Which context describes a difference of rational numbers?
A. Comparing the daily high temperature and low temperature
B. Finding the average of daily high temperatures
C. Recording the temperature hourly
D. Determining the coldest temperature in a month
A. Comparing the daily high temperature and low temperature
Which scenario about books represents finding the difference?
A. Finding the location of a book in a store
B. Finding the number of books remaining after a sale on books
C. Finding the type of books in a store
D. Finding the total number of books in a store when new books arrive
B. Finding the number of books remaining after a sale on books
Which of the following is an irrational number between 5 and 7: 6–√, 12−−√, 27−−√, 36−−√?
The irrational number that lies between 5 and 7 is √6.
The temperature on Monday is −4°C. On Tuesday, it is 13° colder. What is the temperature on Tuesday?
A. −17°C
B. 9°C
C. −9°C
D. 17°C
To find the temperature on Tuesday, we need to subtract the decrease of 13 degrees from the temperature on Monday.
-4°C - 13°C = -17°C
Therefore, the temperature on Tuesday is -17°C.
A. -17°C
Really? I thought it was the square root of 27.
Apologies for the incorrect response.
To find the temperature on Tuesday, we need to subtract 13 degrees from the temperature on Monday, which is -4°C.
-4°C - 13°C = -17°C
Therefore, the temperature on Tuesday is -17°C.
A. -17°C is the correct answer.
Ping dove off a 10 meter platform. He reached a depth of 6 meters in the water. What was the change in height?
A. 60 meters
B. 4 meters
C. 16 meters
D. 64 meters
The change in height is calculated by subtracting the initial height from the final depth.
Initial height: 10 meters
Final depth: 6 meters
Change in height = Final depth - Initial height
Change in height = 6 meters - 10 meters
Change in height = -4 meters
Since the change in height is -4 meters, the correct answer is:
B. 4 meters
What is the largest integer whose square root is an irrational number between 3 and 4?
In order to find the largest integer whose square root is an irrational number between 3 and 4, we need to find the largest perfect square that is less than or equal to 4.
The largest perfect square less than or equal to 4 is 4 itself, which has a square root of 2.
Therefore, the largest integer whose square root is an irrational number between 3 and 4 is:
C. 2
Find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.
To find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, we follow these steps:
1. Add the two numbers together: 2 + 214 = 216.
2. Divide the sum by 2: 216 ÷ 2 = 108.
So, the rational number between 2 and 214 is 108.
To write this as a mixed number, we can express 108 as a whole number and a fraction. Since 108 is greater than 100, we can write it as a mixed number using the whole number part 100 and the fractional part 8/1.
Thus, the rational number between 2 and 214 can be written as:
108 = 100 + 8/1.
The mixed number representation is:
100 8/1.
Find a rational number between 2 and 2/14 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.
To find a rational number between 2 and 2/14 using the method of adding the numbers together and dividing by 2, we follow these steps:
1. Add the two numbers together: 2 + 2/14 = 28/14 + 2/14 = 30/14.
2. Divide the sum by 2: (30/14) / 2 = 30/14 * 1/2 = 30/28.
So, the rational number between 2 and 2/14 is 30/28.
To write this as a mixed number, we can simplify the fraction and express it as a whole number and a fraction. The fraction 30/28 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
30 ÷ 2 / 28 ÷ 2 = 15/14.
Now, we can write the rational number as a mixed number. The whole number part will be 1 because 15 is greater than 14. The fractional part will be 1/14 because after subtracting the whole number part (1), we are left with 1.
So, the rational number between 2 and 2/14 can be written as:
30/28 = 1 + 1/14.
The mixed number representation is:
1 1/14.
A parasail is 1/20 of a meter above the water. Then, after 10 minutes, the parasail is 1/50 of a meter above the water. What is the change in height?
To find the change in height, we need to subtract the initial height from the final height.
Initial height: 1/20 meters
Final height: 1/50 meters
Change in height = Final height - Initial height
Change in height = (1/50) - (1/20)
Change in height = (1/50) - (2/100)
Change in height = (1/50) - (1/50)
Change in height = 0
Therefore, the change in height is 0 meters.
A parasail is 1/20 of a meter above the water. Then, after 10 minutes, the parasail is 1/50 of a meter above the water. What is the change in height?
A. 1/50 meter
B. 3/100 meter
C. 7/100 meter
D. 1/20 meter
To find the change in height, we need to subtract the initial height from the final height.
Initial height: 1/20 meter
Final height: 1/50 meter
Change in height = Final height - Initial height
Change in height = (1/50) - (1/20)
Change in height = (2/100) - (5/100)
Change in height = (2 - 5)/100
Change in height = -3/100
Therefore, the change in height is -3/100 meter.
So, the correct option is:
B. -3/100 meter