1) In 2000, magazine A had 5,000 subscribers more than magazine B. 2) The available options indicate that the subscription numbers for both magazines are dropping. 3) As the years progress from 2000, the subscriber counts for both magazines approach zero.
Question 1: (2.2, -1.4). Question 2: (1.33, 1). Providing a detailed analysis, the equations for the given lines are specified as (1) passing through points (0, 2.5) and (2.2, 1.4), and (2) through (0, -3) and (2.2, -1.4). We are tasked with locating a common solution or intersection of these equations. This leads to finding x = 2.2, and consequently y = -1.4. Therefore, the solution set is (2.2, -1.4). For question 2, the equations yield a solution of (1.33, 1).
Part a) When a page is scaled down to 80%, how much enlargement is necessary to bring it back to its original size?
Let
x---------> the percent enlargement
Given the original size is 100%
This means:
x*80%=100%
x=(100%/80%)
x=1.25--------> 1.25=(125/100)=125%
Thus,
The answer to Part a) is
The percent enlargement required is 125%
Part b) Estimate how many successive copies of a page are needed to make the final copy less than 15% of its original size.
Since the photocopy machine reduces sizes to 80% of the original
Therefore:
Copy N 1
0.80*100%=80%
Copy N 2
0.80*80%=64%
Copy N 3
0.80*64%=51.2%
Copy N 4
0.80*51.2%=40.96%
Copy N 5
0.80*40.96%=32.77%
Copy N 6
0.80*32.77%=26.21%
Copy N 7
0.80*26.21%=20.97%
Copy N 8
0.80*20.97%=16.78%
Copy N 9
0.80*16.78%=13.42%-------------> 13.42% < 15%
Therefore,
The answer to Part b) is
The necessary number of copies to achieve this is 9
Response:
Step-by-step explanation:
We need to form an equation that illustrates the area that Felicia has covered, denoted as y, in relation to the number of tiles she utilized, represented by x.
Let x= Number of tiles
y=Area occupied by Felicia's tiles
The relationship between x and y is constant. Hence, it follows a direct proportion.
The equation for direct proportion is shown as
Where
k=The value of the ratio of x and y
x and y are variable factors
Here, we have k=9
Substituting the known values into the equation
leads us to
This represents the necessary equation depicting the area Felicia covered, y, in terms of the number of tiles utilized, x.
To change the mixed number 83 1/3 into an improper fraction, we compute.
Thus, 83 1/3 converts to 250/3
Next, converting 250/3 into its decimal form gives us 83.33.
Our goal is now to determine 83.33 percent of 384.
We begin by performing the multiplication (83.33) with 384, yielding 83.33 * 384 = 31987.2
Subsequently, we divide by 100 to find the percentage.
Dividing 31987.2 by 100 shifts the decimal two places to the left, resulting in
31987.2/100 = 319.872
Consequently, 83 1/3 percent of 384 equals 319.872.
