Lakshmi is a cashier in a bank. she has currency notes of denominations 100,50 and 10 respectively. the ratio of the number of notes is 2: 3: 5. the total cash with lakshmi is 4. how many notes of each denomination does she have ?

the ratio of the notes is :   2 : 3 : 5  

let her have   2 * n number of rs 100 notes,   3 * n number of rs 50 notes,   and 5 * n   number of rs 10 notes respectively.

the total value of the currency notes :

2 n * rs 100 + 3 n * rs 50 + 5 n * rs 10   =   rs 4, 00, 000

=>     200 n + 150 n + 50 n = rs 4, 00, 000

=>     400 n = rs 4, 00, 000

  =>   n = 1, 000

hence,   there are 2n = 2,000 notes of rs 100   ,   3n = 3,000 notes of rs 50 and   finally ,   5 n = 5, 000 notes of rs 10..  

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240