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ruslelena [56]
3 years ago
9

What is 880005 rounded to the nearest hundred thousand

Mathematics
2 answers:
pentagon [3]3 years ago
6 0
The answer to your question is 900000
erastova [34]3 years ago
4 0
900000 because the ten thousands place is the first number
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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
Two gears in a machine are aligned by a mark drawn from the center of one gear to the center of the other. If the first gear has
Aleksandr [31]

Answer:

5

Step-by-step explanation:

for the first gear

revolutions/teeth

1 / 24

2 / 48

3 / 72

4 / 96

5 / 120

6 / 144

for the second gear

revolutions/teeth

1 / 40

2 / 80

3 / 120

4 / 160

<em>the two marks will meet after 120 teeth, 5 revolutions of the first gear and 3 revolutions of the second.</em>

the way to get that amount of teeth is

24 = 2 \times 2 \times 2 \times 3 =  {2}^{3}  \times 3

40 = 2 \times 2 \times 2 \times 5 =   {2}^{3}  \times 5

the Least Common Multiple equals the product of all factors, but those factors who are repeted for both numbers should be only once.

{2}^{3} \times 5 \times 3 = 120

120 teeth are 5 revolutions for gear1 and 3 por gear2

8 0
3 years ago
A circular dance stage has a perimeter of 28(3.14) feet. What is the area, in square feet, of this dance stage?
tiny-mole [99]
The perimeter (circumference) = 28 * PI.
This means the diameter = 28.
The area = PI*radius^2
area = PI * 14^2
area = PI * <span> <span> <span> 196 </span> </span> </span>
area = <span> <span> <span> 615.7521601036 </span> </span> </span> square feet


4 0
3 years ago
A store pays $119 for a scooter. The store marks up the price by 40%.
Inessa [10]

Answer:

Step-by-step explanation:

if the store marks up the price by 40%

119*(40/100)=47.60

119+47.60=166.60

5 0
3 years ago
Helpppppppppp fasttttttttttttttttttt
horrorfan [7]

Answer:

first 2 , second 50, third 8

Step-by-step explanation:

5 0
3 years ago
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