Answer:
12
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 9)² + (y - 4)² = 36 ← is in standard form
with r² = 36 ⇒ r = = 6
diameter = 2 × r = 2 × 6 = 12
Answer:
≈ 18.8 cm
Step-by-step explanation:
The arc length is calculated as
arc = circumference of circle × fraction of circle
The central angle is equal to the arc subtending it, that is 60°
arc = 2πr ×
= 2π × 18 ×
= 36π ×
= 6π ≈ 18.8 cm ( to 1 dec. place )
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:
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.