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adoni [48]
3 years ago
6

Suppose that G(x) = F(x - 6) - 3. Which statement best compares the graph of G(x) with the graph of F(x)?

Mathematics
2 answers:
Debora [2.8K]3 years ago
8 0
From the given, G(x) = F(x - 6) - 3, the graph is shifted to 6 units to the right and 3 units down. Thus, the answer is letter A. It should be noted that for horizontal shifting, negative means to the right and down for vertical shifting. 
lilavasa [31]3 years ago
8 0

Answer:

 Option A -The graph of G(x) is the graph of F(x) shifted 6 units to the right and 3 units down.

Step-by-step explanation:

Given : G(x)=F(x-6)-3

We can compare graph of G(x) with graph of F(x) by looking at a and b values in G(x)=F(x-a)-b

where, a=6 and b=3

For the value of a :

If some unit is subtract from the x value then the graph shifted to right by that unit.

mathematically we can write,  

f(x)→ f(x-a) →  f(x) shift right with a units.

Therefore, in G(x)=F(x-6)-3

F(x)→ F(x-6) →  F(x) shift right with 6 units.

⇒Graph of G(x) is the graph of F(x)  shifted 6 units right.

For the value of b:

If some units is subtract from the function then the graph shifted downward by that unit.

mathematically we can write,  

f(x)→ f(x)-b →  f(x) shift down with b units.

Therefore, in G(x)=F(x-6)-3

F(x)→ F(x)-3 →  F(x) shift down with 3 units.

⇒Graph of G(x) is the graph of F(x) shifted 3 units down.

Therefore, option A is correct that the graph of G(x) is the graph of F(x) shifted 6 units to the right and 3 units down.








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2.A production process manufactures items with weights that are normally distributed with mean 10 pounds and standard deviation
Vesna [10]

Answer:

Step-by-step explanation:

Given that:

population mean = 10

standard deviation = 0.1

sample mean = 9.8 < x > 10.2

The z score can be computed as:

z = \dfrac{\bar x - \mu}{\sigma}

if x > 10.2

z = \dfrac{10.2- 10}{0.1}

z = \dfrac{0.2}{0.1}

z = 2

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z = \dfrac{9.8- 10}{0.1}

z = \dfrac{-0.2}{0.1}

z = -2

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the probability of acceptable = 1 - the probability of defectives

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the probability of acceptable = 0.9545

the probability of acceptable = 95.45%

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sampling distribution of proportions:

sample size n=1000

p = 0.0455

The z - score for this distribution at most 5% of the items is;

z = \dfrac{0.05 - 0.0455}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}

z = \dfrac{0.0045}{\sqrt{\dfrac{0.04342975}{1000}}}

z = \dfrac{0.0045}{\sqrt{4.342975 \times 10^{-5}}}

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From the z tables

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p-value = 1 - 0

p-value = 1

Thus, the probability that at least 85% of these items in a given batch will be acceptable = 1

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