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Effectus [21]
3 years ago
11

Express 3a^2b^-1 with positive exponents.

Mathematics
1 answer:
Marizza181 [45]3 years ago
5 0
Your answer would come down to be 3a^2/b
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9x^3y^6/xy^6<br> Solve using only positive exponents
DedPeter [7]

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6 0
3 years ago
From the top of a tower 120m high the angle of depression of a stone on the ground is found to be 30°. How far is the stone from
gogolik [260]

Step-by-step explanation:

so from this, I think the difference is 207.84 m

:)

8 0
2 years ago
How do you find the area of a square
Lubov Fominskaja [6]

Answer:

width times length

Step-by-step explanation:


7 0
3 years ago
The mean height of women in a country (ages 20-29) is 64 4 inches A random sample of 50 women in this age group is selected What
Simora [160]

Answer:

0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.

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.

Mean of 64.4 inches, standard deviation of 2.91

This means that \mu = 64.4, \sigma = 2.91

Sample of 50 women

This means that n = 50, s = \frac{2.91}{\sqrt{50}}

What is the probability that the mean height for the sample is greater than 65 inches?

This is 1 subtracted by the p-value of Z when X = 65. So

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

By the Central Limit Theorem

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

Z = \frac{65 - 64.4}{\frac{2.91}{\sqrt{50}}}

Z = 1.46

Z = 1.46 has a p-value of 0.9279

1 - 0.9279 = 0.0721

0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.

8 0
2 years ago
Ryan is trying a low-carbohydrate diet. He would like to keep the amount of carbs consumed in grams between the levels shown in
pentagon [3]

Compound inequality combines multiple single inequalities.

The solution and interpretation of the inequality is:

<em />x > 50<em> and </em>x < 150<em>.  Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.</em>

<em />

We have:

110 < 2x + 10 and 2x + 10< 310

Solve for x in both inequalities

110 < 2x + 10

110 -10 < 2x

100 < 2x

Divide both sides by 2

50 < x

Rewrite as:

x > 50

Also, we have:

2x + 10< 310

2x< 310 - 10

2x< 300

Divide by 2

x < 150

So, the solutions to the inequalities are:

x > 50 and x < 150

This means that Ryan needs to consume more than 50 but less than 150 grams of carbohydrates.

Hence, (a) is correct

Read more about compound inequalities at:

brainly.com/question/13290962

8 0
2 years ago
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