Answer:
Step-by-step explanation:
Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year. This means that for each year, her income is 104% of the previous year. So the rate of increase is 104/100 = 1.04. This rate is in geometric progression. The formula for the sum of n terms of a geometric sequence is expressed as
Sn = a(r^n - 1)/r-1
Where
Sn is the nth term
a is the first term
n is the number of terms.
r is the rate or common ratio
From the information given,
a = 33000
r = 1.04
The formula for Alexis total earning over n years will be
Sn = 33000(1.04^n - 1)/(1.04 - 1)
Her earnings for the next 15 years would be
S15 = 33000(1.04^15 - 1)/(1.04 - 1)
S15 = 33000(0.8009) / 0.04
S15 = $668167.50
Answer:
15km
Step-by-step explanation:

Answer:
2u-1/3v = (4, -2)
Step-by-step explanation:
Given vector u and v,
v = (-6, -6)
u = (1, -2)
2*u = (2*1, -2*2) = (2, -4)
1/3*v = (1/3*-6, 1/3*-6) = (-2, -2)
So, 2u = (2, -4) and 1/3*v = (-2, -2)
We have 2u-1/3v = (2, -4) - (-2, -2) = (4, -2)
Therefore, 2u-1/3v = (4, -2)
Answer:
a) 

And we can use the complement rule and we got:


And replacing we got:

b) 

And we can use the complement rule and we got:


And replacing we got:

Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the length of time waiting to be seated of a population, and for this case we know the distribution for X is given by:
Where
and
Part a
For this cae we want to find this probability:

And if we use the conditional probability formula we got:

We can solve the problem using the z score formula given by:



And we can use the complement rule and we got:


And replacing we got:

Part b

We can solve the problem using the z score formula given by:



And we can use the complement rule and we got:


And replacing we got:

Answer:
Applying the Pythagorean theorem, the diagonal is calculated by:
D = sqrt(40^2 + 9^2) = 41
Hope this helps!
:)