Write four hundred seven trillion, six million, one hundred five thousand, twenty-eight in standard form.

contractor wishes to build 9 houses, each different in design. In how many ways can he place these houses on a street if 6 lots

Tju [1.3M]

The houses can be placed in 362,880 ways.

Step-by-step explanation:

The 9 houses are each in different design.

The each lot can place any of the 9 houses.

The 1st lot can place anyone house of all the 9 houses.
The 2nd lot can place one of remaining 8 houses.
The 3rd lot can place one of remaining 7 houses.

Similarly, the process gets repeated until the last house is placed on a lot.

From the above steps, it can be determined that :

The number of ways to place the 9 houses in 9 lots = 9!

⇒ 9×8×7×6×5×4×3×2×1

⇒ 362880 ways.

Therefore, the houses can be placed in 362880 ways.

5 0

2 years ago

Maryanne throws a ball off the top of a building. The table shows the height of the ball in feet, f(t), at t seconds.

grigory [225]

Answer:

quadratic

Step-by-step explanation:

i just took it on edge

7 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

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

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

$X - 128 = 1.28*23$

$X = 157.44$

So

157.44mmHg

6 0

2 years ago

over the course of numbering every page in a book, a mechanical stamp printed 2929 individual digits. How many pages does the bo

Kazeer [188]

1. Page 1-9 (1digit/page x 9page) = 9 digits = 9 page

2. Page 10-99 (2digits/page x 90page)= 180 digits = 90 page

3. Page 100-999 (3digits/page x 900page)= 2700 digits = 900 page

2,929 total digits – (9 digits + 180 digits + 2700 digits)= 40 digits

Since there are only 4 digits after page 999 we divide 40/4 = 10, thus there are 10 more pages after 999

So the book has 1009 pages.

Hope this answer will be a good help for you.

4 0

2 years ago

How are the two functions f(x) = 0.7(6)x and g(x) = 0.7(6)–x related to each other?

Harlamova29_29 [7]

The answer
f(x) = 0.7(6)x = f(x) = 0.7(6)^x, and g(x) = 0.7(6)–x= g(x) = 0.7(6)^-x=1/0.7(6)^x
so 
g(x) =1/0.7(6)^x=1 /f(x)

 the relationship between f and g are g(x) =1 /f(x) or g(x) . f(x) = 1

7 0

2 years ago

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