Write the expression as a polynomial: (5–2a+a^2)(4a^2–3a–1)
1 answer:
Answer: 4a^4 - 11a^3 + 25a^2 - 13a - 5
Explanation:
Check out the attached image below for the box method diagram. It's basically a 3 by 3 box showing all the 9 terms, some of which combine together (only the like terms though).
Each inner box or inner cell is the result of multiplying the outer terms. For example, in row 2, column 2 we have the outer terms -3a and -2a multiply to get 6a^2. Figure 1 shows the full table filled out while figure 2 has that same table highlighted with different colors to show the like terms.
The like terms are:
-15a and 2a, which combine to -13a
20a^2, 6a^2 and -a^2 which combine to 25a^2
-8a^3 and -3a^3 which combine to -11a^3
Those results are added to the other terms but we do not combine them (as they are not like terms). That's how we end up with the final answer. This is a quartic polynomial as the degree (largest exponent) is 4. There are five terms in this polynomial when fully simplified.
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First, distribute 3 into the parenthesis(multiply it to every term inside):
Add 21 to both sides:
Subtract 15m to both sides:
Divide -11 to both sides:
To check our work we can plug this back into the original equation for 'm':
Multiply:
Distribute 3 into the parenthesis:
Subtract:
Both sides are equal to each other, so we solved it correctly.
For this case we must resolve the following inequality:
Subtracting 150 from both sides of the inequality we have:
We divide between 750 on both sides of the equation:
We simplify, dividing by 5 numerator and denominator:
We simplify, dividing by 5 numerator and denominator:
We simplify, dividing by 2 numerator and denominator:
Thus, the solution is given by all values of x less strict than
Answer:
Answer:
Between (253400;256600)
Step-by-step explanation:
Data given
reprsent the population mean
represent the population standard deviation
The Chebyshev's Theorem states that for any dataset
- We have at least 75% of all the data within two deviations from the mean.
- We have at least 88.9% of all the data within three deviations from the mean.
- We have at least 93.8% of all the data within four deviations from the mean.
Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least:
So using this theorem and the part "We have at least 75% of all the data within two deviations from the mean". And using the theorem we have this:
And solving for k we have this:
So then we need the limits between two deviations from the mean in order to have at least 75% of the data will reside.
Lower bound:
Upper bound:
So the final answer would be between (253400;256600)