Given the figure of a cyclic quadrilateral
The sum of the opposite angles = 180
so, we can write the following equations:
we will find (x) from equation (1):
x = 180 - 100 = 80
We will find (y) from equation (2):
2y = 180 - 102
2y = 78
y=78/2 = 39
So, the answer will be:
x = 80
y = 39
We know that the population is declining at a rate of 14% per year.
The expression is:
N ( x ) = 206 * ( 0.86 ) ^ x
where x stays for years.
If we want to find the rate at which the population is declining per month we have to find:
![\sqrt[12]{0.86} = 0.9875](https://tex.z-dn.net/?f=%20%5Csqrt%5B12%5D%7B0.86%7D%20%3D%200.9875%20%20)
And 0.9875 ≈ 0.99
There are 12 months in a year so the exponent is: x/12
Answer:
b. ( .99 ) ^ x/12
Answer:
P(4≤x≤7) = 2/3
Step-by-step explanation:
We'll begin by obtaining the sample space (S) i.e possible outcome of rolling both dice at the same time. This is illustrated below:
1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
Adding the outcome together, the sample space (S) becomes:
2 3 4 5 6 7
3 4 5 6 7 8
4 5 6 7 8 9
5 6 7 8 9 10
6 7 8 9 10 11
7 8 9 10 11 12
Next, we shall obtain the event of 4≤x≤7. This is illustrated below:
4 5 6 7
4 5 6 7
4 5 6 7
4 5 6 7
4 5 6 7
4 5 6 7
Finally, we shall determine P(4≤x≤7). This can be obtained as follow:
Element in the sample space, n(S) = 36
Element in 4≤x≤7, n(4≤x≤7) = 24
Probability of 4≤x≤7, P(4≤x≤7) = ?
P(4≤x≤7) = n(4≤x≤7) / nS
P(4≤x≤7) = 24/36
P(4≤x≤7) = 2/3
18 is the right answer. The two fractions must be porportional
the 3rd vertex is on the x axis line which means Y =0
since the longer leg is twice as long as the shorter leg and the length of the shorter leg is a, then twice the length would be 2a ( 2 times a)
so the 3rd vertex is (2a,0)
