Happy is four times as old as Grumpy. The sum of their age is 100. How old are Happy and Grumpy?
2 answers:
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The statement "<span>The rate of change of y with respect to x is inversely proportional to y^4" can be written mathematically as dy/dx = k/y^4
To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
![y= \sqrt[5]{Bx+C}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%5B5%5D%7BBx%2BC%7D%20)
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To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
Answer:
The sample statistics are attached.
First, we need to determine the hypothesis.
The null hypothesis should be: .
The alternative hypothesis should be:
The next step is about calculating the<em> t statistics </em>based on the samples. This <em>t test </em>will give the probability value or p-value, which determines if there's enough to reject the null hypothesis. The formula we need to use to find the t-value is:
Replacing all the values into the formula, we have:
Therefore, the t-value is -3.2.
Now, we using a level of significance of 0.01, and a degree of freedom (df) of 34, we use the t-table to find the p-value for this results. (df = N -1; in this case, we take the smaller sample, which is 35, giving us 34 of df).
Therefore, according to the table attached, <em>the p-value is less than 0.01,</em> which is less than our level of significance. This result means that the null hypothesis is rejected. In other words, there's enough evidence to say that <em>the life expectancy of people in Africa is less than the life of expectancy of people in Asia.</em>
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