Math Homework with answer

Question 1




Answer

f (x) = 𝑥 2 − 𝑥

The slope of the tangent line is given by f’(x).
𝑑[𝑥 2 −𝑥]
f’(X) =
𝑑𝑥

𝑑𝑥 2 𝑑𝑥
= -
𝑑𝑥 𝑑𝑥

=2x-1

The slope of the tangent line at the point x= 2 is given by f’ (2).

Slope= f’(2)

=2×2-1

=3

The correct option is given by

o b.3

,Question 2




Answer

Given,

E(X) = 6

Np = 6

Var(X) = 4.2

Npq = 4.2

So,

𝑛𝑝 6
=
𝑛𝑝𝑞 4.2

We get,

q= 0,7

p=1-q=0.3

Therefore,

P=0.3

And

, 6
N= =20
0.3

So, n=20 and p=0.3

P(X ≤ 6) = P( X = 1) + P( X = 2 ) + P( X = 3 ) + P( X = 4 ) + P( X = 5 ) + P( X
=6)

We use the formula
𝑛
P(X= r) = ( ) 𝑝𝑟 𝑞 𝑛−𝑟
𝑟

Therefore,
0.0798
P(X=0) =
100

0.684
P(X=1) =
100

2.7846
P(X=2) =
100

7.16
P(X=3) =
100

13.042
P(X=4) =
100

17.886
P(X=5) =
100

19.164
P(X=6) =
100

60.8004
P(X≤ 6) =
100

P(X≤ 6) = 0.608

ANS -> TRUE(T)