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xeze [42]
2 years ago
7

I have a bad memory,i learned this but I forgot it (I swear I'm not lying)

Mathematics
1 answer:
mihalych1998 [28]2 years ago
3 0

Answer:

b

Step-by-step explanation:

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Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the ar
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Answer:

<u>Alternative Hypothesis:H₁:</u><em> μ ≠ 0.41</em>

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the newscast reaches 41% of the viewing audience in the area

The mean of the Population = 0.41

Given that In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station

Given that the mean of the sample = 0.36

<u><em>Step(ii):-</em></u>

<u><em>Null hypothesis:</em></u><em> The sample statistic does not differ significantly from the hypothetical parameter value.</em>

<em>Given data </em>

<em>Null hypothesis: H₀ : μ = 0.41</em>

<u>Alternative Hypothesis:</u><em> Any hypothesis which is complementary to the Null hypothesis</em>

<u>Alternative Hypothesis:H₁:</u><em> μ ≠ 0.41</em>

<em> </em>

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2 years ago
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\text{Goal: Find } x \text{ such that:} \\ 2^x > 4x + 12

2^x > 4x + 12 \\ 2^x > 4(x + 3) \\ 2^{x - 2} > x + 3

\text{A lemma: } \\ \text{It is given that: } \\ 2^n > 2n + 1, \text{ } n > 3
\text{This can be proven by Mathematical Induction.}
\text{Using this lemma, we can manipulate the expression:} \\ 2^{x - 2} > 2(x - 2) + 1 = 2x - 3, \text{ } x > 5 \\ 2\cdot 2^{x - 2} > 2(2x - 3) \\ 2^{x - 1} > 4x - 12 \\ 2^{x - 1} + 24 > 4x + 12

\text{Observe the following: } 2^x \text{ will always grow faster than } 2^{x - 1} \\ \text{This implies that } 2^{x} > 2^{x - 1} + 24 > 4x + 12, \text{ given that } x > 5

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