A grid with 3 rows and 52 columns is tiled with 78 identical 2x1 dominoes. How many ways can this be done such that exactly two of the dominoes are vertical?
There are 39 ways that exactly two of the dominoes are vertical.
Answer:
i)32C16
ii)1185408
<em><u>Explanation</u></em><em><u>:</u></em>
i)Total number of selected/eligible is 7+9+8+8=32
Total ways of selecting dance committee of 16 is
<em><u>3</u></em><em><u>2</u></em><em><u>C</u></em><em><u>1</u></em><em><u>6</u></em>
ii)Total ways of selecting 3 seniors from 8 is 8C3
and Total ways of selecting 6 juniors from 8 is 8C6
ways of selecting 2 sopho from 9 is 9C2
ways of selecting 5 freshman from 7 is 7C5
now, total way of selection come to be
8C3×8C6×9C2×7C5
=56×28×36×21
=1185408
✌️
M<2 = 90 - 64 = 26
answer
26
Answer:
The initial mass of the sample was 16 mg.
The mass after 5 weeks will be about 0.0372 mg.
Step-by-step explanation:
We can write an exponential function to model the situation.
Let the initial amount be A. The standard exponential function is given by:
Where r is the rate of growth/decay.
Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:
After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.
Therefore, when x = 12, P(x) = 2. By substitution:
Solve for A. Simplify:
Simplify:
Thus, the initial mass of the sample was:
5 weeks is equivalent to 35 days. Therefore, we can find P(35):
About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.
Answer:
x=14
Step-by-step explanation:
(7x - 1)° + (6x - 1)° = 180°
(13x - 2)° = 180°
13x = 182°
x = 182°/13
x = 14