Questions: Question 7 of 21 Nine percent of Americans get 5 or fewer hours of sleep each night or 87% get 5 or more hours of sleep each night. 2% get 7 or more hours of sleep each night. The truth value of the simple statement "Nine percent of Americans get 5 or fewer hours of sleep each night" is The truth value of the simple statement "87% get 5 or more hours of sleep each night" is The truth value of the simple statement "62% get 7 or more hours of sleep each night" is The truth value of the compound statement is

Question 7 of 21
Nine percent of Americans get 5 or fewer hours of sleep each night or 87% get 5 or more hours of sleep each night.
2% get 7 or more hours of sleep each night.
The truth value of the simple statement "Nine percent of Americans get 5 or fewer hours of sleep each night" is
The truth value of the simple statement "87% get 5 or more hours of sleep each night" is
The truth value of the simple statement "62% get 7 or more hours of sleep each night" is
The truth value of the compound statement is

Transcript text: Question 7 of 21 Nine percent of Americans get 5 or fewer hours of sleep each night or $87 \%$ get 5 or more hours of sleep each night. $2 \%$ get 7 or more hours of sleep each night. The truth value of the simple statement "Nine percent of Americans get 5 or fewer hours of sleep each night" is $\square$ The truth value of the simple statement " $87 \%$ get 5 or more hours of sleep each night" is $\square$ The truth value of the simple statement " $62 \%$ get 7 or more hours of sleep each night" is $\square$ The truth value of the compound statement is $\square$

Solution

Solution Steps

To determine the truth value of each statement, we need to compare the given percentages with the actual survey data. The truth value of a statement is "True" if the statement matches the data and "False" otherwise. For the compound statement, we use logical operators to combine the truth values of the individual statements.

To solve the given problem, we need to determine the truth values of the provided statements based on the survey data. Let's break down the problem into steps.

Step 1: Analyze the Statements

We have the following statements to evaluate:

"Nine percent of Americans get 5 or fewer hours of sleep each night."
"$87\%$ get 5 or more hours of sleep each night."
"$62\%$ get 7 or more hours of sleep each night."

Step 2: Determine the Truth Value of Each Statement

Statement 1: "Nine percent of Americans get 5 or fewer hours of sleep each night."

We need to verify if $9\%$ of Americans indeed get 5 or fewer hours of sleep each night.
If the survey data confirms this percentage, the statement is true; otherwise, it is false.

Statement 2: "$87\%$ get 5 or more hours of sleep each night."

We need to verify if $87\%$ of Americans indeed get 5 or more hours of sleep each night.
If the survey data confirms this percentage, the statement is true; otherwise, it is false.

Statement 3: "$62\%$ get 7 or more hours of sleep each night."

We need to verify if $62\%$ of Americans indeed get 7 or more hours of sleep each night.
If the survey data confirms this percentage, the statement is true; otherwise, it is false.

Step 3: Evaluate the Compound Statement

The compound statement is not explicitly given, but it seems to involve the truth values of the above statements. Typically, a compound statement could be a logical combination (e.g., AND, OR) of the simple statements.

Final Answer

Since the problem does not provide specific survey data to verify the truth values, we cannot definitively determine the truth values of the statements. However, based on the structure of the problem, we can summarize the expected answers as follows:

Truth value of the simple statement "Nine percent of Americans get 5 or fewer hours of sleep each night" is $\boxed{\text{unknown}}$.
Truth value of the simple statement "$87\%$ get 5 or more hours of sleep each night" is $\boxed{\text{unknown}}$.
Truth value of the simple statement "$62\%$ get 7 or more hours of sleep each night" is $\boxed{\text{unknown}}$.

The truth value of the compound statement is also $\boxed{\text{unknown}}$ due to the lack of specific data.

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