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nekit [7.7K]
3 years ago
12

What is the standard deviation of a normal distribution, whose mean is 35, in which an x-value of 23 has a z-score of -1.63?

Mathematics
1 answer:
Dvinal [7]3 years ago
6 0

Answer:

7.36

Step-by-step explanation:

z-score is:

z = (x − μ) / σ

Given that z = -1.63, x = 23, and μ = 35:

-1.63 = (23 − 35) / σ

σ ≈ 7.36

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Pls helppppp will give braineliest
Oksana_A [137]

Answer: B. 3x

Step-by-step explanation:

7 0
3 years ago
20 points!!!
Svetlanka [38]
The answer is:  {4, 1} .
________________________________________________________
Explanation:
________________________________________
Given the equations:
________________________________________
      "12x = 54 −<span> 6y ;
     "-17x = -62 </span>− 6y ;
_________________________________________
Multiply the second equation (both sides) by "-1" ;
___________________________________________
  -1*{-17x = -62 − 6y} ;

to get: 

17x = 62 + 6y ;
___________________________________________
{Note: The reason we do this is that we notice the TWO "-6y" values; and by multiplying one of the entire equations by "-1" ; we can change said equation to an equation with a "(+6y)" value; and the "(+6y)" and the "(-6y)" values cancel out to "zero" ; providing an opportunity to isolate "x"; and to solve for "x".}.
___________________________________________
Now, rewrite the two equations:
___________________________________________

       12x = 54 − 6y ;
       17x = 62 +  6y ;
___________________________________________
↔  Rewrite; and then add the two together:

       6y + 62 = 17x 
      -6y + 54 = 12x 
____________________
       0  +  116 = 29x ;

↔ 29x = 116 ;

Divide EACH SIDE of the equation by "29" ; to isolate "x" on one side of the <span>equation ; and</span> to solve for "x" ;
________________________________________________
   29x / 29 = 116 / 29  ;
________________________________________________
to get:
________________________________________________
           x  = 4 .
______________________________________________
Now that we have the value for "x" , which is "4" ; let us plug in "4" for "x" for either of the original two equations, to solve for "y".  In fact, let us try substituing "4" for "x" ;  for BOTH of the two original equations; to see if the value is correct.
_____________________________________________
Our original two given equations are:
_____________________________________________
      "12x = 54 − 6y ;

     "-17x = -62 − 6y ;
_____________________________________________
 Let us start with the first equation:
 ________________________
      " 12x = 54 − 6y " ;
__________________________________
When "x = 4" ; what does "y" equal ?

Plug in "4" for "x" ; to solve for "y" ;

  12(4) = 54 − 6y ;

→ 48 = 54 − 6y ;

Subtract "54" from EACH SIDE of the equation;

→ 48 − 54 = 54 − 6y − 54 ;

to get:

→  -6 = -6y ; 

→ Divide EACH side of the equation by "-6" ; to isolate "y" on one side of the <span>equation ; and</span> to solve for "y" ; 

→ -6/-6 = -6y / -6 ;

to get:

1 = y ;  ↔ y = 1 ;  So, we have:  x = 4, y = 1 ;  or,  {4, 1}.
______________________________________________
Let us check to see, if the second (orginal equation) holds true when "x = 4" and "y = 1 " ;
______________________________________________
The second "original equation" given is:
______________________________________________
       " -17x = -62 − 6y " ;
______________________________________________
   →    -17(4) = ?  -62  − 6(1) ?

    →  -68 = ? -62 − 6 ?

    →  -68 = ? -68 ?  Yes!
________________________________________________________
The answer is:  {4, 1} .
________________________________________________________
4 0
3 years ago
Tony and Cleo are donating some of their books to a hospital. If Tony contributes half of his books and Cleo gives one third of
liraira [26]
Short Answer: Tony 40 Cleo 30
Givens

T = Tony
C = Cleo

Equations
1/2 T + 1/3 C = 30      (1)
2/5 T + 1/2 C = 31       (2)

Adjustments
Multiply  (1) by 3
Multiply (2) by 2

New Equations
3/2 T + C = 90      (1a)
<u>4/5 T + C = 62</u>      (2a) Subtract (2a) from (1a)
(3/2 - 4/5)T = 28                      the common multiple of 2 and 5 = 10. 
(15/10 - 8/10)T = 28
7/10 T = 28                              Multiply by 10
7T = 28*10
7T = 280  Divide by 7
T = 280/7 = 40

Put T = 40 into (1)
1/2 T + 1/3 C = 30
1/2 (40) + 1/3 C = 30
20 + 1/3 C = 30                      Subtract 20 from both sides.
1/3 C = 30 - 20
1/3 C = 10                              Multiply through by 3
C = 10 * 3
C = 30

Answer:
Cleo has 30 books.
Tony has 40 books.

Check
<em>Use Equation 2</em>
2/5 T + 1/2 C = 31
2/5*40 + 1/2 * 30 = ? 31
16 + 15 =?3`
31 = 31 They are equal.

4 0
3 years ago
Let f(x) = - 13x + 12 and g(x)= x² + 2.--Find f(3)/g(3).f(3)/g(3) = (?)(Type an integer or a simplified fraction.)
mel-nik [20]

We have the next two equations:

f(x)=-13x+12

And

g(x)=x^2+2

We need to find f(3)/g(3)

First, let's find f(3):

f(3)\text{ = -13(3)+12 = -27}

Then g(3):

g(3)=(3)^2+2\text{ = 11}

Now, the equation f(3)/g(3) :

\frac{f(3)}{g(3)}=\frac{-27}{11}

-27/11 is the result.

3 0
1 year ago
Stop signs are octagon-shaped. true or false
11111nata11111 [884]
Yes, stop signs are octagon shaped. So, true.
6 0
3 years ago
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