How much is it that’s my question
The samples he chose may not be a representative sample because the number of students per foreign language class may not be the same. One class may have a very large number of students while another may have only a few. Taking equal number of students per class is not a representative sample.<span />
Well this is simple a calculator type problem...but if you are curious as the the algorithm used by simple calculators and such...
They use a Newtonian approximation until it surpasses the precision level of the calculator or computer program..
A newtonian approximation is an interative process that gets closer and closer to the actual answer to any mathematical problem...it is of the form:
x-(f(x)/(df/dx))
In a square root problem you wish to know:
x=√n where x is the root and n is the number
x^2=n
x^2-n=0
So f(x)=x^2-n and df/dx=2x so using the definition of the newton approximation you have:
x-((x^2-n)/(2x)) which simplifies further to:
(2x^2-x^2+n)/(2x)
(x^2+n)/(2x), where you can choose any starting value of x that you desire (though convergence to an exact (if possible) solution will be swifter the closer xi is to the actual value x)
In this case the number, n=95.54, so a decent starting value for x would be 10.
Using this initial x in (x^2+95.54)/(2x) will result in the following iterative sequence of x.
10, 9.777, 9.774457, 9.7744565, 9.7744565066299210578124802523397
The calculator result for my calc is: 9.7744565066299210578124802523381
So you see how accurate the newton method is in just a few iterations. :P
Answer:
51.877 kg
Step-by-step explanation:
a
See attachment for calculations
b
The amount of salt in the tank after 4 hours is gotten by simply replacing t in the equation from a, with 4 hours. Since the t gotten in a above is in minutes, we'd convert hours to minute as well. If we do that, we have
t = 4 hours = 4 * 60 minutes = 240 minutes
y = 160/3 (1 - e^((-3 * 240)/200))
y = 160/3 (1 - e^(-720/200))
y = 160/3 (1 - 0.0273)
y = 160/3 (0.9727)
y = 51.877 kg
Therefore, the amount of salt in the tank after 4 hours is 51.877 kg
correct option is D) exponential growth.
<u>Step-by-step explanation:</u>
An exponential function is a function in which the independent variable is an exponent. Exponential functions have the general form , where a > 0, a≠1, and x is any real number. The reason a > 0 is that if it is negative, the function is undefined for . Restricting a to positive values allows the function to have a domain of all real numbers. In this example, a is called the base of the exponential function. Here , we have
, this is an increasing exponential function as , value of x increases value of y increases exponentially . And so function y = (1/2)(3)^x or is an example of exponential growth.
Therefore, correct option is D) exponential growth.