The conclusions are :
- The number of bass decreased over time
- The number of catfish increased over time.
Step-by-step explanation:
Form the table as shown to visualize and make conclusions
Year Trout Catfish Bass Total
1 77 57 58 192
2 83 76 40 199
3 92 80 31 203
From the table;
- The number of bass decreases over time.
- The number of catfish increased over time
- The number of Trout increased over time
- The fish population increased over time
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Keywords: random,samples,years,table,fish,years
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Full Question:
The 4th term of a g.p. is 40 and the 10th term in the sequence is 2560, what is the 11th term in the sequence ?
Answer:
the 11 the term is 5120
Step-by-step explanation:
Given
Geometry Progression
4th term = 40
10th term = 2560
Required
11 term.
The nth term of a geometric sequence is calculated as follows
Tₙ = arⁿ⁻¹
For the 4th term, n = 4 and Tₙ = 40
Substitute these in the given formula; this gives
40 = ar⁴⁻¹
40 = ar³. --;; equation 1
For the 10th term, n = 10 and Tₙ = 2560
Substitute these in the given formula; this gives
2560 = ar¹⁰⁻¹
2560 = ar⁹. --;; equation 2
Divide equation 2 by 1. This gives
2560/40 = ar⁹/ar³
64 = r⁹/r³
From laws of indices
64 = r⁹⁻³
64 = r⁶
Find 6th root of both sides
(64)^1/6 = r
r = (2⁶)^1/6
r = 2
Substitute r = 2 in equation 1
40 = ar³. Becomes
40 = a * 2³
40 = a * 8
40 = 8a
Divide both sides by 8
40/8 = 8a/8
5 = a
a = 5.
Now, the 11 term can be solved using Tₙ = arⁿ⁻¹ where n = 11
So,
Tₙ = arⁿ⁻¹ becomes
Tₙ = 5 * 2¹¹⁻¹
Tₙ = 5 * 2¹¹⁻¹
Tₙ = 5 * 2¹⁰
Tₙ = 5 * 1024
Tₙ = 5120.
Henxe, the 11 the term is 5120
It would be: 4 3/10 * 6
43/10 * 6
4.3 * 6 = 25.8 miles
I have included the returned journey, as he has to do so to continuing for next one!!
Answer:
a) 
b) 
c) 
Step-by-step explanation:
Given the curve
a) If the x-coordinate of P is 
, then the y-coordinate is 
so point P has coordinates 
If the x-coordinate of Q is 
, then the y-coordinate is 
so point Q has coordinates 
b) The gradient of the secant RQ is
c) If 
then the gradient 
The answer:
According to the image, <span>the length of line segment GF can be found with
</span>GF= GC +CF
CF is one the radius, so CF=7.5
to find GC, we can apply Pythagorean theorem on the right triangle GEC
it is
GC² =GE² + EC² = 10² +7.5² =156.25, and then GC= sqrt(156.25)=12.5
therefore, GF= GC +CF=12.5+7.5=20
so the answer is <span>20.0 units</span>
