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3 years ago

Factor the trinomial. x^2-4x-5

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

7 0

<h3>Answer: Choice C. (x+1)(x-5)</h3>

We need to find two numbers that

Multiply to -5 (last term)
Add to -4 (middle coefficient)

Through trial and error, those two numbers are 1 and -5

1 times -5 = -5
1 plus -5 = -4

So this means x^2-4x-5 factors to (x+1)(x-5)

This is the same as (x-5)(x+1) since the order of multiplication doesn't matter.

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In a multiple choice quiz there are 5 questions and 4 choices for each question (a, b, c, d). Robin has not studied for the quiz

Ahat [919]

Answer:

a) There is a 18.75% probability that the first question that she gets right is the second question.

b) There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

c) There is a 10.35% probability that she gets the majority of the questions right.

Step-by-step explanation:

Each question can have two outcomes. Either it is right, or it is wrong. So, for b) and c), we use the binomial probability distribution to solve this problem.

Binomial probability distribution

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

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

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

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

And $\pi$ is the probability of X happening.

In this problem we have that:

Each question has 4 choices. So for each question, Robin has a $\frac{1}{4} = 0.25$ probability of getting ir right. So $\pi = 0.25$ . There are five questions, so $n = 5$ .

(a) What is the probability that the first question she gets right is the second question?

There is a 75% probability of getting the first question wrong and there is a 25% probability of getting the second question right. These probabilities are independent.

$P = 0.75(0.25) = 0.1875$

There is a 18.75% probability that the first question that she gets right is the second question.

(b) What is the probability that she gets exactly 1 or exactly 2 questions right?

This is: $P = P(X = 1) + P(X = 2)$

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

$P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955$

$P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637$

$P = P(X = 1) + P(X = 2) = 0.3955 + 0.2637 = 0.6592$

There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

(c) What is the probability that she gets the majority of the questions right?

That is the probability that she gets 3, 4 or 5 questions right.

$P = P(X = 3) + P(X = 4) + P(X = 5)$

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

$P(X = 3) = C_{5,3}.(0.25)^{3}.(0.75)^{2} = 0.0879$

$P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0146$

$P(X = 5) = C_{5,5}.(0.25)^{5}.(0.75)^{0} = 0.001$

$P = P(X = 3) + P(X = 4) + P(X = 5) = 0.0879 + 0.0146 + 0.001 = 0.1035$

There is a 10.35% probability that she gets the majority of the questions right.

6 0

3 years ago

find the number of possible combinations choose one of three books and one of eight CDs to bring on a bus trip

SVEN [57.7K]

There is a possibility of 24 combinations I believe

6 0

3 years ago

Read 2 more answers

12 Times 12 = 144 right?

REY [17]

Answer:

yes it is u are correct

Step-by-step explanation: plz mark brainliest

5 0

3 years ago

Sistema de ecuaciones.5x+2y=-152x-2y=-6

Zolol [24]

Tnemos el sisema de ecuaciones:

$\begin{gathered} 5x+2y=-15 \\ 2x-2y=-6 \end{gathered}$

Podemos resolverlo por eliminación sumando ambas ecuaciones y eliminando y. Asi podemos resolver para x:

$\begin{gathered} (5x+2y)+(2x-2y)=(-15)+(-6) \\ 7x+0y=-21 \\ x=-\frac{21}{7} \\ x=-3 \end{gathered}$

Ahora podemos resolver para y con cualquiera de las dos ecuaciones:

$\begin{gathered} 2x-2y=-6 \\ 2\cdot(-3)-2y=-6 \\ -6-2y=-6 \\ -2y=-6+6 \\ -2y=0 \\ y=0 \end{gathered}$

Respuesta: x=-3, y=0

7 0

1 year ago

Joan has 1/2 yard of felt. She will use 1/3 of it to make place cards. How much felt will she will use for place cards?

-Dominant- [34]

ANSWER

$\frac{1}{6} \: yards$

EXPLANATION

It was given that, Joan has

$\frac{1}{2} \: yard \: of \: felt$

and she will use

$\frac{1}{3}$
of it to make place cards.

We want to find how felt she will use for place cards.

We just have to find,

$= \frac{1}{3} \: of \: \frac{1}{2}$

$= \frac{1}{3} \times \frac{1}{2}$

$= \frac{1}{6}$

Therefore Joan will use

$\frac{1}{6}$

yards of felt for the place cards.

7 0

3 years ago