Step-by-step explanation:
:
1. Let's denote the distance from the pole to the tower as \( x \) feet and the distance from the pole to the stake as \( y \) feet.
2. We know that the pole is 5 feet tall, so it acts as the height of the right triangle formed by the guy wire, the distance to the tower, and the distance to the stake.
3. Using the Pythagorean Theorem, we have:
\[ x^2 + 5^2 = y^2 \]
This equation represents the relationship between the distances to the tower, to the stake, and the length of the guy wire.
4. Given the values of \( x \) and \( y \), we can now solve for the length of the guy wire, which is \( y \). After substituting the known values into the equation above, you can find the length of the guy wire to the nearest foot.
By following these steps and calculations, you can determine the length of the guy wire accurately. This method helps to visualize and solve the problem effectively using the Pythagorean Theorem.
A community center rents a hall for special events. They have a fixed fee of $200 plus an hourly fee of $22.50. Lin has $300 to spend on renting the hall for a fundraiser. A) Using the only money she has, can Lin pay for a 6-hour event? Explain or show your reasoning. B) Using the money she has, can Lin pay for a 3-hour event? Explain or show your reasoning? C) Write and solve an equation to determine the number of hours Lin can rent the community center. D) Write and solve an inequality in this situation. Explain what the solution to the inequality means in the situation.
Brainly Ginny character avatar
There was an error while retrieving the answer.
Jackie played in 5 basketball games. She always scored more than 5 points. She scored in double-digits once. Her median score was 8. What might her 5 scores be so that her mean is also 8?
Brainly Ginny character avatar
AI-generated answer
To find Jackie's scores so that her mean is 8, we can consider the following:
1. Since Jackie played 5 games and scored more than 5 points in each game, one of her scores must be in double-digits (10 or more).
2. If the median score is 8, and she has one score in double-digits, the other three scores must be below 8 to keep the median at 8.
3. To maintain a mean score of 8, we can distribute the points evenly among the 5 games. Here's one possible set of scores that satisfies the conditions:
- Game 1: 6 points
- Game 2: 7 points
- Game 3: 8 points
- Game 4: 8 points
- Game 5: 11 points
4. This distribution gives a total of 40 points (6 + 7 + 8 + 8 + 11 = 40) over 5 games, resulting in a mean score of 8 (40 / 5 = 8).
5. Therefore, one set of Jackie's scores that meets the conditions would be: 6, 7, 8, 8, and 11.
Answer:
6, 7, 8, 9, and 10
Step-by-step explanation:
To find Jackie's five scores so that her mean is 8, we need to consider her median score and the fact that she scored in double-digits once.
Let's denote Jackie's five scores as [tex] a [/tex], [tex] b [/tex], [tex] c [/tex], [tex] d [/tex], and [tex] e [/tex], where [tex] a \leq b \leq c \leq d \leq e [/tex].
Given:
Jackie's median score is 8, which means the third score out of five is 8.
She scored in double-digits once, which means at least one of her scores is greater than 9.
Her mean score is also 8.
To find her scores, let's first arrange the scores in ascending order:
[tex]\sf a, b, 8, d, e [/tex]
Given that the mean is 8, the sum of the scores is:
[tex] 5 \times 8 = 40 [/tex]
So, we have the equation:
[tex]\sf a + b + 8 + d + e = 40 [/tex]
Now, since [tex] b [/tex] is less than or equal to 8, and at least one score must be greater than 9, the only possibility for the other scores is:
[tex]\sf a = 6, b = 7, d = 9, e = 10 [/tex]
Now, let's check if this configuration satisfies all the given conditions:
[tex]\dfrac{6+7+8+9+10}{5}=8[/tex]
So, her five scores could be 6, 7, 8, 9, and 10.
