Yes I think you are correct.
Answer:
30189.155
Step-by-step explanation:
Recall the compound interest formula :
A = P(1 + r/n)^nt
P = principal = 10000
r = rate = 3.7% = 0.037
n = quarterly = 4
t = 30
A = 10000(1 + 0.037/4)^30*4
A = 10000(1 + 0.00925) ^120
A = 10000(1.00925)^120
A = 10000 * 3.0189155
A = 30189.155
<u>Given</u>:
The arithmetic sequence is represented in the table.
The general form of the arithmetic sequence is given by

We need to determine the value of the missing term.
<u>First term:</u>
From the table, we need to determine the first term of the arithmetic sequence.
From the table, the value of the first term is 3.
Thus, 
Hence, the first term is 3.
<u>Common difference:</u>
From the table, we can determine the common difference of the arithmetic sequence.
Thus, we have;
12 - 3 = 9
Hence, the common difference is 
<u>Value of the missing term:</u>
The value of the term 45 can be determined by substituting n = 45 in the general form 
Thus, we have;




Hence, the value of the term 45 is 399.
Thus, the value of the missing term is 399.
Answer:
3003
Step-by-step explanation:
The number of differents menus containing 10 main courses that the restaurant can make if it has 15 main courses from which to chose is calculated through the combination: 15C10. The formula of the combination is: nCr = n! / ((r!) x(n - r)!)
Where r=10 and n=15
Substituting the values to the equation: 15C10 = 15! / (10!)x(10 - 5)! = 3003
Then there are 3003 different menus that a restaurant can makeif it has 15 main courses from which to choose.