Mathematics, 19.11.2020 18:20 Ezekielcassese

A local business was looking for a cleaning service to work on their property. They narrowed their choices down to companies. Molly maids company charges a flat rate of $100 per hour. Sparkly clean company charges $80 per hour plus $260 equipment fee. A) determine and state the number of hours that must be worked for the cost of both companies to be the same. B) if it is estimated to take at least 30 hours to company the job, which company will be less expensive? Justify your answer.

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Answer from: emmdolzx

A. 13 hours

B. Sparkly clean company

Step-by-step explanation:

Step one:

given

Molly maids company

charges a flat rate of $100 per hour

let the total charges be y

let the number of hours be x

the expression for the total charges for Molly maids is

y=100x1

Step two:

Sparkly clean company

charges $80 per hour

equipment fee=$260

let the total charges be y

let the number of hours be x

the expression for the total charges for Sparkly clean is

y=80x+2602

A) determine and state the number of hours that must be worked for the cost of both companies to be the same.

Equate equations 1 and 2

100x=80x+260

solve for x, collect like terms

100x-80x=260

20x=260

divide both sides by 20

x=260/20

x=13 hours

B) if it is estimated to take at least 30 hours to company the job, which company will be less expensive

x=30

Molly maids company

y=100x

y=100*30

y=3000

$3000

Sparkly clean company

y=80x+260

y=80*30+260

y=2400+260

$2660

Sparkly clean company will be less expensive for a 30 hour work

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Answer from: Quest

tried on you are knowing that we can't leave the picture in the graph ok no problem now you need to send it in the question group

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