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3 years ago

Use the zero product property to find the possible solutions to the equation x2 – 13x + 30 = 0.

Mathematics

2 answers:

7nadin3 [17]3 years ago

7 0

x² - 13x + 30 = 0

Factorise:

(x - 3) (x - 10) = 0

Apply zero product property:

x - 3 = 0 or x - 10 = 0

Evaluate:

x = 3 or x = 10

Answer: x = 3 or x = 10

ehidna [41]3 years ago

5 0

First we factor the equation, like this:

(x + 10)(x + 3)

Then we just find the answers, like this:

x = -10, x = -3.

Hope this helped! c:

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Answer:

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Step by step explanation:

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3 years ago

Let X be a Binomial Random Variable with 8 trials and a probability of success as 0.37. Suppose you want to find k such that P(X

larisa86 [58]

Answer:

k = 4

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$n = 8, p = 0.37$ . So

P(X < k) = 0.6625

k only assumes discrete values, so

$P(X < k) = P(X \leq k-1) = 0.6625$

We have to find the cummulative distribution until we hit 0.6625. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{8,0}.(0.37)^{0}.(0.63)^{8} = 0.0248$

$P(X \leq 0) = P(X = 0) = 0.0248$

$P(X = 1) = C_{8,1}.(0.37)^{1}.(0.63)^{7} = 0.1166$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0248 + 0.1166 = 0.1414$

$P(X = 2) = C_{8,2}.(0.37)^{2}.(0.63)^{6} = 0.2397$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0248 + 0.1166 + 0.2397 = 0.3811$

$P(X = 3) = C_{8,3}.(0.37)^{3}.(0.63)^{5} = 0.2814$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0248 + 0.1166 + 0.2397 + 0.2814 = 0.6625$

$P(X \leq 3) = P(X < 4) = 0.665$

So k = 4

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