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3 years ago

How do I find the simplest form of a square root?

Mathematics

1 answer:

lozanna [386]3 years ago

3 0

Answer:

A General Note: The Product Rule for Simplifying Square Roots. If a and b are nonnegative, the square root of the product a b \displaystyle ab ab is equal to the product of the square roots of a and b.

Step-by-step explanation:

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It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minute

Genrish500 [490]

Answer:

a) 0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes

b) 0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes

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.

Mildly obese:

Mean 376 minutes and standard deviation 67 minutes, which means that $\mu = 376, \sigma = 67$

Sample of 6

This means that $n = 6, s = \frac{67}{\sqrt{6}} = 27.35$

Lean

Mean 520 minutes and standard deviation 110 minutes, which means that $\mu = 520, \sigma = 110$

Sample of 6

$n = 6, s = \frac{110}{\sqrt{6}} = 44.91$

A) What is the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes?

This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for mildly obese people. So

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

By the Central Limit Theorem

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

$Z = \frac{420 - 376}{27.35}$

$Z = 1.61$

$Z = 1.61$ has a pvalue of 0.9463

1 - 0.9463 = 0.0537

0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes.

B) What is the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?

This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for lean people. So

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

$Z = \frac{420 - 520}{44.91}$

$Z = -2.23$

$Z = -2.23$ has a pvalue of 0.0129

1 - 0.0129 = 0.9871

0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes

5 0

3 years ago

The sum of two numbers is 12 and their difference is 5. Find each of the numbers.

vivado [14]

The two number would be 3.5 and 8.5

4 0

3 years ago

Read 2 more answers

Find the coordinate point for A that would make ABDC a rhombus. coordinate plane with points B 3 comma 4, and C at 2 comma 1, an

mixer [17]

Answer:

B. (1, 3)

Step-by-step explanation:

We know the rhombus has perpendicular diagonals and the diagonals bisect each other.

The diagonals are AD and BC.

Note. The points C and D should have swapped coordinates. This becomes ABDC.

The midpoint of BC is:

([3 + 2]/2,[4 + 1]/2) = (2.5, 2.5)

Use A(x, y) and midpoint formula for the other diagonal AD:

(x + 4)/2 = 2.5 ⇒ x + 4 = 5 ⇒ x = 1
(y + 2)/2 = 2.5 ⇒ y + 2 = 5 ⇒ y = 3

Point A has coordinates (1, 3)

Correct choice is B

See the picture

7 0

3 years ago

Read 2 more answers

Cargo pants that regularly sell for $36 are now on sale for 30% off how much is the discount

Andre45 [30]

0.30 times 36 equals 10.80. The answer is $10.80

5 0

3 years ago

Plzzzzz help i'm in desprate need of help with this

Ainat [17]

Answer:

Obtuse

Step-by-step explanation:

Right = has angle measure of 90°

Acute = has angle measure less than 90°

Equilateral = 2 or more angles whose angle measures are congruent to others

Circle = measures 360°

Obtuse = Angle measure greater than 90° and less than 180°

Hope this helps!

5 0

3 years ago