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2 years ago

A roller of radius 14.25 cm turns at 10 revolutions per second. What is the linear velocity of the roller in meters per second?

Mathematics

2 answers:

Sveta_85 [38]2 years ago

8 0

Answer:

Linear velocity, v = 8.95 m/s

Step-by-step explanation:

It is given that,

Radius of the roller, r = 14.25 cm = 0.1425 m

Angular velocity, $\omega=10\ rev/s=62.83\ rad/s$

We need to find the linear velocity of the roller. Th linear velocity of the roller is given by :

$v=r\times \omega$

$v=0.1425\times 62.83$

v = 8.95 m/s

So, the linear velocity of the roller is 8.95 m/s. Hence, this is the required solution.

ddd [48]2 years ago

5 0

A point on the edge of the roller travels the circumference of the roller in 1 revolution, so that its linear velocity is

(10 rev/s) * (2*(14.25 cm)*pi cm/rev) = 285 pi cm/s

or about 895.4 cm/s.

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The heights of students at a college are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. One might

frosja888 [35]

Answer:

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 175cm

Standard deviation = 6 cm

Percentage of students below 163 cm

163 = 175 - 2*6

So 163 is two standard deviations below the mean.

By the Empirical rule, 95% of the heights are within 2 standard deviations of the mean. The other 100-95 = 5% are more than 2 standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of them are more than 2 standard deviations below the mean(so below 163cm) and 2.5% are more than two standard deviations above the mean.

2.5% of the students have heights less than 163cm.

Out of 1000

0.025*1000 = 25

25 is the answer

8 0

2 years ago

Read 2 more answers

a table is 6 feet long and 3 feet wide. You extend the table by inserting two identical table leaves. The longest side length of

Marianna [84]

Your awser would be 74

3 0

2 years ago

Solve for x 3x−91>−87 OR 21x−17>25

klasskru [66]

Answer:

x > 4/3

Step-by-step explanation:

The first inequality can be solved this way ...

3x -91 > -87

3x > 4 . . . . . . . add 91

x > 4/3 . . . . . . divide by 3

The second inequality has solution ...

21x -17 > 25

21x > 42 . . . . . . add 17

x > 2 . . . . . . . . . divide by 21

The solution set is the union of these overlapping solutions, so will be equal to the first solution:

x > 4/3

5 0

2 years ago

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According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

Sati [7]

Answer:

a) Mean blood pressure for people in China.

b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg

f) 157.44mmHg

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If X is two standard deviations from the mean or more, it is considered unusual.

In this question:

$\mu = 128, \sigma = 23$

a.) State the random variable.

Mean blood pressure for people in China.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the pvalue of Z when X = 135.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{135 - 128}{23}$

$Z = 0.3$

$Z = 0.3$ has a pvalue of 0.6179

1 - 0.6179 = 0.3821

38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the pvalue of Z when X = 141.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{141 - 128}{23}$

$Z = 0.565$

$Z = 0.565$ has a pvalue of 0.7140

71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the pvalue of Z when X = 125 subtracted by the pvalue of Z when X = 120. So

X = 125

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{125 - 128}{23}$

$Z = -0.13$

$Z = -0.13$ has a pvalue of 0.4483

X = 120

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{120 - 128}{23}$

$Z = -0.35$

$Z = -0.35$ has a pvalue of 0.3632

0.4483 - 0.3632 = 0.0851

8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From b), when X = 135, Z = 0.3

Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then

X = 120

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 128}{23}$

$X - 128 = 1.28*23$

$X = 157.44$

157.44mmHg

6 0

2 years ago

Elena bikes 20 minutes each day for exercise. Write an equation to describe the relationship between her distance in miles, D, a

nika2105 [10]

Answer:

<h2>D= 3.9 miles</h2>

Step-by-step explanation:

Given data

speed v= 13 miles per hour

time taken t= 20min to hour 0.3 hours

the distance D

We know that the relationship between speed, time, and distance

speed=distance/time

13=D/0.3

(the expression above describes the relationship between distance, speed, and time)

making D subject of formula we have

D= 0.3*13

D= 3.9 miles

hence the distance is 3.9miles

6 0

2 years ago