Which number line shows the sum of -8, 4, and -2?
1 answer:
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Answer:
420 meters
Step-by-step explanation:
Q. Benjamin is riding a unicycle. The tire of his unicycle has a circumference of 2.8 m, and the tire revolves 1.5 times per second. What is the distance Benjamin travels in 100 seconds?
<u>Given</u>:
Circumference of circular tire = 2.8 meters
Tire revolves per second = 1.5 times
<u>Question asked:</u>
What is the distance Benjamin travels in 100 seconds?
<u>Solution:</u>
Circumference of circular tire means distance covered by the unicycle's tire when it revolves 1 time that is 2.8 meters.
<em><u>Now, by unitary method:</u></em>
In 1 second, tire revolves = 1.5 times
In 100 seconds, tire revolves = 1.5 100
= 150 times
Distance covered by the tire when it revolves 1 time = 2.8 m
Distance covered by the tire when it revolves 150 times = 2.8 150
= 420 meters
Therefore, Benjamin travels 420 meters in 100 seconds.
Answer:
(a) The probability that proportion of heads is between 0.30 and 0.70 is 1.
(b) The probability that proportion of heads is between 0.40 and 0.65 is 0.9759.
Step-by-step explanation:
Let <em>X</em> = number of heads.
The probability that a head occurs in a toss of a coin is, <em>p</em> = 0.50.
The coin was tossed <em>n</em> = 100 times.
A random toss's result is independent of the other tosses.
The random variable <em>X</em> follows a Binomial distribution with parameters n = 100 and <em>p</em> = 0.50.
But the sample selected is too large and the probability of success is 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of <em> </em>(sample proportion of <em>X</em>) if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
Check the conditions as follows:
Thus, a Normal approximation to binomial can be applied.
So,
(a)
Compute the probability that proportion of heads is between 0.30 and 0.70 as follows:
Thus, the probability that proportion of heads is between 0.30 and 0.70 is 1.
(b)
Compute the probability that proportion of heads is between 0.40 and 0.65 as follows:
Thus, the probability that proportion of heads is between 0.40 and 0.65 is 0.9759.