Answer:
a. Yes(n=500>=5, n(1-p)=25>=5)
b. 0.15241
Step-by-step explanation:
a. A normal approximation to the binomial can be used 
5 and n(1-p)>=5:
#We calculate our p as follows:
=x/n=470/500=0.94
n=500
n(1-p)=500(1-0.95)=25
Hence, we can use the normal approximation.
b. This is a normal approximation.
-Given that p=0.95(95%)
-We verify if our distribution can be approximated to a normal:
Hence, we can use the normal approximation of the form:
Hence, the probability of the sample proportion is the same as the proportion of the sample found is 0.15241
Answer:
<h2>The answer is 75 and 75</h2>
Step-by-step explanation:
hope this helps!!
The factorization of the expression of 43x³ + 216y³ is
(7x + 6y)(49x² - 42xy + 36y²)
Step-by-step explanation:
The sum of two cubes has two factors:
1. The first factor is ![\sqrt[3]{1st}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1st%7D)
+ ![\sqrt[3]{2nd}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2nd%7D)
2. The second factor is ( )² - ( ) ( ) + ( )²
Ex: The expression a³ + b³ is the sum of 2 cubes
The factorization of a³ + b³ is (a + b)(a² - ab + b²)
∵ The expression is 343x³ + 216y³
∵ ![\sqrt[3]{343x^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B343x%5E%7B3%7D%7D)
= 7x
∵ ![\sqrt[3]{216y^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B216y%5E%7B3%7D%7D)
= 6y
∴ The first factor is (7x + 6y)
∵ (7x)² = 49x²
∵ (7x)(6y) = 42xy
∵ (6y)² = 36y²
∴ The second factor is (49x² - 42xy + 36y²)
∴ The factorization of 43x³ + 216y³ is (7x + 6y)(49x² - 42xy + 36y²)
The factorization of the expression of 43x³ + 216y³ is
(7x + 6y)(49x² - 42xy + 36y²)
Learn more:
You can learn more about factors in brainly.com/question/10771256
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