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3 years ago

Find the 70th term of the arithmetic sequence -26, -19, -12

Mathematics

1 answer:

zaharov [31]3 years ago

6 0

Answer:

457

Step-by-step explanation:

The general term of an arithmetic sequence is given by ...

an = a1 +d(n -1)

where a1 is the first term (-26), and d is the common difference (7).

The 70th term of your sequence can be found by putting the numbers into this formula:

a70 = -26 +7(70 -1) = -26 +483

a70 = 457

The 70th term of the sequence is 457.

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The ability of lizards to recognize their predators via tongue flicks can often mean life or death for lizards. Seventeen juveni

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Answer:

Confidence level is (380.7133, 533.2867)

Step-by-step explanation:

Responses in number of tongue flicks per 20 minutes of lizards, are: 727,217, 268, 438, 625, 319, 200, 591, 574, 727, 693, 336, 302, 761, 268, 353, 370

n = 17

Mean (μ) is:

$\mu=\frac{{\Sigma}x}{n} = \frac{727+217+ 268+ 438+ 625+ 319+ 200+ 591+ 574+ 727+ 693+ 336+ 302+ 761+ 268+ 353+ 370}{17} = 439.3529$

Standard deviation (σ) is:

$\sigma=\sqrt{\frac{\Sigma(x-\mu^2)}{n} } =\sqrt{\frac{(727-457)^2+(217-457)^2+...+(370-457)^2}{17} } =191.2$

The confidence interval (c) = 90% = 0.9

$\alpha=1-0.9=0.1\\\frac{\alpha }{2} = 0.05\\Z_{\frac{\alpha }{2} }=1.64$

Margin of error (e) = $=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }=1.64*\frac{191.2}{\sqrt{17} }=76.2867$

Confidence level = μ ± e = 457 ± 76.2867 = (380.7133, 533.2867)

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