Solve the equation with special factors. (Please show all steps) 4p^4 - 25p^2 = -16p^2
2 answers:
Answer:
p = 0 , p = ±
Step-by-step explanation:
4 - 25p² = - 16p² ( add 16p² to both sides )
4 - 9p² = 0 ← factor out p² from both sides
p²(4p² - 9) = 0 ← factor is a difference of squares
p²(2p - 3)(2p + 3) = 0
Equate each factor to zero and solve for p
p² = 0
p = 0 ( multiplicity of 2 )
2p - 3 = 0 ⇒ 2p = 3 ⇒ p =
2p + 3 = 0 ⇒ 2p⇒ = - 3 ⇒ p = -
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Using the z-distribution, it is found that the needed sample sizes are:
a) 242
b) 1842
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which z is the z-score that has a p-value of .
The margin of error is:
99% confidence level, hence, z is the value of Z that has a p-value of
, so
.
Item a:
The estimate is:
The sample size is <u>n for which M = 0.03</u>, then:
Rounding up, a sample of 242 is needed.
Item b:
No prior estimates, hence is used.
Rounding up, a sample of 1842 is needed.
For more on the z-distribution, you can check brainly.com/question/25404151