Using the binomial distribution, it is found that:
a) 0.1271 = 12.71% probability of obtaining at least three defects in the sample, if the entire shipment has 5% defectives. 5% defective is between 1 and 2 defects, but since this probability is more than the unlikely threshold 5%, more than 2 defects could still mean that Intel has provided a shipment which is consistent with the contract.
b) The mean is of 1.25 defective chips and the standard deviation is of 1.09 defective chips.
c) 0.8908 = 89.08% probability that more than 17 chips in the sample are good.
For each chip, there are only two possible outcomes, either it is defective, or it is not. The probability of a chip being defective is independent of any other chip, which means that 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]
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:
25 chips are tested, thus, [tex]n = 25[/tex].Item a:
Supposing 5% defective, we have that [tex]p = 0.05[/tex].
The probability is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{25,0}.(0.05)^{0}.(0.95)^{25} = 0.2774[/tex]
[tex]P(X = 1) = C_{25,1}.(0.05)^{1}.(0.95)^{24} = 0.3650[/tex]
[tex]P(X = 2) = C_{25,2}.(0.05)^{2}.(0.95)^{23} = 0.2305[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2774 + 0.3650 + 0.2305 = 0.8729[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.8729 = 0.1271[/tex]
0.1271 = 12.71% probability of obtaining at least three defects in the sample, if the entire shipment has 5% defectives. 5% defective is between 1 and 2 defects, but since this probability is more than the unlikely threshold 5%, more than 2 defects could still mean that Intel has provided a shipment which is consistent with the contract.
Item b:
The mean is:
[tex]E(X) = np = 25(0.05) = 1.25[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{25(0.05)(0.95)} = 1.09[/tex]
The mean is of 1.25 defective chips and the standard deviation is of 1.09 defective chips.
Item c:
20% are defective, so 80% are good, which means that [tex]p = 0.8[/tex]
The probability is:
[tex]P(X > 17) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 18) = C_{25,18}.(0.8)^{18}.(0.2)^{7} = 0.1108[/tex]
[tex]P(X = 19) = C_{25,19}.(0.8)^{19}.(0.2)^{6} = 0.1633[/tex]
[tex]P(X = 20) = C_{25,20}.(0.8)^{20}.(0.2)^{5} = 0.1960[/tex]
[tex]P(X = 21) = C_{25,21}.(0.8)^{21}.(0.2)^{4} = 0.1867[/tex]
[tex]P(X = 22) = C_{25,22}.(0.8)^{22}.(0.2)^{3} = 0.1358[/tex]
[tex]P(X = 23) = C_{25,23}.(0.8)^{23}.(0.2)^{2} = 0.0708[/tex]
[tex]P(X = 24) = C_{25,24}.(0.8)^{24}.(0.2)^{1} = 0.0236[/tex]
[tex]P(X = 25) = C_{25,25}.(0.8)^{25}.(0.2)^{0} = 0.0038[/tex]
Then:
[tex]P(X > 17) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25) = 0.1108 + 0.1633 + 0.1960 + 0.1867 + 0.1358 + 0.0708 + 0.0236 + 0.0038 = 0.8908[/tex]
0.8908 = 89.08% probability that more than 17 chips in the sample are good.
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Given f(x) = 2x - 3, find f(8)
***EXPLANATION NEEDED***
Answer:
f(8) = 13
Step-by-step explanation:
Step 1: Plug in 8 for the value of x.
[tex]f(8) = 2(8) - 3[/tex]Step 2: Multiply 2 by 8.
[tex]f(8) = 16 - 3[/tex]Step 3: Subtract 3 from 16.
[tex]f(8) = 13[/tex]Therefore, f(8) = 13.
Answer:
Step-by-step explanation:
Hi there!
Given;
f(x) = 2x - 3
To find: f(8)
Replace 8 in each place where there is "x" in f(x).
or, f(8) = 2*8 -3
= 16-3
= 13
Therefore, f(8) = 13.
Hope it helps!
I dont understand Analyze and solve percent problems
Answer:
okay, well, is there any link u wanna post for us to help u? maybe we can explain it?
Step-by-step explanation:
Help Please, Missing Geometry Class because I am sick and don't understand this.
