Answer:
Number of fish in 2006 = 845 fishes (Approx.)
Step-by-step explanation:
Given;
Number of fish in 2000 = 1,150 fishes
Decreasing rate = 5% per year
Find:
Number of fish in 2006
Computation:
Exponential decay function:
F = P[1-r]ⁿ
Number of year = 2006 - 2000
Number of year = 6 year
Number of fish in 2006 = 1,150[1-5%]⁶
Number of fish in 2006 = 1,150[1-0.05]⁶
Number of fish in 2006 = 1,150[0.95]⁶
Number of fish in 2006 = 1,150[0.735]
Number of fish in 2006 = 845.25
Number of fish in 2006 = 845 fishes (Approx.)
A little Algebra, and we're home free!
We are given R = 20 and r2 = 75. We need to find r1.
The formula is 1/R = 1/r1 + 1/r2. Plug-in:
1/20 = 1/r1 + 1/75
1/20 - 1/75 = 1/r1
0.0366 = 1/r1
r1 = 1/0.03666
r1 = 27.272
Our answer is r1 = 27 ohms.
Answer:
77 "
Step-by-step explanation:
'mean' is the average of all of the heights
( 84 + 84 + 77 + 63 + 70 + 70 + x) / 7 = 75
x = 77
Answer:
m∠x = 10°
Step-by-step explanation:
Since we are dealing with a <u>right triangle</u> and its two sides and one angle, we can use <u>trigonometry ratios</u>. Remember them all with the acronym SohCahToa.
"o" is for opposite side, "a" is for adjacent side, "h" is for hypotenuse side.
The ratios are:
sinθ = opposite/hypotenuse
cosθ = adjacent/hypotenuse
tanθ = opposite/adjacent
θ means the "angle of reference", or the angle you know or want to find. This determines which side is adjacent (touching) or opposite (not touching). The hypotenuse (longest side) does not change.
In this triangle, θ = x. The sides we know are hypotenuse and opposite. Therefore, we will use the sinθ ratio.
sinθ = opposite/hypotenuse
sinx = CB/AB Substitute the labels in the diagram
sinx = 4/23 Substitute known values (side lengths)
x = sin⁻¹(4/23) Isolate 'x'. Use calculator to solve.
x = 10.015....° Exact answer
x ≈ 10° Round to the nearest degree
Therefore the measure of angle x (m∠x) is 10°.
MISSING DETAILS
Yoko's fish tank has 17 liters of water in it. She plans to add 5 liters per minute until the tank has at least 57 liters. What are the possible numbers of minutes Yoko could add water?
Answer:
Minutes = 8 minutes
Step-by-step explanation:
Topic: Inequality
Given:
Available Size of water = 17 liters
Increment = 5 liters/minute
Size of water needed = At least 57 liters
Putting the above together, as have
17 + 5m > 57
where m represents total minutes and > represent at least
Solving the Inequality
5m > 57 - 17
5m > 40 ------ Divide through by 5
5m/5 > 40/5
m > 8
So, Yoko will need to add water for at least 8 minutes before she fills her tank to 57 liters.
