Ne Friday night, a group of friends bought 5 containers of popcorn and 4 granola bars at the movie theatre for $42.50. The next

week, the same group of friends bought 3 containers of popcorn and 6 granola bars for $34.50. Let p represent the cost of one container of popcorn. Let g represent the cost of one granola bar. Which system of equations will solve for p and g?

Mathematics

You might be interested in

Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month

AnnZ [12381]

Answer:

a) The first inequality is 100 + 55x > 150 + 51x;

b) The final inequality results in x > 12.5

c) Sal's mother will need to use the second phone for at least 13 months.

Step-by-step explanation:

a) Let x represent the number of months.

1. The first phone is priced at $100, with a monthly fee of $55 for unlimited use, leading to a total cost of $(100 + 55x) for x months.

2. The second phone costs $150 with a monthly fee of $51 for unlimited use, resulting in a total of $(150 + 51x) for x months.

3. For the second phone to be cheaper, we set up the inequality:

150 + 51x < 100 + 55x

which simplifies to

100 + 55x > 150 + 51x

b) Now solve this:

55x - 51x > 150 - 100

4x > 50

so x > 12.5

c) This means Sal's mother has to retain the second phone for at least 13 months (since x > 12.5).

8 0

3 months ago

Read 2 more answers

Upgrading a certain software package requires installation of 68 new files. Files are installed consecutively. The installation

lawyer [12517]

Answer:

The chance of completing the entire package installation in under 12 minutes is 0.1271.

Step-by-step explanation:

We define X as a normal distribution representing the time taken in seconds to install the software. According to the Central Limit Theorem, X is approximately normal, where the mean is 15 and variance is 15, giving a standard deviation of √15 = 3.873.

To find the probability of the total installation lasting less than 12 minutes, which equals 720 seconds, each installation should average under 720/68 = 10.5882 seconds. Thus, we seek the probability that X is less than 10.5882. To do this, we will apply W, the standard deviation value of X, calculated via the formula provided.

Utilizing $\phi$ , we reference the cumulative distribution function of the standard normal variable W, with values found in the attached file.