Answer:
niether do i
Step-by-step explanation:
5(Y-1)=3(2Y-5)-(1-3Y)
Answer: =11/4
Step-by-step explanation:
Answer:
[tex]y = 2 \frac{3}{4} \\ [/tex]
Step-by-step explanation:
[tex]5(y - 1) = 3(2y - 5) - (1 - 3y) \\ 5y - 5 = 6y - 15 - 1 + 3y \\ 5y - 5 = 9y - 16 \\ 16 - 5 = 9y - 5y \\ 11 = 4y \\ \frac{11}{4} = y \\ 2 \frac{3}{4} = y \\ [/tex]
The principal of a school is hosting a small luncheon for her staff. She plans to prepare two sandwiches for each person. Some staff members offer to bring salads and beverages.
The principal has a budget of $225 and expects at least 16 people to attend. Sandwiches cost $3 each.
Select all of the equations and inequalities that could represent the constraints in the situation, where n is the number of people attending and s is the number of sandwiches.
Copied for free from openupresources.org
Select all that apply:
A. n ≥ 16
B. n ≥ 32
C. s < 32
D. s = 2n
E. 3n ≤ 225
F. 3s ≤ 225
The constraints in the question are given by the definition of the variables;
The constraints are represented by the following equation and inequalities.
A. n ≥ 16D. s = 2·nF. 3s ≤ 225Reasons:
The budget of the principal = $225
Number of people expected = 16 people
Number of sandwich per person = 2
Cost of each sandwich = $3
Required:
To select the inequalities that represent the situation's constraint
Solution:
The variable that represent the number of people attending = n
The number of sandwiches = s
From the question , we have;
The number of sandwich per attendee = 2 sandwiches
The total number of sandwich, s, for n attendees = 2·n
Therefore, we have;
s = 2·n
The number of people attending is at least 16, therefore;
n ≥ 16
The cost of the s sandwich = $3 × s
The total cost should be less than or equal to given budget of $225,
therefore;
3s ≤ 225
The equations and inequalities that could represent the constraints are;
A. n ≥ 16, D. s = 2·n, and F. 3s ≤ 225
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In 3 years Xavier will be 3 times older than Joanne is today. Joanne is 24. How old is Xavier?
Answer: he is currently 69 years old
Step-by-step explanation:
24x3=72-3=69 lol funni number
Answer:
78 years old
Step-by-step explanation:
In 3 years Joanne will be 27. Xavier is 3 times that age by the time Joanne is 27. 27×3=81. but we're looking for Xaviers age today. so we take 81 and subtract 3 which leaves us with 78
A manufacturer of bicycles has determined that 550 bikes per month will be sold at a price of $250. At a price of $150, it is estimated that 750 bikes will be sold. a) Determine a linear function (equation) that predicts the number of bikes that will be sold each month at any given price. b) Use your equation from question a to predict how many bikes will be sold at $350.
Answer:
A is the answer
trust me
here is your answer and please follow me and Mark me As brain list
A manufacturer of bicycles has determined that 550 bikes per month will be sold at a price of $250. At a price of $150, it is estimated that 750 bikes will be sold.
a) Determine a linear function (equation) that predicts the number of bikes that will be sold each month at any given price.
b) Use your equation from question a to predict how many bikes will be sold at $350.
Step-by-step explanation:
Option A os Correct
a line that is parallel to y=-3x+2 and contains the point (3,-3)
Answer:
y = -3x + 6
Step-by-step explanation:
Two lines that are parallel will have the same slope. All we need to do is find the new y-intercept.
-3 = -3(3) + b
-3 = -9 + b
6 = b
Now we can input the stuff we know and solved for back into the original formula [ y = mx + b ].
y = -3x + 6
Best of Luck!
A parallel line means our new line will have a slope equal to the original line.
The original line is in slope-intercept form, y = mx + b, where m is the slope and b is the value of the y-intercept. This tells us that the slope we want to use is m = -3
By using a slope of -3, with the given point (3,-4), we can now use the point-slope formula to find our new line.
