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3 years ago

Write an equivalent expression by distributing the "-−" sign outside the parentheses:

Mathematics

1 answer:

saw5 [17]3 years ago

6 0

Answer:

1.5q - 5r = 2

Step-by-step explanation:

All you need to do here is negate each term inside the brackets, which allows you to get rid of the minus sign and the brackets.

-(-1.5q + 5r) = 2

is exactly the same as saying:

-1 × (-1.5q + 5r) = 2

And if we multiply each term in the brackets by negative one, we get:

(1.5q - 5r) = 2

And now the brackets can go, leaving you with:

1.5q - 5r = 2

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It is known that 25% of inhabitants of a community favour a political party A.

Keith_Richards [23]

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i) $P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669$

ii) $P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317$

$P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211$

$P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669$

And replacing we got:

$P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883$

iii) $P(X$

Step-by-step explanation:

Let X the random variable of interest "number of inhabitants of a community favour a political party', on this case we now that:

$X \sim Binom(n=20, p=0.25)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Part i

We want this probability:

$P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669$

Part ii

We want this probability:

$P(X\geq 3)$

And we can use the complement rule and we have:

$P(X\geq 3) = 1-P(X$

And if we find the individual probabilites we got:

$P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317$

$P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211$

$P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669$

And replacing we got:

$P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883$

Part iii

We want this probability:

$P(X$

And replacing we got:

$P(X$

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