Write the following fraction as tenths in fraction and decimals.4/10

Mathematics

2 answers:

Veseljchak [2.6K]3 years ago

3 0

If you wanted to write 4/10 as a decimal it would be .4

Nataly [62]3 years ago

3 0

The decimal would be 0.4 and the simplest form of fractions would be 2/5

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Please solve the problem

jek_recluse [69]

Treat the matrices on the right side of each equation like you would a constant.

Let 2X + Y = A and 3X - 4Y = B.

Then you can eliminate Y by taking the sum

4A + B = 4 (2X + Y) + (3X - 4Y) = 11X

==> X = (4A + B)/11

Similarly, you can eliminate X by using

-3A + 2B = -3 (2X + Y) + 2 (3X - 4Y) = -11Y

==> Y = (3A - 2B)/11

It follows that

$X=\dfrac4{11}\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\dfrac1{11}\begin{bmatrix}7&-10\\-7&11\end{bmatrix} \\\\ X=\dfrac1{11}\left(4\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\left(\begin{bmatrix}48&-12\\40&88\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\begin{bmatrix}55&-22\\33&99\end{bmatrix} \\\\ X=\begin{bmatrix}5&-2\\3&9\end{bmatrix}$

Similarly, you would find

$Y=\begin{bmatrix}2&1\\4&4\end{bmatrix}$

You can solve the second system in the same fashion. You would end up with

$P=\begin{bmatrix}2&-3\\0&1\end{bmatrix} \text{ and } Q=\begin{bmatrix}1&2\\3&-1\end{bmatrix}$

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A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide i

Vilka [71]

Answer:

The probability that exactly 10 insects will die

P( X = 10 ) = 0.06385

Step-by-step explanation:

Step(i):-

Given a certain insecticide kills 60% of all insects in laboratory experiments

Given proportion p = 0.60

q = 1 - 0.60 = 0.40