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Nina [5.8K]
3 years ago
12

The volume of a cylinder is 252pi cm^3 and its height is 7 cm

Mathematics
1 answer:
ser-zykov [4K]3 years ago
5 0

Answer:

Step-by-step explanation:

volume= (pi)(radius^2)(h)

252(pi)=(pi)(radius^2)(7)

divide both sides by pi

252=(radius^2)(7)

divide both sides by 7

36=(radius^2)

square root each side

6=radius

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2 years ago
Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboa
KengaRu [80]

Answer:

a. <u>0.5 or 50%</u>

b. <u>0.496 or 49.6%</u>

c. <u>0.8185 or 81.85%</u>

d. <u>Yes, it would be just 0.0013 or 0.13% of probability to find a typist whose speed exceeds 105 wpm</u>

e. <u>0.0252 or 2.52%</u>

f. <u>The qualifying speed would be 47.4 wpm.</u>

Step-by-step explanation:

a. Let's find the z-score this way:

μ  = 60 σ= 15

z-score = (x - μ)/σ

z-score = (60 - 60)/15

z-score = 0

Now, let's calculate the p value for z-score = 0, using the z-table:

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b. z-score = (x - μ)/σ

z-score = (59.9 - 60)/15

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Now, let's calculate the p value for z-score = -.0.01, using the z-table:

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If the question were less or equal than 60, a and b would have the same answer. But in this case, the question is "less than 60 wpm".

c.

z-score = (x - μ)/σ

z-score = (45 - 60)/15

z-score = - 1

Now, let's calculate the p value for z-score = -1, using the z-table:

p (z = -1) = 0.1587

z-score = (x - μ)/σ

z-score = (90 - 60)/15

z-score = 2

Now, let's calculate the p value for z-score = 2, using the z-table:

p (z = 2) = 0.9772

<u>In consequence,</u>

<u>p (-1 ≤ z ≤ 2) = 0.9772 - 0.1587 = 0.8185 or 81.85%</u>

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z-score = (105 - 60)/15

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Now, let's calculate the p value for z-score = 3, using the z-table:

p (z = 3) = 0.9987

In consequence,

p (z > 3) = 1 - 0.9987 = 0.0013

<u>Yes, it would be just a 0.13% of probability to find a typist whose speed exceeds 105 wpm.</u>

e. z-score = (x - μ)/σ

z-score = (75 - 60)/15

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Now, let's calculate the p value for z-score = 1, using the z-table:

p (z = 1) = 0.8413

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and if the two typists are independently selected, then

p = 0.1587 * 0.1587

<u>p = 0.0252 or 2.52%</u>

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z-score = (x - μ)/σ

-0.84 = (x - 60)/15

-12.6 = x - 60

-x = -60 + 12.6

-x = - 47.4

x = 47.4

<u>The qualifying speed would be 47.4 wpm.</u>

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