What is the x-coordinate of the point that divides the directed line segment from k to j into a ratio of 1:3? x = (startfraction
1 answer:
The x-coordinate of the point which divide the line segment is 3.
Given the coordinates in the figure are J(1,-10) and K(9,2) and the 1:3 is the ratio in which the line segment is divided.
When the ratio of the length of a point from both line segments is m:n, the Sectional Formula can be used to get the coordinate of a point that is outside the line.
To find the x-coordinate we will use the formula x=(m/(m+n))(x₂-x₁)+x₁.
Here, m:n=1:3 and x₁=1 from the point J(1,-10) and x₂=9 from the point K(9,2).
Now, we will substitute these values in the formula, we get
x=(1/(1+3))(9-1)+1
x=(1/4)(8)+(1)
x=8/4+1
x=3
Hence, the x-coordinate of the point that divides the directed line segment from k to j into a ratio of 1:3 is 3 units.
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Answer:
The probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.
Step-by-step explanation:
The complete question is:
Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm Anew book will be printed on 500 sheets of this paper. Approximate the probability that the thicknesses at the entire book (excluding the cover pages) will be between 49.9 mm and 50.1 mm. Note: total thickness of the book is the sum of the individual thicknesses of the pages Do not round your numbers until rounding up to two. Round your final answer to the nearest hundredth, or two digits after decimal point.
Solution:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e S, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
And the standard deviation of the distribution of the sum of values of X is given by,
The information provided is:
As <em>n</em> = 500 > 30, the central limit theorem can be used to approximate the total thickness of the book.
So, the total thickness of the book (S) will follow N (50, 0.045²).
Compute the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm as follows:
Thus, the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.