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1 year ago

4 (hx - 1) -3 (x +h) ≡ 5 (x + k) Work out the value of h and k H and k are integer constants

Mathematics

1 answer:

vladimir1956 [14]1 year ago

6 0

Answer:

4hx - 8x - 3h - 4

k = ------------------------

8x + 5k + 4

h = ------------------------

4x - 3

Step-by-step explanation:

4 (hx - 1) - 3 (x + h) = 5 (x + k)

4hx - 4 - 3 (x + h) = 5 (x + k)

4hx - 4 - 3x - 3h = 5 (x + k)

4hx - 4 - 3x - 3h = 5x + 5k add 3h both sides

4hx - 4 - 3x - 3h + 3h = 5x + 5k + 3h simplify

4hx - 4 - 3x = 5x + 5k + 3h add 4 both sides

4hx - 4 - 3x + 4 = 5x + 5k + 3h + 4 simplify

4hx - 3x = 5x + 5k + 3h + 4 subtract 5x from both sides

4hx - 3x - 5x = 5x + 5k + 3h + 4 - 5x simplify

4hx - 8x = 5k + 3h + 4

4hx - 8x - 3h - 4 = 5k

4hx - 8x - 3h - 4

k = ------------------------

solving for h;

4hx - 3h = 8x + 5k + 4

h(4x - 3) = 8x + 5k + 4

8x + 5k + 4

h = ------------------------

4x - 3

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Answer:

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Step-by-step explanation:

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The pivotal quantity for a 99% confidence interval for the true mean shell length is given by;

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where, $\bar X$ = sample mean shell length = 51.3 cm

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Now, the 99% confidence interval for $\mu$ = $\bar X \pm t_(_\frac{\alpha}{2}_) \times \frac{s}{\sqrt{n} }$

Here, $\alpha$ = 1% so $(\frac{\alpha}{2})$ = 0.5%. So, the critical value of t at 0.5% significance level and 5 (6-1) degree of freedom is 4.032.

So, 99% confidence interval for $\mu$ = $51.3 \pm 4.032 \times \frac{6.6}{\sqrt{6} }$

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The interpretation of the above result is that we are 99% confident that the true mean shell length lie within the above interval of [40.44 cm, 62.16 cm].

The assumption about the distribution of shell lengths must be true in order for the confidence interval, part a, to be valid is that;

C. The population has a relative frequency distribution that is approximately normal.

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