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2 years ago

Need Answered ASAP

Mathematics

1 answer:

kicyunya [14]2 years ago

6 0

Answer:

The possible rational roots are: +1, -1 ,+3, -3, +9, -9

Step-by-step explanation:

The Rational Root Theorem tells us that the possible rational roots of the polynomial are given by all possible quotients formed by factors of the constant term of the polynomial (usually listed as last when written in standard form), divided by possible factors of the polynomial's leading coefficient. And also that we need to consider both the positive and negative forms of such quotients.

So we start noticing that since the leading term of this polynomial is $x^3$ , the leading coefficient is "1", and therefore the list of factors for this is: +1, -1

On the other hand, the constant term of the polynomial is "9", and therefore its factors to consider are: +1, -1 ,+3, -3, +9, -9

Then the quotient of possible factors of the constant term, divided by possible factor of the leading coefficient gives us:

+1, -1 ,+3, -3, +9, -9

And therefore, this is the list of possible roots of the polynomial.

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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

2 years ago

I’m confused please help

Law Incorporation [45]

So x equals 30 because u did 180-150 and y is also 30 since you found x you then add 90 plus 30 and it will give u 120 then 180 minus 120 will be 60 then 90 - 60 because u are trying to find y, and u will get 30.

3 0

2 years ago

PLEASE I NEED HELP!!!!!!!!

leonid [27]

Use distributive property in order to find the equivalent pieces of oi

5 0

2 years ago

Which expression is equivalent to -35 3/5

Alex787 [66]

You can look at -32 as being -2^5 so if you write (-2^5)^3/5 the 5's cancel out making it -2^3 which equals -8

5 0

2 years ago