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A manufacturer of light bulbs claims that its light bulbs have a mean life of 2000 hours with a standard deviation of 2. A random sample of 200 such bulbs is selected for testing. If the sample produces a mean value of 1992 hours and a sample standard deviation of 81, is there sufficient evidence to claim that the mean life is significantly less than the manufacturer claimed at 5% significant level
A school has 1000 students. The principal of the school thinks that the average IQ of its students is at least 110. To prove her point, she administers an IQ test to 200 randomly selected students. Among the sampled students, the average IQ is 108 with a standard deviation of 10. Based on these results, should the principal accept or reject her original hypothesis? Assume a significance level of 1%
An electric charge q caused an electric potential of V = -218 V at point A 10.6 m from q. What is the electric charge q?
A fixed mass of a gas occupies 100cm cubed ,at-15cm cubed and 650mmHg pressure at what temperature will it have a volume of 150cm cubed if the pressure is adjusted to 680 mmHg?
2.Construct a program in C++ to compute the sum of the digits of the numbers input from the user. Apply all the control structures. Display the number input by the user as well as the sum. Use for loop control structure.
Example display in Console Application
Input number: 93
———output——-
You input number 9 and 3.
The sum of the digits 9 and 3 is 12.
1. Create a C++ program that asks the user to input full name 5times using for, do while and while loop. Then,display.
1.a. For loop
1.b. While loop
1.c Do while loop
Example display in console application
—-This program can accept 5 full names from the user——
Please enter five full names :
Carlo Adam
Justin Doe
Liam Baird
Mike Tan
John Davis
//Expected output:
You entered the following names:
Carlo Adam
Justin Doe
Liam Baird
Mike Tan
John Davis
Congratulations!
Oxygen gas inside a 1.5 L gas tank has a pressure of 0.95 atm. Provide the temperature remains constant, how much pressure is needed to reduce it's volume by 1/2
a) Does the sequence (3+(-1)n) converge to 2? Justify.
b) Show that "\\lim _{x\\to \\infty }\\left(\\frac{x-3}{x+1}\\right)^x=e^{-4}"
c) Check whether the sequence fn (x) = "\\frac{3x}{1+nx^2}" where x ∈ [2,∞ [ is uniformly
convergent in [2,∞ [
1.The pH sample of human blood was measured to be 7.41 at 25 degrees celsius. Calculate the hydrogen ion concentration, H' and hydroxide ion, OH for the sample.
a) Find "\\ lim_{x\\to 0}\\frac{\\left(tanxsec^2x-x\\right)}{x^3}"
b) Examine whether the equation, x3- 11x +9 =0 has a real root in the interval [0,1]
c) Check whether the following series are convergent or not (4)
i) "\\sum _{n=1}^{\\infty }\\:\\frac{\\left(3n-1\\right)}{7^n}"
(ii) "\\sum _{n=1}^{\\infty }\\frac{\\left(\\:\\sqrt{n^2+3}-\\sqrt{n^2-3}\\right)}{\\sqrt{n}}\\:"
