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Pavlova-9 [17]
3 years ago
7

Solve the following system of equations

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
8 0

Answer:

x = -9

y = -3

Step-by-step explanation:

We can first multiply the 2nd equation by -6, so we have:

-6*[-0.8x+0.4y=6]\\=4.8x-2.4y=-36

Now, we add up this equation to the 1st equation given to eliminate y and solve for x. Shown below:

1.2x+2.4y=-18\\4.8x-2.4y=-36\\---------\\6x=-54\\x=-9

So, we have the value of x to be -9

Now, we substitute this value in 1st equation and solve for y:

1.2x+2.4y=-18\\1.2(-9)+2.4y=-18\\-10.8+2.4y=-18\\2.4y=-7.2\\y=-3

The value of y is -3

So,

<u>x = -9</u>

<u>y = -3</u>

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Given:

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Probability of population is 65 or older is 10.5%.

This date follows the binomial distribution,

\begin{gathered} n=25,p=0.105 \\ X\rightarrow B(n=25,p=0.105) \end{gathered}

To find the probability that at most 2 are 65 or older,

\begin{gathered} P(X=x)=^nC_x(p)^x(1-p)^{n-x} \\ P(0\leq X\leq2)=P(X=0)+P(X=1)+P(X=2) \\ =^{25}C_0(0.105)^0(1-0.105)^{25-0}+^{25}C_1(0.105)^1(1-0.105)^{25-1}+^{25}C_2(0.105)^2(1-0.105)^{25-2} \\ =0.0625+0.1832+0.2579 \\ =0.5036 \\ \approx0.504 \end{gathered}

Answer: Probability is 0.504 .

8 0
1 year ago
The graph below shows the solution to which system of inequalities?
nlexa [21]

Answer:

Option D.

Step-by-step explanation:

Consider option D. y\leq \frac{3x}{4}+10\,,\,y\leq \frac{-x}{2}-3

Take point (0,0)

On putting this point in inequation y\leq \frac{3x}{4}+10 , we get

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On putting (0,0) in inequation y\leq \frac{-x}{2}-3 , we get 0\leq -3 which is false , so solution is region away from the origin i.e region below line y= \frac{-x}{2}-3 including the line itself .

So, common solution to both the inequations is the shaded part in the given figure .

In other words, we can say that the graph shown in the given figure represents system of equations: y\leq \frac{3x}{4}+10\,,\,y\leq \frac{-x}{2}-3

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