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3 years ago

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

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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3 years ago

the ordered pairs (0,-1),(1,0),(2,3),(3,8),(4,15) represent a function what is a rule that represents this function? Please help

yarga [219]

Answer:

The function rule is

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

Step-by-step explanation:

The given ordered pairs are (0,-1), (1,0),(2,3),(3,8),(4,15)

We can observe the following pattern.

$f(0) = {0}^{2} - 1 = - 1$

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$f(4) = {4}^{2} - 1 = 15$

When we generalize this pattern, we obtain:

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

This is the function equation.

The function rule is

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

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