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The curve has an equation y = e*. Compute the area bounded by the
curve from x = 0 to x = 1.
A curve has an equation of y=sin x. If the area of the curve
y=sin x from x=0 to X=pi is revolved about the y-axis, what is the
volume generated?
Two curves having an equation of x=2√y and y=2√x intersect each
other. Compute the area between the two curves.
The average zone of inhibition (in mm) for mouthwash H as tested by medical technology
students have been known to be 9mm. A random sample of 10 mouthwash H was tested
and the test yielded an average zone of inhibition of 7.5 mm with a variance of 25mm. Is
there enough reason to believe that the antibacterial property of the mouthwash has
decreased? Test the hypothesis that the average zone of inhibition of the mouthwash is
no less than 9mm using 0.05 level of significance.
Check whether or not the function f, defined on R by
f(x) = { 3x^2sin(1/2x), when x≠0
{ 0 ,when x=0
is derivable on R. If it is, is f' continuous at x=0? If f is not derivable , then define a derivable function on R
Find an equation of the line through the point (3, 5) that cuts off the least area from the first quadrant?
A family has four children find the probability that the family has equal number of sons and daughter.
It is claimed that last year, 65% of the people believed that there was an improvement in the country’s economy.
Suppose this year, only 270 out of the 450 people randomly selected believe that there is an improvement in the country’s
economy. Does this indicate that there is a decrease in the number of people who believes that there is an improvement in
the country’s economy? Use 0.05 significance level.
(Use critical value method)
A History teacher claims that the average height of Filipino males is 163 centimeters. A student taking up Statistics
randomly selects 20 Filipino males and measures their heights. Their heights in cm are shown below.
163 164 165 177
167 163 159 169
159 160 163 163
165 169 163 165
162 174 163 167
Do the collected data present sufficient evidence to indicate that the average heights of Filipino male is different
from 163 cm? Use 0.05 level of significance and assume that the population follows a normal distribution.
(Use critical value method)
The cashier of a fastfood restaurant claims that the average amount spent by customers for dinner is P 120. 00. A sample
of 50 customers over a month period was randomly selected and it was found out that the average amount spent for dinner
was P 112. 50. Using a 0.05 level of significance, can it be concluded that the average amount spent by customers is more
than P 120. 00? Assume that the population standard deviation is P 6.50.
(Use the critical value method)
