Answer: She started with $160.
It will take 6 weeks before she has less than half of what she originally invested.
Step-by-step explanation:
If her money is decreasing in value by 11% each week, it means that the rate at which it is decreasing is exponential.
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the value of the investment after t weeks.
t represents the number of weeks.
P represents the initial value of the investment.
r represents rate of depreciation.
From the information given,
A = $142.40
r = 11% = 11/100 = 0.11
t = 1
Therefore
142.40 = P(1 - 0.11)^1
142.40 = P(0.89)
P = 142.4/0.89
P = 160
For her to have half of what she invested originally, then
80 = 160(0.89)^t
80/160 = (0.89)^t
0.5 = (0.89)^t
Taking log of both sides to base 10
Log 0.5 = log0.89^t = tlog0.89
- 0.3010 = - 0.051t
t = - 0.3010/- 0.051
t = 5.9
Approximately 6 weeks
Answer: The total purchase price is $ 29,032
Step-by-step explanation:
Hi, to solve this problem you have to solve the percentages of each taxes first.
So :
- state taxes =$24,500 × 5.5% = $1,347.5
- federal tax = $24,500 × 13% = $3,185
The next step is adding the taxes results to the speedboat cost.
so:
speedboat = $24,500
speedboat + taxes = $24,500 + $1,347.5 +$3,185 = $29,032
The total purchse price for the speedboat is $29,032.
Answer:
125π√3/3 cm³ ≈ 226.72 cm³
Step-by-step explanation:
The length of the circular edge of the half-circle is ...
(1/2)C = (1/2)(2πr) = πr = 10π . . . . cm
This is the circumference of the circular edge of the cone, so the radius of the cone is found from ...
C = 2πr
10π = 2πr . . . . fill in the numbers; next, solve for r
r = 5 . . . . cm
The slant height of the cone is the original radius, 10 cm, so the height of the cone from base to apex is found from the Pythagorean theorem.
(10 cm)² = h² + r²
h = √((10 cm)² -(5 cm)²) = 5√3 cm
And the cone's volume is ...
V = 1/3·πr²h = (1/3)π(5 cm)²(5√3 cm)
V = 125π√3/3 cm³ ≈ 226.72 cm³
Answer:
(-21,-19)
Standard form
Step-by-step explanation:
We are given the equation of circle
General equation of circle:
Centre: (-g,-f)
Radius: 
Compare the equation to find f, g and c from the equation
Centre: (-21,-19)
Radius (r) 
Standard form of circle:
The centre of circle at the point (-21,-19) and its radius is .
The general form of the equation of a circle that has the same radius as the above circle is standard form.
