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3 years ago

If 8 pigs can fit in a pen, how many pens are necessary to make sure 71 pigs are all in a pen?

Mathematics

1 answer:

Ulleksa [173]3 years ago

7 0

Answer:

Step-by-step explanation:

Each pen can only hold 8 pigs, and pens cannot be split up into fractions.

Divide. 71 / 8 = 8.875

There is no 7/8 of a pen, so you must round up.

8.875 → 9.

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( I NEED THIS FAST)A speedometer has a percent error of 10%. The actual speed of the car is 40 mph. Select from the drop-down me

ikadub [295]

Answer = 36.0 mph

As per the question,

Actual speed of the car = 40 mph.

Speedometer has a percent error of 10%.

The error can be negative as well as positive.

If the error is negative, it means speedometer is showing less speed than actual speed= - 10%

10 % of 40 = 4

speed shown by speedometer = 40 - (10% of 40) = 36 mph

If the error is positive, it means speedometer is showing more speed than actual speed = +10%

speed shown by speedometer = 40 + ( 10% of 40) = 44 mph

as per the given options, correct option is 36.0 mph

6 0

3 years ago

Read 2 more answers

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

Round 425.919 to the nearest whole number

Alika [10]

Rounded to the nearest whole number would be 426

8 0

3 years ago

Read 2 more answers

Courtney reads around 110 words per minute. She procrastinated and now has less than a week to finish her reading assignment. If

Fynjy0 [20]

820 pages X 350 words = 287,000 words

287,000 / 110 = 2.609.09 minutes 

2.609.09 / 60 = 43.48 hours 

It would take about 2 days of non-stop reading to finish her assignment

5 0

3 years ago

-2.7+17.8+29.5+8.9=?

BARSIC [14]

Answer:

64.5

Step-by-step explanation:

64.5

6 0

2 years ago

Read 2 more answers