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erma4kov [3.2K]
3 years ago
8

What are the restrictions on the domain of g o h?

Mathematics
2 answers:
anzhelika [568]3 years ago
8 0

Answer:

6

Step-by-step explanation:

100%

umka21 [38]3 years ago
5 0

g(x) = \sqrt{x-4} and h(x)= 2x-8

g o h is a composition function

First we find g o h

g o h is g(h(x))

We plug in h(x) in g(x)

We replace x  with 2x-8 in g(x)

g(h(x)) = g (2x-8) = \sqrt{2x-8-4} = \sqrt{2x-12}

g(h(x)) = \sqrt{2x-12}

To find domain we look at the domain of h(x) first

Domain of h(x) is set of all real numbers

now we look at the domain of g(h(x))

Negative number inside the square root is imaginary. so we ignore negative number inside the square root

So to find domain we set 2x - 12 >=0   and solve for x

2x - 12 >=0

add both sides by 12

2x >= 12

divide both sides by 2

x > = 6



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What is the y-intercept of f (x) = 3.4’x?
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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
3 years ago
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