Yeah you did it right but good job!
Answer:
A= 57° , a= 7.79 and c = 14.30
Step-by-step explanation:
In a given right triangle,
We have, b =12 ,B =33° and C =90°
We can find Angle A.
Angle sum property of triangle:
i.e A + B + C = 180°
A + 33° + 90° = 180°
A = 57°
Next, by using trigonometry
tanB = Perpendicular /Base = a /b
Here B =33° , a = ? , b = 12
So, tan 33° = a/12
0.6494 = a/12
a = 7.79
So we got a and b. By using Pythagoras theorem we determine c.
c^2 = a^2 + b^2
c^2 = 7.79^2 + 12^2
c = √(2046841) = 14.30
First one is -1. The second one is 1/2.
Answer:
In the photo
Step-by-step explanation:
If A and B are two different events then, P(A U B) = P(A) + P(B) - P(A ∩ B)
Explanation of the formula:
If you look at the Venn Diagram, if you add 2 areas : P(A) and P(B), P(A ∩ B) is overlapping. This is why you should remove P(A ∩ B).
However, in this case, we should find P(A ∩ B) and all the other values are given in the question. Hence, we implement them and find P(A ∩ B).
Answer:
proportion of gamers who prefer console does not differ from 29%
Step-by-step explanation:
Given :
n = 341 ; x = 95 ; Phat = x / n = 95/341 = 0.279
H0 : p = 0.29
H1 : p ≠ 0.29
The test statistic :
T = (phat - p) ÷ √[(p(1 - p)) / n]
T = (0.279 - 0.29) ÷ √[(0.29(1 - 0.29)) / 341]
T = (-0.011) ÷ √[(0.29 * 0.71) / 341]
T = -0.011 ÷ 0.0245725
T = - 0.4476532
Using the Pvalue calculator from test statistic score :
df = 341 - 1 = 340
Pvalue(-0.447, 340) ; two tailed = 0.654
At α = 0.01
Pvalue > α ; We fail to reject the null and conclude that there is no significant evidence that proportion of gamers who prefer console differs from 29%