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This question is concerning the completion of the square by using plane geometry
The area of a square of length x is : x
2
The area of a rectangle of sides x and y is : xy
Consider the expression : x
2 + 10x
Such can be considered as the sum of two areas viz square x
2 and a rectangle 10x
Now do the following (sketch essential)
Divide the rectangle into two equal areas viz 5x and 5x
Next to the square place the two rectangles with the side x in common. One to the RHS and the other below.
You will now have a ’nearly complete’ square
a) What is the length of each side of the ’missing square’ in your diagram
b) If you add the area of the missing square to make a big square, what is the area of the complete (big) square
c) By using the areas from your sketch, find the expressions ? and ?? in the following:
x
2 + 10x + (?)2 = (??)
The average height of students in a freshman class of a certain school has been 161.27 cm with a population standard deviation of 6.5 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 45 students in the present freshman class has an average height of 150.6 cm? Use a 0.05 level of significance.
Let X be a random variable with the following probability distribution:
x. -3 , 6 , 9
P(X=x). 1/6 , 1/2 , 1/3
Find ug(x), where g(X)= (2X+1)^2
Assume your run the statistics to test the hypothesis and your result is 0.06, and then what will be your decision as a researcher, at P is 5%?
Chinovac Labs tried a new vaccine on 165 randomly selected individuals. From the experiment, it was determined that 82 of them developed immunity. Calculate a 95% confidence interval for the proportion p of individuals in the population for whom the vaccine would help. What is the lower bound of this interval?
11. Q10. Assume your run the statistics to test the hypothesis and your result is 0.06, and then what will be your decision as a researcher, at P is 5%?
Chinovac Labs tried a new vaccine on 189 randomly selected individuals. From the experiment, it was determined that 104 of them developed immunity. Calculate a 95% confidence interval for the proportion p of individuals in the population for whom the vaccine would help. What is the upper bound of this interval?
6 % of the 100 students in Emmie Xi Hem International School students said that they had been late in their first-period classes. What is the upper bound of the 99% confidence interval for the proportion of students in the said school who had been late in their first-period classes?
Chinovac Labs tried a new vaccine on 126 randomly selected individuals. From the experiment, it was determined that 118 of them developed immunity. Calculate a 95% confidence interval for the proportion p of individuals in the population for whom the vaccine would help. What is the point estimate of this interval?
The Malayo Colleges Mindanao recently conducted a study analyzing the privacy management habits of teen internet users. In a group of 116 teens, 80 reported having more than 100 followers on Twitter. Find the upper bound of a 90% confidence interval for the true proportion of teens who would report having more than 100 followers on Twitter.