Point-slope formula: y - y1 = m(x - x1) where m is the slope and the line passes through the point (x1,y1)
Combining our point and slope, we get:
y + 4 = -3(x - 3)
If we wish, we can rearrange this by distributing on the right hand side.
y + 4 = -3x + 9
We can then subtract 4 from both sides to get our answer in slope-intercept form
y + 4 - 4 = -3x + 9 - 4
y = -3x + 5
I will gladly give brainliest.
4 ( 2x - 3) -2 ( x + 1)
Answer:
6x - 14
Step-by-step explanation:
4(2x - 3) - 2(x + 1)
1. Expand both brackets
(8x - 12) - (2x + 2)
2. Simplify
8x - 2x = 6x
-12 - 2 = -14
Therefore, 4(2x - 3) - 2(x + 1) = 6x - 14
QUIZ:
Add Signed Decimals
Add.
-2.34 + (-1.052)
Enter your answer in the box.
Answer:
-3.392
Step-by-step explanation:
Math-way
What are the solutions of the quadratic equation
4x2 - 8x – 12 = 0 ?
A) x = -1 and x = -3
B) x = -1 and x = 3
C) x = 1 and x = -3
D) x = 1 and x = 3
Answer:
Step-by-step explanation:
4x2 - 8x -12 = 0
divide through by 4
x2 - 2x - 3 = 0
x2 - 3x + x - 3 = 0
(x2 - 3x) + (x - 3) = 0
x(x - 3) + 1(x - 3) = 0
(x + 1) (x - 3) = 0
x + 1 = 0 and x - 3 = 0
x = -1 and x = 3
Answer:
B IS THE ANSWER
Step-by-step explanat
(22x2 - 8x) - 12 = 0
4x2 - 8x - 12 = 4 • (x2 - 2x - 3)
The first term is, x2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -2 .
-3 + 1 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 1
x2 - 3x + 1x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-3)
Add up the last 2 terms, pulling out common factors :
1 • (x-3)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-3)
Which is the desired factorization
4 • (x + 1) • (x - 3) = 0
A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
Any solution of term = 0 solves product = 0 as well.
Solve : x+1 = 0
Subtract 1 from both sides of the equation :
x = -1
Solve : x-3 = 0
Add 3 to both sides of the equation :
x = 3
What are the three major responsibilities of the county sheriff? (Site 1)
Answer:1. They make policies
2. They perform executive duties
3. They plan environmental and land use policy
Step-by-step explanation:
Answer:
To become rich
Step-by-step explanation:
I'm rich so
How many intervals are there in the hisogram in figure 1.4?
Answer: 5 to 20 intervals.
Step-by-step explanation:
Complete the square to rewrite y = x^2 - 6x + 16 in vertex form. Then state wether the vertex is a maxium or minimum and give its coordinates.
A. Maximum at (3,7)
B. Maximum at (-3,7)
C. Minimum at (3,7)
D. Minimum at (-3,7)
will give brainly!!’
Answer:
C) Minimum at (3,7)
Step-by-step explanation:
Recall that vertex form is [tex]y=a(x-h)^2+k[/tex]:
[tex]y=x^2-6x+16[/tex]
[tex]y=(x^2-6x+9)+7[/tex]
[tex]y=(x-3)^2+7[/tex]
Therefore, the vertex is [tex](h,k)[/tex] or [tex](3,7)[/tex] in this case. Because the parabola is positive, then the vertex has to be the minimum of the parabola, making choice C correct.
x = - 23
y = - 5
z = - 10
[tex](x-12)/ (y+z)\\[/tex]
i had to do the answer as a pic cuz my iPad is gonna die.
sorry <:)
Answer:
7/3Step-by-step explanation:
x = - 23
y = - 5
z = - 10
(x - 12)/(y+z)=
(-23 - 12)/(-5-10)=
45/15=
7/3
What is 449,650 rounded to the nearest ten thousand?
400,000
440,000
449,000
450,000
Answer:
450,000
Step-by-step explanation:
The ten thousand digit is 4 and if we compare it to 9, it is bigger then 5 therefore it is rounded up and you get the answer of 450,000
Explain why rational numbers are "friendly."
Answer:
What makes a number friendly?
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself. Two numbers with the same "abundancy" form a friendly pair; n numbers with the same "abundancy" form a friendly n-tuple.
