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2 years ago

Which ratio best defines experimental probability?

Mathematics

2 answers:

Lostsunrise [7]2 years ago

8 0

B. Total number of times the activity is performed: Number of times an event occurs

FrozenT [24]2 years ago

7 0

B what the other person said

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Write the equation in it's simplest form or as

allsm [11]

9514 1404 393

Answer:

2∛7

Step-by-step explanation:

Putting the expression in simplest form will factor cubes from under the radical.

$\displaystyle\sqrt[3]{56}=\sqrt[3]{2^3\cdot7}=\boxed{2\sqrt[3]{7}}$

7 0

2 years ago

65/100=55.24/x what is the answer?

ANEK [815]

Answer:

DDKEFD

Step-by-step explanation:

4 0

3 years ago

5x -6y=-32

erastovalidia [21]

So this question is already perfectly set up. Since the 6 and -6 cancel you’ll be left with 5x + 3x which is 8x and -32 + 48 which is 16. 8x=16. Isolate x to get that x=2. Plug 2 back into one of the equations. 5(2) -6y = -32. Solve for y now. -10-32 equals -42. Divide -42 by -6 to get 7. So the final coordinate where the two equations will intersect is (2,7)

3 0

3 years ago

A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat

zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

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.

In this question, we have that:

$\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5$

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

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

X = 205

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

$Z = \frac{205 - 200}{5}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

X = 195

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

$Z = \frac{195 - 200}{5}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

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

$Z = \frac{210 - 200}{5}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772.

X = 195

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

$Z = \frac{190 - 200}{5}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0

3 years ago

Help with these please.

zepelin [54]

For numbers 15-17, we need to remember that two of a triangle's angles are always acute and the third angle will allow us to classify the triangle based on its angles. now that we know this, let's look at #15. the first two angles listed are acute, and the third is an obtuse angle, therefore it is an obtuse triangle. on #16 we have three acute angles, so it is an acute triangle. #17 has two acute angles and a right angle so it is a right triangle.
on numbers 21-23, we need to know that a triangle with all congruent sides is called equilateral, a triangle with two equal sides is isosceles, and a triangle with no equal sides is called scalene. #21 shows two equal sides so it is an isosceles triangle. #22 has three equal sides so it is an equilateral triangle. #23 has no equal sides so it is scalene. hope this helped! :)

7 0

3 years ago