Please show work for both problems
1 answer:
(1) The value of x is 25
(2) The measure of ∠CBD is 60°
Explanation:
(1) The given two angles are vertical angles. Since, vertical angles are equal, we can add the two angles to determine the value of x.
Thus, we have,
Subtracting 5x from both sides, we have
Adding 10 to both sides , we have,
Thus, the value of x is 25.
(2) It is given that the measure of ∠ABC = (x+7)° and ∠CBD = (2x+14)°
Since, these two angles are supplementary angles and supplementary angles add upto 90°
Thus, we have,
Simplifying, we get,
Thus, substituting the value of x in ∠CBD = (2x+14)° to determine its value.
Thus, the measure of ∠CBD is 60°
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Answer:
a) There is a 16.6% probability that doubles were rolled.
b) Given that the roll resulted in a sum of 6 or less, there is a 20% probability that doubles were rolled.
c) There is a 30.55% probability that at least one die is a 1.
Step-by-step explanation:
The probability formula is the number of desired outcomes divided by the number of total outcomes.
(a) Find the probability that doubles were rolled. (i.e. the two outcomes are equal)
There are six desired outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)
There are 36 total outcomes. So:
There is a 16.6% probability that doubles were rolled.
(b) Given that the roll resulted in a sum of 6 or less, find the conditional probability that doubles were rolled.
The following rolls result in a sum of 5 or less:
(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1)
So, there are 15 total outcomes.
3 of them are doubled: (1,1), (2,2), (3,3). So
Given that the roll resulted in a sum of 6 or less, there is a 20% probability that doubles were rolled.
(c) Find the probability that at least one die is a 1
The following outcomes have at least one die that is 1:
(1,1), (1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(3,1),(4,1),(5,1),(6,1)
So, there are 11 desired outcomes out of 36.
There is a 30.55% probability that at least one die is a 1.