Answer:
<h3>
a₁₈ = 10</h3>
Step-by-step explanation:
aₙ₊₁ = aₙ + d
a₁₉ = a₁₈ + d
- 7 = a₁₈ + (-17)
a₁₈ = - 7 +17
a₁₈ = 10
Answer:
The probability that the good exam belongs to student <em>X</em> is 0.8571.
Step-by-step explanation:
It is provided that the probability that <em>X</em> did well in the exam is, P (X) = 0.90 and the probability that <em>X</em> did well in the exam is, P (Y) = 0.40,
Compute the probability that exactly one student does well in the exam as follows:
![P(Either\ X\ or\ Y\ did\ well)=P(X\cap Y^{c})+P(X^{c}\cap Y)\\=P(X)P(Y^{c})+P(X^{c})P(Y)\\=P(X)[1-P(Y)]+[1-P(X)]P(Y)\\=(0.80\times0.60)+(0.20\times0.40)\\=0.56](https://tex.z-dn.net/?f=P%28Either%5C%20X%5C%20or%5C%20Y%5C%20did%5C%20well%29%3DP%28X%5Ccap%20Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%5Ccap%20Y%29%5C%5C%3DP%28X%29P%28Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%29P%28Y%29%5C%5C%3DP%28X%29%5B1-P%28Y%29%5D%2B%5B1-P%28X%29%5DP%28Y%29%5C%5C%3D%280.80%5Ctimes0.60%29%2B%280.20%5Ctimes0.40%29%5C%5C%3D0.56)
Then the probability that <em>X</em> is the one who did well in the exam is:
![P(X\ did\ well\ in\ the\ exam)=\frac{P(X\cap Y^{c})}{P(X\cap Y^{c})+P(X^{c}\cap Y)}\\ =\frac{P(X)[1-P(Y)]}{P(X\cap Y^{c})+P(X^{c}\cap Y)} \\=\frac{0.80\times0.60}{0.56}\\=0.857143\\\approx0.8571](https://tex.z-dn.net/?f=P%28X%5C%20did%5C%20well%5C%20in%5C%20the%5C%20exam%29%3D%5Cfrac%7BP%28X%5Ccap%20Y%5E%7Bc%7D%29%7D%7BP%28X%5Ccap%20Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%5Ccap%20Y%29%7D%5C%5C%20%3D%5Cfrac%7BP%28X%29%5B1-P%28Y%29%5D%7D%7BP%28X%5Ccap%20Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%5Ccap%20Y%29%7D%20%5C%5C%3D%5Cfrac%7B0.80%5Ctimes0.60%7D%7B0.56%7D%5C%5C%3D0.857143%5C%5C%5Capprox0.8571)
Thus, the probability that the good exam belongs to student <em>X</em> is 0.8571.
Function P . . . . . y = 5x + 3
Function Q . . . . . y = 2x + 4
Function P rate of change = 5
Function Q rate of change = 2
The first one is => 3 <= more than second one.
Answer:
5 = side a
3 = side c
angle B = 62 degrees
JK is side b
Use the Law of Cosines to find the length of side b.
b^2 = a^2 + c^2 − 2ac cos(B)
b^2 = (5^2 + 3^2) − ( 2 x 5 x 3) cos(62°)
b^2 = (25 + 9) − 30 x 0.469
b^2 = 34 - 30 x 0.469
b^2 = 34 - 14.084
b^2 = 19.916
b = √19.916
b = 4.463
Rounded to the nearest tenth is 4.5 mm.
Hope this helps!
Step-by-step explanation: