanation:
The perimeter is the sum of the side lengths:
3 cm + 4 cm + 5 cm + 6 cm = 18 cm
_____
Additional comment
If these are the side lengths in order around the figure, it cannot exist. (It will be a line segment 9 units long.)
find the measure of ∠A.
Answer:
68 degrees
Step-by-step explanation:
Supplementary angles have sum 180°
5x+27+5x-7=18010x+27-7=18010x+20=18010x=160x=16<A=
5(16)+2780+27107°Hey everyone! I need some help with this one.
What is the range of this relation?
Answer:
ok so first lets look for the highest y value which is 4
the lowest one is -4
so -4<x>4
The answer is c
Hope This Helps!!!
-2 5/12 - (-10 8/9)
[tex]-2 \dfrac 5{12} - \left( - 10 \dfrac 89 \right)\\\\\\=- \left(2 + \dfrac 5{12} \right) + \left(10 + \dfrac 89 \right) \\\\\\=8 + \dfrac 89 - \dfrac 5{12}\\\\\\=8+ \dfrac{32}{36} - \dfrac{15}{36}\\\\\\= 8 + \dfrac{17}{36}\\\\\\= 8 \dfrac{17}{36}[/tex]
find the value of x in 7/8=49/x
Step-by-step explanation:
,
[tex] \frac{7}{8} = \frac{49}{x} \\ 7x = 392 \\ x = \frac{392}{7} \\ x = 56[/tex]
Answer:
x = 56
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
7/8-(49/x)=0
Step by Step solution:
Step 1:
Simplify 49/x
Equation at the end of step 1:
7/8 - 49/x = 0
Step 2:
Simplify 7/8
Equation at the end of step 2:
7/8 - 49/x = 0
Step 3:
Calculating the Least Common Multiple :
Find the Least Common Multiple
The left denominator is : 8
The right denominator is : x
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 3 0 3
Product of all
Prime Factors 8 1 8
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
x 0 1 1
Least Common Multiple:
8x
Calculating Multipliers :
3.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = x
Right_M = L.C.M / R_Deno = 8
Making Equivalent Fractions :
3.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 7 • x
—————————————————— = —————
L.C.M 8x
R. Mult. • R. Num. 49 • 8
—————————————————— = ——————
L.C.M 8x
Adding fractions that have a common denominator :
3.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
7 • x - (49 • 8) 7x - 392
———————————————— = ————————
8x 8x
STEP
4
:
Pulling out like terms :
4.1 Pull out like factors :
7x - 392 = 7 • (x - 56)
Equation at the end of step
4
:
7 • (x - 56)
———————————— = 0
8x
STEP
5
:
When a fraction equals zero :
5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
7•(x-56)
———————— • 8x = 0 • 8x
8x
Now, on the left hand side, the 8x cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
7 • (x-56) = 0
Equations which are never true:
5.2 Solve : 7 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
5.3 Solve : x-56 = 0
Add 56 to both sides of the equation :
x = 56
One solution was found :
x = 56