A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the s

Answer: 800

Step-by-step solution:

Given: The stadium has total seats.

The portion of seats sold is .

To calculate the tickets sold, multiply the total seats by the sold fraction, resulting in

Tickets sold:

Therefore, 800 tickets were sold.

Answer: The other two observations are 97 and 107.

Explanation:

We know that

Mean = 100

Mode = 98

Range = 10

And from the formula,

Range = Highest - Lowest.

Let’s set the highest observation as x and the lowest as y.

Thus, we have the equation x - y = 10 (equation 1).

The observations can be represented as:

x, 98, 98, y.

Using the mean formula yields:

Mean = .

This means our second equation is:

x + y = 204.

By applying the elimination method to solve these linear equations, we find:

x = 97.

and

.

Therefore, the other two observations are 97 and 107.

Response:

Bob’s best approach is to prepare for sunny conditions, unless he can access a weather forecast for the next day.

Explanation in detail:

This scenario focuses on the potential for gains versus the risk of losses. We will evaluate the options available to Bob in different weather situations.

When Bob buys for rain:

He purchases 500 umbrellas priced at $5 each, leading to a total expenditure of $2500.

In the event of rain, Bob can sell all umbrellas at $10 each, yielding total revenue of $5000. Consequently, his maximum profit equals $2500. Recall that:

Profit = Revenue - Cost

If the weather is sunny, he will only manage to sell 100 umbrellas for $10 each, resulting in a revenue of $1000. Therefore, in this scenario, he faces a maximum profit of -$1500. This indicates that his minimum loss in this case is $1500.

When Bob prepares for Shine:

He opts for purchasing 100 umbrellas at $5 each and 1000 sunglasses at $2 each, totaling an expense of $2500.

On a sunny day, he can sell all umbrellas for $10 each and all sunglasses for $5. This allows him to achieve a total revenue of $6000. Thus, his maximum profit amounts to $3500.

Conversely, during rain, Bob can only dispose of 100 umbrellas at $10 each, but he sells none of the sunglasses, yielding a maximum profit of $1000. Here, the maximum profit still evaluates to -$1500, meaning his minimum loss remains $1500.

In both scenarios, the worst possible outcome for Bob is consistent: a loss of $1500.

However, in the most favorable scenario, purchasing for sunny conditions results in higher profits. Therefore, if the risks are equivalent, it is more advantageous to adopt the strategy that provides greater profitability.