Answer:
x = -11
Step-by-step explanation:
Let the Triangle be named 'ABC'
In Triangle ABC,
∠A = x + 51
∠B = 80 (Intersecting lines, Vertically opposite Angles)
∠C = 60 (Intersecting lines, Vertically opposite Angles)
∠A + ∠B + ∠C = 180 (Sum of angles of Triangle = 180)
x + 51 + 80 + 60 = 180
=> x + 191 = 180
=> x = 180 - 191
=> x = -11
Answer:
P ( x ) = -0.7 (x - 2)²(x + 3)
Step-by-step explanation:
<u>We are given</u> :
P ( x ) , has a root of multiplicity 2 at x = 2
and a root of multiplicity 1 at x = − 3
Then
P ( x ) = a (x - 2)²(x + 3) ; where ‘a’ is a real number.
P ( x ) = a (x - 2)²(x + 3)
= a (x² - 4x + 4)(x + 3)
= a [x³ - 4x² + 4x + 3x² - 12x + 12]
P (0) = -8.4
⇔ a [(0)³ - 4(0)² + 4(0) + 3(0)² - 12(0) + 12] = -8.4
⇔ 12 a = -8.4
⇔ a = (-8,4) ÷ 12
⇔ a = -0,7
<u>Conclusion</u> :
P ( x ) = -0.7 (x - 2)²(x + 3)
Answer:
Binomial distribution requires all of the following to be satisfied:
1. size of experiment (N=27) is known.
2. each trial of experiment is Bernoulli trial (i.e. either fail or pass)
3. probability (p=0.14) remains constant through trials.
4. trials are independent, and random.
Binomial distribution can be used as a close approximation, with the usual assumption that a sample of 27 in thousands of stock is representative of the population., and is given by the probability of x successes (defective).
P(x)=C(N,x)*p^x*(1-p)^(n-x)
where N=27, p=0.14, and C(N,x) is the number of combinations of x items out of N.
So we need the probability of <em>at most one defective</em>, which is
P(0)+P(1)
= C(27,0)*0.14^0*(0.86)^(27) + C(27,1)*0.14^1*(0.86^26)
=1*1*0.0170 + 27*0.14*0.0198
=0.0170+0.0749
=0.0919
In mathematics. 256 is a composite number, with the factorization 256 = 28, which makes it a power of two. 256 is 4 raised to the 4th power, so in tetration notation 256 is 24.