Step-by-step explanation:
Please answer this math riddle for me ASAP!!! please
I am a four-digit number. My first number has no use because the number would be the same without it. My second and third numbers are mirror images and my fourth number is half of my second number.
Answer:
0884
Step-by-step explanation:
Plz help me
I will thank you
Answer: 89674 buckets were produced in 4 months
Answer:
Step-by-step explanation:
First you have to do 5263 / 7 = 751.9 (rounded 751.857143)
Then do 751.9x121.6= 91 431
You get 121.6 because that is how many days are in 4 months.
Hope this helps !!!!
Have a good day/night!!<333
Match the following items.
Determine the functions if θ is a first-quadrant angle, and sin = .
1. cosθ √(15)/5
2. tanθ √(10)/2
3. cscθ √(15)/3
4. secθ √6/3
5. cotθ √6/2
The functions are illustrations of trigonometry ratios
[tex]\mathbf{(a)\ cos\theta = \frac{\sqrt{15}}{5}}[/tex]
The sine of an angle is calculated as follows
[tex]\mathbf{sin\theta = \sqrt{1 - cos^2\theta}}[/tex]
So, we have:
[tex]\mathbf{sin\theta = \sqrt{1 - (\sqrt{15}/5)}}[/tex]
[tex]\mathbf{sin\theta = \sqrt{1 - (15/25)}}[/tex]
Take LCM
[tex]\mathbf{sin\theta = \sqrt{\frac{10}{25}}}[/tex]
[tex]\mathbf{sin\theta = \frac{\sqrt{10}}{5}}[/tex]
[tex]\mathbf{(b)\ tan\theta = \frac{\sqrt{10}}{2}}[/tex]
The tangent of an angle is:
[tex]\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}[/tex]
Using Pythagoras theorem, we have:
[tex]\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}[/tex]
So, we have:
[tex]\mathbf{Hypotenuse^2 = (\sqrt{10})^2 + 2^2}[/tex]
[tex]\mathbf{Hypotenuse^2 = 10 + 4}[/tex]
[tex]\mathbf{Hypotenuse^2 = 14}[/tex]
Take square roots
[tex]\mathbf{Hypotenuse = \sqrt{14}}[/tex]
So, the sine of the angle is:
[tex]\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}[/tex]
[tex]\mathbf{\ sin\theta = \frac{\sqrt{10}}{\sqrt{14}}}[/tex]
Rationalize
[tex]\mathbf{\ sin\theta = \frac{\sqrt{140}}{14}}[/tex]
[tex]\mathbf{(c)\ csc\theta = \frac{\sqrt{15}}{3}}[/tex]
The sine of the angles is:
[tex]\mathbf{sin \theta = \frac{1}{csc\theta}}[/tex]
So, we have:
[tex]\mathbf{sin \theta = \frac{1}{\sqrt{15}/3}}[/tex]
[tex]\mathbf{sin \theta = \frac{3}{\sqrt{15}}}[/tex]
Rationalize
[tex]\mathbf{sin \theta = \frac{3\sqrt{15}}{15}}[/tex]
[tex]\mathbf{sin \theta = \frac{\sqrt{15}}{5}}[/tex]
[tex]\mathbf{(d)\ sec\theta =\frac{\sqrt 6}{3}}}[/tex]
The sine of an angle is calculated as follows
[tex]\mathbf{sin\theta = \sqrt{1 - (1/sec\theta)^2}}[/tex]
So, we have:
[tex]\mathbf{sin\theta = \sqrt{1 - (3/\sqrt 6)^2}}[/tex]
[tex]\mathbf{sin\theta = \sqrt{(1 - 9/6)}}[/tex]
[tex]\mathbf{sin\theta = \sqrt{( - 3/6)}}[/tex]
The sine of the angle does not have a real value
[tex]\mathbf{(e)\ cot\theta = \frac{\sqrt 6}{2}}[/tex]
Start by calculating the tangent of the angle
[tex]\mathbf{tan\theta = \frac{1}{cot\theta}}[/tex]
So, we have:
[tex]\mathbf{tan\theta = \frac{1}{\sqrt 6/2}}[/tex]
[tex]\mathbf{tan\theta = \frac{2}{\sqrt 6}}[/tex]
Rationalize
[tex]\mathbf{tan\theta = \frac{2\sqrt 6}{6}}[/tex]
[tex]\mathbf{tan\theta = \frac{\sqrt 6}{3}}[/tex]
