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2 years ago

Factor the GCF: -6x^4y^5 - 15x^3y^2 + 9x^2y^3

1 answer:

5 0

<span>-6x^4y^5 - 15x^3y^2 + 9x^2y^3

</span>-6x^4y^5 = -2, 3, x, x, x, x, y, y, y, y, y
15x^3y^2 = -5, 3 x, x, x, y, y
9x^2y^3 = 3, 3 x, x, y, y, y

Each group has a 3 in common and each group has 2 x in common and each group has 2 y in common so the GCF = -3x^2y^2

Divide that out and we get
$\frac{-6x^4y^5 - 15x^3y^2 + 9x^2y^3}{-3x^2y^2} =$
$2x^2y^3 + 5x - 3y$
$-3x^2y^2(2x^2y^3 + 5x - 3y)$

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The time a traffic light remains yellow is one second more than 0.05 times the speed limit. What is the yellow time for a traffi

weqwewe [10]

30 * 0.05 + 1 = X
1.5 + 1 = X
2.5 = X

The light remains yellow for 2.5 seconds on a street with a speed limit of 30.

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2 years ago

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

Put these numbers in order from least to greatest 12%, -1/2, 0, -0.22, 0.56

uysha [10]

Answer: -1/2, -0.22, 0, 12%, 0.56

Step-by-step explanation:

-1/2 is equal to -0.50, making it the number with the least value.

-0.22 is closer to 0 than -0.50, meaning it is greater then -0.50 and less than 0.

0 is between the negative and positive numbers, giving it the spot that it has.

12% is equivalent to 0.12, meaning it is more than 0, and less than 0.56, which is the greatest number.

0.56 has more value than any other number in the problem, meaning it goes last in the order.

8 0

2 years ago

Find the value of f(-1) for the function below

mrs_skeptik [129]

Put the value of x = -1 to the equation of a function f(x):

$f(x)=\dfrac{2}{3}\times3^{3x+12}\\\\f(-1)=\dfrac{2}{3}\times3^{3(-1)+12}=\dfrac{2}{3}\times3^{-3+12}=\dfrac{2}{3}\times3^9=\dfrac{2}{1}\times3^8=13,122\to\boxed{B.}$

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2 years ago

Solve this inequality. 7.2-3w<4.5

zlopas [31]

Answer:

w>0.9

Step-by-step explanation:

7.2-3w<4.5

-7.2 -7.2

-3w<-2.7

/-3 /-3

w>0.9

The inequality switches when divided by a negative.

-hope it helps

8 0

2 years ago

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