The probability that you can get N heads in a row would be:
Let <span>p</span> be the probability of flipping a heads. Let <span>x</span> be number of flips needed to achieve <span>h </span>consecutive heads. The solution is <span><span>E(x) = (<span><span>1−<span>p^h) / (</span></span><span><span>p^h</span>(1−p))</span></span></span></span>
This expression may be derived as follows. The probability of being successful immediately is <span><span>p^r.</span></span> However, one might get a tails immediately. In that case, the number of flips needed is <span><span>1+E(x) </span></span>(one flip has been used and we are back to the original position). We might get a heads and then a tails. In this case two flips have been used and we are back to the original position. Continue this up to <span><span>h−1</span></span> heads followed by a tails in which case <span>h</span> flips have been used and we are back to the original position.
Answer:height = 15 yd
Base = 20 yd
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = 1/2 base × height.
From the information given, the area of the triangle is 150 yd.² the height is x +5 and the base is 3x -10.
Therefore,
150 = 1/2 × (3x - 10)(x + 5)
300 = 3x^2 + 15x - 10x - 50
300 + 50 = 3x^2 + 5x
350 = 3x^2 + 5x
3x^2 + 5x - 350 = 0
3x^2 + 35x - 30x - 350 = 0
x(3x + 35) - 10(3x + 35) = 0
x - 10 = 0 or 3x + 35 = 0
x = 10 or x = - 35/3
Since the dimensions cannot be negative, then x = 10
The height = x + 5 = 10 + 5 = 15 yd
The base = 3x - 10 = 3×10 - 10 = 20 yd
The answer is 25!
3 times 7 = 21 + 4 = 25
<em>y</em> - 1/<em>z</em> = 1 ==> <em>y</em> = 1 + 1/<em>z</em>
<em>z</em> - 1/<em>x</em> = 1 ==> <em>z</em> = 1 + 1/<em>x</em>
==> <em>y</em> = 1 + 1/(1 + 1/<em>x</em>) = 1 + <em>x</em>/(<em>x</em> + 1) = (2<em>x</em> + 1)/(<em>x</em> + 1)
<em>x</em> - 1/<em>y</em> = <em>x</em> - (<em>x</em> + 1)/(2<em>x</em> + 1) = (2<em>x</em> ² - 1)/(2<em>x</em> + 1) = 1
==> 2<em>x</em> ² - 1 = 2<em>x</em> + 1
==> 2<em>x</em> ² - 2<em>x</em> - 2 = 0
==> <em>x</em> ² - <em>x</em> - 1 = 0
==> <em>x</em> = (1 ± √5)/2
If you start solving for <em>z</em>, then for <em>x</em>, then for <em>y</em>, you would get the same equation as above (with <em>y</em> in place of <em>x</em>), and the same thing happens if you solve for <em>x</em>, then <em>y</em>, then <em>z</em>. So it turns out that <em>x</em> = <em>y</em> = <em>z</em>.
Answer:
You need to use sohcahtoa to find your answer.
first you gotta identify what sides of the triangle you have.
You're missing the hypotenuse, and you have the value of the adjacent.
since you have the adjacent and need the hypotenuse, you're going to use cosine to find x
cos(65) = 16/x
x = 37.859