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An element with mass 590 grams decays by 19.5% per minute. How much of the element is remaining after 15 minutes, to the nearest 10th of a gram?
A random sample of 900 members is found to have a mean of 4.45 CM can it be reasonably regarded as a sample from a large population whose mean is 5 cm and variance is 4 cm square obtain the 95% confidence limit for the mean in the population
A spider climbing out of a well is affected by the weather. When it rains, he falls back down the well with a probability of 1/10. In dry weather, he only falls back down with probability of 1/25. The probability of rain is 1/5.
(i) Draw the tree diagram of these events.
(ii) Find the probability he falls back down the well.
(iii) Find the probability that given he falls it was a rainy day.
Suppose that the sitting back-to-knee length for a group of adults has a normal distribution with a mean of 24.5in. and a standard deviation of 1.1in. These data are often used in the design of different seats, including aircraft seats, train seats, theater seats, and classroom seats. Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater)0.01 and a value is significantly low if P(x or less)0.01. Find the back-to-knee lengths separating significant values from those that are not significant. Using these criteria, is a back-to-knee length of 26.7in. significantly high?
Show that each of these conditional statements is a tautology
by using truth tables.
a) [¬p ∧ (p ∨ q)] → q
b) [(p → q) ∧ (q → r)] → (p → r)
c) [p ∧ (p → q)] → q
d) [(p ∨ q) ∧ (p → r) ∧ (q → r)] → r
Find the Derivative of the following function
- y = x2 cos x - 2xsinx - 2cosx
- x(cos2x + 3y) = ysinx
The weight (x grams) of a rose is assumed to be distrubuted as N (5, 12.4). A rose is selected randomly .find the probability that the weight of randomly selected flower is less than 4 gram
Given the population 3 5 8 9 and 10. Suppose samples of size 3 are drawn from this population
a consider the normal distribution of IQs with a mean of 100 and a standard deviation of 16. What
percentage of IQs are?
a. greater than 95?
b. less than 120
c. between 90 and 110
A division-wide aptitude test in Science was conducted to 1000 pupils. The mean of the test is 58 and the standard deviation is 12. The scores also approximate the normal distribution. What is the score that divides the distribution into two such that 75% of the cases is below it?
