The least common denominator of two fraction is the least common multiple of the two denominator.
The least common multiple of 4 and 7 is their product 28, because 4 and 7 have no common factor.
Now, we need to manipulate both fractions so that they have denominator 28. Recalling that you can multiply numerator and denominator of a fraction by the same number without affecting its value, we have
So, the sum becomes
In fact, when two fractions have the same denominator, you can directly sum their numerators.
Given:
A line passes through (-5,-3) and perpendicular to .
To find:
The equation of the line.
Solution:
We have,
On comparing this equation with slope intercept form, i.e., , we get
It means, slope of this line is .
Product of slopes of two perpendicular lines is always -1.
Slope of required line is and it passes through the point (-5,-3). So, the equation of the line is
where, m is slope.
Therefore, the equation of required line is .
Answer:
The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.
Step-by-step explanation:
The confidence interval for population variance is given as below:
We are given
Confidence level = 98%
Sample size = n = 81
Degrees of freedom = n – 1 = 80
Sample Variance = S^2 = 3.23
(By using chi-square table)
[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]
[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]
2.3004 < σ^2 < 4.8263
Lower limit = 2.30
Upper limit = 4.83.