Answer:
The explicit rule for the arithmetic sequence is given by:
......[1]
where,
is the first term
n is the number of terms and
d is the common difference for two consecutive terms.
As per the statement:
A recursive rule for an arithmetic sequence is:


The recursive formula for the arithmetic sequence is given by:

then;
On comparing we get;
d = -3
Substitute the given values in [1] we have;

⇒
Therefore, the explicit rule for this sequence is, 
Answer:
50 nickels, 20 quarters.
Step-by-step explanation:
System of equations (q = # of quarters, n = # of nickels):
<em>q + n = 70, 0.25q + 0.05n = 7.50</em>
the first equation can be changed to q = 70 - n, so we are able to <em>substitute q with 70 - n</em>.
So, it will look like <em>0.25*70 - 0.25n + 0.05n = 7.50</em>. This can be simplified to <em>0.2n = 10</em>, which means that n = 50.
Knowing that we can solve <em>q + 50 = 70</em>, which means that q = 20.
Answer:
a) 0.19
b) 0.9689
c) ≈ 6 cars
Step-by-step explanation:
Rate at which cars arrive = 12 cars/hour = 1/5 cars/minute
time needed by each car to complete ATM transaction = 6 minutes = 1/6 car/minute
capacity of lane = 10 car
n = 10
<u>a) Calculate the probability of an arriving not using the ATM because the line is full</u>
p ( not using the ATM ) = 0.19
<u>b) probability that a car will not be able to use the ATM machine immediately on arrival</u>
P ( n > 0 ) = 1 - Po
= 1 - 0.0311 = 0.9689
<u>c) Average number of cars in the lane </u>
Lq = 5.74 ≈ 6 cars
attached below is the detailed solution
Answer:
if it is an equilateral triangle then it should have the same measurements on each side.
Step-by-step explanation:
An equilateral triangle is equal on all three sides, meaning if one side is 24, the rest will be the same/equal.