Answer:
.
Step-by-step explanation:
The equation that represents the function can be written in the slope-intercept form,
.
To create an equation, we need to find the slope (m) and the y-intercept (b) of the function.
First, calculate the slope of the function using two points, (1, 12) and (2, 19).

Next, find b by substituting x = 1, f(x) = 12, and m = 7 into
.


Subtract 7 from each side



Substitute m = 7 and b = 5 into
.
✅Thus, the equation that represents the function would be:
.
Answer: 6
Step-by-step explanation:
Answer:
The correct option is (a) 0.9780.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:

The standard deviation of this sampling distribution of sample proportion is:

As the sample selected is quite large, i.e. <em>n</em> = 110 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample proportion by a Normal distribution.
The mean and standard deviation are:

Compute the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 as follows:


*Use a <em>z</em>-table.
Thus, the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 is approximately equal to 0.9780.
The correct option is (a).
Answer:

Any number multiplied by 2 is even, therefore 2(2n + 16) is even.
If 2(2n + 16) is even, then adding 1 to this makes it odd.
Thus proving that the given expression is an odd number for all 