MATHEMATICS MIDDLE SCHOOL

Write the next three terms of the arithmetic sequence. $(5)/(6)$ , $(2)/(3)$ , $(1)/(2)$ , $(1)/(3)$ , . . .

Answers

Answer 1

Answer:

The next three terms are: 1/6 , 0 and -1/6

Step-by-step explanation:

Given sequence is:

$(5)/(6) , (2)/(3) ,(1)/(2), (1)/(3) ...$

First of all, we have to find the common difference

$here\na_1 = (5)/(6)\na_2 = (2)/(3)\na_3 = (1)/(2)\na_4 = (1)/(3)\nd = a_2-a_1 = (2)/(3) -(5)/(6) = (4-5)/(6) = -(1)/(6)\nd = a_3 - a_2 = (1)/(2) - (2)/(3) = (3-4)/(6) = =(1)/(6)$

The common difference is -1/6

We can simply add -1/6 to the previous term to find the next terms so,

Adding -1/6 to 1/3

$(1)/(3) - (1)/(6) = (2-1)/(6) = (1)/(6)\n(1)/(6) - (1)/(6) = 0\n0-(1)/(6) = -(1)/(6)$

Hence,

The next three terms are: 1/6 , 0 and -1/6

Keywords: Arithmetic sequence, common difference

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Is 87 Prime or Composite

Answers

87 is Composite, not prime

87 :1,3,29,87

Prime numbers have exactly two factors: 1 and itself.
Composites have more than two factors.

There are 107 teams and 19 people on each team. how many people are on teams ?

Answers

Basically, to find this, you just have to multiply the number of teams by the number of people on each team. If there are 107 teams with 19 people on each, then you multiply 107 by 19 to find the total number of people.

107 x 19 = 2033

So, there are 2033 people on teams in total.

the answer is 2033

107 teams with 19 people on each team is 2033

hope i helped
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Darrel earned $2965 in gross pay over the last 2 weeks. How much income tax will be withheld from his paycheck this pay period? Use the table to answer the question. $ 2014 weekly tax table with all amounts in dollars and cents unless noted - first column If your taxable income is (first column Over, second column But not over), second column And your filing status is single (third column Base tax plus fourth column Rate times fifth column Amount over). First row Over 87, But not over 436, Base tax blank, Rate 10 percent, Amount over 87. Second row Over 436, But not over 1,506, Base tax 34.90, Rate 15 percent, Amount over 436. Third row Over 1,506, But not over 3,523, Base tax 195.40, Rate 25 percent, Amount over 1,506. Fourth row Over 3,523, But not over 7,254, Base tax 699.65, Rate 28 percent, Amount over 3,523.

Answers

$383.76 should be withheld from his $2965 gross pay over 2 weeks.

2014 WEEKLY TAX TABLE
OVER   BUT NOT OVER  BASE TAX     RATE
87.00                    436.00                   -   + 10% OVER 87
436.00                 1,506.00            34.90 + 15% OVER 436
1,506.00                 3,523.00          195.40 + 25% OVER 1506    3,523.00                 7,254.00          699.65 + 28% OVER 3523

Since, $2965 is for 2 weeks, we need to divide his pay by 2 to get his weekly pay.

2965 / 2 = 1482.50 per week.

1482.50 is OVER 436 BUT NOT OVER 1506. Therefore, his base tax for the week is 34.90 + 15% OVER 436.

1482.50 - 436 = 1046.50 * 15% = 156.98 + 34.90 = 191.88 tax withheld for the week.

The tax withheld 191.88 should be multiplied by 2 to get the tax withheld for the pay period of 2 weeks.

191.88 * 2 = 383.76 should be withheld from his $2965 gross pay over the last 2 weeks.

Malika charges $7.20 per hour for babysitting.she babysits 4 hours each week.she spends $10 per week and puts the rest of her earnings in a saving account.after 12 weeks,Malika's grandparents put a gift of money in her savings account that is equal to 0.25 times the amount she has saved from babysitting earning.How much money does Malika have in her savings account after the gift from her grandparents? Show your work

Answers

Malika has $282 in her saving account after the gift obtained from her grandparents.

What is an arithmetic operation?

The four fundamental operations of arithmetic are addition, subtracting, multiplying, and dividing two or more numbers. Included is the study of integers, especially the order of operations, which is essential for all other aspects of mathematics, notably algebra, information management, and geometry.

As per the data given in the question,

7.2 × 4= $28.8

$28.8 - 10=18.8

which means that she saves $18.8 per week.

18.8 × 12 = 225.6

She has collected 225.6 dollars over 12 weeks.

225.6 × 0.25 = 56.4

she received $56.4 from her grandparents,

$56.4 + $225.6 = $282

she has $282.

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7.2 times 4=28.8-10=18.8
she saves 18.8 dollars per week.
18.8 times 12=225.6
after 12 weeks she has saved 225.6 dollars
225.6 times 0.25=56.4
her grandparents giver her 56.4 dollars
56.4+225.6=282
she has 282 dollars

2.789 in expanded form