Answer:
341
Step-by-step explanation:
The number of people who know the art of quilting in each successive generation is
1, 4, 16, …
These numbers represent a geometric sequence where each term has the form
aₙ = a₁rⁿ⁻¹
In your sequence, a₁ = 1 and r = 4.
Then, the formula for your sequence is
aₙ = 4ⁿ⁻¹
Sum over five generations
The formula for the sum of the first n terms of a geometric series is
Sum = a₁[(1 - rⁿ)/(1 - r)]
Sum = 1[(1 - 4⁵)/(1 - 4)
= (1 - 1024)/(-3)
= -1023/-3
= 341
If the process continues for five generations, 341 people will know the art of quilting.
Answer:
13.5 = 9.5 + x
x=4
Step-by-step explanation:
In this problem, the price of the baseball cap, which is $9.50, and a baseball, whose price is unknown (and therefore must be the variable), total $13.50. So, to set up the equation add the two prices and set them equal to the total, 9.5+x=13.5.
Then, using the subtraction property of equality subtract 9.5 from both sides. This means x=4, so the baseball cost 4 dollars.
Answer:
<u>The budget for defense can be represented as x + 660.4</u>
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Budget for education is $ 660.4 billion less than budget for defense in some country
x = represents the budget for education, in billion of dollars
2. How can the budget for defense be represented?
x = represents the budget for education, in billion of dollars
x + 660.4 = represents the budget for defense, in billion of dollars also
<u>The correct answer is that the budget for defense can be represented as x + 660.4</u>
10^1 = 10
10^2 = 100 {10 x 10 = 100}
10^3 = 1000 {10 x 10 x 10 = 1,000}
10^4 = 10000 {10 x 10 x 10 x 10 = 10,000}
The exponent represents how many zeros will be used in the answer. For example, 10^6 would include 6 zeros in it’s answer; 1,000,000.
Answer:
2 bears in 2020.
Step-by-step explanation:
We have been given that a new bear population that begins with 150 bears in 2000 decreases at a rate of 20% per year.
We will use exponential decay formula to solve our given problem as:
, where,
y = Final quantity,
a = Initial value,
r = Decay rate in decimal form,
x = Time
Upon substituting our given values in above formula, we will get:
, where x corresponds to year 2000.
To find the population in 2020, we will substitute 
in our equation as:
Therefore, 2 bears are there predicted to be in 2020.
Since population is decreasing so population is best described as exponential decay.
