Write an equation for the 4th degree polynomial graphed below. Use k if your leading coefficient is positive and −k if your lead
ing coefficient is negative. Use y for the dependent variable. You can leave your answer in factored form.
2 answers:
Solution-
The general equation for a 4th degree polynomial with roots a, b, c, and d is:
A root that the graph bounces off signifies it has an even multiplicity.
A root that the graph crosses indicates an odd multiplicity.
The roots identified are -1, 2, and 4. (Since the graph either touches or crosses the x-axis at these points)
At x=2, the graph touches the x-axis, so it has a multiplicity of 2.
Next, we analyze the end behavior or leading coefficient.
and
This means the graph must be portrayed as a function with an even degree and a negative leading coefficient.
Thus, the final equation is:
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Answer:
The anticipated number of tests required to identify 680 acceptable circuits is 907.
Step-by-step explanation:
For any circuit, there are two potential results: it either passes the test or it fails. The likelihood of passing is independent between circuits. Therefore, we apply the binomial probability distribution to address this scenario.
Binomial probability distribution
This distribution calculates the chance of obtaining exactly x successes across n trials, where x has only two possible outcomes.
To find the expected number of trials to achieve r successes with a probability p, the formula is given by:
Circuits from a specific factory pass a certain quality evaluation with a probability of 0.75.
Thus, to determine the expected number of tests needed for 680 acceptable circuits, let’s denote this as E where r = 680.
The expected number of tests necessary to find 680 acceptable circuits is 907.
Answer:
The fat percentage in the blend amounts to 8%.
Step-by-step explanation:
Let
x -----> represent the fat percentage in the mix.
We understand that
The total of milk's volume times its fat percentage, added to cream's volume times its fat ratio, must match the overall mixture's volume times its fat percentage.
Keep in mind that
15% = 15/100 = 0.15
3% = 3/100 = 0.03
therefore
Now, solve for x
Convert that into a percentage