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sergey
2 months ago
13

The price of fuel may increase due to demand and decrease due to overproduction. Marco is studying the change in the price of tw

o types of fuel, A and B, over time.
The price f(x), in dollars, of fuel A after x months is represented by the function below:

f(x) = 2.15(0.98)x

Part A: Is the price of fuel A increasing or decreasing and by what percentage per month? Justify your answer. (5 points)

Part B: The table below shows the price g(m), in dollars, of fuel B after m months.

m (number of months) 1 2 3 4
g(m) (price in dollars) 4.19 3.98 3.78 3.59
Which type of fuel recorded a greater percentage change in price over the previous month? Justify your answer. (5 points)

(10 points)
Mathematics
1 answer:
zzz [12.3K]2 months ago
6 0
Part A: The price of fuel A declines at a rate of 2% monthly. Part B: Fuel B experienced a larger price change percentage from the previous month at 5% compared to fuel A's 2%. For Part A, we need to determine if the price of fuel A is rising or falling and by what percentage monthly. We note that the exponential function's equation indicates a decrease since the rate of change is negative, indicating it follows an exponential decay model. Therefore, the price of fuel A is indeed decreasing by 2% each month. In Part B, analyzing the data shows that fuel B's price changes more significantly than that of fuel A.
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In the xy-plane, point E has coordinates (4,5) and point O has coordinates (0,0). Which of the following is an equation of the l
lawyer [12517]

Answer:

D

Step-by-step explanation:

You should insert the provided x and y coordinates into the equations to determine which one satisfies both points.

D is valid for both:

5 = 5/4(4)

0 = 5/4(0)

6 0
3 months ago
Tanmay had some chocolates with him. He gave one-third of them to Akash and one-fifth of them to Sharad. Tanmay could do so with
babunello [11817]

Answer:

Possible values for X include;

15, 30, 45, 60, and so on

Step-by-step explanation:

The parameters provided are

Number of chocolates Tanmay possessed = X

Number of chocolates given to Akash = 1/3 × X

Number of chocolates given to Sharad = 1/5 × X

Consequently, since both 3 and 5 divide X,

3 × 5 = 15 is the smallest single factor of X.

Thus, the values of X based on this minimum factor are as follows;

15 × 1 = 15

15 × 2 = 30

15 × 3 = 45

15 × 4 = 60

Therefore, potential values for X form an arithmetic series: a + (n - 1) × d

Where:

a = 15

n = 1, 2, 3, 4,...

d = 15

This results in;

15, 30, 45, 60

7 0
2 months ago
1. Darnell reads at a constant rate
Svet_ta [12734]

Answer:

Darnell reads 1,715 words in 7 minutes.

Step by step Explanation:

1. First, determine how many words he can read in a minute by dividing 735 words by 3. The result is 245.

245

______

3)735

6 drop the 3 to form 13

-_____

1 3

12 drop the 5 to make 15

-______

1 5

15

___________

0

2. Next, since he reads 735 words over 3 minutes, multiply that by 2 to find words read in 7 minutes: 3×2=6, thus, 735+735 (735×2) equals 1,470 words.

3. Finally, add 245 to account for the last minute we calculated. Therefore, the total is 1,715 words in 7 minutes.

8 0
2 months ago
Consider the area shown below. The height of the triangle is 8 and the length of its base is 3. We have used the notation Dh for
tester [12383]

Answer:

\text{Riemann sum }=\sum \frac{3}{8}(8-h)Dh

\text{Area =}\int_{a}^{b} \frac{3}{8}(8-h)Dh

Step-by-step explanation:

Given that the triangle's height measures 8 and the base length is 3, we can apply the concept of similar triangles to represent the base of the smaller triangle in relation to h.

The height of the smaller triangle will be (8-h).

Denote x as the base of the smaller triangle. Thus, by utilizing the properties of similar triangles, we can establish ratios of the corresponding sides as illustrated below:

\frac{8-h}{x} =\frac{8}{3} \\x=\frac{3}{8}(8-h)

This allows us to express the area of the small strip with length x and thickness Dh as follows:

DA=x*Dh\\DA=\frac{3}{8}(8-h)Dh

The desired Riemann sum can be articulated as:

\text{Riemann sum }=\sum \frac{3}{8}(8-h)Dh

The necessary areas can be represented as:

\text{Area =}\int_{a}^{b} \frac{3}{8}(8-h)Dh

Your remaining answers are accurate.:)

3 0
2 months ago
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