Answer:
1
Step-by-step explanation:
7 + 2x = 9
Carry over the 7 to the 9.
2x = 9-7
2x= 2
x = 2÷2
x = 1
Answer: 0.79
Step-by-step explanation:
I will suppose that this is not a continuos probability, as the individual probabilites add up to 100%.
If you want to obtain the probability that x ≤ 0, then you need to add the probability for the cases x= 0, x = -1, x = -2 .... etc
This is:
x = 0, p = .16
x = -2, p = .33
x = -3, p = .13
x = -5, p = .17
Then, the probability where x takes a negative value or zero {-5, -3, -2, 0} is:
P = 0.16 + 0.33 + 0.13 + 0.17 = 0.79
Answer:
12.1 cm
Step-by-step explanation:
Using the law of sines, we can find angle C. Then from the sum of angles, we can find angle B. The law of sines again will tell us the length AC.
sin(C)/c = sin(A)/a
C = arcsin((c/a)sin(A)) = arcsin(8.2/13.5·sin(81°)) ≈ 36.86°
Then angle B is ...
B = 180° -A -C = 180° -81° -36.86° = 62.14°
and side b is ...
b/sin(B) = a/sin(A)
b = a·sin(B)/sin(A) = 13.5·sin(62.14°)/sin(81°) ≈ 12.0835
The length of AC is about 12.1 cm.
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<em>Comment on the solution</em>
The problem can also be solved using the law of cosines. The equation is ...
13.5² = 8.2² +b² -2·8.2·b·cos(81°)
This is a quadratic in b. Its solution can be found using the quadratic formula or by completing the square.
b = 8.2·cos(81°) +√(13.5² -8.2² +(8.2·cos(81°))²)
b = 8.2·cos(81°) +√(13.5² -(8.2·sin(81°))²) . . . . . simplified a bit