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AURORKA [14]
3 years ago
10

Which graph represents the function f(x)=-x2+5?

Mathematics
2 answers:
Dafna1 [17]3 years ago
8 0

The top one (keep in mind i think)

nikklg [1K]3 years ago
6 0

Answer:

The graph of given function is shown below.

Step-by-step explanation:

The given function is

f(x)=-x^2+5             .... (1)

We need to find the graph of the function.

The vertex form of the quadratic function is

f(x)=a(x-h)^2+k            .... (2)

On comparing (1) and (2) we get

h=0,k=5

It means the vertex of the function is (0,5).

The table of values is

x                 y

-2               1

-1               4

0              5

1               4

2              1  

Plot all ordered pairs on a coordinate plane and connect them by a free hand curve.

The graph of given function is shown below.

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The probability of a successful optical alignment in the assembly of an optical data storage product is p = 0.7. Assume the tria
zhannawk [14.2K]

Answer:

(a) P(X = 4) = 0.0189

(b) P(X \leq 4) = 0.9919

(c) P(X \geq 4) = 0.027

Step-by-step explanation:

We are given that the probability of a successful optical alignment in the assembly of an optical data storage product is p = 0.7 .

Since we have to find the probabilities for 1st successful alignments, so the probability distribution that we will use here is Geometric distribution.

<u>Geometric distribution</u> is used when we are interested in knowing the chances of our first success.

The probability distribution of geometric distribution is given by;

P(X =x) = p(1-p)^{x-k} ; x = 1,2,3,....

where, x = number of trials

            k = first success = 1

            p = probability of getting success = 0.70

So, X ~ Geo(p = 0.7)

(a) Probability that the 1st successful alignment requires exactly 4 trials is given by = P(X = 4)

Here, x = 4, p = 0.7 and k = 1

So, P(X = 4) = 0.7(1-0.7)^{4-1} = 0.7 \times 0.3^{3} = 0.0189

(b) Probability that the 1st successful alignment requires at most 4 trials is given = P(X \leq 4)

 P(X \leq 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)  

               = 0.7(1-0.7)^{1-1} + 0.7(1-0.7)^{2-1}+0.7(1-0.7)^{3-1}+0.7(1-0.7)^{4-1}

               = 0.7 \times 0.3^{0}+0.7 \times 0.3^{1}+0.7 \times 0.3^{2}+0.7 \times 0.3^{3}

               = 0.7 + 0.21 + 0.063 + 0.0189 = 0.9919

(c) Probability that the 1st successful alignment requires at least 4 trials is given by = P(X \geq 4)

    P(X \geq 4) = 1 - P(X < 4) = 1 - P(X \leq 3)

    P(X \geq 4) = 1 - P(X = 1) - P(X = 2) - P(X = 3)

                  =  1-0.7(1-0.7)^{1-1} + 0.7(1-0.7)^{2-1}+0.7(1-0.7)^{3-1}

                  = 1-0.7 \times 0.3^{0}+0.7 \times 0.3^{1}+0.7 \times 0.3^{2}

                  = 1 - 0.7 - 0.21 - 0.063 = 0.027

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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f(x) =  {x}^{2}  - 1

This is the function equation.

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f:  x\to \:  {x}^{2}  - 1

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