6. How many even prime numbers are there in the set of natural numbers?​

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1. Answer:

   Answer :

   [tex] \large{ \boxed{ \rm{ \pmb{ \pink{x = 11}}}}} [/tex]

   [tex] \boxed{ \bf{ \underline{7 : \pink{11} : : 35 : 55 }}} [/tex]

   Step-by-step explanation :

   • In this question, we are provided with the proportion [tex] \bf 7 : x : : 35 : 55 [/tex] and we have to find the value of x.

   • So, for calculating the value of x, we will apply this method,

   [tex] \boxed{ \tt{ \underline{Product \: of \: means = Product \: of \: extremes }}} [/tex]

   • And lastly we will calculate the value of x.

   Given :

   [tex] \tt 7 : x : : 35 : 55 [/tex]

   To Find :

   The value of x.

   Options given :

   5

   6

   13

   11 [tex] \checkmark [/tex]

   Calculations :

   We know that,

   [tex] \boxed{ \tt{ \underline{Product \: of \: extremes = Product \: of \: means }}} [/tex]

   Putting the values,

   [tex] \mapsto \sf \dfrac{7}{x} = \dfrac{35}{55} [/tex]

   ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

   [tex] \mapsto \sf x = \dfrac{55 \times 7}{35} [/tex]

   On multiplying the numbers [55 × 7]

   [tex] \mapsto \sf x = \dfrac{385}{35} [/tex]

   Performing division,

   [tex] \mapsto \sf x = \cancel \dfrac{385}{35} [/tex]

   ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

   [tex] \mapsto \boxed{ \rm{ \pmb{ \red{ x = 11}}}} \ [/tex]

   Therefore,

   The value of x is 11.

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