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4 years ago

Find the number of terms common to the two A.P.'s 3,7,11,......,407 and 2,9,16,......,709

Mathematics

1 answer:

melomori [17]4 years ago

5 0

Answer: 14 terms

Step-by-step explanation:

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Suppose a simple random sample of size nequals36 is obtained from a population with mu equals 74 and sigma equals 6. (a) Descri

OlgaM077 [116]

Part a)

The simple random sample of size n=36 is obtained from a population with

$\mu = 74$

and

$\sigma = 6$

The sampling distribution of the sample means has a mean that is equal to mean of the population the sample has been drawn from.

Therefore the sampling distribution has a mean of

$\mu = 74$

The standard error of the means becomes the standard deviation of the sampling distribution.

$\sigma_ { \bar X } = \frac{ \sigma}{ \sqrt{n} } \\ \sigma_ { \bar X } = \frac{ 6}{ \sqrt{36} } = 1$

Part b) We want to find

$P(\bar X \:>\:75.9)$

We need to convert to z-score.

$P(\bar X \:>\:75.9) = P(z \:>\: \frac{75.9 - 74}{1} ) \\ = P(z \:>\: \frac{75.9 - 74}{1} ) \\ = P(z \:>\: 1.9) \\ = 0.0287$

Part c)

We want to find

$P(\bar X \: < \:71.95)$

We convert to z-score and use the normal distribution table to find the corresponding area.

$P(\bar X \: < \:71.95) = P(z \: < \: \frac{71.9 5- 74}{1} ) \\ = P(z \: < \: \frac{71.9 5- 74}{1} ) \\ = P(z \: < \: - 2.05) \\ = 0.0202$

Part d)

We want to find :

$P(73\:$

We convert to z-scores and again use the standard normal distribution table.

$P( \frac{73 - 74}{1} \:< \: z$

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3 years ago

Substitution method 2x-y+24 y=-3x+16

Llana [10]

- Using substitution means you are going to solve one equation for one variable and substitute with its value in the other equation in order to get also an equation with one variable.

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3 years ago

Refer to the right triangle ABC below. Identify the correct values for B and C

zaharov [31]

Answer:

B=12.2

C=5.4 is your answer

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3 years ago

3. Write a number that has a value greater than -2.6|

svetoff [14.1K]

Answer:

-1.67539

Step-by-step explanation:

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3 years ago

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if you have a cylinder with a diameter of 15 and height of 12 inches. What is the volume of the largest sphere that will fit ins

Lapatulllka [165]

If we have a cylinder with a smaller height than diameter, the height is our constricting measurement. This means that our sphere's max diameter is 12 inches.

Solving for the volume of a sphere with diameter of 12 inches:
4/3 * pi * r^3
4/3 * 3.14 * 6^3
volume = 904.32 cubic inches

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4 years ago