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sertanlavr [38]
3 years ago
10

One Sunday, 120 days before Christmas, Aldsworth store publishes an advertisement saying ‘120 shopping days until Christmas'. Al

dsworth subsequently publishes similar advertisements every Sunday until Christmas. a. How many times does Aldsworth advertise? b. Find the sum of the numbers of days published in all the advertisements. c. On which day of the week is Christmas?
Mathematics
1 answer:
Lena [83]3 years ago
6 0

Answer:

(a)18

(b)1089

(c)Sunday

Step-by-step explanation:

The problem presented is an arithmetic sequence where:

  • First Sunday, a=1
  • Common Difference (Every subsequent Sunday), d=7

We want to determine the number of Sundays in the 120 days before Christmas.

(a)In an arithmetic sequence:

\text{The nth term}, T_n=a+(n-1)d\\T_n \leq 120\\$Therefore:$\\1+7(n-1) \leq 120\\1+7n-7\leq 120\\7n-6\leq 120\\7n\leq 120+6\\7n\leq 126\\$Divide both sides by 7$\\n\leq 18

Since the result is a whole number, there are 18 Sundays in which Aldsworth advertises.

Therefore, Aldsworth advertised 18 times.

(b)Next, we want to determine the sum of the first 18 terms of the sequence

1,8,15,...

\text{Sum of a sequence}, S_n=\frac{n}{2}( 2a+(n-1)d)\\S_{18}=\frac{18}{2}( 2*1+(18-1)*7)\\=9(2+17*7)\\=9(2+119)\\=9*121\\S_{18}=1089

The sum of the numbers of days published in all the advertisements is 1089.

(c)SInce the 120th day is the 18th Sunday, Christmas is on Sunday.

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Step-by-step explanation:

4(-8x+5) = -32 x 26

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x = -25.375

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2 years ago
A semicircular archway is built in front of a garden using 8 congruent granite tiles, as shown in the diagram. Find the area of
iris [78.8K]
Given: 
8 tiles
radius from the center of the archway to the inner edge of the tile. 7 ft.
radius from the center of the archway to the outer edge of the tile. 8 ft = 7 ft + 1 ft.

Area of a semi circle = π r² / 2 
A = (3.14 * (7ft)²) / 2 = (3.14 * 49ft²) / 2 = 153.86 ft² / 2 = 76.93 ft²
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100.48 ft² - 76.93 ft² = 23.55 ft²
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2 years ago
Two workers finished a job in 12 days. How long would it take each worker to do the job by himself if one of the workers needs 1
Lorico [155]

Two workers finished a job in 7.5 days.

How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

let t = time required by one worker to complete the job alone

then

(t+8) = time required by the other worker (shirker)

let the completed job = 1

A typical shared work equation

7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1

multiply by t(t+8), cancel the denominators, and you have

7.5(t+8) + 7.5t = t(t+8)

7.5t + 60 + 7.5t = t^2 + 8t

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Factor easily to

(t-12) (t+5) = 0

the positive solution is all we want here

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8 0
2 years ago
Read 2 more answers
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
NARA [144]

ANSWER

Step 3

EXPLANATION

The given polynomial expression is:

2 {p}^{2}  - 3p - 7 - (3 {p}^{2}  + p - 5)

Fatau correctly expanded the parenthesis in the first step.

2 {p}^{2}  - 3p - 7 - 3 {p}^{2}   -  p  +  5

Fatau also correctly grouped the like terms to obtain:

(2- 3) {p}^{2}   + (- 3 - 1)p  + (- 7 +  5)

Fatau committed a mistake at the third step.

Instead of obtaining,

- {p}^{2} - 4p   - 2

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3 years ago
There are 8 runners in a race.
lesya692 [45]
STEP 1:
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STEP 2:
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ANSWER: 2/3 of the remaining runners will win a trophy.

Hope this helps! :)


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