We can let r and b represent the numbers of teams in the red and blue divisions, respectively. The total number of goals scored in each division will be the average for that division times the number of teams in that division.

r - b = 1 . . . . . . there is 1 more red team than blue

4.5r +4.2b = 48 . . . . . . total goals scored per week

Solving by substitution, we have ...

r = b +1

4.5(b +1) +4.2b = 48 . . . . substitute for r

8.7b +4.5 = 48 . . . . . . . . simplify

8.7b = 43.5 . . . . . . . . . . subtract 4.5

b = 43.5/8.7 = 5 . . . . . divide by 8.7

r = b +1 = 6 . . . . . . . . . find r

There are 6 red teams and 5 blue teams.

_____

Additional comment

The basic idea is that you make an equation for each relation given in the problem statement. For a problem like this, you do need to have an understanding of how the average number of goals would be calculated and how that relates to the total goals.

8 0

2 years ago

There are 10 boys and 8 girls in the chess club at West Middle School. The principal randomly selects one student from the chess

egoroff_w [7]

Answer:

5/9 of a chance

Step-by-step explanation:

or a 55.55- chance

5 0

3 years ago

According to the Department of Transportation, 27% of domestic flights were delayed in the last year at JFK airport. Five flight

Mars2501 [29]

Answer:

The probability that all the five flights are delayed is 0.2073.

Step-by-step explanation:

Let X = number of domestic flights delayed at JFK airport.

The probability of a domestic flight being delayed at the JFK airport is, P (X) = p = 0.27.

A random sample of n = 5 flights are selected at JFK airport.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={5\choose x}0.27^{x}(1-0.27)^{5-x};\ x=0,1,2...$

Compute the probability that all the five flights are delayed as follows:

$P(X=5)={5\choose 5}0.27^{5}(1-0.27)^{5-5}=1\times 1\times 0.207307=0.2073$

Thus, the probability that all the five flights are delayed is 0.2073.

4 0

3 years ago