What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for π
.(1 point)
Responses
7.07 miles
7.07 miles
14.13 miles
14.13 miles
14.2 miles
14.2 miles
63.59 miles
The circumference of a circle is calculated using the formula C = πd, where C is the circumference and d is the diameter.
Given that the diameter is 4.5 miles, we can calculate the circumference by multiplying the diameter by π.
C = 3.14 * 4.5
C ≈ 14.13 miles
Therefore, the estimated circumference of the circle is 14.13 miles.
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 8/11 as a repeating decimal, we divide 8 by 11.
When we do this long division, we get:
0.727272...
The digits 27 repeat, so we can express 8/11 as 0.72¯¯¯¯¯¯¯¯¯¯.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we define a variable x and set it equal to 0.72¯¯¯¯¯.
x = 0.72¯¯¯¯¯
To remove the repeating decimal, we multiply both sides of the equation by 100:
100x = 72.727272...
Now, we subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 72.727272... - 0.72¯¯¯¯¯
99x = 72
Finally, we simplify the equation by dividing both sides by 99:
x = 72/99
The fraction 72/99 can be simplified further by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = (72/9)/(99/9)
x = 8/11
Therefore, 0.72¯¯¯¯¯ is equal to the rational number 8/11 in simplest form.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
525
5 Start Fraction 2 over 5 end fraction
26−−√
start root 26 end root
517
5 Start Fraction 1 over 7 end fraction
513
A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers.
From the given options, the only number that satisfies this definition is:
5 Start Fraction 2 over 5 end fraction
Therefore, the rational number between 5 and 514 is 5 2/5.
Which of the following is a rational number between 5 and 5/14?(1 point)
Responses
525
5 Start Fraction 2 over 5 end fraction
26−−√
start root 26 end root
517
5 Start Fraction 1 over 7 end fraction
513
A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers.
From the given options, the only number that satisfies this definition is:
5 Start Fraction 1 over 7 end fraction
Therefore, the rational number between 5 and 5/14 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.(1 point)
To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we need to find a number that falls between the two given numbers.
We can start by simplifying the given numbers:
7–√ = 7 - √49 = 7 - 7 = 0
8–√ = 8 - √64 = 8 - 8 = 0
As both numbers simplify to 0, it means that they are equal.
Therefore, there is no rational number with a denominator of 7 that lies between 7–√ and 8–√.