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Aneli [31]
2 years ago
8

Solve the simultaneous equations 5x+2y=25 5x-y=10

Mathematics
1 answer:
Pavlova-9 [17]2 years ago
4 0

<em>5x + 2y = 25;</em>

<em>5x + 2y = 25;5x - y = 10;</em>

5x + 2y = 25;

5x = 10 + y;

(10 + y) + 2y = 25;

5x = 10 + y;

10 + 3y = 25;

5x = 10 + y;

3y = 15;

5x = 10 + y;

y = 5;

5x = 10 + y;

y = 5;

5x = 10 + 5;

y = 5;

5x = 15;

y = 5;

x = 3.

Answer: (3; 5).

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Referring to that finding, if we set initial value less than zero, which means that we are solving 0.5x+1<0 and taking a number in the interval of the solution, which means x ∈ (- ∞, -20). Setting x=-19, we find that F(x)=0.5x+1=-19 and x=-40. In the next iteration, F(x+1)=0.5(x+1)+1=0.5(1-40)+1=-18.5. In the next iteration, F(x+2)=0.5(x+2)+1=0.5(2-40)+1=-18. By this way, we find that even if the initial value is less than zero, value of the successive iterations is increasing. 

Using the function g(x)=-x+2 and taking the initial value equal to 4, we find that g(x)=-x+2=4 and x=-2. In the next iteration, g(x+1)=-(x+1)+2=-(-2+1)+2=3. If we continue the iterations we'll see that they are decreasing.
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8 0
3 years ago
Write the numbers -2.1, -1.8, -2.5 and -2.7 from greatest to least.​
Fiesta28 [93]

Answer:

-1.8, -2.1, -2.5, -2.7

Step-by-step explanation:

the bigger the negative number, the smaller it is

5 0
3 years ago
Read 2 more answers
Consider a t distribution with 7 degrees of freedom. Compute P(-1.29 &lt; t &lt; 1.29). Round your answer to at least three deci
ss7ja [257]

Answer:

a) 0.76197086

b) -1.73406361

Step-by-step explanation:

a)

Consider a t distribution with 7 degrees of freedom. Compute P(-1.29 < t < 1.29)

P(-1.29 < t < 1.29) would be the area under the t distribution curve with 7 degrees of freedom between -1.29 and 1.29, that is in the interval (-1.29, 1.29).

This can be done the old style by looking up in a table or by using the technology with a spreadsheet.

In Excel, the function TDIST(x,n,2) with x>0 gives the area outside the interval (-x, x) of the t distribution with n degrees of freedom.

So TDIST(1.29,7,2) gives the area outside (-1.29, 1.29).

If we subtract this value from 1 we get the desired result

Hence  

P(-1.29 < t < 1.29) = 1 - TDIST(1.29,7,2) = 1 - 0.23802914 = 0.76197086

In OpenOffice Calc, the function is the same replacing “,” with “;”  

That is

P(-1.29 < t < 1.29) = 1 - TDIST(1.29;7;2) = 0.76197086

b)

Consider a t distribution with 18 degrees of freedom. Find the value of c such that P(t≤ c) = 0.05

We are looking for a point c such that the area of the t distribution with 18 degrees of freedom to the left of c is 0.05

In Excel, the inverse function of TDIST is TINV.  

TINV(p*2,n) with p>0 gives the point c such that the area of the t distribution with n degrees of freedom to the right of c is p.  

Since <em>the t distribution is symmetric with respect to 0</em>, -c would be a point such that the area to the left of -c is p.

So we want to compute  in Excel

-TINV(0.05*2,18) = -1.73406361

In OpenOffice Calc  

-TINV(0.05*2;18) = -1.73406361

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