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ladessa [460]
3 years ago
5

You roll a die and then roll the die again. How many possible outcomes are there

Mathematics
2 answers:
siniylev [52]3 years ago
7 0

Answer:

Step-by-step explanation:

If one event has p possible outcomes, and another event has m possible outcomes, then there are a total of p • m possible outcomes for the two events. Rolling two six-sided dice: Each die has 6 equally likely outcomes, so the sample space is 6 • 6 or 36 equally likely outcomes.

nignag [31]3 years ago
4 0

Answer:

There will be 36 possible outcomes and 36 sample spaces

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The 3 inside angles of a triangle need to add up to 180 degrees.

You have two angles of 104 and 36.

A = 180 - 104 - 36 - 40

The answer is 40

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Ollie won 2 games for every 5 games that Noelle won. If Noelle won 15 more
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6

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3 years ago
Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1
svet-max [94.6K]

Answer:

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

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 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.

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that \mu = 8, \sigma = 1.1

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

n = 5 means that s = \frac{1.1}{\sqrt{5}} = 0.4919

This probability is the pvalue of Z when X = 9.3. So

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

By the Central Limit Theorem

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

Z = \frac{9.3 - 8}{0.4919}

Z = 2.64

Z = 2.64 has a pvalue of 0.9959

0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

n = 6 means that s = \frac{1.1}{\sqrt{6}} = 0.4491

This probability is 1 subtracted by the pvalue of Z when X = 9. So

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

Z = \frac{9 - 8}{0.4491}

Z = 2.23

Z = 2.23 has a pvalue of 0.9871

1 - 0.9871 = 0.0129

0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

8 0
3 years ago
Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 8% each week. The following function represents t
dybincka [34]

The function is f(x) = 86(1.01)^7x; grows approximately at a rate of 1% daily

<h3>How to rewrite the function?</h3>

The function is given as:

f(x) = 86(1.08)^x

There are 7 days in a week.

This means that:

1 day = 1/7 week

So, x days is

x day = x/7 week

Substitute x/7 for x in

f(x) = 86(1.08)^(x/7)

Rewrite as:

f(x) = 86(1.08^1/7)^x

Evaluate

f(x) = 86(1.01)^x

In the above, we have:

r = 1.01 - 1

Evaluate

r = 0.01

Express as percentage

r = 1%

Hence, the function is f(x) = 86(1.01)^7x; grows approximately at a rate of 1% daily

Read more about exponential functions at:

brainly.com/question/11487261

#SPJ1

3 0
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