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4 years ago

Find the first term, a1, of an arithmetic sequence if a12 = 38 and a45 = 170.

1 answer:

8 0

Standard formula for arithmetic sequence:
an = a0 + d(n-1)

if we use the two terms given, setting a12 as starting term and a45 as the end term an.

170 = 38 + 33d
170 - 38 = 33d
132 = 33d

132/33 = d
This is the common difference, use it to find the first term.

38 = a0 + (132/33)(12-1)
38 = a0 + (132/33)(11)
38 = a0 + 132/3
38 - 132/3 = a0
38 - 44 = a0
-6 = a0

The starting term is -6

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Marta can vacuum the house in 30 min. It takes her daughter 45 min to vacuum the house. How long would it take them if they

Mamont248 [21]

Answer:

Step-by-step explanation:

This problem is on combined work rate

given that

Marta can vacuum the house in 30 min

then her rate= 1/30

Also, her daughter will take 45 min to vacuum the house

her daughter's rate will be = 1/45

then the combined work rate is

1/30+1/45=1/T

30+45/30*45=1/T

75/1350= 1/T

1/18=1/T

This means that they will both take 18 minutes working together to vacum a house

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3 years ago

What is the distance between nicholas's school and the post office?

aleksklad [387]

Part A:

Given that Nicholas's school is located at point (3, 2) and that the post office is located at point (-2, -2), then the distance between Nicholas's school and the post office is given by:

$d= \sqrt{(-2-3)^2+(-2-2)^2} \\ \\ = \sqrt{(-5)^2+(-4)^2} = \sqrt{25+16} \\ \\ \sqrt{41} =\bold{6.4} \ units$

Part B:

If Nicholas is located at point (– 3 , 2), the distance to get to the grocery store located at point (1,-1) is given by:

$d= \sqrt{(1-(-3))^2+(-1-2)^2} \\ \\ = \sqrt{(1+3)^2+(-3)^2} = \sqrt{(4)^2+9} \\ \\ = \sqrt{16+9} = \sqrt{25} =\bold{5}$

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3 years ago

A recent poll of 80 randomly selected Californians showed that 38% ( = 0.38) believe they are doing all that they can to conserv

Elanso [62]

The margin of error given the proportion can be found using the formula

$z* \sqrt{ \frac{p(1-p)}{n} }$

Where
$z*$ is the z-score of the confidence level
$p$ is the sample proportion
$n$ is the sample size

We have
$z*=2.58$
$p=0.38$
$n=80$

Plugging these values into the formula, we have:
$2.58 \sqrt{ \frac{0.38(1-0.38)}{80} } =0.14$

The result 0.14 as percentage is 14%

Margin error is 38% ⁺/₋ 14%

8 0

3 years ago

Read 2 more answers

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Anna007 [38]

Answer:

8n - 4

Step-by-step explanation:

The numbers here go up in 8, so you have 8n. Afterwards, use the term and the 8 times tables. Eg. 4 is the first term and the first 8 multiple is 8, so 4-8. You have to subtract 4 from 8 to get the first term. Sorry if this didn't help but yeah...

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3 years ago

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