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spayn [35]
3 years ago
13

Arithmetic of Functions problem.

Mathematics
2 answers:
FromTheMoon [43]3 years ago
5 0

Answer:

(f o g)(4) = 45  

Step-by-step explanation:

We have given two functions and we have to find their composition.

f(x) = 4x+1   , g(x) = x²-5  

Firstly, we have to find (f o g)(x)

Then, we have to find (f o g)(x).

(f o g)(x) = f(g(x))

Putting the given values of functions in above formula , we have

(f o g)(x) = f(x²-5)

(f o g)(x) = 4(x²-5)+1

simplifying

(f o g)(x) = 4x²-20+1

adding like terms, we have

(f o g)(x) = 4x²-19

Putting x = 4   to above equation , we have

(f o g)(4) = 4(4)²-19

(f o g)(4) = 4(16)-19

(f o g)(4) = 64-19

(f o g)(4) = 45  which is the answer.

lidiya [134]3 years ago
4 0

Answer:

(f o g)(4) = 45

Step-by-step explanation:

f(x)=4x+1

g(x)=x²-5

(f o g)(4)=?

(f o g)(4) = f(g(4))


Calculating g(4):

x=4→g(4)=4²-5

g(4)=16-5

g(4)=11


Replacing g(4)=11

(f o g)(4) = f(g(4))

(f o g)(4) = f(11)


Calculating f(11)

x=11→f(11)=4(11)+1

f(11)=44+1

f(11)=45


Replacing f(11)=45:

(f o g)(4) = f(11)

(f o g)(4) = 45

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Answer:

Step-by-step explanation:

Hello!

The parameter of interest in this exercise is the population proportion of Asians that would welcome a person of other races in their family. Using the race of the welcomed one as categorizer we can define 3 variables:

X₁: Number of Asians that would welcome a white person into their families.

X₂: Number of Asians that would welcome a Latino person into their families.

X₃: Number of Asians that would welcome a black person into their families.

Now since we are working with the population that identifies as "Asians" the sample size will be: n= 251

Since the sample size is large enough (n≥30) you can apply the Central Limit Theorem and approximate the variable distribution to normal.

Z_{1-\alpha /2}= Z_{0.975}= 1.965

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If 79% would welcome a white person, then the expected value is:

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With a 95% confidence level, you'd expect that the interval [185.62; 210.96] contains the number of Asian people that would welcome a White person in their family.

2. 95% CI for Asians that would welcome a Latino person.

If 71% would welcome a Latino person, then the expected value is:

E(X)= n*p= 251*0.71= 178.21

And the Standard deviation is:

V(X)= n*p*(1-p)= 251*0.71*0.29= 51.6809

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You can construct the interval as:

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With a 95% confidence level, you'd expect that the interval [164.08; 192.34] contains the number of Asian people that would welcome a Latino person in their family.

3. 95% CI for Asians that would welcome a Black person.

If 66% would welcome a Black person, then the expected value is:

E(X)= n*p= 251*0.66= 165.66

And the Standard deviation is:

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You can construct the interval as:

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165.66±1.965*7.50

[150.92; 180.40]

With a 95% confidence level, you'd expect that the interval [150.92; 180.40] contains the number of Asian people that would welcome a Black person in their family.

I hope it helps!

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