AB = 6 cm, AC = 12 cm, CD = ?
In triangle ABC, ∠CBA = 90°, therefore in triangle BCD ∠CBD = 90° also.
Since ∠BDC = 55°, ∠CBD = 90°, and there are 180 degrees in a triangle, we know ∠DCB = 180 - 55 - 90 = 35°
In order to find ∠BCA, use the law of sines:
sin(∠BCA)/BA = sin(∠CBA)/CA
sin(∠BCA)/6 cm = sin(90)/12 cm
sin(∠BCA) = 6*(1)/12 = 0.5
∠BCA = arcsin(0.5) = 30° or 150°
We know the sum of all angles in a triangle must be 180°, so we choose the value 30° for ∠BCA
Now add ∠BCA (30°) to ∠DCB = 35° to find ∠DCA.
∠DCA = 30 + 35 = 65°
Since triangle DCA has 180°, we know ∠CAD = 180 - ∠DCA - ∠ADC = 180 - 65 - 55 = 60°
In triangle DCA we now have all three angles and one side, so we can use the law of sines to find the length of DC.
12cm/sin(∠ADC) = DC/sin(∠DCA)
12cm/sin(55°) = DC/sin(60°)
DC = 12cm*sin(60°)/sin(55°)
DC = 12.686 cm
Answer: y= 4/3x-9
Step-by-step explanation:
Answer:
5.3%
Step-by-step explanation:
The final probability is calculated by means of the quotient of the specific combinations and the total of total combinations
Let's start with the specific ones,
First the number of combinations of 4 of the 30 students getting a spot, i.e .:
A combinations are equal to:
nCx = n! / x! * (n-x)!
Replacing:
30C4 = 30! / (4! * 26!) = 27405
Segundo the number of combinations of the other audience members filling the other 4 (8-4) spots n = 110, 140 - 30
110C4 = 110! / (4! * 106!) = 5773185
Now the total combinations of possible 8 contestants from the audience
140C8 = 140! / (8! * 132!) = 2.98 * 10 ^ 12
Finally, the probability is equal to:
P = (30C4 * 110C4) / 140C8
replacing:
P = 27405 * 5773185 / 2.98 * 10 ^ 12
P = 0.053
Therefore the probability is 5.3%
Count what fraction receive Karen, James and Frank in total:
since
Karen receives - 
,
James receives - 
,
Frank receives - 
,
then 
.
All inheritance is the whole 1, then for Dan remains 
.
Answer: Dan receives one quarter of the inheritance.
Answer: .6 ft. every hour
Step-by-step explanation: when you add the amount of feet added each hour you get .6 ft.
