Ray AD, since D is at 105°
Answer:
No
Step-by-step explanation:
It will be a right triangle if it follows Pyhthagoras Theorem . Where the sum of squares of two smaller sides is equal to the square of the 3rd side. Let's check ,
→ 11²+ 12² = 13²
→ 121 + 144 = 169
→ 265 ≠ 169
<h3>Hence the ∆ is not a right angled triangle </h3>
p(x) = 90 / (9 + 50 * e^(-x))
e = 2.718, so we can use e = 2.7 as a quick substitute
p(3) =>
90 / (9 + 50 * e^(-3)) =>
90 / (9 + 50 * 2.7^(-3)) =>
90 / (9 + 50 / 2.7^3) =>
90 / ((9 * 2.7^3 + 50) / 2.7^3) =>
90 * 2.7^3 / (9 * 2.7^3 + 50)
2.7^3 =>
(27/10)^3 =>
27^3 / 1000 =>
729 * 27 / 1000 =>
2187 * 9 / 1000 =>
6561 * 3 / 1000 =>
19683 / 1000 =>
19.683
90 * 2.7^3 / (9 * 2.7^3 + 50) =>
90 * 19.683 / (9 * 19.683 + 50)
9 * 19.683 =>
9 * (20 - 0.317) =>
180 - 9 * 0.317 =>
180 - 9 * 0.3 - 9 * 0.017 =>
180 - 2.7 - 9 * 0.01 - 9 * 0.007 =>
177.3 - 0.09 - 0.063 =>
177.3 - 0.153 =>
177.15 - 0.003 =>
177.147
90 * 19.683 / (9 * 19.683 + 50) =>
10 * 177.147 / (177.147 + 50) =>
1771.47 / 227.147 =>
1771470 / 227147 =>
1770000 / 225000 =>
1770/225 =>
4 * 1770 / 900 =>
4 * 177 / 90 =>
708/90 =>
70.8 / 9 =>
23.6 / 3 =>
(21 + 2.6) / 3 =>
7 + 0.866666.... =>
7.8666666...
Actual value: 7.8333389811057471507345888320992.....
Not bad for some estimates, is it?
The lengths of the sides of the triangles are:
<span>AU = 20x + 108,
UB = 273,
BC = 703,
UV = 444,
AV = 372 and
AC = 589.
Similarity implies: AB / BC = AU / UV
And AB = AU + UV = 20x + 108 + 273 = 20x + 381
=> (20x + 381) / (703) = (20x + 108) / 444
=> (20x + 381) (444) = (20x + 108)(703)
=> 8880x + 169164 = 14060x + 75924
=> 14060x - 8880x = 169164 - 75924
=> 5180x = 93240
=> x = 93240 / 5180
=> x = 18
Answer: 18
</span>
The estimate would be 1200.
We will set up a proportion for this. 10 out of 60 of the sample were tagged, so that is the first ratio. The 200 that were tagged would be in the numerator of the second ratio (10 was the portion tagged, and 200 is the portion tagged, so they both go on top). We do not know the total number so we use a variable:
10/60 = x/200
Cross multiply:
10*x = 60*200
10x = 12000
Divide both sides by 10:
10x/10 = 12000/10
x = 1200