All these are true when X and Y are independent events:
1) The occurrence or lack of event X does not influence the occurrence of event Y, and the occurrence or lack of event Y does not influence the occurrence of event X.
2) P(X∩Y) = P(X) * P(Y)
3) P(X | Y) = P(X).... this is the probability of X given Y is equal to the probability of X.
4) P (Y | X) = P(Y)
5) P(A∪B) = P(A) + P(B) - P(A∩B)
Answer:
B. 1/25
Step-by-step explanation:
This question asks us to find (-2), or f(x) when x is equal to -2.
We know that f(x)=5^x. We also know that we are trying to find f(-2). Therefore, we must substitute -2 in for x.
f(x)=5^x
x= -2
f(-2)= 5^-2
Negative exponents follow the rule:
x^-b= 1/x^b
Rewrite the exponent according to this rule.
5^-2=1/5^2
f(-2)= 1/5^2
Evaluate the exponent in the denominator.
5^2=5*5=25
f(-2)=1/25
f(-2) is equal to 1/25, therefore B is the correct answer.
Answer:
\sqrt(217)
Step-by-step explanation:
(19)^2=(12)^2
361 - 144 + 217
\sqrt(217)
The answer is A because a sample of 500 boys and girls from middle schools across the state represents the population.
This is the concept of sinusoidal, to solve the question we proceed as follows;
Using the formula;
g(t)=offset+A*sin[(2πt)/T+Delay]
From sinusoidal theory, the time from trough to crest is normally half the period of the wave form. Such that T=2.5
The pick magnitude is given by:
Trough-Crest=
2.1-1.5=0.6 m
amplitude=1/2(Trough-Crest)
=1/2*0.6
=0.3
The offset to the center of the circle is 0.3+1.5=1.8
Since the delay is at -π/2 the wave will start at the trough at [time,t=0]
substituting the above in our formula we get:
g(t)=1.8+(0.3)sin[(2*π*t)/2.5]-π/2]
g(t)=1.8+0.3sin[(0.8πt)/T-π/2]
