Monique measured the widths of several stamps in her collection of world stamps. The measurements are 158in., 11116in., 134in., and 112in. What is the width of the widest stamp?(1 point)
The width of the widest stamp is 158 inches.
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
14.13 miles
14.13 miles
7.07 miles
7.07 miles
14.2 miles
14.2 miles
63.59 miles
The circumference of a circle can be calculated using the formula: C = πd, where C is the circumference and d is the diameter.
Given a diameter of 4.5 miles, we can calculate the circumference using the value of π as 3.14:
C = 3.14 * 4.5 = 14.13 miles.
Therefore, the estimated circumference of the circle is 14.13 miles.
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To convert 811 to a repeating decimal, we divide 811 by 9:
811 ÷ 9 = 90 with a remainder of 1
Now, we take the remainder (1) and multiply it by 10:
1 × 10 = 10
We divide 10 by 9:
10 ÷ 9 = 1 with a remainder of 1
We continue this process, multiplying the remainder by 10 and dividing by 9 until we see a repeating pattern:
1 × 10 = 10
10 ÷ 9 = 1 with a remainder of 1
1 × 10 = 10
10 ÷ 9 = 1 with a remainder of 1
The repeating pattern of the decimal digits is 1. Therefore, 811 as a repeating decimal is:
811 = 90.1 (repeating)
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To convert 8/11 into a repeating decimal, we perform long division:
0.727 (repeating)
___________
11 | 8.000
We start by dividing 8 by 11. The quotient is 0, which we place to the right of the decimal point. We then write a decimal point and a 0 above the division symbol. Next, we multiply 0 by 11 and subtract it from 8 to get a remainder of 8. We bring down a 0 and repeat the process.
0.727 (repeating)
___________
11 | 8.000
- 0.000
___________
8.000
We then divide 80 by 11, which gives a quotient of 7, followed by a decimal point and a 2 above the division symbol. We multiply 7 by 11 and subtract it from 80, giving a remainder of 3. We bring down another 0 and continue:
0.727 (repeating)
___________
11 | 8.000
- 0.000
___________
8.000
- 7.000
___________
1.000
When we divide 10 by 11, the quotient is 0, followed by a decimal point and a 9 above the division symbol. We multiply 9 by 11 and subtract it from 10, which results in a remainder of 1. Since we have already encountered this situation before, we know that the pattern repeats.
Thus, 8/11 as a repeating decimal is 0.727 (repeating), with the cycle of repeating digits marked by a bar over 27.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can use the method of infinite geometric series.
Let's call the repeating decimal x:
x = 0.72¯¯¯¯¯
To eliminate the repeating part, we can multiply x by 100, since we have two digits repeating:
100x = 72.72¯¯¯¯¯
Now, we can subtract x from 100x to eliminate the repeating part:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Dividing both sides of the equation by 99:
99x/99 = 72/99
Simplifying:
x = 24/33
Further simplifying the fraction by dividing both the numerator and denominator by the greatest common divisor, which is 3:
x = (24/3) / (33/3)
x = 8/11
Therefore, the repeating decimal 0.72¯¯¯¯¯ is equivalent to the rational number 8/11 in simplest form.
To find the width of the widest stamp, you have to compare the measurements and identify the largest value. In this case, Monique measured the widths of several stamps: 158in., 11116in., 134in., and 112in.
To find the largest value, you can follow these steps:
1. Compare the first measurement, 158in., to the others.
2. Compare the second measurement, 11116in., to the others.
3. Compare the third measurement, 134in., to the others.
4. Compare the fourth measurement, 112in., to the others.
By comparing all the measurements, you will find that the widest stamp has a width of 11116in.
Therefore, the width of the widest stamp is 11116in.