The appropriate method to use in solving the given question is permutation. Then, the numbers of ways to arrange the buttons is 1320 ways.
In the given question, the order of arrangement is important, so that the number of ways that Fiona could order the buttons can be determined by permutation method.
i.e 
= 
Red 6
Green 3
Yellow 3
Total 12
Since no two neighbouring buttons of the same colour is allowed, then 3 buttons would be arranged at a time.
Thus, n = 12 and r = 3;
= 
= 
= 
= 12 x 11 x 10
= 1320
Therefore the buttons can be arranged in 1320 ways without two neighbors having the same colour.
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Way 1:
a triangle with sides 3,4,5 will make a triangle. because this isn't 3,4,5 triangle it wont work.
way 2:
By using Heron's formula you can find the area of the flower bed.
<span>s=(a+b+c) ÷2
</span><span>Area =√s(s-a)(s-b)(s-c)
</span>so, 3+4+8= 15
15÷2 =7.5
√7.5(7.5-3)(7.5-4)(<span>7.5-8)
</span>Now because 7.5-8 gives you a negative number and you can't have a negative number under a square root unless you want to use an imaginary number, it won't form a triangle.
Answer:
9
Step-by-step explanation:
a^2 + b^2 = h^2
15^2= 12^2 + b^2
225=144+b^2
81=b^2
9
The law of cosines states that, if 
is the angle between sides b and c,
So, plugging our values, we have
This is equal to
Answer:
0.625
Step-by-step explanation:
Given :
Ambell company uses or procures batteries from two manufacturers.
The life of a battery in critical tool is at = 32 hours
Ambell uses 70% of its batteries from manufacturer 1 and out of that 90% batteries lasts for about 40 hours.
Similarly, 75% of the batteries procured from the manufacturer 2 lasts for about 40 hours.
Therefore, the probability that a battery is form manufacturer 1 is :
= 0.625
