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alina1380 [7]
3 years ago
15

Aston challenges his fater to a 100-m race. Aston asks to race again but wants to be given a head start. How much of a start sho

uld Aston's fater give him to make it a close race? Explain your answer.
Mathematics
1 answer:
photoshop1234 [79]3 years ago
7 0
Ah hah ! You said in there "race AGAIN". Tell us something about how the first race turned out, and we may have some information we can use to answer with. Right now we got nuttn.
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Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X deno
Roman55 [17]

Answer:

a) P(X>np+3\sqrt{np(1-p)}=0.017

b) P(x>1)=0.190

c) P(Y>1)=0.651

Step-by-step explanation:

This a binomial experiment where success is denoted by parts that need rework.

X ∼ B(n, p); n = 20; p = 0.01

The expected value of X is: E(X) = np =20×0.01= 0.2

The variance is: Var(X) = np(1 − p) = 0.2 × 0.99 = 0.198,

The standard deviation SD(X)= \sqrt{0.198} ≈ 0.445

a) P(X>np+3\sqrt{np(1-p)}=P(X>0.2+3×0.445)=P(X>1.535)=P(X≥2)

Probability function is given by:

\frac{n!}{x!(n-x)!} *p^x*(1-p)^{(n-x)}

P(X≥2)=1-P(X<2)=1-P(X=1)-P(X=0)= 1 - \frac{20!}{1!(20-1)!} *(0.01)^{1}*(1-0.01)^{(20-1)}-\frac{20!}{0!(20-0)!} *(0.01)^{0}*(1-0.01)^{(20-0)}

P(X≥2)=1-0.165-0.818=0.017

b) p=0.04

P(x>1)=P(x≥2)= 1 - P(x=1) - P(x=0)= 1 - \frac{20!}{0!(20-1)!} *(0.04)^{1}*(1-0.04)^{(20-1)} - \frac{20!}{0!(20-0)!} *(0.04)^{0}*(1-0.04)^{(20-0)}

P(x>1)= 1 - 0.368 - 0.442=0.190

c) In this case we consider p=0.19 (Probability that X exceeds 1)

In this experiment Y is the number of hours and n= 5 hours.

Then, we check the probability in each hour:

P(Y>1)=1- P(Y=0)

P(Y=0)=\frac{5!}{0!(5-0)!} *(0.19)^{0}*(1-0.19)^{(5-0)}=0.349

P(Y>1)=1-0.349=0.651

3 0
2 years ago
what is the equation for A 450-gallon tank full of water is draining at a rate of 20 gallons per minute.
zhuklara [117]

Answer: 150

Step-by-step explanation:

4 0
3 years ago
Write ACUTE, RIGHT, OBTUSE, STRAIGHT or REFLEX for each of the following: ( 5 marks)
soldier1979 [14.2K]

Answer:

a. obtuse angle

b. right angle

c. reflex angle

d. straight

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3 years ago
Triangle abc is an isosceles right triangle. What is the measure of one base angle? 30ş 45ş 60ş 90ş.
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Answer:

  45°

Step-by-step explanation:

The acute angles of a right triangle are complementary. The base angles of an isosceles triangle are congruent. If x is the measure of the base angles, this requires ...

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The measure of a base angle of an isosceles right triangle is 45°.

__

It can be useful to remember this fact.

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Answer:

No; he did the survey incorrectly.

He surveyed 107 people, not 100.

Step-by-step explanation:

Draw a Venn diagram, when you are presented with information like this;

Presenting it in a Venn diagram would look like what is shown in the pic.

P.S. when drawing a Venn diagram, start with the information regarding individuals who fit in all categories and then work your way to the individuals who fit in just in one category.

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