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gregori [183]
2 years ago
12

5x + 2y = 7 y = x + 1 What is the solution set of the given system? {(5/7, 12/7)} {(12/7, 5/7)} {(9/7, 16/7)} {(16/7, 9/7)}

Mathematics
1 answer:
Rama09 [41]2 years ago
5 0

5x+2y=7

y=x+1

5x+2(x+1) =7

5x +2x+2=7

7x +2 =7

7x = 5

x = 5/7

y=5/7 +1

y =12/7

(5/7, 12/7)

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The sampling distribution used when making inferences about a single population variance is?
melamori03 [73]

We use the chi-square distribution when making inferences about a single population variance.

Short Description of Chi-Square Distribution

The continuous probability distribution known as the chi-square distribution. The number of degrees of freedom (k) a chi-square distribution has determines its shape. This type of sampling distribution has a variance of 2k and a mean equal to its number of degrees of freedom (k). The range is of a chi-square distribution is from 0 to ∞.

Variance plays a key role in the analysis of risk and uncertainty. The sample variance, an unbiased estimator of population variance, is expressed by the following formula of core statistic for a sample size 'n' and Y' as the sample mean:

S² = ∑(Yₓ - Y') / (n-1)

The formula, (n-1)S² / σ² has the central chi-square distribution as χ²ₙ₋₁. Here (n-1) represents the degrees of freedom.

Learn more about chi-square distribution here:

brainly.com/question/13857280

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4 0
1 year ago
Solve 2x3 + x2 - 15x completely by factoring.
zhuklara [117]
Answer:  [D]:  " x = 0, -3, 5/2 "  .

{Assuming:  " 2x³ + x²  − 15x = 0 ".}.
__________________________________________
Explanation:
___________________________________
Given:
_________________________________
     2x³ + x² − <span>15x ;
 __________________________________
</span>        →  (2x³ + x²) − 15x ;
  
        →   2x³ + x² − 15x  =   x * (2x² + x − 15) ;
         
        →  Factor the expression:  "(2x² + x − 15)" ;
                                     
             → (2x² + x − 15) =  
            
            →   2x² − 5x + 6x − 15 ;

           →  Add the "first TWO (2) terms", and pull out the "like factors" ;                                       →  x*(2x − 5) ;

           →  Add the "last TWO (2) terms, pulling out "common factors";
                            →  3*(2x − 5) ;

           →  Now, add up the previous FOUR (4) terms; to get:

                            → (x + 3)(2x − 5) ;  

           → Now, we have factored the:

                    "(2x² + x − 15)" of:  " x*(2x² + x − 15) " ; 

           →  So we add the "x"; and write the entire factored expression:
______________________________________________________
                      →  x*(x + 3)(2x − 5) ;           
_____________________________________
Now, assume the question is asking to solve for "x" by factoring;
   when the expression is "equal to zero" ;
_______________________________________
That is, when:  

                →  x*(x + 3)(2x − 5) = 0 ;
____________________________________________
Since we have THREE (3) multiplicands;  and anything times "0" equals "0" ;
    this equation holds true when:
________________________________
  1) x = 0 ;
_______________
  2) (x + 3) = 0 ;
  
Subtract "3" from each side of the equation;

   x + 3 − 3 = 0 − 3 ; 
  
         x = -3 ; 
_______________________
3)  2x − 5 = 0 ; 

Add "5" to each side of the equation;

2x − 5 + 5 = 0 + 5 ;

2x = 5 ; Now, divide EACH side of the equation by "2" ; to isolate "x" on one side of the equation; and to solve for "x" ; 

2x/2 = 5/2 ;

x = 5/2; or, write as 2.5; or write as 2<span>½ .
</span>_____________________________________
Put simply, the equation is true when:
_________________________________________
    x = 0, -3, 5/2 ;  which is: Answer choice: [D].
_________________________________________

7 0
3 years ago
How many different ways can an after school club of 13 students line up?
maksim [4K]

Answer:

13! or 6227020800

Step-by-step explanation:

With no restrictions, we can figure out the answer to be 13! by the following analysis:

For the first position in line, there are 13 different students who could fill that spot. If we fill it and proceed to the next position in line, there are now only 12 students left who can fill it, since one is already in line. Then the next position only has 11 possibilities, and the next 10, and so on.

Multiplying all of this together gives us 13*12*11*10*9*8*7*6*5*4*3*2*1 or 13!

3 0
2 years ago
Read 2 more answers
Helppppp pleaseeeee fasttttt thankkkkk youuuuu
Digiron [165]
Pretty sure it is nine. I hope I helped
8 0
3 years ago
What is the explicit rule for the arithmetic sequence shown in the graph?​
Afina-wow [57]

Answer:

Step-by-step explanation:

Looking at the given graph, the slope of the line is expressed as

Slope = (y2 - y1)/(x2 - x1)

y2 = 19.5

y1 = 9.5

x2 = 6

x1 = 1

Slope = (19.5 - 9.5)/(6-1)

Slope = 10/5 = 2

The successive terms is increasing by 2

The formula for the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a is the first term of the sequence

n is the number of terms in the sequence.

d is the common difference.

From the information given,

a = 9.5

Tn = an

d = 2

The explicit rule for the arithmetic sequence will be

an = 9.5 + 2(n-1)

8 0
2 years ago
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