The tangent of an angle is:
[tex]\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}[/tex]
Using Pythagoras theorem, we have:
[tex]\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}[/tex]
So, we have:
[tex]\mathbf{Hypotenuse^2 = (\sqrt{6})^2 + 3^2}[/tex]
[tex]\mathbf{Hypotenuse^2 = 6 + 9}[/tex]
[tex]\mathbf{Hypotenuse^2 = 15}[/tex]
Take square roots
[tex]\mathbf{Hypotenuse = \sqrt{15}}[/tex]
So, the sine of the angle is:
[tex]\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}[/tex]
[tex]\mathbf{\ sin\theta = \frac{\sqrt{6}}{\sqrt{15}}}[/tex]
Rationalize
[tex]\mathbf{\ sin\theta = \frac{\sqrt{90}}{15}}[/tex]
Rewrite as:
[tex]\mathbf{\ sin\theta = \frac{3\sqrt{10}}{15}}[/tex]
[tex]\mathbf{\ sin\theta = \frac{\sqrt{10}}{5}}[/tex]
Read more about trigonometry ratios at:
https://brainly.com/question/24888715
A plumber charges 1/4 of the cost of materials as a labor fee. If the materials for the current job cost $130.00, how much will the plumber charge the client?
Answer:32.5
Step-by-step explanation: i used a calculator
Answer:
$162.50
Step-by-step explanation:
A store buys 10 shirts at a whole sale price of $5 each. They want to mark up the
price by 50%. How much do they sell each t-shirt for?
$100
$7.50
$55
$5.50
PLS I NEED HELPPP
Answer:
the answer is 5.50 or the last one
Step-by-step explanation:
hope this helps
Answer:
answer is $7.5
Step-by-step explanation:
1shirt=$5
10 shirt= ?
10*5= $50
$5= 100%
what about 150%
(5*150)÷100= $7.5
Aashi buys
2 packets of bread rolls costing £1.40 for each packet
1 bottle of ketchup costing £1.80
3 packets of sausages
Aashi pays with a £10 note.
She gets 45p change.
Work out the price in pounds (£) of one pack of sausages.
(you will get brainliest) !! :D
Price of one unit Sausage = 1.65
Sum ( Price x Quantity) = Total Expenditure
Price of Bread x Quantity of Bread + Price of Ketchup x Quantity of Ketchup + Price of Sausage x Quantity of Sausage
Total Expenditure Value = 10 - 0.45 = 9.55
Let price of sausage = P
Therefore, 2 (1.40) + 1 (1.80) + 3 P = 9.55
2.80 + 1.80 + 3 Ps = 9.55
4.6 + 3 P = 9.55
3P = 9.55 - 4.60 = 4.95
P = 4.95 / 3 = 1.65
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विपरीत अर्थवाले शब्द लिखिए ।
1. नदी २. इच्छा ३. आशा ४. अपकार
Answer:
sorry I can't understand the word
what is the quotient of 2x+5/4 ÷ 2x+5/6
a. 1/4
b. 1/2
c. 2/3
d. 3/2
Please answer. Don't spam!
Hello Gumiho!
[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
Find the distance.
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
Refer to the attached picture for the steps.
Answer :- The answer will be (c) [tex]\boxed{\boxed{\tt\sqrt{a^{2} + b^{2}}}}[/tex]
__________________
Hope it'll help you!
ℓu¢αzz ッ
Answer fast, please!!
Choose the numbers to find the product shown by the model.
-
0.5 x ? = ?
Answers: (this one is for what it was multiplied by)
A) 0.01
B) 0.1
C) 1
D) 10
Answers to the question:
E) 0.005
F) 0.05
G)0.5
H)5
Answer: A F D G
Step-by-step explanation:
what is the sum of 1/6 and 5/12
Answer:
7/12
1/6 to 2/12 add 5/12 to get 7/12
how to multiply 21 x 25 in oldschool way