Answer:
1. The quotient in simplest form is 4
2. It take him 8 minutes to run 1 mile.
Step-by-step explanation:
Given:
9 divided by 2 1/4.
Sean runs 3 1/2 miles in 28 minutes.
Now, to find the quotient in simplest form and the time it takes Sean to run 1 mile.
1. 9 divided by 2 1/4.
![9\div 2\frac{1}{4}](https://tex.z-dn.net/?f=9%5Cdiv%202%5Cfrac%7B1%7D%7B4%7D)
Converting mixed fraction into improper:
= ![9\div \frac{9}{4}](https://tex.z-dn.net/?f=9%5Cdiv%20%5Cfrac%7B9%7D%7B4%7D)
Converting 9/4 into decimal:
= ![9\div 2.25](https://tex.z-dn.net/?f=9%5Cdiv%202.25)
= ![4.](https://tex.z-dn.net/?f=4.)
Therefore, the quotient in simplest form is 4.
2. Sean runs 3 1/2 miles in 28 minutes.
Sean runs 7/2 miles in 28 minutes.
Now, solving it by unitary method:
Sean runs 7/2 miles in 28 minutes.
Sean runs 1 mile in =
.
= ![28\div 3.5](https://tex.z-dn.net/?f=28%5Cdiv%203.5)
= ![8\ minutes.](https://tex.z-dn.net/?f=8%5C%20minutes.)
Therefore, it take him 8 minutes to run 1 mile.
<u>Answer</u>:
A regular polygon first maps directly onto itself after rotating 20 degrees has 18 sides
<u>Explanation</u>:
Given:
Angle rotated=20 degrees
To find:
Number of sides the polygon has=?
Solution:
![\text { The number of sides the polygon have }=\frac{\text { total angle }}{\text { angle rotated }}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20The%20number%20of%20sides%20the%20polygon%20have%20%7D%3D%5Cfrac%7B%5Ctext%20%7B%20total%20angle%20%7D%7D%7B%5Ctext%20%7B%20angle%20rotated%20%7D%7D)
![\text { We know that the total angle of polygon }=360^{\circ}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20We%20know%20that%20the%20total%20angle%20of%20polygon%20%7D%3D360%5E%7B%5Ccirc%7D)
![\text { The number of sides the polygon have }=\frac{360^{\circ}}{20^{\circ}}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20The%20number%20of%20sides%20the%20polygon%20have%20%7D%3D%5Cfrac%7B360%5E%7B%5Ccirc%7D%7D%7B20%5E%7B%5Ccirc%7D%7D)
![\text { The number of sides the polygon have }=18\\](https://tex.z-dn.net/?f=%5Ctext%20%7B%20The%20number%20of%20sides%20the%20polygon%20have%20%7D%3D18%5C%5C)
RESULT:
Hence the number of sides the polygon has =18
The area of the frame not covered by the painting is 192 square inches
<em><u>Solution:</u></em>
Given that, A rectangular painting is 24 inches wide and 20 inches tall without the frame
The area of rectangle is given as:
![Area = length \times width](https://tex.z-dn.net/?f=Area%20%3D%20length%20%5Ctimes%20width)
<em><u>Find the area of painting without frame:</u></em>
Length = 20 inches
Width = 24 inches
![Area\ Without\ Frame = 20 \times 24 = 480](https://tex.z-dn.net/?f=Area%5C%20Without%5C%20Frame%20%3D%2020%20%5Ctimes%2024%20%3D%20480)
Thus area of painting without frame is 480 square inches
With the frame, it is 28 inches wide and 24 inches tall
<em><u>Find the area of painting with frame:</u></em>
Length = 24 inches
Width = 28 inches
![Area\ with\ frame = 24 \times 28 = 672](https://tex.z-dn.net/?f=Area%5C%20with%5C%20frame%20%3D%2024%20%5Ctimes%2028%20%3D%20672)
Thus area of painting with frame is 672 square inches
<em><u>What is the area of the frame not covered by the painting</u></em>
Area of the frame not covered by the painting = Area with farme - Area without frame
Area of the frame not covered by the painting = 672 - 480 = 192
Thus the area of the frame not covered by the painting is 192 square inches
Answer:
D. The students are not part of the population
Step-by-step explanation:
The first three options are true of this sample. D is the only option that is not true.