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3 years ago

The 9th term of an arithmetic series is 5/2

Mathematics

1 answer:

Verdich [7]3 years ago

8 0

Answer:

- 8050

Step-by-step explanation:

The n th term of an arithmetic sequence is

$a_{n}$ = a + (n - 1)d

where a is the first term and d the common difference.

We require to find both a and d

Given the 9 th term is 2.5 , then

a + 8d = 2.5 → (1)

Given the sum of the second and fifth term is 27, then

a + d + a + 4d = 27, that is

2a + 5d = 27 → (2)

Multiply (1) by - 2 and add to (2) to eliminate a

- 2a - 16d = - 5 → (3)

Add (2) and (3) term by term

- 11d = 22 ( divide both sides by - 11 )

d = - 2

Substitute d = - 2 into (1) and solve for a

a - 16 = 2.5 ( add 16 to both sides )

a = 18.5

The sum to n terms of an arithmetic sequence is

$S_{n}$ = $\frac{n}{2}$ [ 2a + (n - 1)d ], thus

$S_{100}$ = 50 [ (2 × 18.5) + (99 × - 2) ] = 50(37 - 198) = 50(- 161) = - 8050

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Elden [556K]

If we take the perimeter of the park as being equivalent to the distance that Anwar walks, then we can calculate the number of blocks he walks and then multiply this by the width of each block, thus:

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5 0

3 years ago

Read 2 more answers

A random sample of adult female reaction times has a sample mean of x¯=394.3 milliseconds and sample standard deviation of s=84.

s2008m [1.1K]

Answer:

99.7%

Step-by-step explanation:

Given that mean (μ) = 394.3 ms and standard deviation (σ) = 84.6 ms.

The empirical rule states that for a normal distribution:

68% falls within one standard deviation (μ ± σ)
95% falls within two standard deviation (μ ± 2σ)
99.7% falls within three standard deviation (μ ± 3σ)

one standard deviation = 394.3 ± 84.6 = (309.7, 478.9). 68% falls within 309.7 and 478.9 ms

two standard deviation = 394.3 ± 2 × 84.6 = (225.1, 563.5). 95% falls within 225.1 and 563.5 ms

three standard deviation = 394.3 ± 3 × 84.6 = (140.5, 648.1). 99.7% falls within 140.5 and 648.1 ms

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3 years ago

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wolverine [178]

(4,3) (-3,4)(-3,2)(-1,2)

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3 years ago

*Help ASAP Please! Studying for finals and I'm stuck on this question!*

Nezavi [6.7K]

First I am going to assume that these are both right triangles based off of look and because it is much easier. Without it you have to use law of sines or law of cosines...
So to find x you must first find y which can be done simply by using the pythagorean theorem. This theorem is defined as the sum of the squared legs is equal to the sum of the hypotenuse or x^2 + y^2 = z^2

If we substitute in the known values 16^2 + y^2 = 20^2 and solve for y we get that y = sqrt(20^2 - 16^2), this then simplifies to y = 12

Finding x is much more annoying, the easiest way I can immediately see is to find the upper angles by doing sin(16/20) and then 90 - sin(16/20) since the complementary angle is the one you want. I don't have a calculator or a trig table with me right now but I will tell you that x will be equal to 12 ÷ the inverse cosine of the angle (90degrees - sin(16/20)).

I am pretty sure the answer is D though because we know for sure y = 12 and x has to be greater than y because the hypotenuse must be larger than both legs. It could be E but you won't know unless you do the math for x. So it is either D or E but I would be surprised if a Professor made you do all of the work just to say it doesn't work...

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3 years ago

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White raven [17]

Answer:

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question 2= you already did it

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Step-by-step explanation:

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3 years ago