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3 years ago

Find the indicated sum. Select your choice and click Submit to check your answer.

Mathematics

1 answer:

Ivahew [28]3 years ago

3 0

Answer:

$S_4=50$

Step-by-step explanation:

Sum Of Arithmetic Sequence

Given an arithmetic sequence

$a_1,\ a_1+r,\ a_1+2r,....,\ a_1+(n-1)r$

The sum of the n first terms is

$\displaystyle S_n=\frac{(a_1+a_n)n}{2}$

Or equivalently

$\displaystyle S_n=\frac{[2a_1+(n-1)r]n}{2}$

The given sequence is

5, 8, 11 ...

We can see the common difference between terms is r=3

We are asked to find the sum of the terms 2 to 5, it means that

$a_1=8, n=4, r=3$

$\displaystyle S_4=\frac{[2(8)+(4-1)3]4}{2}$

$\displaystyle S_4=\frac{100}{2}$

$\boxed{S_4=50}$

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Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

The distance between New York City, NY, and Louisville, KY is 720 miles. One morning a train traveling 80 mph left from New York

beks73 [17]

Answer:

2 hours

Step-by-step explanation:

Given : The distance between New York City, NY, and Louisville, KY is 720 miles. One morning a train traveling 80 mph left from New York. Two hours later a slower train, traveling at 60 mph, left Louisville.

To find : How many hours will the slower train travel for before both trains will arrive at the same point?

Solution : Let the distance covered by NY is x

and let the distance covered by KY is y

Total distance covered is $x+y=720$ ........[1]

→ New York city,

Distance traveled = x

Speed of the train = 80 mph

Time taken = t+2

Formula is $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

$t+2=\frac{x}{80}$ .......[2]

→ Louisville,

Distance traveled = y

Speed of the train = 60 mph

Time taken = t

Formula is $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

$t=\frac{y}{60}$ .......[3]

Put the value of t from [3] into [2]

$\frac{x}{80}- \frac{y}{60}=2$ ......[4]

Now, we solve equation [1] and [4],

Put the value of y from [1] and put back in [4], $y=720-x$

$\frac{x}{80}- \frac{y}{60}=2$

$\frac{x}{80}- \frac{720-x}{60}=2$

$\frac{60x-80(720-x)}{80\times60}=2$

$60x-57600+80x=9600$

$140x-57600=9600$

$140x=57600+9600=67200$

$x=\frac{67200}{140}=480$

Put x=480 in [1]

$x+y=720$

$480+y=720$

$y=240$

So, The distance covered by train from New York city is x=480 miles

The distance covered by train from Louisville is y=240 miles.

Now put value of y in [3] to get time,

$t=\frac{y}{60}$

$t=\frac{240}{60}$

$t=4$

So, The time taken by train from Louisville is 4 hr.

The time taken by train from New York city is t+2=4+2=6 hr.

→ 6-4=2 hours will the slower train travel for before both trains will arrive at the same point.

7 0

3 years ago

Given: BAD = CAD. Find the perimeter of ABC.

11111nata11111 [884]

Answer:

34 units

Step-by-step explanation:

Since the triangles are equal, the bottom length of triangle CAD will be the same as the bottom length of BAD. This means that the total length of the bottom of triangle ABC is 6 (3 + 3).

Next, you need to find the length of AC and again, since they're the same triangle, AB will be the same as AC, 14.

The three side lengths of the triangle will be 6, 14, and 14, so the perimeter is

6 + 14 + 14 = 34 units

4 0

3 years ago

The table below shows the typical hours worked by employees at a company. A new employee is offered an annual salary of $37,000.

Mademuasel [1]

Answer:

Salaried pay is preferable for a new employee

Step-by-step explanation:

As per table, hours worked per week:

0+ 8.5+ 9.5+ 7.5+ 8+ 8.5+ 4 = 46

Employee gets paid for 46 hours per week:

$40*14 + (46- 40)*$21 = $686

Average yearly salary would be:

$686/7*365 = $35770

Comparing with annual salary, we see:

$37000 > $35770

As we see, hourly employees get paid less, so the new employee should choose annual salary option

7 0

3 years ago

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aleksandr82 [10.1K]

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SO the correct answer are...............................

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3 years ago