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The value of x is 28
Solution:
The approximate image of the question is attached below.
Given data:
The angles of the triangle are x°, (2x + 5)° and (3x + 7)°.
By triangle sum theorem,
<em>Sum of all the angles of the triangle = 180°</em>
x° + (2x + 5)° + (3x + 7)° = 180°
x° + 2x° + 5° + 3x° + 7° = 180°
6x° + 12° = 180°
Subtract 12° from both sides of the equation, we get
6x° = 168°
Divide by 6° on both sides of the equation, we get
x° = 28°
x = 28
The value of x is 28.
The tree diagram is constructed and attached as an image below.
80% of the participants received medication, this means 20% received placebo. Among those who received medication, 76% reported improvement, this means rest 24% reported no improvement. Among those who received Placebo, 62% reported no improvement, this means rest 38% reported improvement.
The probability of P(Placebo and Improvement) will be = 20% x 38%
P(Placebo and Improvement) = 0.20 x 0.38 = 0.076 = 7.6%
This means there is 7.6% probability that those who received Placebo reported Improvement.
80% of the participants received medication, this means 20% received placebo. Among those who received medication, 76% reported improvement, this means rest 24% reported no improvement. Among those who received Placebo, 62% reported no improvement, this means rest 38% reported improvement.
The probability of P(Placebo and Improvement) will be = 20% x 38%
P(Placebo and Improvement) = 0.20 x 0.38 = 0.076 = 7.6%
This means there is 7.6% probability that those who received Placebo reported Improvement.