Answer: a) 1/64
Step-by-step explanation:
The quantity of distance measures in miles depends on the quantity of time measured in hours. is your best choice.
The quantity of time is an independent variable, as it continues to go no matter how much you travel, and so it is the independent.
The quantity of distance depends on your speed and time, and because it depends on these two factors, it is the dependent.
hope this helps
In a geometric sequence each number after the first is found by multiplying the previous number by a fixed number called the common ratio.
In an arithmetic sequence, each term is equal to the previous term plus or minus a constant called the common difference.
In your problem we have a sequence of numbers that appears to be decreasing in value, but on the surface it doesn't appear to be by any constant number... but if you look closely, the denominator 34 is exactly twice the other denominator 17. This would lead me to look at a common denominator to see if anything takes shape...
9/17 = 18/34
15/34
6/17 = 12/34
9/34
Now we see that each number is the previous number minus 3/34, so we have a common difference of 3/34.
This would match the definition of an arithmetic sequence and NOT a geometric sequence.
Given:
Cost to build a bookshelf = $20
Cost to build a table = $45
Amount available to spend = $600
Let x = number of bookshelves built.
Let y = number of tables built.
The total number of bookshelves and tables = 18.
Therefore
x + y = 18.
That is,
y = 18 - x (1)
The total amount available to build x bookshelves and y tables = $600. Therefore
20x + 45y = 600
That is (dividing through by 5),
4x + 9y = 120 (2)
Substitute (1) into (2).
4x + 9(18 - x) = 120
4x + 162 - 9x = 120
-5x = -42
x = 8.4
From (1),obtain
y = 18 - 8.4 = 9.6
Because we cannot have fractional bookshelves and tables, we shall test values of x=8, 9 and y=9,10 for profit
Note: The profit is $60 per bookshelf and $100 per table.
If x = 8, then y = 18-8 = 10.
The profit = 8*60 + 10*100 = $1480
If x = 9, then y = 18-9 = 9.
The profit = 9*60 + 9*100 = $1440
The choice of 8 bookshelves and 10 tables is more profitable.
Answer: 8 bookshelves and 10 tables.
