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trasher [3.6K]
2 years ago
10

2. (8 points) If you have n gold coins with one a fake that you know is slightly lighter, how many weighings on the pan balance

will you need to ensure that you can find the fake? Explain your answer.
Mathematics
1 answer:
pogonyaev2 years ago
5 0

Answer:

Only 1 Time

Step-by-step explanation:

Since you know that one coin is fake and that the coin is lighter than the rest , then you would only need to weigh all the coins together 1 time to ensure that you will find the fake coin. We can determine this by doing the following.

<u>Example:</u>

Lets say we have 100 coins that weigh 1 gr each. Meaning that the total weight of the 100 coins would be (100coins*1gr = 100gr) <em><u>IF</u></em> there are no fake coins in the batch.

Knowing this we can weigh the entire batch 1 time and if the total weight is less than 100gr we know that the fake coin is in that batch.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

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The bill for your dinner was $12 and you paid $4 gratuity. What percent gratuity did you<br> give?
inysia [295]

Answer:

33.333333333333%

Rounded: 33%

3 0
2 years ago
A popular soft drink is sold in 2-liter (2000 milliliter) bottles. Because of variation in the filling process, bottles have a m
andrezito [222]

Answer:

a) 0.27% probability that the mean is less than 1995 milliliters.

b) 2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

Step-by-step explanation:

To solve this problem, it is important to understand the normal probability distribution and the central limit theorem

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 2000, \sigma = 18

A) If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1995 milliliters?

So n = 100, s = \frac{18}{\sqrt{100}} = 1.8

This probability is the pvalue of Z when X = 1995. So

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

By the Central Limit Theorem

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

Z = \frac{1995 - 2000}{1.8}

Z = -2.78

Z = -2.78 has a pvalue of 0.0027

So 0.27% probability that the mean is less than 1995 milliliters.

B) What mean overfill or more will occur only 10% of the time for the sample of 100 bottles?

This is the value of X when Z has a pvalue of 1-0.1 = 0.9.

So it is X when Z = 1.28

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

1.28 = \frac{X - 2000}{1.8}

X - 2000 = 1.8*1.28

X = 2002.3

2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

3 0
2 years ago
When three times the sum of a number and seven is increased by ten, the result is four. What is the number ?
densk [106]

Answer:

x=9   :))

Step-by-step explanation:

First set up your equation.

"3 times" is multiplication

"THE SUM of A NUMBER and seven" that is parenthesis because of the multiplication before it

"is increased by ten" that is an addition at the end

Now we have 3(x+7)+10=4

Solve your equation!

Distribute the 3 now we have 3x+21+10=4

Add like terms

now it should look like this... 3x+31=4

Subtract 31 from both sides and it looks like...

3x=27

Divide by the x-value

x=9

4 0
3 years ago
The sum of a number and its additive inverse is
BlackZzzverrR [31]

Answer:

1+1=2 additive inverse 1/2

Step-by-step explanation:

hope it helps

8 0
2 years ago
What is the mean median mode and range of the numbers 31 28 30 31 30 ...?
mamaluj [8]
1. Mean is the number you get when you add all these numbers and then divide by the number of numbers. So, (31 + 28 + 30 + 31 + 30) / 5 = 150 / 5 = 30
2. The median is the middle number in the list of numbers, so, the answer is 30 as well.
3. Mode is the number that appears most often, so here it is 30 and 31 because they both appear 2 times.
4. Range is the difference between the largest and smallest number, so 31 - 28 = 3. 
5 0
2 years ago
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