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
C. $122.10
20 first hour
20+0.1*20 = 22 second hour
22+0.1*22 = 24.2 third hour
24.2+0.1*24.2 = 26.62 fourth hour
26.62+0.1*26.62 = 29.282 fifth hour
Total=$122.10
Given :
A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla.
To Find :
1. How many batches can you make with 15 cups of flour and 6 teaspoons of vanilla?
2. How much flour and vanilla would you need for 5 batches of cookies?
Solution :
Let, 1 cup of flour contains x gm of flour.
Let, 2 teaspoons of vanilla contains y gm of vanilla.
So, 1 batch requires :
1 batch = 5x + 2y
It is given that 15 cups of flour and 6 teaspoons of vanilla are their so batches are :
x = 15x + 6y = 3( 5x + 2y ) = 3 batches.
Now,
For 5 batches of cookies 5×5 = 25 cups of flour and 5×2 = 10 teaspoons of vanilla.
Hence, this is the required solution.
Answer:
15. y = 6x
16. x = 11
Step-by-step explanation:
15. A direct variation equation is of the form ...
y = kx
Solving for k, we find ...
k = y/x = 42/7 = 6
The equation is y = 6x.
__
16. Filling in the given values, we have ...
66 = 6x
11 = x . . . . . . . divide by 6
Answer:
Perimeter is 130r units
Area is n*r^2 square units
Step-by-step explanation:
So, something special happens to perimeter and area if you scale a figure by some factor. let's say you make a figure twice as big, well, the perimeter also gets twice as big. Area though will get 4 times as big. more generally, if you scale a figure by x, the perimeter also scales by x, while the area scales by x^2.
So for this triangle, the perimeter of abc is 30 + 40 + 60, then when you scale them by r the perimeter becomes 30r + 40r + 60r or (30 + 40 +60)r. of course 30 + 60 + 40 is 130 so the perimeter of xyz is 130r
Now for area, the problem just vices us the area as n. Scaling the sides by r makes the area n*r^2. This is for all shapes. If you want to check try on a random triangle, or more easily a square