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3 years ago

When multiplying a binomial by a trinomial, is the degree of the product always 5? Explain.

Mathematics

2 answers:

Naya [18.7K]3 years ago

4 0

Given that a binomial is multiplied by a trinomial.

A binomial means containing two terms normally

x+a

Trinomial is containing 3 terms may be

ax^2+bx+c

When we multiply we can get degree 3 also as shown above.

Hence the statement is false.

When a binomial is multiplied by a trinomial getting a product of degree 5 is only occasional and not always.

DedPeter [7]3 years ago

4 0

Answer:

...

Step-by-step-by-step explanation:

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) Determine the probability that a bit string of length 10 contains exactly 4 or 5 ones.

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Answer: 0.4512

Step-by-step explanation:

A bit string is sequence of bits (it only contains 0 and 1).

We assume that the 0 and 1 area equally likely to any place.

i.e. P(0)= P(1)= $\dfrac{1}{2}$

The length of bits : n = 10

Let X = Number of getting ones.

Then , $X \sim Bin(n=10,\ p=\dfrac{1}{2})$

Binomial distribution formula : $P(X=x)=^nC_x p^x q^{n-x}$ , where p= probability of getting success in each event and q= probability of getting failure in each event.

Here , $p=q=\dfrac{1}{2}$

Then ,The probability that a bit string of length 10 contains exactly 4 or 5 ones.

$P(X= 4\ or\ 5)=P(x=4)+P(x=5)\\\\=^{10}C_4(\dfrac{1}{2})^{10}+^{10}C_4(\dfrac{1}{2})^{10}$

$=\dfrac{10!}{4!6!}(\dfrac{1}{2})^{10}+\dfrac{10!}{5!5!}(\dfrac{1}{2})^{10}$

$=(\dfrac{1}{2})^{10}(\dfrac{10!}{4!6!}+\dfrac{10!}{5!5!})$

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