height of ladder = 12 feet
let x be the distance from the wall to the base of the ladder then
height = 2x + 2
Using Pythagoras' identity
(2x + 2)² + x² = 13² ( expand bracket and simplify left side )
4x² + 8x + 4 + x² = 169 ( rearrange into standard form )
5x² + 8x - 165 = 0 ← in standard form
consider the factors of the product 5 × - 165 = - 825
which sum to the coefficient of the x- term + 8
These are + 33 and - 25
split the middle term using these factors
5x² - 25x + 33x - 165 = 0 ( factor by grouping )
5x(x - 5) + 33(x - 5) = 0 ( take out the common factor (x - 5) )
(x - 5)(5x + 33) = 0
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
5x + 33 = 0 ⇒ x = -
but x > 0 ⇒ x = 5
Hence height of ladder = (2 × 5 ) + 2 = 12 feet
Both of the fractions have different numerators.
Answer:
The percentage that of people who gave the movie a rating between 6.8 and 8.8
<em>P(6.8≤X≤8.8) = 83.9≅ 84 percentage</em>
Step-by-step explanation:
<u> Step(i):-</u>
Mean of the Population = 8.3 points
Standard deviation of the Population = 0.5 points
Let 'X' be the random variable in normal distribution
<em>Let X = 6.8</em>
Let X = 8.8
The probability that of people who gave the movie a rating between 6.8 and 8.8
<em>P(6.8≤X≤8.8) = P(-3≤Z≤1)</em>
= P(Z≤1)- P(Z≤-3)
= 0.5 + A(1) - ( 0.5 -A(-3))
= A(1) + A(3) (∵A(-3)=A(3)
= 0.3413 +0.4986 (∵ From Normal table)
= 0.8399
<u><em>Conclusion:-</em></u>
The percentage that of people who gave the movie a rating between 6.8 and 8.8
<em>P(6.8≤X≤8.8) = 83.9≅ 84 percentage</em>
B) 1/5.....................