two fields at a state park on 1000 from each other on a map to to filter 8 cm apart what scale is a map using
1 answer:
Two fields at a state park are 1,000 meters from each other. On a map, the two field are 8 centimeters apart. What scale is the map using?
Answer:
Step-by-step explanation:
Given
two fields are 1000 meters from each other on a map, and the two fields are 8cm apart.
We have to express the scale of the map as unit of measure. So we need to figure out how many actual meters for each cm in the map.
If 1000 meters is equal to 8 cm, how many meters (let's calls this x) is equal to 1 cm?
Therefore, the scale is
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Answer:
- CDs — $10,000
- bonds — $80,000
- stocks — $45,000
Step-by-step explanation:
Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:
c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested
0.0275c +.045b +0.104s = 8555 . . . . . total income earned
-c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs
Using the third equation to write an expression for b, we can substitute into the other two equations.
b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b
c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation
2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify
.0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn
.0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify
Using [eq4], we can write an expression for s that can be substituted into [eq5].
s = 65000 -2c . . . . . . . expression we can substitute for s
0.0725c +0.104(65000 -2c) = 5405
-0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify
c = 1355/.1355 = 10,000
s = 65000 -2×10000 = 45,000
b = 70000 +10000 = 80,000
The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.
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Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...