First difference
12-5 = 7
21-12 = 9
32-21 = 11
Second difference
9-11 = 2
11-9 = 2
second difference is constant so it could defined by quadratic formula,
u(x) = ax^2 + bx + c
because 2a = Second difference = 2
so a = 1
then u(x) = x^2 + bx + c
build equations from known values to find b and c
for x=1, u(1) = 5 = 1^2 + b(1) + c
b + c = 4 ...(1)
x=2, u(2) = 12 = 2^2 + b(2) + c
2b + c = 8 ... (2)
solve b = 4, c =0
so u(x) = x^2 + 4x ... formula for n term (i use x not n here)
difference between consecutive term is 245, we have
245 = u(x+1) - u(x)
245 = (x+1)^2 + 4(x+1) - (x^2 + 4x)
245 = x^2 + 2x + 1 + 4x + 4 - x^2 - 4x
245 = 2x + 5
x = 120
it's between term 120 and 121
graph is y=2
Using proportions, it is found that there is a 0.54 = 54% probability that a randomly selected household owns a cat.
<h3>What is a proportion?</h3>
A proportion is a fraction of total amount.
In this problem, the proportions associated with owning a cat are given by:
- 70% of 60%(also have a dog).
- 30% of 40%(do not have a dog).
Hence:
p = 0.7(0.6) + 0.3(0.4) = 0.42 + 0.12 = 0.54.
0.54 = 54% probability that a randomly selected household owns a cat.
More can be learned about proportions at brainly.com/question/24372153
Answer:
Cost to arrange the event for 5 attendees will be $20.
Step-by-step explanation:
We have to solve this question by calculating the unit rates or unitary method.
Since cost to arrange corporate team building event for 3 attendees is = $12
Cost to arrange the event for 1 attendee will be = = $4
Therefore, cost to arrange the event for five attendees will be = 5×4 = $20
<span>0 = x² + 10x + 16
Subtract </span><span>x^2+10x+16 from each side
</span><span>0−<span>(<span><span>x^2+10x</span>+16</span>) </span></span>= x^2+10x+16−(<span>x^2+10x+16</span>)
<span><span>−x^2−10x</span>−16</span>=<span>0
</span>
Factor left side
<span><span>(<span>−x−2</span>)</span><span>(x+8)</span></span>=<span>0
</span>
Set all factors to equal 0
<span><span><span>−x</span>−2</span>=<span><span><span>0<span> or </span></span>x</span>+8</span></span>=<span>0
</span>
The solutions are x = -2 and x = -8