The diagram shows a circle with a centre o which is
sp divided into 9 sectors. the angles of the sectors forms an
arithmetic progression with the first sector of 4°

calculate
(a) the common difference
(b)the angle of the largest sector

see explanation

Step-by-step explanation:

The first 3 terms of the arithmetic progression are

4, 13, 22, ...

(a)

with d = 13 - 4 = 22 - 9 = 9 ← common difference

(b)

The largest sector is the 9 th and the n th term is

= a + (n - 1)d

where a is the first term = 4, thus

= 4 + (8 × 9 ) = 4 + 72 = 76°

 a) 9

               b) 76

Step-by-step explanation:

The given arithmetic sequence is: {4, 13, 22, ... }

where a₁ = 4, a₂ = 13, a₃ = 22

The difference (d) is a₂ - a₁   -->   13 - 4 = 9

The explicit rule for an arithmetic sequence is:

Since we are looking for the 9th term, solve for a₉

a₉ = 4 + 9(9 - 1)

    = 4 + 9(8)

    = 4 + 72

    = 76

Check: by adding 9 to each previous term

{4, 13, 22, 31, 40, 49, 58, 67, 76, ... }

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000     [12% converted to decimal as 0.12]

= $3720