The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
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Answer: x=2.375937.... sorry I give you the wrong one but here the steps O here x=2.96423 will it can be any one of the two answer I give you now.
Step-by-step explanation: Hope this help :D
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Answer: 
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n starts at 1, and n is a positive whole number (1,2,3,...)
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Explanation:
The sequence is arithmetic with first term 40 and common difference 10. Meaning we add 10 to each term to get the next one.
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a1 = 40 = first term
d = 10 = common difference

is the general nth term of this arithmetic sequence
Plug in n = 1 and you should get 
Plug in n = 2 and you should get 
and so on
Answer:
False
Step-by-step explanation:
It makes no sense......
Answer: B. 0.036
Step-by-step explanation:
Formula for standard error :

, where p = Population proportion and n= sample size.
Let p be the population proportion of the people who favor new taxes.
As per given , we have
n= 170

Substitute these values in the formula, we get

Hence, the standard error of the estimate is 0.036.
∴ The correct answer is OPTION B. 0.036