$a_1=-9\\\\a_2=a_1-8\to a_2=-9-8=-17\\\\a_3=a_2-8\to a_3=-17-8=-25\\\\a_4=a_3-8\to a_4=-25-8=-33\\\\\text{The general term of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\a_1-first\ term\\d-common\ difference\\\\\text{We have}\ a_1=-9\ \text{and}\ d=-8.\ \text{Substitute:}\\\\a_n=-9+(n-1)(-8)=-9-8n+8=-8n-1\\\\\text{Put n = 43 and calculate}\ a_{43}\\\\a_{43}=-8(43)-1=-344-1=-345\\\\Answer:\ \boxed{?=-345}$

4 0

3 years ago

The blue dot is at what value on the number line? 5

Eduardwww [97]

Answer:

value of blue dot is -6

Step-by-step explanation:

-6 is visible if you go 3 units to the left of -3. -3 - 3 = -6.

4 0

2 years ago

Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2725hours is a

Ivan

Answer:

a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

$P(X >2) = 1-P(X\leq 2) = 1-(1- e^{-0.367 *2})=e^{-0.367 *2}= 0.48$

At most 3 hours?

$P(X \leq 3) = F(3) = 1-e^{-0.367*3}= 1-0.333 =0.667$

b) What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

$P(X > 2.725 + 2*5.540) = P(X>13.62) = 1-P(X$

What is the probability that it is less than the mean value by more than one standard deviation?

$P(X$

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}$