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algol13
3 years ago
14

Describe the difference between algebraic expressions and numerical expressions.

Mathematics
1 answer:
Mila [183]3 years ago
7 0
The difference between an algebraic expression and a numerical expression is that algebraic expressions contain numbers and variables. Numerical expressions only contain numbers. 

Ex:
Algebraic Expression- 5x+9
Numerical Expression- 4+2
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Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 25% of these tanks
Gnesinka [82]

Answer:

a) 3.75

b) 23.61% probability that fewer than 3 tanks will be found to be leaking

c) 0% the probability that at least 600 of these tanks are leaking

Step-by-step explanation:

For each tank there are only two possible outcomes. EIther they leak, or they do not. The probability of a tank leaking is independent of other tanks. So we use the binomial probability distribution to solve this question.

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}.p^{x}.(1-p)^{n-x}

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

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

And p is the probability of X happening.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

To solve question c), i am going to approximate the binomial distribution to the normal.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

It is estimated that 25% of these tanks leak.

This means that p = 0.25

15 tanks chosen at random

This means that n = 15

a.What is the expected number of leaking tanks in such samples of 15?

E(X) = np = 15*0.25 = 3.75

b.What is the probability that fewer than 3 tanks will be found to be leaking?

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134

P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668

P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361

23.61% probability that fewer than 3 tanks will be found to be leaking

c.Now you do a larger study, examining a random sample of 2000 tanks nationally. What is the probability that at least 600 of these tanks are leaking?

Now we have n = 2000. So

\mu = E(X) = np = 2000*0.25 = 500

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2000*0.25*0.75} = 19.36

This probability is 1 subtracted by the pvalue of Z when X = 600. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{600 - 500}{19.36}

Z = 5.16

Z = 5.16 has a pvalue of 0.

0% the probability that at least 600 of these tanks are leaking

4 0
3 years ago
How do i solve divide 5/8 by 50%
Ede4ka [16]
50% is \frac{50}{100}
We have two ways to do this, pick your favor:
either by fractions:
\frac{5}{8} ÷ \frac{1}{2}
(\frac{50}{100} =  \frac{1}{2}
Multiply by the reciprocal of \frac{1}{2} which is 2(flip it)

\frac{5}{8} × 2 = \frac{5}{4} = 1.25

Or change them to decimals:
\frac{5}{8} = 0.625
\frac{50}{100} = 0.5

0.625 ÷ 0.5

0.5 I 0.625
multiply by 10 to make it easier to divide(it still gives us the same answer)
0.5 × 10 = 5
0.625 × 10 = 6.25
     1.25
5 I 6.25
    -5
     12
    -10
       25
      -25
         0

0.625 ÷ 0.5 = 1.25

7 0
2 years ago
A business owner would like to know if the new marketing strategy improves their sales. They recorded their average income befor
Savatey [412]
The answer is 220.214 is the correct answer because you see the the income and if you add that up that’s the how much level will come up
7 0
2 years ago
If a = 8 and b = 15, then c<br> =
Anika [276]
Then c = 22 just keep adding 7
8+7=15 15+7=22
4 0
3 years ago
How do you write the equation 4x + 2y = 16 in function form? Please answer with an explanation!
kramer
F(x)=-2x+8 This is because f(x) is the same as writing y so therefore you have to change the equation to 4x+2y=16 so you have Y=-2x+8
3 0
2 years ago
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