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Westkost [7]
3 years ago
15

Find an explicit rule for the nth term of the sequence. 3, -12, 48, -192, ...

Mathematics
2 answers:
Burka [1]3 years ago
8 0

Answer: a_n=3(-4)^{n-1}

Step-by-step explanation:

Given sequence : 3, -12, 48, -192, ...

Here, First term a_1=3

Second term a_2=-12

and  Ratio=r=\frac{a_2}{a_1}=\frac{-12}{3}=-4

Third term a_3=48

Ratio=r=\frac{a_3}{a_2}=\frac{48}{-12}=-4

Fourth term a_4=-192

Ratio=r=\frac{a_4}{a_3}=\frac{-192}{48}=-4

Thus, the given sequence is geometric sequence with the common ratio r = -4.

The explicit rule for for the nth term in geometric sequence is given by

a_n=a_{1}r^{n-1}

Then the explicit rule for the nth term of the given sequence will be :-

a_n=3(-4)^{n-1}

Nimfa-mama [501]3 years ago
6 0
Hello,
u_{1}=3
u_{2}=3*(-4)
u_{3}=3*(-4)^2

u_{n}=3*(-4)^{n-1}


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Step-by-step explanation:

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Give at least four different symbols that have been used to represent specific statistical measures. Describe what measure each
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Answer:

Variance                    0²

standard deviation   0×

mean                          α

median                      x-bar

Step-by-step explanation:

these are the four different symbols that have been used to represent specific statistical measures like for example, mean which is used to calculate the average value of a sample or population. Variance is the what is expected from the squared standard deviation of a random variable from is average vale/ mean. Median is the value that lies in the middle in a random sample and lastly the standard deviation is the square root of the variance and it measures how the values of sample are spread or how far are they from the mean. these are also commonly use in excel a lot to calculate and evaluate data.

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3 years ago
X -5x -14=0 quadratic formula
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8 0
3 years ago
3. The adult men of the Dinaric Alps have the highest average height of all regions. The
ahrayia [7]

Using the normal distribution, it is found that:

  • 3 - a) The 40th percentile of the height of Dinaric Alps distribution for men is of 72.2 inches.
  • 3 - b) The minimum height of man in the Dinaric Alps that would place  him in the top 10% of all heights is of 76.84 inches.
  • 4 - a) The 25th percentile for the math scores was of 71.6 inches.
  • 4 - b) The 75th percentile for the math scores was of 78.4 inches.

<h3>Normal Probability Distribution </h3>

In a <em>normal distribution </em>with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It 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, which is the percentile of X.

Question 3:

  • The mean is of 73 inches, hence \mu = 73.
  • The standard deviation is of 3 inches, hence \sigma = 3.

Item a:

The 40th percentile is X when Z has a p-value of 0.4, so <u>X when Z = -0.253</u>.

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

-0.253 = \frac{X - 73}{3}

X - 73 = -0.253(3)

X = 72.2

The 40th percentile of the height of Dinaric Alps distribution for men is of 72.2 inches.

Item b:

The minimum height is the 100 - 10 = 90th percentile is X when Z has a p-value of 0.9, so <u>X when Z = 1.28</u>.

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

1.28 = \frac{X - 73}{3}

X - 73 = 1.28(3)

X = 76.84

The minimum height of man in the Dinaric Alps that would place  him in the top 10% of all heights is of 76.84 inches.

Question 4:

  • The mean score is of 75, hence \mu = 75.
  • The standard deviation is of 5, hence \sigma = 5.

Item a:

The 25th percentile is X when Z has a p-value of 0.25, so <u>X when Z = -0.675</u>.

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

-0.675 = \frac{X - 75}{5}

X - 75 = -0.675(5)

X = 71.6

The 25th percentile for the math scores was of 71.6 inches.

Item b:

The 75th percentile is X when Z has a p-value of 0.25, so <u>X when Z = 0.675</u>.

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

0.675 = \frac{X - 75}{5}

X - 75 = 0.675(5)

X = 78.4

The 75th percentile for the math scores was of 78.4 inches.

To learn more about the normal distribution, you can take a look at brainly.com/question/24663213

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2 years ago
3. The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equ
ikadub [295]

Answer:

The equation that models the cost of each bracelet is 72=9x+9. Cost of each bracelet is $7.

Step-by-step explanation:

Let the cost of each bracelet is defined by the variable x.

Cost of 9 bracelet is 9x. The shipping cost is $9. Therefore the total cost of 9 bracelets, including shipping is

\text{Total Cost}=9x+9

The total cost for 9 bracelets, including shipping is $72.

72=9x+9

Subtract 9 from both sides

72-9=9x+9-9

63=9x

Divide both sides by 9.

7=x

Therefore the cost of each bracelet without shipping changes is $7.

8 0
3 years ago
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