Find a and b to make the following matrices equal.
2 answers:
You might be interested in
Answer:
True.
Step-by-step explanation:
The explicit form for an arithmetic sequence is:
where is the first term and
is the common difference.
The common difference here is 2 because the y's are going up by 2 while the x's are going up by 1.
Yes, the common difference is the slope.
So we have d=2.
The first term is 9.5 because that is what happens when x=1.
x is n.
y is .
So the answer is true.
----
You can also verify by plugging in numbers for n and see if you get the outputs mentioned in the pairs given:
Let n=1:
Let n=2:
Let n=3:
Let n=4:
Let n=5:
Let n=6:
We have confirmed that we get all 6 of the mentioned points using the equation they gave.
Answer:
The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we select appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sum of values of <em>X</em>, i.e ∑<em>X</em>, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
And the standard deviation of the distribution of the sum of values of X is given by,
The information provided is:
<em>μ</em> = $970
<em>σ</em> = $129
<em>n</em> = 102
Since the sample size is quite large, i.e. <em>n</em> = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.
Then,
Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.