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A geometric progression has a second term of 12 and a sum to infinity of 54. Find the possible values of the first term of the progression
Suppose that in a casino, a certain slot machine pays out an average of Php 15, with a standard deviation of Php 5,000. Every play of the game costs a gambler Php 20.
a. Why is the standard deviation so large?
b. If your parent decides to play with this slot machine 5 times, what are the mean and standard deviation of the casino's profit?
c. If the gamblers play with this slot machine 1000 times in a day, what are the mean and standard deviation of the casino's profits?
Prove that the premises P → Q, Q → R, S → ¬R and P ∧ S are inconsistent.
1.)Determine if the proposition is satisfiable or not by providing any possible combination of inputs that yields a TRUE result.
(p ∧ q) ∨ (¬p ∧¬q)→r
2.)Prove or disapprove the given proposition using a truth table or rules of logic.
¬(¬p ∧ q) ∨ q ⇔ q → p
Can you make use of the normal curve to find for the probability of a large value? How?
The base of the rectangle is changing at the rate of 3in/min. if its height remains constant, determine the rate of change of its perimeter with respect to time?
Suppose 𝑓 is odd and differentiable everywhere. Prove that for every positive
number 𝑏, there exists a number 𝑐 in (−𝑏, 𝑏) such that 𝑓′(𝑐) = 𝑓(𝑏)/𝑏.
The Altitude of a triangle is increasing at a rate of 8cm/s while its area is increasing at the rate of 12cm^2/s. At what rate is the base of the triangle changing when the altitude is 20 cm and the area is 100 cm^2 ?
A cone of radius 𝑟 centimeters and height ℎ centimeters is lowered point first at
a rate of 1 cm/s into a tall cylinder of radius 𝑅 centimeters that is partially filled with
water. How fast is the water level rising at the instant the cone is completely
submerged
Show that the length of the portion of any tangent line to the asteroid 𝑥^2/3 + 𝑦^2/3 = 𝑎^2/3 cut off by the coordinate axes is constant.
