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enyata [817]
3 years ago
13

I’m stuck on this please someone help

Mathematics
1 answer:
kakasveta [241]3 years ago
6 0

Answer:   \bold{a_{n+1}=\dfrac{1}{2}a_n}

<u>Step-by-step explanation:</u>

Term-to-term rule is also called the recursive rule.

The recursive rule for a geometric sequence is: a_{n+1}=a_n\cdot r  where

  • a_n\ \text{is the previous term}
  • r is the common ratio

The common ratio (r) is the second term divided by the first term <em>(which is the same ratio for each term divided by its previous term) </em>

In the given sequence {64, 32, 16, 8, 4}, r=\dfrac{32}{64}\quad \rightarrow \quad r=\dfrac{1}{2}

So, the recursive rule is: {a_{n+1}=a_n\cdot \dfrac{1}{2}

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Extreme cold and hot temperatures are known to affect the operation of electronic components. Winter is approaching and you are
Musya8 [376]

Answer:

A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F

Test statistic(Z) = 2.31

P-value = 0.0104

Step-by-step explanation:

Step 1

Null hypothesis: The average damaging temperature of nine iPods is 5°F

Alternate hypothesis: The average damaging temperature of nine iPods differs from 5°F

Step 2

Mean=5°F, Sd=3, df=n-1=9-1=8

The t-value corresponding to 8 degrees of freedom and 95% confidence level (5% significance level) is 2.306

Confidence Interval(CI) = (mean + or - t×sd/√n)

CI = (5 + 2.306×3/√8) = 5 + 6.918/2.828= 5+2.45=7.45°F

CI = (5 - 2.306×3/√8) = 5-2.45 = 2.55°F

Z = (sample mean - population mean)/(sd÷√n) = (5-2.55)/(3÷√8) = 2.45/1.061 = 2.31

Step 3

Using the standard distribution table, the cumulative area to the left of Z = 2.31 is 0.9896

P-value = 1 - 0.9896 = 0.0104

Step 4

Conclusion: A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F

7 0
3 years ago
Explain how to write 45,100,000 in scientific notation.
Komok [63]

Step-by-step explanation:

45,100,000  \\  = 4.51 \times  {10}^{7}

5 0
3 years ago
Try to work out this equation! Type your answer below!<br> 65 x 589 x 653 - 65 + 36
neonofarm [45]

Answer:

25000076

Step-by-step explanation:

Hope this helps! :)

8 0
3 years ago
Solve for x in the equation.
oksano4ka [1.4K]
x^2 + 20x + 100 = 36

(x + 10)^2 = 36

x + 10 = \pm \sqrt{36}

x + 10 = 6   or   x + 10 = -6

x = -4   or   = -16
5 0
3 years ago
It is an unfair coin with unknown probability of head and tail. Can you generate even odds using this coin?
Vladimir79 [104]

Answer:

Yes, it can be generated if p = \frac{n}{n+1}, where n is a positive even integer.

Step-by-step explanation:

An odds for an event, is the probability or chance that this event will occur, divided by the probability that it will not occur.

Assume that the probability of getting tail when throwing the coin is p, therefore, the probability of getting a head is (1-p) and the odds for the event of getting tail is \frac{p}{1-p}.

If k is a positive integer, and we assume that the odds of getting a tail are even, then:

\frac{p}{1-p} = 2k

p = 2k - 2kp

p = \frac{2k}{2k+1}

Conclusion: if p = \frac{2k}{2k+1}, for some positive integer k, even odds are generated. For example: p = 2/3, 4/5, 6/7, ...

6 0
3 years ago
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