Using the normal distribution, it is found that there is a 0.0668 = 6.68% probability a randomly selected box has less than the 34 ounces of advertised weight.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean 
and standard deviation 
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
.
The probability a randomly selected box has less than the 34 ounces of advertised weight is the <u>p-value of Z when X = 34</u>, hence:
Z = -1.5
Z = -1.5 has a p-value of 0.0668.
0.0668 = 6.68% probability a randomly selected box has less than the 34 ounces of advertised weight.
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The interest rate needed to double the investment in 18 years is 6%.
<h3>What is the interest rate?</h3>
Interest earned is a function of the amount invested, interest rate and time. The future value of the investment is to be $6000 (3000 x 2). Interest earned would be $3000 (6000 - 3000)
Interest rate = interest earned / (amount invested x time )
$3000 / ($3000 x 18) = 6%
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Answer:
2x+8
Step-by-step explanation:
I actually did the math
Let <em>a</em> (<em>n</em>) denote the <em>n</em>-th term in the progression. Consecutive terms in the sequence differ by a fixed constant - call it <em>c</em> - such that
<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + <em>c</em>
Let <em>a</em> = <em>a</em> (1) be the first term in the sequence. We can solve for <em>a</em> (<em>n</em>) in terms of <em>a</em> alone:
<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + <em>c</em>
<em>a</em> (<em>n</em>) = (<em>a</em> (<em>n</em> - 2) + <em>c</em>) + <em>c</em> = <em>a</em> (<em>n</em> - 2) + 2<em>c</em>
<em>a</em> (<em>n</em>) = (<em>a</em> (<em>n</em> - 3) + <em>c</em>) + <em>c</em> = <em>a</em> (<em>n</em> - 3) + 3<em>c</em>
and so on, down to
<em>a</em> (<em>n</em>) = <em>a</em> + (<em>n</em> - 1) <em>c</em>
The sum of the first <em>n</em> terms is then
Since this is equal to 3<em>n</em> ^2 + 5<em>n</em>, it follows that
<em>c</em>/2 = 3 => <em>c</em> = 6
<em>a</em> - <em>c</em>/2 = 5 => <em>a</em> = 8
So the sequence is
<em>a</em> (<em>n</em>) = 8 + (<em>n</em> - 1) 6 = 6<em>n</em> + 2
