For the linear function (x)=7x-2, which of the following is true?
1)it has a slope of 7 and a y-intercept of -2.
2)it has a slope of -2 and a y-intercept of 7.
3)it has a slope of 7x and a y-intercept of -2.
4)it has a slope of -2 and a y-intercept of 7x.

Correct option is : 1) It has a slope of 7 and a y-intercept of -2.

Step-by-step explanation:

The given function is :

                   .....1

The general form of equation of a linear function is given by :

                 .....2

where, y is the dependent variable, x is the independent variable, m is the slope of the function and c is the y-intercept.

On comparing equations 1 and 2, we get:

m = 7,c = -2

Thus, we can conclude that : Slope of equation is 7 and y-intercept is -2.

Thus, only option 1 satisfies the given solution.

(a)7.185

(b)0.000371

(c) 0.019

(d)Sample variance and Sample standard deviation

Step-by-step explanation:

We are given the following sample data.

7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.17, 7.18.

(a) Calculate the sample mean. Round your answer to 3 decimal places.

The formula for sample mean =

Sum of terms/Number of terms

= 7.15 + 7.20+ 7.18+7.19+7.21+7.20+7.17+ 7.18/8

= 57.48/8

= 7.185

(b) Calculate the sample variance. Round your answer to 6 decimal places.

The formula for sample Variance =

(x - mean)²/n - 1

n = 8

Sample variance = (7.15 - 7.185)² + (7.20-

7.185)²+ (7.18 -7.185)² + (7.19 -7.185)² + (7.21 - 7.185)² + (7.20 - 7.185)² + (7.17 - 7.185)² + (7.18 - 7.185)² /8 - 1

= 0.001225 + 0.000225+ 0.000025+ 0.000025 + 0.000625 + 0.000225 + 0.000225 + 0.000025/7

= 0.0026/7

= 0.000371428571

Approximately to 6 decimal places = 0.000371

(c) Calculate the sample standard deviation. Round your answer to 3 decimal places.

The formula for Sample Standard Deviation = √Sample variance

= √0.000371428571

= 0.01927248223

To 3 decimal places = 0.019

(d) Which of the following are potential major sources of variability in the experiment

Sample variance

Sample standard deviation