The draws are independent, so

There is a total of 11 marbles in the bag, so

and

So

Answer:
He stepped back 59.71 feet.
Step-by-step explanation:
Start by making 2 triangles. One has 68 degrees as the acute angle at the base of the triangle and the other has 41 degrees as the acute angle at the base of the triangle. The side opposite of said angle on both triangles will be 80, the height of the tree. You're solving for the bottom (horizontal) side for both triangles.
For the triangle with an acute base angle of 68, the formula to solve for the horizontal side is tan(68) = 80/x.
Get x by itself to get 80/tan(68) = x
x = 32.32.
For the next triangle, the equation is the same but the angle is changed to 41.
tan(41) = 80/x
80/tan(41) = x
x = 92.03
Finally, subtract the smaller distance from the larger:
92.03 - 32.32 = 59.71 steps.
Answer:
x ≥ -4
Step-by-step explanation:
-3x + 2 ≤ 14
Subtract 2 from each side
-3x+2-2 ≤ 14-2
-3x ≤ 12
Divide each side by -3 . Remember that dividing by a negative flips the inequality.
-3x/-3 ≥12/-3
x ≥ -4
Each part of diagram Venn is shown below
We have:
Total students = 800
Students in Gymnastic team = 20
Students in Chess team = 10
Students in both team = 3
The Venn diagram showing these values is shown in the second picture below