When asked how old she is, a teacher responded with this riddle: “my age is a two digit number. when multiplied by seven, the result is a three digit number. when the digit 6 is written after the three digit number, that number is increased by 1833.” how old is the teacher?

Let x be the age of the teacher.

We know that 7x is a three digit number.

Writing 6 after this number means to multiply this number by 10 (this adds a zero after the number) and then add 6.

So, we actually only need the last information:

Solving this equation is quite trivial: subtract 7x  and 6 from both sides and you get

This is indeed a two digit number, and if you multiply it by 6 it becomes 174, a three digits number.

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation:

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation: