Anyone who is extremely smart in Math please help me with my online homework and I'm struggling with this assignments.
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Answer:
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
Step-by-step explanation:
Given that M is a polynomial of degree 3.
So, it has three zeros.
Let the polynomial be
M(x) =a(x-p)(x-q)(x-r)
The two zeros of the polynomial are -4 and 4i.
Since 4i is a complex number. Then the conjugate of 4i is also a zero of the polynomial i.e -4i.
Then,
M(x)= a{x-(-4)}(x-4i){x-(-4i)}
=a(x+4)(x-4i)(x+4i)
=a(x+4){x²-(4i)²} [ applying the formula (a+b)(a-b)=a²-b²]
=a(x+4)(x²-16i²)
=a(x+4)(x²+16) [∵i² = -1]
=a(x³+4x²+16x+64)
Again given that M(0)= 53.12 . Putting x=0 in the polynomial
53.12 =a(0+4.0+16.0+64)
=0.83
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
Answer: The test statistic needed to test this claim= 10.92
Step-by-step explanation:
We know that the probability of giving birth to a boy : p= 0.5
i..e The population proportion of giving birth to a boy = 0.5
As per given , we have
Null hypothesis :
Alternative hypothesis :
Since is right-tailed , so the hypothesis test is a right-tailed z-test.
Also, it is given that , the sample size : n= 291
Sample proportion:
Test statistic : , where n is sample size ,
is sample proportion and p is the population proportion.
i.e. the test statistic needed to test this claim= 10.92
Critical value ( one-tailed) for 0.01 significance level =
Decision : Since Test statistic value (10.92)> Critical value (2.326), so we reject the null hypothesis .
[When test statistic value is greater than the critical value , then we reject the null hypothesis.]
Thus , we concluded that we have enough evidence at 0.01 significance level to support the claim that the YSORT method is effective in increasing the likelihood that a baby will be a boy.