Answer:
0.150 < (Proportion of Sandy's pie) < 0.167
15% < (Percentage of Sandy's pie) < 16.7%
Step-by-step explanation:
Total percentage of pie = 100% or 1
George, Sandy, Carlos, and Michelle all ate a piece of the pie.
George ate a fraction of 0.150
Michelle ate a fraction of (1/6) = 0.167
Carlos ate a fraction of (1/7) = 0.143
The amount of pie left = 1 - 0.15 - (1/6) - (1/7) = 0.5405
And Sandy is known to eat more than two of her friends, but less than one of them.
Of the amount of pie eaten by the first 3 friends, (1/6) is the highest proportion.
Hence, it is evident that Sandy ate more than 0.143 and 0.150 (Carlos and George) but less than Michelle (0.167).
So, mathematically, the possible proportion of cake that Sandy ate is
0.150 < (Proportion of Sandy's pie) < 0.167
Hope this Helps!!!
Answer:
Step-by-step explanation:
In order for a triangle to be a right triangle, it has to fit into Pythagorean's Theorem:
where c is the hypotenuse.
We need to figure out which is the longest side in each of those triangles and that is the hypotenuse.
In the first set, the sqrt of 443 is 21.04, but that is not the longest side; 24 is. So the Theorem formula for that is:
which gives us
443 + 289 = 576, but 732 does not equal 576, so that one is not right.
In the second set, the sqrt of 725 is the longest side, so that formula is:
which gives us
725 = 196 + 529, and 725 does equal 725, so that one is right.
In the third set, the sqrt of 890 is the longest side, so:
, which gives us
890 = 361 + 529, and 890 = 890, so that is a right triangle as well. That's how you know those are right, compared to the first one that is not.
Answer:
704
Step-by-step explanation:
7000 + 40 (7 thousands + 4 Tens) Divide that by 10.
7040/10 = 704
I think it's 7 hope its right sorry if not
Check the picture below.
so the perimeter of the polygon is the sum of all its sides, namely, AB + BC + CD + DA.
now, let's check how long each side is,
![\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &A&(~{{ -6}} &,&{{ -4}}~) % (c,d) &B&(~{{ -3}} &,&{{ 6}}~) \end{array} \\\\\\ d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\ -------------------------------\\\\ AB=\sqrt{[-3-(-6)]^2+[6-(-4)]^2} \\\\\\ AB=\sqrt{(-3+6)^2+(6+4)^2} \\\\\\ AB=\sqrt{3^2+10^2}\implies \boxed{AB=\sqrt{109}}\\\\ -------------------------------](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26A%26%28~%7B%7B%20-6%7D%7D%20%26%2C%26%7B%7B%20-4%7D%7D~%29%20%0A%25%20%20%28c%2Cd%29%0A%26B%26%28~%7B%7B%20-3%7D%7D%20%26%2C%26%7B%7B%206%7D%7D~%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0AAB%3D%5Csqrt%7B%5B-3-%28-6%29%5D%5E2%2B%5B6-%28-4%29%5D%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AAB%3D%5Csqrt%7B%28-3%2B6%29%5E2%2B%286%2B4%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AAB%3D%5Csqrt%7B3%5E2%2B10%5E2%7D%5Cimplies%20%5Cboxed%7BAB%3D%5Csqrt%7B109%7D%7D%5C%5C%5C%5C%0A-------------------------------)
![\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &B&(~{{ -3}} &,&{{6}}~) % (c,d) &C&(~{{ 4}} &,&{{ 0}}~) \end{array} \\\\ -------------------------------\\\\ BC=\sqrt{[4-(-3)]^2+[0-6]^2}\implies BC=\sqrt{(4+3)^2+(0-6)^2} \\\\\\ BC=\sqrt{7^2+(-6)^2}\implies \boxed{BC=\sqrt{85}}\\\\ -------------------------------](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26B%26%28~%7B%7B%20-3%7D%7D%20%26%2C%26%7B%7B6%7D%7D~%29%20%0A%25%20%20%28c%2Cd%29%0A%26C%26%28~%7B%7B%204%7D%7D%20%26%2C%26%7B%7B%200%7D%7D~%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0ABC%3D%5Csqrt%7B%5B4-%28-3%29%5D%5E2%2B%5B0-6%5D%5E2%7D%5Cimplies%20BC%3D%5Csqrt%7B%284%2B3%29%5E2%2B%280-6%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0ABC%3D%5Csqrt%7B7%5E2%2B%28-6%29%5E2%7D%5Cimplies%20%5Cboxed%7BBC%3D%5Csqrt%7B85%7D%7D%5C%5C%5C%5C%0A-------------------------------)

![\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &D(~{{ 2}} &,&{{-1}}~) % (c,d) &A&(~{{ -6}} &,&{{ -4}}~) \end{array}\\\\ -------------------------------\\\\ DA=\sqrt{[-6-2]^2+[-4-(-1)]^2}\\\\\\ DA=\sqrt{(-6-2)^2+(-4+1)^2} \\\\\\ DA=\sqrt{(-8)^2+(-3)^2}\implies \boxed{DA=\sqrt{73}}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26D%28~%7B%7B%202%7D%7D%20%26%2C%26%7B%7B-1%7D%7D~%29%20%0A%25%20%20%28c%2Cd%29%0A%26A%26%28~%7B%7B%20-6%7D%7D%20%26%2C%26%7B%7B%20-4%7D%7D~%29%0A%5Cend%7Barray%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0ADA%3D%5Csqrt%7B%5B-6-2%5D%5E2%2B%5B-4-%28-1%29%5D%5E2%7D%5C%5C%5C%5C%5C%5C%20DA%3D%5Csqrt%7B%28-6-2%29%5E2%2B%28-4%2B1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0ADA%3D%5Csqrt%7B%28-8%29%5E2%2B%28-3%29%5E2%7D%5Cimplies%20%5Cboxed%7BDA%3D%5Csqrt%7B73%7D%7D)
sum those sides up, and that's the perimeter of the polygon.