There is only 1 remaining side
We have 2 sides and an included angle, we use the Law of Cosines to solve the third side:
c^2 = a^2 + b^2 -2ab *cos(C)
c^2 = .5^2 + .333333333...^2 - 2 * .5 * .3333333... * cos (95)
c^2 = .25 + .1111111111111111... -2*.5*.3333333333...* -0.087156
c^2 = 0.3611111111 + 0.029052
c^2 = 0.3901631111
c = 0.6246303796
Answer:
a₄₂ = 107
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₂₇ = 66 , then
a₁ + 26d = 66 , that is
- 12 + 26d = 66 ( add 12 to both sides )
26d = 78 ( divide both sides by 26 )
d = 3
Then
a₄₂ = - 16 + (41 × 3) = - 12 + 123 = 111
Answer:
A. 0.47 ; B. 0.40 ; C. 0.73 ; D. 0.23 & 4.26
Step-by-step explanation:
- Total Animals = Total Possible Outcomes = 8 + 12 + 6 + 5 + 11 = 42
- Probability = No. of Possible Outcomes / No.of total outcomes
- Odds in favour of event = Prob (Event) / Prob (No Event) ; Odds in against event = Prob (No Event) / Prob (Event)
A. Probability of choosing a Cat = All no. of cats / Total no. of animals
= ( 8 + 12 ) / 42 = 20 / 42 = 0.47
B. Probability of choosing a Common Cat or a Labrador Retriever :-
No. of common cats + no.of labrador retrievers / Total Animals
= (12 + 5) / 42 = 17 / 42 = 0.40
C. Probability of selecting non 'mixed breed' dog :-
No. of animals except mix breed dogs / Total Animals
= ( 8 + 12 + 6 + 5 ) / 42 = 31 / 42 = 0.73
D. Probability of choosing Siamese cat = Siamese Cat / Total Animals = 8 / 42 = 0.19 ; Probability Not choosing Siamese Cat = 1 - Prob (Siamese Cat) = 1- 0.19 = 0.81.
Odds in favour of choosing Siamese Cat :-
Prob (Siamese cat) / Prob (Not Siamese Cat) = 0.19 / 0.81 = 0.23
Odds against choosing Siamese Cat :-
Prob (Not Siamese Cat) / Siamese Cat = 0.81 / 0.19 = 4.26
C is the y intercept of the line
Answer:
8.50 cm²
Step-by-step explanation:
The dimension of each square is given as 0.5cm by 0.5cm
The area of the a square is, a²
Where, a = side length
Area of each square = 0.5² = 0.25cm
The number of blue colored squares = 34
The total area of the blue colored squares is :
34 * 0.25 = 8.50cm²
