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Sphinxa [80]
3 years ago
9

*PLEASE ANSWER ASAP* John is playing a game with two friends. Using the spinner pictured, one friend spun a three, and the other

friend spun a five. John needs to spin a number higher than both friends in order to win the game, and he wants to calculate his probability of winning. How many desired outcomes should John use in his probability calculation?

Mathematics
1 answer:
levacccp [35]3 years ago
5 0

Answer:

3

Step-by-step explanation:

he wants a 6,7,or8

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The sum of two numbers is 28. one number is 14 more. find the numbers
ruslelena [56]
The numbers are:  "7 " and "21 " .
_______________________________________
Explanation:
_______________________________________
The numbers are:  "x"  and "x + 14" .

x + (x + 14) = 28 .  Solve for "x" ; and then solve for "x + 14" .
_______________________________________
 → x + (x + 14) = 28 ;

Rewrite as:

 →  x + x + 14 = 28 ;

 →  1x + 1x + 14 = 28 ;

 →  2x + 14 = 28 ; 
  
 Subtract "14" from each side of the equation;
 
 →  2x + 14 − 14 = 28 <span>− 14 ;

</span> →  2x = 14  ;

Divide EACH SIDE of the equation by "2" ;
     to isolate "x" on one side of the equation; & to solve for "x" ;

 →  2x / 2 = 14 / 2 ;

 →  x = 7 . 
_________________________________________
So;  one of the numbers is:  " 7 " .

The other number is:  " x + 14 " ; which equals: " 7 + 14 = 21".

The other number is:  "21 " .
_________________________________________
The numbers are:  "7 " and "21 " .
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3 years ago
Factor 7(x − 3)2 − 4(x − 3) − 3 completely.
Nezavi [6.7K]
7(x-3)^2-4(x-3)-3\\\\substitute\ t=x-3,\ then\ we\ have\\\\7t^2-4t-3\\\\a=7;\ b=-4;\ c=-3\\\\\Delta=b^2-4ac\\\\\Delta=(-4)^2-4\cdot7\cdot(-3)=16+84=100\\\\t_1=\dfrac{-b-\sqrt\Delta}{2a};\ t_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{100}=10\\\\t_1=\dfrac{-(-4)-10}{2\cdot7}=\dfrac{4-10}{14}=\dfrac{-6}{14}=-\dfrac{3}{7}\\\\t_2=\dfrac{-(-4)+10}{2\cdot7}=\dfrac{4+10}{14}=\dfrac{14}{14}=1\\\\7t^2-4t-3=7\left(t+\dfrac{3}{7}\right)(t-1)=(7t+3)(t-1)\\\\=(7(x-3)+3)(x-3-1)=(7x-21+3)(x-4)\\\\=\boxed{(7x-18)(x-4)}
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