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Explanation:
There are 18 ways to pick the first topping and 18-1 = 17 ways to pick the next topping. Picking the same topping again doesn't make much sense (though I suppose it could mean that you just want more of that topping than usual?), so that's why we have the 18 drop to 17 when making that second selection.
If the order of toppings mattered, then we'd have 18*17 = 306 permutations. However, the order of toppings doesn't matter. All that matters is the group rather than the individual toppings. When counting out the 306 permutations, we've overcounted by a factor of 2. In other words, we've double counted.
So we must divide by 2 to fix this double count. That leads to 306/2 = 153 combinations
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The alternative method involves using the nCr combination formula
Use n = 18 and r = 2 in this formula
the exclamation marks indicate factorial.
Answer/Step-by-step explanation:
Total Distance = 3Ft
a) Determine the amplitude and period of a sinusoidal function that models the bobbing buoy.
Amplitude = 3/2 = 1.5 period = 10 second
No ph. Shift
b) Write an equation of a function that models the buoy with x=0 at its highest point.
y= 1.5 cos ( )
Answer:
The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.
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 and standard deviation
, the z-score of a measure X is given by:
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 and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean $39725 and standard deviation $7320.
This means that
Sample of 125
This means that
The probability that the sample mean would be at least $39000 is about?
This is 1 subtracted by the pvalue of Z when X = 39000. So
By the Central Limit Theorem
has a pvalue of 0.1335
1 - 0.1335 = 0.8665
The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.
Answer:
The answer is A. .
Step-by-step explanation:
To find the difference of this problem, start by simplifying the denominator, which will look like . Next, multiply
by
to create a fraction with a common denominator in order to subtract from
. The problem will now look like
.
Then, simplify the terms in the problem by first multiplying and
, which will look like
. The next step is to combine the numerators over the common denominator, which will look like
.
Next, simplify the numerator, and to simplify the numerator start by factoring 3 out of , which will look like
. Then, subtract 14 from -7, which will look like
. The final answer will be
.