Math/Algebra - please help!?

Question

please help with answers/solutions:

1. Park rangers catch, tag, and release 200 deer back into a wildlife refuge. Two weeks later they catch a sample of 150 deer, of which 5 are tagged. Assuming that the ratio of tagged deer in the sample holds for all deer in the refuge, how many deer are there in the park?

2. The term grade is used to describe the inclination of a road. A 7% grade means that for every horizontal distance of 100feet, the road rises or drops 7 feet. A road rises 50 feet vertically over a horizontal distance of 625 feet. Find the grade of the road.

3.The temperature, t, in degrees Celsius, inside the earth is a function of depth below the surface, d, in kilometers. At the surface, the temperature is 20 celsius. THe temperature increases by 10 celsius for each kilometer of depth. what is the temp at 30 km below surface?

4. a car purchased for 12000 has a loss in value of $1250 per year. write an equation that models the value, v of the car after x years. ty

Answer 1

(1) 5/150 = 0.0333
200/x = 0.3333
x = 6000

(2) 50/625 = 0.08
8%

(3) t = 20 + 10(d)
t = 20 + 10(30)
t = 320

(4) v = 12000 - 1250x

Answer 2

1) The tag ratio is 5/150 = 1/30. You know that 200 deer are tagged, so the population = 20/(1/30) = 6000.

2) grade = vertical distance/horizontal distance. Just plug in the numbers.

3) Make an equation. y = -10x + 20 where y = temperature and x = distance in km. Again, plug in the numbers.

4) you know that the value = 12000 in year 0 and that one year later the value is 12000 - 1250 = 10750. This gives you two points: (0,12000) and (1,10750). Use the point-slope form to create your linear equation.

Answer 3

1. This is like saying:

200 / X = 5 / 150

200(150) = 5X

X = 6000 deer


2. 7% = 7 / 100 = 0.07 so,

X% = 50 / 625 = 0.08

X% = 8%


3. T = 20 + 10(x)

T = 20 + 10(30)

T = 320 deg. celcius


4. V = 12,000 - 1250x

Answer 4

1. 5/150 = 3%
3% * Total = 500
500/3% = Total
Total = 15000

2. 50/625 = 8%

3. Surface Temp = 20 C
Temp = Surface Temp + 10C * km
Temp = 20C + 10C * 30
Temp = 320 C

4. V = 12000 - 1250x