Answer :
Let's go through each of the provided questions and write the inequalities.
### 21. All real numbers between -5 and 7 (inclusive)
To represent all real numbers between -5 and 7 inclusively, we can use the inequality:
[tex]\[ -5 \leq x \leq 7 \][/tex]
Here, [tex]\(\leq\)[/tex] indicates that -5 and 7 are included in the set of numbers.
### 22. A welterweight boxer's weight is greater than 140 lbs (non-inclusive), but no more than 147 lbs (inclusive)
To express this condition, we can use the following inequality:
[tex]\[ 140 < w \leq 147 \][/tex]
Here, the inequality [tex]\(<\)[/tex] for 140 means 140 lbs is not included, and the inequality [tex]\(\leq\)[/tex] for 147 means 147 lbs is included.
### 23. The posted speed limit on a residential street is 25 mph (miles per hour)
To write an inequality indicating that the speed [tex]\(s\)[/tex] should be at most 25 mph, we can use:
[tex]\[ s \leq 25 \][/tex]
This means a vehicle should not exceed the speed limit of 25 mph.
### Calculations:
Given the problem description with specific numerical results:
1. Lower Bound Calculation:
[tex]\[ z_{\text{lower}} = -2.1275871824522046 \][/tex]
2. Upper Bound Calculation:
[tex]\[ z_{\text{upper}} = 0.7091957274840682 \][/tex]
3. Probability Calculation:
The probability that the sample mean falls between the lower and upper bounds is:
[tex]\[ 0.7442128248197002 \][/tex]
In summary, the inequalities can be written as:
1. [tex]\( -5 \leq x \leq 7 \)[/tex]
2. [tex]\( 140 < w \leq 147 \)[/tex]
3. [tex]\( s \leq 25 \)[/tex]
And the calculated numerical results:
1. [tex]\( z_{\text{lower}} = -2.1275871824522046 \)[/tex]
2. [tex]\( z_{\text{upper}} = 0.7091957274840682 \)[/tex]
3. Probability [tex]\( = 0.7442128248197002 \)[/tex]
### 21. All real numbers between -5 and 7 (inclusive)
To represent all real numbers between -5 and 7 inclusively, we can use the inequality:
[tex]\[ -5 \leq x \leq 7 \][/tex]
Here, [tex]\(\leq\)[/tex] indicates that -5 and 7 are included in the set of numbers.
### 22. A welterweight boxer's weight is greater than 140 lbs (non-inclusive), but no more than 147 lbs (inclusive)
To express this condition, we can use the following inequality:
[tex]\[ 140 < w \leq 147 \][/tex]
Here, the inequality [tex]\(<\)[/tex] for 140 means 140 lbs is not included, and the inequality [tex]\(\leq\)[/tex] for 147 means 147 lbs is included.
### 23. The posted speed limit on a residential street is 25 mph (miles per hour)
To write an inequality indicating that the speed [tex]\(s\)[/tex] should be at most 25 mph, we can use:
[tex]\[ s \leq 25 \][/tex]
This means a vehicle should not exceed the speed limit of 25 mph.
### Calculations:
Given the problem description with specific numerical results:
1. Lower Bound Calculation:
[tex]\[ z_{\text{lower}} = -2.1275871824522046 \][/tex]
2. Upper Bound Calculation:
[tex]\[ z_{\text{upper}} = 0.7091957274840682 \][/tex]
3. Probability Calculation:
The probability that the sample mean falls between the lower and upper bounds is:
[tex]\[ 0.7442128248197002 \][/tex]
In summary, the inequalities can be written as:
1. [tex]\( -5 \leq x \leq 7 \)[/tex]
2. [tex]\( 140 < w \leq 147 \)[/tex]
3. [tex]\( s \leq 25 \)[/tex]
And the calculated numerical results:
1. [tex]\( z_{\text{lower}} = -2.1275871824522046 \)[/tex]
2. [tex]\( z_{\text{upper}} = 0.7091957274840682 \)[/tex]
3. Probability [tex]\( = 0.7442128248197002 \)[/tex]
