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andrezito [222]
3 years ago
6

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. a) Simplify the express

ion and explain each step. (2 points) 4 ( 3 x + 2 ) − 2 b) Factor the expression completely. (1 point) 20 b − 16
Mathematics
1 answer:
SOVA2 [1]3 years ago
6 0

Answer:

Step-by-step explanation:

To simplify the expression:

4(3x+2) - 2

The first step is to open the brackets

= 4 * 3x + 4* 2 - 2

= 12x + 8 - 2

= 12x - 6

Factor out the above expression, we get;

= 6(2x - 1)

To factor out the expression:

20b - 16

the factor that can be divided by 20 and 16 without remainder is 4;

So, we have:

= 4(5b - 4)

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If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight au
Alex17521 [72]

Answer:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305  

And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Solution to the problem

Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:  

X \sim Binom(n=8, p=0.9)  

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!}  

And for this case we want to find this probability:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305  

And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

3 0
2 years ago
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Answer:

The perimeter is 16 units

Step-by-step explanation:

Add up all the sides together

1+1+7+7 = 16

6 0
3 years ago
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