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3 years ago

X^2+4x+3 factor each polynomial

Mathematics

1 answer:

Lapatulllka [165]3 years ago

6 0

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Which of the ratios below can be used to finish the proportion

AysviL [449]

The correct ones are A,B, D&E

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4 years ago

The number of typographical errors on a page of the first booklet is a Poisson random variable with mean 0.2. The number of typo

muminat

Answer:

The required probability is 0.55404.

Step-by-step explanation:

Consider the provided information.

The number of typographical errors on a page of the first booklet is a Poisson random variable with mean 0.2. The number of typographical errors on a page of second booklet is a Poisson random variable with mean 0.3.

Average error for 7 pages booklet and 5 pages booklet series is:

λ = 0.2×7 + 0.3×5 = 2.9

According to Poisson distribution: $P(k{\text{ events in interval}})={\frac {\lambda ^{k}e^{-\lambda }}{k!}}$

Where $\lambda$ is average number of events.

The probability of more than 2 typographical errors in the two booklets in total is:

$P(k > 2)= 1 - {P(k = 0) + P(k = 1) + P(k = 2)}$

Substitute the respective values in the above formula.

$P(k > 2)= 1 - ({\frac {2.9 ^{0}e^{-2.9}}{0!}} + \frac {2.9 ^{1}e^{-2.9}}{1!}} + \frac {2.9 ^{2}e^{-2.9}}{2!}})$

$P(k > 2)= 1 - (0.44596)$

$P(k > 2)=0.55404$

Hence, the required probability is 0.55404.

4 0

3 years ago

lilavasa [31]

The count of the equilateral triangle is an illustration of areas

There are 150 small equilateral triangles in the regular hexagon

<h3>How to determine the number of equilateral triangle </h3>

The side length of the hexagon is given as:

L = 5

The area of the hexagon is calculated as:

$A = \frac{3\sqrt 3}{2}L^2$

This gives

$A = \frac{3\sqrt 3}{2}* 5^2$

$A = \frac{75\sqrt 3}{2}$

The side length of the equilateral triangle is

l = 1

The area of the triangle is calculated as:

$a = \frac{\sqrt 3}{4}l^2$

So, we have:

$a = \frac{\sqrt 3}{4}*1^2$

$a = \frac{\sqrt 3}{4}$

The number of equilateral triangles in the regular hexagon is then calculated as:

$n = \frac Aa$

This gives

$n = \frac{75\sqrt 3}{2} \div \frac{\sqrt 3}4$

So, we have:

$n = \frac{75}{2} \div \frac{1}4$

Rewrite as:

$n = \frac{75}{2} *\frac{4}1$

$n = 150$

Hence, there are 150 small equilateral triangles in the regular hexagon