Given that√7=2.65 and √70=8.37,find the value of (a)√0.07
(b)√0.0007
(c)√0.7
(d)√0.007
(e)√0.000007
(f)√0.00007

A) 0.265

B) 0.0265

C) 0.837

D) 0.0837

E) 0.00265

F) 0.00837

Step-by-step explanation:

We are given;

√7 = 2.65 and √70 = 8.37

A) √0.07 can be rewritten as;

√(7 × 1/100)

Let's deal with the digits in the bracket.

Square root of 100 is 10. Thus;

√(7 × 1/100) = (1/10)√7 = (1/10) × 2.65 = 0.265

B) √0.0007

Rewrite to get;

√(7 × 1/10000)

Square root of 1/10000 is 1/100

Thus;

√(7 × 1/10000) = (1/100)√7 = (1/100) × 2.65 = 0.0265

C) √0.7

Like above;

√0.7 = √(70 × (1/100))

>> (1/10)√70 = (1/10) × 8.37 = 0.837

D) √0.007

Like above;

Rewrite to get;

√(70 × 1/10000)

Square root of 1/10000 is 1/100

Thus;

√(70 × 1/10000) = (1/100)√70 = (1/100) × 8.37 = 0.0837

E) √0.000007

Rewritten to;

√(7 × (1/1000000))

√(1/1000000) = 1/1000

Thus; √(7 × (1/1000000)) = 1/1000 × √7 = 1/1000 × 2.65 = 0.00265

F)√0.00007

Rewritten to;

√(70 × (1/1000000))

√(1/1000000) = 1/1000

Thus; √(70 × (1/1000000)) = 1/1000 × √70 = 1/1000 × 8.37 = 0.00837

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.

in 2010, the population of the state of california is 37.29 × 10⁶

step-by-step explanation:

population of los angeles = 3.79 × 10⁶

population of california = 9.84 × population of los angeles

                                        = 9.84 × 3.79 × 10⁶

                                        = 37.2936 × 10⁶

                                        = 37.29 × 10⁶

∴ in 2010, the population of the state of california is 37.29 × 10⁶