A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone wrong in the manufacturing process, at most 7 chips each lot would be defective, but if something does go wrong, there could be far more defective chips. If something goes wrong with a given lot, they discard the entire lot. It would be prohibitively expensive to test every chip in every lot, so they want to make the decision of whether or not to discard a given lot on the basis of the number of defective chips in a simple random sample. They decide they can afford to test 100 chips from each lot. You are hired as their statistician.
There is a tradeoff between the cost of eroneously discarding a good lot, and the cost of warranty claims if a bad lot is sold. The next few problems refer to this scenario.
Problem 8. (Continues previous problem.) A type I error occurs if (Q12)
Problem 9. (Continues previous problem.) A type II error occurs if (Q13)
Problem 10. (Continues previous problem.) Under the null hypothesis, the number of defective chips in a simple random sample of size 100 has a (Q14) distribution, with parameters (Q15)
Problem 11. (Continues previous problem.) To have a chance of at most 2% of discarding a lot given that the lot is good, the test should reject if the number of defectives in the sample of size 100 is greater than or equal to (Q16)
Problem 12. (Continues previous problem.) In that case, the chance of rejecting the lot if it really has 50 defective chips is (Q17)
Problem 13. (Continues previous problem.) In the long run, the fraction of lots with 7 defectives that will get discarded erroneously by this test is (Q18)
Problem 14. (Continues previous problem.) The smallest number of defectives in the lot for which this test has at least a 98% chance of correctly detecting that the lot was bad is (Q19)
(Continues previous problem.) Suppose that whether or not a lot is good is random, that the long-run fraction of lots that are good is 95%, and that whether each lot is good is independent of whether any other lot or lots are good. Assume that the sample drawn from a lot is independent of whether the lot is good or bad. To simplify the problem even more, assume that good lots contain exactly 7 defective chips, and that bad lots contain exactly 50 defective chips.
Problem 15. (Continues previous problem.) The number of lots the manufacturer has to produce to get one good lot that is not rejected by the test has a (Q20) distribution, with parameters (Q21)
Problem 16. (Continues previous problem.) The expected number of lots the manufacturer must make to get one good lot that is not rejected by the test is (Q22)
Problem 17. (Continues previous problem.) With this test and this mix of good and bad lots, among the lots that pass the test, the long-run fraction of lots that are actually bad is (Q23)

Answer:

[tex]a + 2b -3 c + - 3a + b + 2c + 2a - 3b + c \\ = a - 3a + 2a + 2b + b - 3b - 3c + 2c + c \\ 0a + 0b + 0c \\ thank \: you[/tex]

a+2b-3c+(-3a+b+2c) +(2a-3b+c)

=a+2b-3c-3a+b+2c+2a-3b+c

=a-3a+2b+2b+b-3b-3c++2b+c

=0a+0b+0c

=0

Therefore, the addition of the expressions, a+2b-3c+(-3a+b+2c) +(2a-3b+c) is zero or 0.

To know more about algebraic expressions

https://brainly.com/question/28307605

Answer:

y=-2/3x+3

Step-by-step explanation:

the equation of line J is y=3/2x-5

perpendicular slope would be -2/3

you want it at point (6, -1) so sub the points into y=-2/3x+b

-1=-2/3(6)+b

-1=-4+b

3=b

y=-2/3x+3

Answer:

13

Step-by-step explanation:

If we have a right triangle, we can use the Pythagorean theorem to find the hypotenuse

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = c^2

25+144= c^2

169 = c^2

Take the square root of each side

sqrt(169) = sqrt(c^2)

13= c

Answer:

The length of the hypotenuse is 13.

Step-by-step explanation:

[tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex]

[tex]a^2 = 12^2 + 5^2[/tex]

[tex]a^2 = 144 + 25[/tex]

[tex]a^2 = 169[/tex]

a=[tex]\sqrt{169}[/tex]

a= 13

Here we use the idea of the Pythagoras' theorem. Which suggests that [tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex] in which  [tex]a^{2}[/tex] is the hypotenuse of the triangle and [tex]b^2[/tex] and [tex]c^{2}[/tex] are the two other lengths of the triangle.

HOPE THIS HELPED

Answer:

0.0286 = 2.86% probability that today is Monday.

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.

In this question:

Event A: Dressed correctly

Event B: Monday

Probability of being dressed correctly:

100% = 1 out of 4/7(mom dresses).

(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So

[tex]P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625[/tex]

Probability of being dressed correctly and being Monday:

The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:

[tex]P(A \cap B) = 0.125\frac{1}{7} = 0.0179[/tex]

What is the probability that today is Monday?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286[/tex]

0.0286 = 2.86% probability that today is Monday.

Answer:

D. Find the cost of 1 week of guitar lessons for each store and compare.

Step-by-step explanation:

Find the cost for 1 week of guitar lessons by finding the slope of the data.

[tex]\frac{y_2-y_1}{x_2-x_1}\\\\ A.)\frac{132-66}{6-3}=\frac{66}{3}=22\\\\ B.)\frac{168-84}{8-4}=\frac{84}{4}=21[/tex]

Therefore, Store B would be the best choice.

Answer:

x = 14

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

3x - 5 = 37

Step 2: Solve for x

Answer:

54ft

Step-by-step explanation:

if 3foot is 4ft tall

then a shadow of 72 ft will be how tall?= x

4x =3ft by 72ft

4x= 216ft

x= 216/4

×=54

Answer:

180 Feet Per Minute

Step-by-step explanation:

Please mark me as brainliest and rate 5 stars!

Answer: Distance: 2250

Step-by-step explanation:

Find GCF of 450 and 250

Answer:

1. 8+(30/(2+4)) = 8+(30/6) = 8+5 = 13

2. ((8+30)/2)+4 = (38/2)+4 = 19+4 = 23

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

23:

(8 + 30) ÷ 2 + 4

13:

8 + 30 ÷ (2 + 4)

please give me the brainliest if u can

(1) D

[tex]L_s\left\{t\right\} = \displaystyle\int_0^\infty te^{-st}\,\mathrm dt[/tex]

Integrate by parts, taking

[tex]u = t \implies \mathrm du=\mathrm dt[/tex]

[tex]\mathrm dv = e^{-st}\,\mathrm dt \implies v=-\dfrac1se^{-st}[/tex]

Then

[tex]L_s\left\{t\right\} = \displaystyle \left[-\frac1ste^{-st}\right]\bigg|_{t=0}^{t\to\infty}+\frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{t\right\} = \displaystyle \frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{t\right\} = \displaystyle -\frac1{s^2}e^{-st}\bigg|_{t=0}^{t\to\infty}[/tex]

[tex]L_s\left\{t\right\} = \displaystyle \boxed{\frac1{s^2}}[/tex]

(2) A

[tex]L_s\left\{1\right\} = \displaystyle\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{1\right\} = \displaystyle\left[-\frac1se^{-st}\right]\bigg|_{t=0}^{t\to\infty}[/tex]

[tex]L_s\left\{1\right\} = \displaystyle\boxed{\frac1s}[/tex]

Answer:

A

Step-by-step explanation:

(because -4 is equal to -4 and meets the condition of the top inequality, you plug in -4 into the top function)

[tex]g(-4)=\sqrt[3]{(-4)+5}\\\\g(-4)=\sqrt[3]{1} =1[/tex]

Answer:

YWX = DFE

Step-by-step explanation:

AAS means angle angle side. so, we need 2 angles and 1 side.

we have 1 side and one angle confirmed.

so, we need one of the other two angles (W or Y vs. F or D) confirmed.

they probably want W and F as answer, as Y and D would make it a special case of AAS : ASA.

Answer:

(x-7) and (x+12) are the factors and the rest are non factors...

Answer:

$4,966.25

Step-by-step explanation:

3 x 15 = 45

After 15 years, Naomi would have earned a total of 45% interest rate.

