Andy claims that his bird can do single-digit multiplication. He shows the bird 12 cards with simple multiplication problems tha
2 answers:
Answer:
The expected number of cards is 6.
Step-by-step explanation:
We know that,
'Expected value = Total number of trials × Probability of each trial'
Let C is the event of correct cards and C' is the event of incorrect cards.
Given,
Total number of cards = 12
Also, the correctness of the card is 9 times out of 12,
Thus, the number of correct cards,
n(C) = 9,
⇒ The number of incorrect cards,
n(C') = 12 - 9 = 3
Also, A card can be can be correct or incorrect,
Thus, The probability of correct card,
And, the probability of incorrect card,
Thus, the expected number of cards = expected number of correct card + expected number of incorrect card
= n(C) × P(C) + n(C') × P(C')
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Answer:
The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.
Approximation at points (1.1,1.9) is 0.7
Step-by-step explanation:
Given:
Tangent plane to a surface z=5x+2y-10 as the function at point (1,2)
To find :
f(x,y) at (1,2)
partial derivatives of function w.r.t. (x and y) and value of that function at given points.
Solution:(refer the attachment also)
Now we know that
the equation of tangent plane at given points to the surface is given by,
f(x1,y1,z1) and z=f(x,y)
z-z1=Fx(x1,y1)*(x-x1)+Fy(x1,y1)*(y-y1)
here Fx(x1,y1) and Fy(x1,y1) are the partial derivatives of x and y.
now
taking partial derivative w.r.t. x we get
Fx(x1`,y1)=
=5.
Then w.r.t y we get
Fy(x1,y1)=
=2.
The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.
Using the Linearization or linear approximation we get
L(x,y)=f(x1,y1)+Fx(x,y)*(x-x1)+Fy(x,y)(y-y1)
=-1+5(x-1)+2(y-2)
=5x+2y-10
Approximation at F(1.1,1.9)
=5(1.1)+2(1.9)-10
=5.5+3.8-10
=0.7
Approximation at points (1.1,1.9) is 0.7
