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 = ![\left[\begin{array}{ccc}7&1&0\\7&0&1\\7&-1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%261%260%5C%5C7%260%261%5C%5C7%26-1%261%5Cend%7Barray%7D%5Cright%5D)
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.
Given:
The cost of each carnival ticket is $5.
To find:
The equation, table of values and graph for the given problem.
Solution:
Let x be the number of tickets and y be the total money spent on tickets.
Cost of one ticket = $5
Cost of x tickets = $5x
So, total cost is
The required equation is .
At x=1,
At x=2,
At x=3,
The required table of values is
x y
1 5
2 10
3 15
So, the required table of values is table A.
From the above table, it is clear that the graph passes through the point (1,5), (2,10) and (3,15). The graph B passes through these points.
So, the required graph is graph B.
Since the required answers are , table A, graph B, therefore the correct option is B.
<u>Answer:</u>
The probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made is 0.7744
<u>Solution:</u>
Total number of coils = number of good coils + defective coils = 88 + 12 = 100
p(getting two good coils for two selection) = p( getting 2 good coils for first selection ) 
p(getting 2 good coils for second selection)
p(first selection) = p(second selection) = 
Hence, p(getting 2 good coil for two selection) = 
Answer:
C
Step-by-step explanation:
We are given that FGH is a triangle, which means that...
Angle F + Angle G + Angle H = 180
Start by substituting the given angle measurements into the equation:
4x+2+13x-7+3x+5=180
Combine like terms
20x=180
Divide both sides by 20 to isolate x
x=9
Plug 9 back in for x to solve for each angle
Angle F = 4(9)+2=36+2=38
Angle G = 13(9)-7=117-7=110
Angle H = 3(9)+5=27+5=32
Well since the pattern is odd, even, odd, even you are just as likley to pull on odd (<span>not evenly divisible by 2) numebr as an even number, so the option is C.
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