3,425 x 1.45 = 4,966.25

Don't use .45 as the multiplier

3,425 x .45 = 1,541.25 <- incorrect

Answer:

A. 50º

Step-by-step explanation:

we are given the exterior angles 140º and 90º

exterior angles + corresponding interior angles = 180º

that means the two other angles of the triangle are:

180 - 140 = 40º

and

180 - 90 = 90º

the sum of interior angles in a triangle = 180

p = 180 - (40 + 90)

p = 180 - 130

p = 50º

Answer:

total = m/n * c

m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid

Answer:

16 days

Step-by-step explanation:

Here,

By the question,

4 men takes 4 days working each day 4 hours to complete 4 units of work..

then..

if 1 man works 1 hour each day then i would take ( 4×4×4 ) days

= 64days

then..

if 2 men work for 2 hours per day then.

it would take

4×4×4 / 2×2 days

= 16 days

Answer:

2y^3-7y^2+7y

Step-by-step explanation:

7y - 2y^3 + 5y^2 - (  12y^2 – 4y^3)

Distribute the minus sign

7y - 2y^3 + 5y^2 - 12y^2 + 4y^3

Combine like terms

2y^3-7y^2+7y

It looks like you are trying to compute the improper integral,

[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]

or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then

[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]

Answer:

x=30°

hopefully this answer can help you to answer the next question

Answer:

-7

Step-by-step explanation:

x = y - 6

2x = 5y - 9

Use the internet for full steps

x = -7

y = -1

Notice that

6 + 7 = 13

13 + 7 = 20

so if the pattern continues, the underlying sequence in this series is arithmetic with first term a = 6 and difference d = 7. This means the k-th term in the sequence is

a + (k - 1) d = 6 + 7 (k - 1) = 7k - 1

The last term in the series is 111, which means the series consists of 16 terms, since

7k - 1 = 111   ==>   7k = 112   ==>   k = 16

Then in summation notation, we have

[tex]\displaystyle 6+13+20+\cdots+111 = \boxed{\sum_{k=1}^{16}(7k-1)}[/tex]

Answer:

Step-by-step explanation:

CD/6.5 = 2.6/4.9    This is the result of the angle bisector theorem.

The theorem basically says that the side opposite the angle being bisected is divided  the ratio of the sides enclosing the angle.

Multiply both sides of the proportion by 6.5

CD = 2.6 * 6.5 / 4.9

CD = 3.4489

CD = 3.4 rounded.

Answer:

153/50

Step-by-step explanation:

3.06

Rewriting as

There are two numbers after the decimal so we put the number over 100

306/100

Divide top and bottom by 2

153/50

To write 3.06 as a fraction you have to write 3.06 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

3.06 = 3.06/1 = 30.6/10 = 306/100

And finally we have:

3.06 as a fraction equals 306/100

Answer:

Step-by-step explanation:

If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:

[tex]11=-5t^2+30t+1[/tex] and

[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get

t = .35 seconds and t = 5.6 seconds

Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.

Answer:

The value 138 means that this height (138cm) is less than the average height of a 4th grader.

Answer: No credit wanted

Step-by-step explanation:

The other guy is completely right.

9514 1404 393

Answer:

Step-by-step explanation:

The attached shows the predicted mileage for cars built in 2025 to be 46.3 mpg, 76.2 mpg for cars built in 2050.

__

No doubt, the function is valid over the time period used to derive it. It may or may not be valid for predicting MPG beyond that period.

Virtually any function that predicts future increases without bound will turn out to be unreliable at some point. In this universe, there are always limits to growth.

Answer:

See below

Step-by-step explanation:

a)

[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]

[tex]\therefore x=\dfrac{4\pi }{3}[/tex]

But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution

Therefore,

[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]

This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.

Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]

b)

[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]

Once

[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]

As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

[tex]\therefore x=-\dfrac{\pi }{6}[/tex]

c)

[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]

Therefore,

[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]

[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The solutions are

[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]