Answer: Assume the cross section is taken at the same height where the circumference was measured. Then
48/3 = 16 inches, close enough, actually. Trees aren't cylinders.
48 × 7 / 22 inches = 15.2727272
48/3.1415926 = 15.2788747
48/pi = 15.2788745368219522338128412837... ☺️
Step-by-step explanation:
circumference / diameter = pi = 3.1415926......
So diameter = circumference / pi.
2y+3=-2/3(x-3)
minus 3 both sides
2y=-2/3(x-3)-3
divide both sides by 2
y=-1/3(x-3)-3/2
ok, so one thing we can do is evaluate numbers super close to it
when x=3.00001, then the result is aprox -1.5
when x=2.99999, the result is -1.5
the value of the limit is -1.5 or -3/2
Answer:
the mistake they made was the wrong offset from point (0,0) into the y direction. the incline of the line was correct.
the correct equation is y = 1/2×x - 2, because this line contains both points (4,0) and (0,-2)
Step-by-step explanation:
we are looking for a line equation
y = a×x + b
the 2 points give us 2 equations to solve for the 2 variables a and b :
0 = a×4 + b
-2 = a×0 + b
=> b = -2
=> -b = a×4, => a = -b/4 = 2/4 = 1/2
so, the right equation for the line going through both points is
y = 1/2×x - 2
the difference to the original equation is simply the offset from the x- axis in the y direction.
the original equation would be parallel to the correct equation but hit the y-axis at (0,4) instead of (0,-2), and it would hit the x-axis at (-8,0) instead of (4,0)
Answer:
Angle CAD is 44 degrees
Angle ACD is 44 degrees
Angle ACB is 136 degrees
Angle ABC is 22 degrees
Explanation:
29. Triangle ADC is an isosceles triangle because it has two equal sides.
If segments AD and DC are congruent, then segment AC is the base and the base angles of an isosceles triangle are equal.
Let x be angle CAD.
Let's go ahead x;
![\begin{gathered} 92+x+x=180\text{ (sum of angles in a triangle)} \\ 92+2x=180 \\ 2x=180-92 \\ 2x=88 \\ x=\frac{88}{2} \\ \therefore x=44^{\circ} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2092%2Bx%2Bx%3D180%5Ctext%7B%20%28sum%20of%20angles%20in%20a%20triangle%29%7D%20%5C%5C%2092%2B2x%3D180%20%5C%5C%202x%3D180-92%20%5C%5C%202x%3D88%20%5C%5C%20x%3D%5Cfrac%7B88%7D%7B2%7D%20%5C%5C%20%5Ctherefore%20x%3D44%5E%7B%5Ccirc%7D%20%5Cend%7Bgathered%7D)
Therefore, measure of angle CAD is 44 degrees.
30. Measure of angle ACD is 44 degrees (Base angles of an isosceles triangle are equal)
31. Let angle ACB be y,
Let's go ahead and find measure of angle ACB;
![\begin{gathered} 44+y=180\text{ (angles on a straight line)} \\ y=180-44 \\ \therefore y=136^{\circ} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2044%2By%3D180%5Ctext%7B%20%20%20%20%20%28angles%20on%20a%20straight%20line%29%7D%20%5C%5C%20y%3D180-44%20%5C%5C%20%5Ctherefore%20y%3D136%5E%7B%5Ccirc%7D%20%5Cend%7Bgathered%7D)
So measure of angle ACB is 136 degrees.
32. Let angle ABC be z.
Triangle ACB is also an isosceles triangle so the base angles are the same.
Let's go ahead and find z;
![\begin{gathered} 136+z+z=180_{}\text{ (sum of angles in a triangle)} \\ 138+2z=180 \\ 2z=180-136 \\ 2z=44 \\ z=\frac{44}{2} \\ \therefore z=22^{\circ} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20136%2Bz%2Bz%3D180_%7B%7D%5Ctext%7B%20%20%20%20%28sum%20of%20angles%20in%20a%20triangle%29%7D%20%5C%5C%20138%2B2z%3D180%20%5C%5C%202z%3D180-136%20%5C%5C%202z%3D44%20%5C%5C%20z%3D%5Cfrac%7B44%7D%7B2%7D%20%5C%5C%20%5Ctherefore%20z%3D22%5E%7B%5Ccirc%7D%20%5Cend%7Bgathered%7D)
So measure of angle ABC is 22 degrees.
Answer:
The probability of passing the course given that the course taken was statistics = P(pass|C) = 0.7414
Step-by-step explanation:
This is a combined probability question
PASS FAIL Withdrew TOTAL
(C) .238 .044 .039 .321
(S) .559 .051 .069 .679
(T) .797 .095 .108 1
C represents probability data from Calculus exam and S represents probability data from Statistics exam
Compute the probability of passing the course given that the course taken was statistics = P(pass|C)
Mathematically, this is given by
P(pass|C) = P(pass n C)/P(C)
Probability of passing Calculus, P(pass n C) = 0.238 (from the table)
Probability of offering Calculus, P(C) = 0.321 (from the table)
the probability of passing the course given that the course taken was statistics is P(pass|C)
P(pass|C) = 0.238/0.321 = 0.7414