Kara wanted to round to the nearest ten to estimate the sum of 405 and 385. She wrote 400+400=800. Do you agree with Kara? Expla
2 answers:
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Answer:
13.76 square meters
Step-by-step explanation:
The side of square is 8 meters.
So, the diameter of circle = 8 meters.
⇒ Radius = (diameter of circle) ÷ 2 = 8 ÷ 2 = 4 meters
Shaded region = Area of square - Area of circle
= (Side × Side) - π × (radius)²
= 8 × 8 - π × 4 × 4 {∵ π = 3.14 or 22÷7}
= 64 - 50.24
= 13.76 square meter
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.