Answer:
In common scientific notation, any nonzero quantity can be expressed in two parts: sufficient whose absolute value is greater than or equal to 1 but less than 10, and a power of 10 by which the coefficient is multiplied. In some writings, the coefficients are closer to zero by one order of magnitude. In this scheme, any nonzero quantity is expressed in two parts: a coefficient whose absolute value is greater than or equal to 0.1 but less than 1, and a power of 10 by which the coefficient is multiplied. The quantity zero is denoted as 0 unless precision is demanded, in which case the requisite number of significant digits are written out
Question:
A population of insects, in thousands, can be modeled using the function
, where t is time in months. Which statement best
describes the population of insects?
A. The population is decaying at a rate of 3% each month.
B. The population is decaying at a rate of 25% each month.
C. The population is growing at a rate of 75% each month.
D. The population is growing at a rate of 97% each month.
Answer:
A. The population is decaying at a rate of 3% each month.
Step-by-step explanation:
Given

Required
True statement about the function
From the options, we can see that we are to answer the question on the basis of decay and growing rates.
An exponential form is:

Compare to 

If
, then
r represents growth rate
else,
r represents decay rate
Since b < 0.97:





Answer:
1,2,3 and 6 are similar triangles by AA similarity
Step-by-step explanation:
1) ∠DEC ≅ ∠FEG {Vertically opposite angles}
DC // GF
∠ECD ≅ ∠EGF {Alternate interior angles}
∠EDC ≅ ∠EFG {Alternate interior angles}
ΔDEC & ΔFEG are similar triangles by AA similarity
2)MN // QP
∠LQP ≅ ∠QMN {Corresponding angles }
∠LPQ ≅ ∠PNM {Corresponding angles}
ΔLQP & ΔLMN are similar triangles by AA similarity
3) In ΔSYE ,
∠S = 180 - 90 - 39
∠S = 51°
In ΔCHW,
∠H = 180 - 51 - 90
∠H = 39
ΔSYE and ΔCHW
∠S ≅ ∠W = 51°
∠Y ≅ ∠C = 90°
∠E ≅∠H = 39°
ΔSYE & ΔWCH are similar triangles by AA similarity
6) ∠P ≅ ∠Z {Given}
∠PXQ ≅∠ZXY {Vertically opposite angles}
ΔPXQ & ΔZXY are similar triangles by AA similarity
Answer:
Assuming the area is made up of a square and a semicircle.
<u>Perimeter</u>
The side length of the square = 18 ft
We can see 3 full side lengths plus one side length from which we need to subtract 12 ft (see attached diagram).
⇒ perimeter of the square = (3 x 18) + (18 - 12)
= 54 + 6
= 60 ft
Circumference of a circle =
d (where d is the diameter)
⇒ arc length of the semicircle = 1/2 circumference
= 1/2 ·
· 12
= 6
ft
Total perimeter = 60 + 6
= 78.8 ft (nearest tenth)
<u>Area</u>
Area of a square = s² (where s is the side length)
⇒ area of square = 18²
= 324 ft²
Diameter = 2r ⇒ r = 1/2 diameter
Area of a circle =
r² (where r is the radius)
⇒ area of the semicircle = 1/2 ·
· 6²
= 18
ft²
Total area = 324 + 18
= 380.5 ft² (nearest tenth)