This sequence is decreasing by 3 each time. =)
Answer: You will need 3.5lbs of the cheaper candy
and 5 lbs of the expensive candy.
Step-by-step explanation:
Let x represent the number of pounds of the cheaper candy that you would need.
Let y represent the number of pounds of the expensive candy that you would need.
You would like to have 8.5 lbs of a candy mixture. It means that
x + y = 8.5
You have one type of candy that sells for $1.70/lb and another type of candy that sells for $3.40/lb. The candy mixture would sell for $2.70/lb. It means that the total cost of the mixture would be 8.5 × 2.7 = $22.95. The expression would be
1.7x + 3.4y = 22.95- - - - - - - - - - - 1
Substituting x = 8.5 - y into equation 1, it becomes
1.7(8.5 - y) + 3.4y = 22.95
14.45 - 1.7y + 3.4y = 22.95
- 1.7y + 3.4y = 22.95 - 14.45
1.7y = 8.5
y = 8.5/1.7
y = 5
x = 8.5 - y = 8.5 - 5
x = 3.5
The scientific notation is 1.92 x 10^6.
Remark
The formula for this series is
t_n = n^2 - 1
Explanation
If the series ends at 288, then the highest value n can have is 17
So you would write t_n = n^2 - 1 {n| 1 ≤ n ≤17}
If you said this to someone, you would say "t_n = n squared minus 1 where n is such that 1 is greater than or equal to 1 or less than or equal to 17"
Example
What is the 4th term in this series?
t_4 = 4^2 - 1
t_4 = 16 - 1
t_4 = 15
Answer:
Step-by-step explanation:
Use the Pythagorean Theorem to test it.
6² + 8² ≟ 10²
36+64 ≟ 100
100 = 100
It is a right triangle.
