Can get some help on this question please?

Mathematics

2 answers:

Sergio [31]3 years ago

8 0

Answer:

(a) 8

(b) 16

(d) The ratios are the same

Step-by-step explanation:

(a) For inputs -5 and -4, the difference of outputs is ...

-3 -(-11) = 8

(b) For inputs 0 and 2, the difference of outputs is ...

45 -29 = 16

(c) For inputs -3 and 0, the difference of outputs is ...

29 -5 = 24

(d) The ratios of output difference over input difference are ...

8/1 = 16/2 = 24/3 = 8 . . . . . they are all the same

This is yet another confirmation that the slope of a line is the same everywhere, and over any interval.

zloy xaker [14]3 years ago

5 0

Answer:

Step-by-step explanation:

The input is x on the first row

The output is f(x) on the second row

a) to determine the difference of outputs of any two inputs that are 1 unit apart, let us take x = -4 and x = -5

The outputs at these inputs are -3 and - 11 respectively

Difference in output = - 3 - - 11 = 8

b) to determine the difference of outputs of any two inputs that are 2 units apart, let us take x = -3 and x = -5

The outputs at these inputs are 5 and - 11 respectively

Difference in output = 5 - - 11 = 16

c)to determine the difference of outputs of any two inputs that are 3 units apart, let us take x = -2 and x = -5

The outputs at these inputs are 13 and - 11 respectively

Difference in output = 13 - - 11 = 24

d) as the difference in interval of the input increased by 1, the difference in outputs of the corresponding inputs increased by 8. A constant increment in the interval between inputs led to a constant increment in the intervals of the corresponding outputs

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Find the population mean or sample mean as indicated. Sample: 19, 15, 6, 11, 24 Compute the sample mean for this data set. Selec

yKpoI14uk [10]

Answer:

$\overline{x}=15$

Step-by-step explanation:

the mean is given by:

$\overline{x} = \dfrac{\sum\limits_{i=1}^n x_i}{n} \quad\text{or}\quad \dfrac{\text{sum of all items}}{\text{number of items}}$

In our case this is:

$\overline{x} = \dfrac{19+15+6+11+24}{5} \Rightarrow \dfrac{75}{5}\\\\\overline{x} = 15\\\\$

side note: the main difference between sample mean and population mean is in the 'context'. However, the method to calculate them is the same.

By context I mean: if this the items are taken from some larger category for example: the ages of a few 'students' from a 'class'. Here 'students' are the sample from a larger set that is 'class'. The mean of the 'few students' will be called sample mean. In contrast, if we take the mean of the ages of the whole class then this is called population mean. (population mean == mean of the whole set)

In our case we aren't told exactly where these numbers come from, is this the whole set or a sample from it, the lack of context allows us to assume that the mean can either be population mean or sample mean. So we can safely use any symbol $\mu$ or $\overline{x}$ .