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tensa zangetsu [6.8K]
3 years ago
7

Solve by unfolding: a0=2, and, n>=1, a_n=7a_n-1.

Mathematics
1 answer:
vodomira [7]3 years ago
6 0
We are told that the first term is 2.  The next term is 7(2) = 14; the third term is 7(14) = 98.  And so on.  So, the first term and the common ratio (7) are known.

The nth term of this geometric series is a_n = 2(7)^(n-1).

Check:  What is the first term?  We expect it is 2.  2(7)^(1-1) = 2(1) = 2.  Correct.

What is the third term?  We expect it is 98.  2(7)^(3-1) = 2(7)^2 = 98.  Right.<span />
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In the flowering plant, white flowers (B) are dominant over red flowers (b), and short plants (E) are dominant over tall flower
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<u>Question Completion</u>

(a)What is your null hypothesis?

(b)What is your expected phenotypic ratio based on Mendelian inheritance?

(c)Calculate the expected number of flowers you should have gotten based on the Mendelian inheritance. Then calculate a chi-square value, degrees of freedom, and a p-value.

  • Chi-square statistic: _____
  • Degrees of freedom (# phenotypes -1):
  • P-value:

(d)Interpret your results. Do you reject it or fail to reject your null hypothesis (please restate the null)?

Answer:

(a)H_0:$The given data fit the predicted phenotype

(b)9:3:3:1

(c)

  • Chi-square statistic: 3.8914
  • Degrees of freedom (# phenotypes -1) =3
  • P-value:  0.2734

(d)We fail to reject the null hypothesis.

Step-by-step explanation:

In the flowering plant, white flowers (B) are dominant over red flowers (b), and short plants (E) are dominant over tall flowers (e). An F2 generation was created by crossing two F1 individuals (each BbEe).

(a)The null hypothesis is:

H_0:$The given data fit the predicted phenotype

(b)The gametes are BE, Be, bE and be.

The offsprings are presented in the table below:

\left|\begin{array}{c|cccc}&BE&Be&bE&be\\--&--&--&--&--\\BE&BE&BE&BE&BE\\Be&BE&Be&BE&Be\\bE&BE&BE&bE&bE\\be&BE&Be&bE&be\end{array}\right|

The expected phenotypic ratio based on Mendelian inheritance

BE:Be:bE:be=9:3:3:1

(c)

\left|\begin{array}{c|c|c|c|c|c}$Phenotype&Observed&$Expected&O-E&(O-E)^2&\dfrac{(O-E)^2}{E} \\-----&--&--&--&--&--\\$White short(BE)&206&\frac{9}{16}*404 \approx 227 &-21&441&1.9427\\$Red, short(bE)&83&\frac{3}{16}*404 \approx 78 &5&25&0.3205\\$White, tall(Be)&85&\frac{3}{16}*404 \approx 78 &7&49&0.6282\\$Red, tall(be)&30&\frac{1}{16}*404 \approx 25 &5&25&1\\-----&--&--&--&--&--\\$Total&404&--&--&--&3.8914\end{array}\right|

Therefore:

  • Chi-square statistic: 3.8914
  • Degrees of freedom (# phenotypes -1):  4-1 =3
  • P-value:  0.2734

(d) Our null hypothesis is:

H_0:$The given data fit the predicted phenotype

Since p>0.05, the given data fit the predicted phenotypic ratio.

We, therefore, fail to reject the null hypothesis.

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