Hi plz help, if you can ill mark you 5 starz! :)

Simplify the function. Than determine the key aspects of the function

Tom [10]

To simplify the function, we need to know some basic identities involving exponents.

1. b^(ax)=(b^x)^a=(b^a)^x

2. b^(x/d) = (b^x)^(1/d) = ((b^(1/d)^x)

Now simplify f(x), where

f(x)=(1/3)*(81)^(3*x/4)

=(1/3)(3^4)^(3*x/4) [ 81=3^4 ]

=(1/3)(3^(4*3*x/4) [ rule 1 above ]

=(1/3) (3^(3*x)

=(1/3)(3^(3x)) [ or (1/3)(27^x), by rule 1 ]

(A) Initial value is the value of the function when x=0, i.e.

initial value

= f(0)

=(1/3)(3^(3x))

=(1/3)(3^(3*0))

=(1/3)(3^0)

=(1/3)(1)

=1/3

(B) the simplified base base is 3 (or 27 if the other form is used)

(C) The domain for an exponential function is all real values ( - ∞ , + ∞ ).

(D) The range of an exponential function with a positive coefficient and without vertical shift is ( 0, + ∞ ).

8 0

4 years ago

the scale on a map is 1:240000. What is the actual distance represented by 1 centimetre. Give your answer in kilometres

allsm [11]

Answer:

0.24 kilometres

Step-by-step explanation:

1cm represents 240000cm on actual map

therefore to get the actual representation

1km=1000000cm

? =240000cm

Do cross multiplication;

(240000cm x 1km)/1000000cm

=0.24km

5 0

2 years ago

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were de

olga2289 [7]

Answer:

Se=1.2

Step-by-step explanation:

The standard error is the standard deviation of a sample population. "It measures the accuracy with which a sample represents a population".

The central limit theorem (CLT) states "that the distribution of sample means approximates a normal distribution, as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population distribution shape"

The sample mean is defined as:

$\bar X =\frac{\sum_{i=1}^n x_i}{n}$

And the distribution for the sample mean is given by:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

Let X denotes the random variable that measures the particular characteristic of interest. Let, X1, X2, …, Xn be the values of the random variable for the n units of the sample.

As the sample size is large,(>30) it can be assumed that the distribution is normal. The standard error of the sample mean X bar is given by:

$Se=\frac{\sigma}{\sqrt{n}}$