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3 years ago

A 19 = 548 and a 33 = 968 Find a 27

Mathematics

1 answer:

s2008m [1.1K]3 years ago

4 0

Answer:

The value of a₂₇ is 788

Step-by-step explanation:

a₁₉ = 548

a₃₃ = 968

Now,

a₁₉ = 548 can be written as

a + 18d = 548 ...(1) and

a₃₃ = 968 can be written as

a + 32d = 968 ...(2)

Now, from equation (2) we get,

a + 32d = 968

a + 18d + 14d = 968

548 + 14d = 968 (.°. <u>a + 18d = 548</u>)

14d = 968 - 548

14d = 420

d = 420 ÷ 14

d = 30

Now, for the value of a put the value of d = 30 in equation (1)

a + 18d = 548

a + 18(30) = 548

a + 540 = 548

a = 548 - 540

a = 8

Now, For a₂₇

a₂₇ = a + 26d

a₂₇ = 8 + 26(30)

a₂₇ = 8 + 780

a₂₇ = 788

Thus, The value of a₂₇ is 788

<u>-TheUnknownScientist</u>

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3 years ago

Sample annual salaries (in thousands of dollars) for employees at a company are listed. 42 36 48 51 39 39 42 36 48 33 39 42 45 (

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Answer:

a) Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45

$\bar X = 41.538$

$s = 5.317$

b) 44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25

$\bar X = 43.615$

$s= 5.583$

c) 3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75

$\bar X= 3.462$

$s = 0.443$

d) As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3.462).

And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.

And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.

Step-by-step explanation:

For this case we can use the following formulas for the mean and standard deviation:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Part a

Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45

And if we calculate the mean we got:

$\bar X = 41.538$

$s = 5.317$

Part b

For this case we know that each value present a 5% of rise so we just need to multiply each value bu 1.05 and we have this new dataset:

44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25

And if we calculate the new mean and deviation we got:

$\bar X = 43.615$

$s= 5.583$

Part c

The new dataset would be each value divided by 12 so we have:

3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75

And the new mean and deviation would be:

$\bar X= 3.462$

$s = 0.443$

Part d

As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3,462).

And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.

And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.

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2. To complete the trip, 38 more kilometers left

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Let total trip be x kilometers.

So we can say