Answer:
Step-by-step explanation:
Given a total of 12 diesel engines
out of which 2 are defective
Company have to choose 5 good engines to ship.
Therefore no of ways in good engines are selected is
no of ways in which any 5 engines are selected from a total of 12 engines is
Therefore the required probability =
==0.318
Given that,
Gabe went to the amusement park with $40 to spend
His ticket cost $26.50
Therefore,
Total amount she has = $ 40
Ticket cost = $ 26.50
Let "x" be the amount he might spend on souvenirs and snacks
Therefore,
Remaining amount = 40 - 26.50
Remaining amount = 13.5
Thus she can spend less than or equal to $ 13.5 on souvenirs and snacks
Which is represented in inequality as:
Thus the inequality is found
Answer: the answer is -1
Step-by-step explanation:
Answer:
The set of polynomial is Linearly Independent.
Step-by-step explanation:
Given - {f(x) =7 + x, g(x) = 7 +x^2, h(x)=7 - x + x^2} in P^2
To find - Test the set of polynomials for linear independence.
Definition used -
A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero determinant.
The set is dependent if the determinant is zero.
Solution -
Given that,
f(x) =7 + x,
g(x) = 7 +x^2,
h(x)=7 - x + x^2
Now,
We can also write them as
f(x) = 7 + 1.x + 0.x²
g(x) = 7 + 0.x + 1.x²
h(x) = 7 - 1.x + 1.x²
Now,
The coefficient matrix becomes
A =
Now,
Det(A) = 7(0 + 1) - 1(7 - 7) + 0
= 7(1) - 1(0)
= 7 - 0 = 7
⇒Det(A) = 7 ≠ 0
As the determinant is non- zero ,
So, The set of polynomial is Linearly Independent.