Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 8 and 8.5
between 8 and 8.5
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 7 and 7.5
The whole number and rational number to the nearest half that 58-√ falls between is between 7.5 and 8.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 8 and 8.5
between 8 and 8.5
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 7 and 7.5
Apologies for the confusion in my previous response. The correct answer is between 7.5 and 8.
Express 8 over 11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 8/11 as a repeating decimal, we can use long division:
0.727272...
First, we divide 8 by 11:
__0.7272 (first digit is 7)
11 | 8.0000
- 7.07 (7 times 11 equals 77)
10
- 9.09 (9 times 11 equals 99)
10
-9.09
10
From the long division, we see that the decimal representation of 8/11 is 0.727272... The cycle of repeating digits is 72, which is marked with a bar over them: 0.72̅.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can assign a variable to the repeating part of the decimal and solve for it.
Let x = 0.727272...
Now, we can multiply both sides of the equation by 100 to move the decimal point two places to the right:
100x = 72.727272...
Now, let's subtract the original equation from this equation to eliminate the repeating part:
100x - x = 72.727272... - 0.727272...
99x = 72
Dividing both sides of the equation by 99, we get:
x = 72/99
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 9:
x = (72 ÷ 9) / (99 ÷ 9)
x = 8/11
Therefore, the rational number in simplest form equivalent to the repeating decimal 0.72¯¯¯¯¯ is 8/11.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
525
5 Start Fraction 2 over 5 end fraction
517
5 Start Fraction 1 over 7 end fraction
26−−√
start root 26 end root
513
A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers.
Among the given options, the rational number between 5 and 514 is 5 1/7.
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction.(
To find a rational number with a denominator of 7 between 7−√ and 8−√, we can express both numbers in the form a√b, where a and b are integers.
For 7−√, we can rewrite it as √49−√, which is √(7^2)−√1. This means a = 7 and b = 1.
For 8−√, we can rewrite it as √64−√, which is √(8^2)−√1. Again, a = 8 and b = 1.
To find a rational number between these two expressions, we can average the values of a. The average of 7 and 8 is 7.5.
Therefore, the rational number with a denominator of 7 between 7−√ and 8−√ is (7.5/7) or 15/14 as an improper fraction.
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.
Rational numbers and whole numbers are related, but they are not the same.
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. Rational numbers include integers, decimals (finite or repeating), and fractions.
On the other hand, whole numbers are a subset of integers. Whole numbers include all positive integers (1, 2, 3, ...) and zero (0). Whole numbers do not include negative integers or fractions.
Therefore, not all rational numbers are whole numbers because rational numbers can include fractions and decimals. For example, 1/2 and 3.14 are rational numbers but not whole numbers.
However, all whole numbers are rational numbers. This is because every whole number can be expressed as a fraction with a denominator of 1. For example, 3 can be written as 3/1, and 0 can be written as 0/1.
In summary:
- All whole numbers are rational numbers.
- Not all rational numbers are whole numbers.
Find the measures of center—mean, median, and mode—for the given dataset.
10, 17, 11, 24, 12, 7, 15, 17, 20, 5, 11, 21, 16, 17
(2 points)
mean:
; median:
; mode:
To find the measures of center for the given dataset, we can calculate the mean, median, and mode.
Mean:
To find the mean, we add up all the values in the dataset and divide by the total number of values.
mean = (10 + 17 + 11 + 24 + 12 + 7 + 15 + 17 + 20 + 5 + 11 + 21 + 16 + 17) / 14
mean = 213 / 14
mean = 15.2143 (rounded to 4 decimal places)
Median:
To find the median, we arrange the values in ascending order and find the middle value.
Arranging the values in ascending order: 5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
Median of the dataset is the middle value, which is 15.
Mode:
The mode is the value that appears most frequently in the dataset.
In the given dataset, the mode is 17 as it appears 3 times, which is more frequently compared to other values.
Therefore, the measures of center for the given dataset are:
mean: 15.2143
median: 15
mode: 17
its not 15 or 15.2143
Apologies for the error. Let's re-calculate the measures of center for the given dataset:
Arranging the values in ascending order: 5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
Mean:
mean = (5 + 7 + 10 + 11 + 11 + 12 + 15 + 16 + 17 + 17 + 17 + 20 + 21 + 24) / 14
mean = 198 / 14
mean = 14.1429 (rounded to 4 decimal places)
Median:
Since the dataset has an even number of values, we find the average of the two middle values.
median = (12 + 15) / 2
median = 27 / 2
median = 13.5
Mode:
The mode is the value that appears most frequently in the dataset.
In the given dataset, the mode is 17 as it appears three times, which is more frequently compared to other values.
Therefore, the correct measures of center for the given dataset are:
mean: 14.1429
median: 13.5
mode: 17
thats not the anser can you give me another answer
Apologies for the error once again. Let's re-calculate the measures of center for the given dataset:
Arranging the values in ascending order: 5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
Mean:
mean = (5 + 7 + 10 + 11 + 11 + 12 + 15 + 16 + 17 + 17 + 17 + 20 + 21 + 24) / 14
mean = 198 / 14
mean = 14.1429 (rounded to 4 decimal places)
Median:
Since the dataset has an even number of values, we find the average of the two middle values.
median = (12 + 15) / 2
median = 27 / 2
median = 13.5
Mode:
The mode is the value that appears most frequently in the dataset.
In the given dataset, the mode is 17 as it appears three times, which is more frequently compared to other values.
Therefore, the measures of center for the given dataset are:
mean: 14.1429
median: 13.5
mode: 17
People that live in Florida experience hot weather in July. People that live in Australia experience cold weather in July. Why?(1 point)
Responses
The Northern Hemisphere is experiencing day time while the Southern Hemisphere is experiencing night time.
The Northern Hemisphere is experiencing day time while the Southern Hemisphere is experiencing night time.
The Northern Hemisphere is tilted more toward the sun than the Southern Hemisphere in July.
The Northern Hemisphere is tilted more toward the sun than the Southern Hemisphere in July.
Australia is closer to the sun that Florida in July.
Australia is closer to the sun that Florida in July.
Florida is closer to the equator during the month of July.
Florida is closer to the equator during the month of July.
Question 2