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3 years ago

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A balance scale shows that 12 + 5 = 17. If five units are removed from one side, what needs to be done to the other side to keep

the scale in balance?

1 answer:

DerKrebs [107]3 years ago

6 0

You would need to add 5 to the opposite side so the balance scale stays 17.

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Please solve this quickly

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Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

At a new exhibit in the Museum of Science, people are asked to choose between 94 or 220 random draws from a machine. The machine

Tresset [83]

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, 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 normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

The machine is known to have 99 green balls and 78 red balls.

This means that $p = \frac{99}{99+78} = 0.5593$

Mean and standard deviation:

$\mu = p = 0.5593$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5593*0.4407}{99+78}} = 0.0373$

a. Calculate the probability of getting more than 61% green balls.

This is 1 subtracted by the pvalue of Z when X = 0.61. So

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

By the Central Limit Theorem

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

$Z = \frac{0.61 - 0.5593}{0.0373}$

$Z = 1.36$

$Z = 1.36$ has a pvalue of 0.9131

1 - 0.9131 = 0.0869

0.0869 = 8.69% probability of getting more than 61% green balls.

8 0

3 years ago

What is the following product?

IrinaK [193]

Answer:

mathamistics and im not smart order of operations

4 0

3 years ago

X^2+3x^3+27-x <br> Arrange the polynomial so that the powers of x are in decending order

Monica [59]

Answer:

3x^3 + x^2 -x + 27

8 0

3 years ago

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machin

aev [14]

Answer:

The answer to your question is letter C

Step-by-step explanation:

This is a problem with the inverse rule of three because we expect that more machines can complete the same work in fewer days.

6 machines ------------------ 12 days

x machines ------------------- 8 days

x machines = $\frac{(8 days)(6 machines)}{12 days}$

$x machines = \frac{48 machines}{12}$

x = 4 machines

3 0

3 years ago