Multiply 9 by 2
18 = 4
Then subtract 4 from both sides
18 - 4 = 0 will become
14 = 0
Since 14 ≠ 0, there are no solutions
6x = 16 +14
6x = 30
30 / 6 =5
x= 5
The conditional, <span>If four points are non-coplanar, then they are non-collinear, </span>is true:
This is, coplanarity is a necessary condition to be collinear.
The converse, <span>If four points are non-collinear, then they are non-coplanar, is false.
A counterexample that disproves this statement is the 4 vertices of a paralelogram, of course they are in a same plane and are not collinear.
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Answer:
a) the probability that the minimum of the three is between 75 and 90 is 0.00072
b) the probability that the second smallest of the three is between 75 and 90 is 0.396
Step-by-step explanation:
Given that;
fx(x) = { 1/5 ; 50 < x < 100
0, otherwise}
Fx(x) = { x-50 / 50 ; 50 < x < 100
1 ; x > 100
a)
n = 3
F(1) (x) = nf(x) ( 1-F(x)^n-1
= 3 × 1/50 ( 1 - ((x-50)/50)²
= 3/50 (( 100 - x)/50)²
=3/50³ ( 100 - x)²
Therefore P ( 75 < (x) < 90) = ⁹⁰∫₇₅ 3/50³ ( 100 - x)² dx
= 3/50³ [ -2 (100 - x ]₇₅⁹⁰
= (3 ( -20 + 50)) / 50₃
= 9 / 12500 = 0.00072
b)
f(k) (x) = nf(x) ( ⁿ⁻¹_k₋ ₁) ( F(x) )^k-1 ; ( 1 - F(x) )^n-k
Now for n = 3, k = 2
f(2) (x) = 3f(x) × 2 × (x-50 / 50) ( 1 - (x-50 / 50))
= 6 × 1/50 × ( x-50 / 50) ( 100-x / 50)
= 6/50³ ( 150x - x² - 5000 )
therefore
P( 75 < x2 < 90 ) = 6/50³ ⁹⁰∫₇₅ ( 150x - x² - 5000 ) dx
= 99 / 250 = 0.396
<u>Answer:</u>
Limit = -1
<u>Step-by-step explanation:</u>
We are given the following function:
We are to calculate the limit of this function as x approaches zero.
For that, we will use direct substitution method and substitute the x with 0 in the given function to calculate its limit as follows:
Therefore, the limit is -1.
