Answer:
P(inside larger square and outside smaller) = 
Step-by-step explanation:
Probability is the result of the division of the number of possible outcome by the number of an event.
In the question, for a point chosen, the point can be in the small square only or in the area or region between the small square and the big square as such,
Area of larger square = area of region between both squares + area of smaller square
Where the area of a square is S × S where S is the side of a square
Area of larger square = 10 × 10
= 100 cm square
Area of smaller square = 7 × 7
= 49 cm square
Area of the region between both squares
= 100 - 49
= 51 cm square
The probability that a dot selected is inside the larger square and outside the smaller is
P(inside larger square and outside smaller) = Area of region between both square/ Area of larger square
P(inside larger square and outside smaller) =
We need to define our outcomes and events.
Finding the probability<span> of each event occurring
separately, and then multiplying the probabilities is the step to <span>finding
the probability</span> of two
independent events that occur in
sequence.
</span>
<span>
To solve this problem, we take note of this:</span>
The roll of the two dice are denoted by the pair
(I, j) ∈ S={ (1, 1),(1, 2),..., (6,6) }
Each pair is an outcome. There are 36 pairs and each has
probability 1/36. The event “doubles” is { (1, 1),(2, 2)(6, 6) } has
probability p= 6/36 = 1/6. If we define ”doubles” as a successful roll, the
number of rolls N until we observe doubles is a geometric (p) random variable
and has expected value E[N] = 1/p = 6.
Answer:
y − 3 = 2(x − 1)
Step-by-step explanation:
The point-slope form of the equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
You have m=2, h=1, k=3, so the equation is ...
y -3 = 2(x -1)
1st box:
m<A + m<B + m<C = 180
2nd box:
substitution property
3rd box:
division property of equality
Hope it helps.
I suppose you just have to simplify this expression.
(2ˣ⁺² - 2ˣ⁺³) / (2ˣ⁺¹ - 2ˣ⁺²)
Divide through every term by the lowest power of 2, which would be <em>x</em> + 1 :
… = (2ˣ⁺²/2ˣ⁺¹ - 2ˣ⁺³/2ˣ⁺¹) / (2ˣ⁺¹/2ˣ⁺¹ - 2ˣ⁺²/2ˣ⁺¹)
Recall that <em>n</em>ª / <em>n</em>ᵇ = <em>n</em>ª⁻ᵇ, so that we have
… = (2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺³⁾ ⁻ ⁽ˣ⁺¹⁾) / (2⁽ˣ⁺¹⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾)
… = (2¹ - 2²) / (2⁰ - 2¹)
… = (2 - 4) / (1 - 2)
… = (-2) / (-1)
… = 2
Another way to get the same result: rewrite every term as a multiple of <em>y</em> = 2ˣ :
… = (2²×2ˣ - 2³×2ˣ) / (2×2ˣ - 2²×2ˣ)
… = (4×2ˣ - 8×2ˣ) / (2×2ˣ - 4×2ˣ)
… = (4<em>y</em> - 8<em>y</em>) / (2<em>y</em> - 4<em>y</em>)
… = (-4<em>y</em>) / (-2<em>y</em>)
… = 2
