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2 years ago

In the triangle of ABC, D is a point on AB , AC = 7, AD = 6, and BC = 18. The length of DB could be

Mathematics

1 answer:

Ray Of Light [21]2 years ago

8 0

Answer:

19 > DB > 5

Step-by-step explanation:

In a triangle Δ ABC, AC = 7, and BC = 18.

Therefore, the length of the third side of the triangle Δ ABC i.e. length of AB can have a maximum value of < (7 + 18) i.e. 25 and the minimum value of the length AB will be > (18 - 7) i.e. 11

Hence, the length of AB will be given by 25 > AB > 11.

Now, AB = AD + DB = 6 + DB {Since length of AD is given to be 6}

Therefore, 25 > 6 + DB > 11

⇒ 19 > DB > 5 (Answer)

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To test the null hypothesis $H_0: p_1=p_2$ against the alternate hypothesis $H_1:p_1 \neq p_2$ .

Let $\hat p_1, \hat p_2$ denotes the respective sample proportions and the $n_1, n_2$ represents the sample size respectively.

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$n_2=155$

The test statistic can be written as :

$$z=\frac{(\hat p_1 - \hat p_2)}{\sqrt{\frac{\hat p_1 \times (1-\hat p_1)}{n_1}} + \frac{\hat p_2 \times (1-\hat p_2)}{n_2}}}$

which under $H_0$ follows the standard normal distribution.

We reject $H_0$ at $0.05$ level of significance, if the P-value or if $|z_{obs}|>Z_{0.025}$

Now, the value of the test statistics = -1.368928

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Hence we conclude that the two population proportion are not significantly different.

Conclusion :

There is not sufficient evidence to conclude that the $\text{proportion}$ of the seeds that $\text{germinate differs}$ with the percent of the $\text{mushroom compost}$ in the soil.