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3 years ago

Write your answer using only positive exponents. (-2x^6y^-2)^3

Mathematics

1 answer:

Alinara [238K]3 years ago

6 0

Firstly, the rule with raising a power by a power is to multiply the two powers. In our case, it'll look like this:

$(-2x^6y^{-2})^3\\ (-2)^3x^{6*3}y^{-2*3}\\ -8x^{18}y^{-6}$

Now the rule from negative exponents to fractions is $x^{-m}=\frac{1}{x^m}$ . Applying this to y^-6, your final answer is going to be $\frac{-8x^{18}}{y^{6}}$

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3 years ago

Babies born after a gestation period of 32-35 weeks have a mean weight of 2700 grams and a standard deviation of 700 grams, whil

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Answer:

The 33 week gestation period baby has the higher z-score, so he weighs more relative to other babies of the same gestation period.

Step-by-step explanation:

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.

Who weighs more relative to other babies of the same gestation period?

Whoever has the higer z-score

33 - week baby.

Babies born after a gestation period of 32-35 weeks have a mean weight of 2700 grams and a standard deviation of 700 grams. A 33-week gestation baby weighs 2950 grams.

We have to find z when $\mu = 2700, \sigma = 700, X = 2950$ . So

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

$Z = \frac{2950 - 2700}{700}$

$Z = 0.357$

40-week baby

Mean weight of 3000 grams and a standard deviation of 490 grams. 40-week gestation baby weighs 3150 grams.

We have to find Z when $\mu = 3000, \sigma = 490, X = 3150$ . So

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

$Z = \frac{3150 - 300}{490}$

$Z = 0.306$

The 33 week gestation period baby has the higher z-score, so he weighs more relative to other babies of the same gestation period.

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4 years ago

At a dog competition, a dog is awarded 10 points if it runs through 4 pipes, makes 10 jumps, and walks on 2 beams. If Roofy gets

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Answer:

Butch should be awarded with 9,2 points

Step-by-step explanation:

Roofy gets 9 points out of 10 missing only a pipe, that means that each pipe is awarded with 1 point

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So points are awarded as follows

1 point by pipe then 4 points for 4 pipes

2 points by beam then 4 points for 2 beams

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Finally as Butch missed 4 jumps, Butch should be awarded with 9,2 points

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3 years ago

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Answer:

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Step-by-step explanation:

Confidence interval is given as mean +/- margin of error (E)

mean = (17+20+26)/3 = 63/3 = 21

sd = sqrt[((17-21)^2 + (20-21)^2 + (26-21)^2) ÷ 3] = sqrt(42÷3) = sqrt(14) = 3.74

n = 3

degree of freedom = n-1 = 3-1 = 2

confidence level (C) = 95% = 0.95

significance level = 1 - C = 1 - 0.95 = 0.05 = 5%

critical value (t) corresponding to 2 degrees of freedom and 5% significance level is 4.303.

The critical value is 4.303

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Lower limit of mean = mean - E = 21 - 9.291 = 11.709

Upper limit of mean = mean + E = 21 + 9.291 = 30.291

95% confidence interval is (11.709, 30.391)

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