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4 years ago

PLEASE HELP!!! PLZ!!!

Mathematics

1 answer:

Helen [10]4 years ago

7 0

We can use the vertex form
$y = a {(x - h)}^{2} + k$
to find the equation of the graph. We know that a is the coefficient, and since the graph opens upwards and is slightly stretched vertically, we know that a is 1/3. On the graph, we see that the vertex of the parabola is at (0,-1). Therefore, h is 0 and k is -1.
Our vertex form equation is
$y = \frac{1}{3} {x}^{2} - 1$
Which is D

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A.) (1 - p)^n

B.) 1 - (1 - p)^n

C.) (1 - p)^n + np*(1-p)^(n-1)

D.) 1 - (1 - p)^n - np*(1-p)^(n-1)

Step-by-step explanation:

General form of a binomial probability :

P(x = x) = nCx * p^x * q^(n-x)

q = 1 - p ; n = number of trials ; x = number of successes ; p = probability of success

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P(x = 0) = nC0 * p^0 * (1 - p)^(n-0)

P(x = 0) = 1 * 1 * (1 - p)^n

P(x = 0) = (1 - p)^n

Probability of atleast one success = 1 - P(no success)

P(x ≥ 1) = 1 - P(x = 0)

P(x = 0) = (1 - p)^n

P(x ≥ 1) = 1 - P(x = 0) = 1 - (1 - p)^n

Probability of at most one success

P(x ≤ 1) = p(x = 0) + p(x = 1)

P(x = 0) = (1 - p)^n

P(x = 1) = nC1 * p^1 * (1 - p)^(n-1)

P(x = 1) = n * p * (1 - p)^(n-1) = np*(1-p)^(n-1)

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Probability of atleast two successes:

(1 - probability of at most 2 successes)

P(x ≥ 2) = 1 - P(x ≤ 1)

P(x ≥ 2) = 1 - (p(x = 0) + p(x = 1))

P(x ≥ 2) = 1 - p(x = 0) - p(x = 1))

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