2x-y+z=9 x+y-2z=-1 -x+2y+2z=-5

Explain how negative powers of 10 can be helpful when writing and comparing small numbers

Luba_88 [7]

Answer:

See explanation

Step-by-step explanation:

Powers of 10 is a very useful way of writing down large or small numbers.

Instead of having lots of zeros, you show how many powers of 10 will make that many zeros.

When you work with small numbers, you should use the negative powers of 10. Just remember for negative powers of 10, move the decimal point to the left. For example,

$0.36=3.6\cdot 10^{-1}\ [\text{Move the decimal point one place to the left}]\\ \\0.036=3.6\times 10^{-2}\ [\text{Move the decimal point two places to the left}]\\ \\0.0036=3.6\times 10^{-3}\ [\text{Move the decimal point three places to the left}]\\ \\...$

When comparing small numbers, write these numbers in scientific notation (only one non-xero digit must be before point) and then

if the powers of 10 are the same in compared numbers are the same, just compare the numbers which are multiplied by these powers of 10. For example, $3.6\times 10^{-6}>2.6\times 10{-6},$ because powers are the same (-6) and $3.6>2.6$
if the powers are different, then the smaller is power, the smaller is number (number with the smaller negative power has more places after decimal point). For example, $3.6\times 10^{-6}> 2.6\times 10^{-7},$ because $-6>-7$

8 0

3 years ago

A grocery store offers 3 different size boxes of peanuts shown below PLEASE HELP

labwork [276]

Tutu Bru ur ur rubrubru

3 0

2 years ago

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8= -2/5c c=<br> What does c= ?

Murljashka [212]

Answer:

c = -20

Step-by-step explanation:

8/-0.4=-20.

8 = (-2/5) * 20

3 0

2 years ago

Miss Krin has $300 deducted from her checking account every month for her car payment she also has $150 deducted every month for

n200080 [17]

Did the question mention what her current checking account balance was ?

5 0

2 years ago

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Assume the average height for American women is 64 inches with a standard deviation of 2 inches. A sorority on campus wonders if

satela [25.4K]

Answer:

a) s = 0.4

b) Z = 2.5

c) 99th percentile.

d) The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

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 establishes 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.

Assume the average height for American women is 64 inches with a standard deviation of 2 inches

This means that $\mu = 64, \sigma = 2$

A) Calculate the standard error for the distribution of means.

Sample of 25 means that $n = 25$ , so $s = \frac{2}{\sqrt{25}} = 0.4$ .

B) Calculate the z statistic for the sorority group.

Sample mean of 65 means that $X = 65$ .

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{0.4}$

$Z = \frac{65 - 64}{0.4}$

$Z = 2.5$

C) What is the approximate percentile for this sample? Enter as a whole number.

Z = 2.5 has a p-value of 0.9938, so 0.99*100 = 99th percentile.

D) If the sorority actually had 36 members (still with an average of 65 inches), would you expect the percentile value to increase or decrease? why?

The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

3 0

2 years ago