Write as a decimal number.<br> 9-10

Which of the following are geometric sequences?<br> Check all that apply.

kolezko [41]

Answers:

Step-by-step explanation:

There are two general types of sequences that follow a pattern, geometric and arithmetic. Let's see the difference between the two:

An arithmetic sequence is produced by adding the same number to all the terms in the sequence.

EXAMPLE:

5, 7, 9, 11, 13, 15, 17 (The number 2 is added to all terms)

To figure out if a sequence is arithmetic, subtract the first term from the second, then the second from the third and so on until you have checked all the terms.

7 - 5 = 2

9 - 7 = 2

11 - 9 = 2

13 - 11 = 2

15 - 13 = 2

17 - 15 = 2

All results equal 2, so the sequence is arithmetic

From your list: The following sequences are arithmetic

A. 5, 10, 15, 20, 25 (common difference of 5)

The next type of sequence is the geometric sequence.

A geometric sequence is produced when the all the terms in the sequence are multiplied or divided by the same number.

EXAMPLE:

100, 50, 25 (Each term is divided by 2)

To figure this out, we divide each term in the sequence by the next term.

100 / 50 = 2

50 / 25 = 2

All results are two, so this sequence can be confirmed to be geometric

From your list: The following sequences are geometric

C. 10, 5, 2.5, 1.25, 0.625, 0.3125 (common quotient of 2)

D. -9, -3, -1, -1/3, -1/9, -1/27 (common quotient of -3)

There is one final type of sequence, which has no common difference, sum, quotient, or product.

EXAMPLE:

5, 6, 8, 9, 11, 12, 14, 15

This sequence has a pattern, the differences between the numbers are not common.

6 - 5 = 1

8 - 6 = 2

9 - 8 = 1

11 - 9 = 2

12 - 11 = 1

14 - 12 = 2

15 - 14 = 1

From your list: The following sequences are neither geometric nor arithmetic

B. 1, 1, 2, 3, 5, 8, 13 (No pattern)

I'n always happy to help :)

6 0

3 years ago

The amount of protein that an individual must consume is different for every person. There are solid theoretical ideas that sugg

amid [387]

Answer:

The proportion of the population that have a protein requirement less than 0.60 g P • kg-1 • d-1 is 0.239, that is, 239 persons for every 1000, or simply 23.9% of them.

$\\ 0.239 =\frac{239}{1000}\;or\;23.9\%$

Step-by-step explanation:

From the question, we have the following information:

The distribution for protein requirement is <em>normally distributed</em>.
The population mean for protein requirement for adults is $\\ \mu= 0.65 gP*kg^{-1}*d^{-1}$
The population standard deviation is $\\ \sigma =0.07 gP*kg^{-1}*d^{-1}$

We have here that protein requirements in adults is normally distributed with defined parameters. The question is about <em>the proportion</em> <em>of the population</em> that has a requirement less than $\\ x = 0.60 gP*kg^{-1}*d^{-1}$ .

For answering this, we need to calculate a <em>z-score</em> to obtain the probability of the value <em>x </em>in this distribution using a <em>standard normal table</em> available on the Internet or on any statistics book.

<h3>z-score</h3>

A z-score is expressed as

$\\ z = \frac{x - \mu}{\sigma}$

For the given parameters, we have:

$\\ z = \frac{0.60 - 0.65}{0.07}$

$\\ z = -0.7142857$

<h3>Determining the probability</h3>

With this value for <em>z</em> at hand, we need to consult a standard normal table to determine what the probability of this value is.

The value for z = -0.7142857 is telling us that the requirement for protein is below the population mean (negative sign indicates this). However, most standard normal tables give a probability that a statistic is less than z and for values greater than the mean (in other words, positive values). To overcome this, we need to take the complement of the probability given for z-score z = 0.7142857, that is, subtract from 1 this probability, which is possible because the normal distribution is <em>symmetrical</em>.

Tables have values for <em>z</em> with two decimal places, then, for z = 0.7142857, we need to rewrite it as z = 0.71. For this value, the <em>standard normal table</em> gives a value of P(z<0.71) = 0.76115.

Therefore, the cumulative probability for values less than x = 0.60 which corresponds to a z-score = -0.7142857 is approximately:

$\\ P(x$

$\\ P(x$ (rounding to three decimal places)

That is, the proportion of the population that have a protein requirement less than 0.60 g P • kg-1 • d-1 is

$\\ 0.239 =\frac{239}{1000}\;or\;23.9\%$

See the graph below. The shaded area is the region that represents the proportion asked in the question.

5 0

3 years ago

There are 88 Keyes on a piano.some keys are black and some keys are white .

shepuryov [24]

It would be C.88-x and there are 36 black keys on an 88 key piano

5 0

3 years ago

Read 2 more answers

A randomized trial tested the effectiveness of diets on adults. Among 36 subjects using Diet 1, the mean weight loss after a yea

seropon [69]

Answer:

The 95% confidence interval is

$0.45 < \mu_1 - \mu_2 < 5.35$

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 36$

The first sample mean is $\= x_1 = 3.5$

The first standard deviation is $\sigma_1 = 5.9 \ pounds$

The second sample size is $n_2 = 36$

The second sample mean is $\= x_2 = 0.6$

The second standard deviation is $\sigma = 4.4$

Generally the degree of freedom is mathematically represented as

$df = \frac{ [ \frac{s_1^2 }{n_1 } + \frac{s_2^2 }{n_2} ]^2 }{ \frac{1}{(n_1 - 1 )} [ \frac{s_1^2}{n_1} ]^2 + \frac{1}{(n_2 - 1 )} [ \frac{s_2^2}{n_2} ]^2 }$

=> $df = \frac{ [ \frac{5.9^2 }{34 } + \frac{4.4^2 }{34} ]^2 }{ \frac{1}{(34 - 1 )} [ \frac{5.9^2}{34} ]^2 + \frac{1}{(34- 1 )} [ \frac{4.4^2}{ 34} ]^2 }$