Answer:
Radius= 2r
Step-by-step explanation:
Surface area of hemisphere
=2 x 22/7 x (2r)^2
=44/7 x 4 r^2
=174/7 r^2
=25.14 r^2
Answer: 180 people
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Answer:
The new function is g(x) = x² +1
Step-by-step explanation:
<u><em>Explanation:-</em></u>
Given that the function f(x) = x²
From graph ,
The parabola y = x² is shifting to up with '1' units
y = x² +1
The new function is g(x) = x² +1
<u><em>Verification:-</em></u>
y = x²+1
Put x=0 ⇒ y =1
The point (0,1) lies on the parabola y = x²+1
similarly put x =1 and y = 2
The Point (1,2) lies on the Parabola y = x²+1
∴ The new graph y = x²+1
Answer:
341
Step-by-step explanation:
The number of people who know the art of quilting in each successive generation is
1, 4, 16, …
These numbers represent a geometric sequence where each term has the form
aₙ = a₁rⁿ⁻¹
In your sequence, a₁ = 1 and r = 4.
Then, the formula for your sequence is
aₙ = 4ⁿ⁻¹
Sum over five generations
The formula for the sum of the first n terms of a geometric series is
Sum = a₁[(1 - rⁿ)/(1 - r)]
Sum = 1[(1 - 4⁵)/(1 - 4)
= (1 - 1024)/(-3)
= -1023/-3
= 341
If the process continues for five generations, 341 people will know the art of quilting.
We can use the binomial theorem to find the probability that 0 out of the 15 samples will be defective, given that 20% are defective.
P(0/15) = (15C0) (0.2)^0 (1 - 0.2)^15 = (1)(1)(0.8)^15 = 0.0352
Then the probability that at least 1 is defective is equal to 1 - 0.0352 = 0.9648. This means there is a 96.48% chance that at least 1 of the 15 samples will be found defective. This is probably sufficient, though it depends on her significance level. If the usual 95% is used, then this is enough.
