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3 years ago

Find the 4th term in the sequence with the following definition: a1 = 0 an = 2(an-1 -3)

Mathematics

1 answer:

bonufazy [111]3 years ago

7 0

Answer:

-42

Step-by-step explanation:

$a_{1}=0\\a_{n}=2(a_{n-1}-3)\\a_{2}=2(a_{1}-3)=2(0-3)=-6\\a_{3}=2(a_{2}-3)=2(-6-3)=-18\\a_{4}=2(a_{3}-3)=2(-18-3)=-42$

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I have 30 coins consisting of nickels, and quarters. The total value of the coins is $4.10. How many of each kind do I have?

Vedmedyk [2.9K]

A=#nickels, b=#quarters

5a + 25b = 410 total value

5(a + 5b) = 410

a + 5b = 82

a + b = 30 total no. of coins

subtracting . . . 4b = 52

thus b = 13 and a = 17

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4 years ago

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3 years ago

Read 2 more answers

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son4ous [18]

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3 years ago

Given the relation R = {(-2, 3), (a, 4), (1,9), (0,7)}.

aniked [119]

Answer:

The answer would be 4

Step-by-step explanation:

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3 years ago

A random sample of 25 glass sheets is obtained and their thicknesses are measured. The sample mean is x= 3.54 mm and sample stan

lisabon 2012 [21]

Answer: (3.46, 3.62)

Step-by-step explanation:

The formula to find the confidence interval for population mean is given :-

$\overline{x}\ \pm\ t_{\alpha/2}\dfrac{s}{\sqrt{n}}$

, where n = sample size.

$t_{\alpha/2}$ = Two-tailed t-value for significance level of $(\alpha)$ and degree of freedom df= n-1.

$s$ = sample standard deviation.

As per given , we have

$\overline{x}= 3.54$ mm

s= 0.20 mm

n= 25

Significance level $=\alpha=1-0.95=0.05$

Since population standard deviation is not given , it means the given problem has t- distribution.

Two-tailed t-value for significance level of $(0.05)$ and degree of freedom df= 24:

$t_{\alpha/2\ ,df}=t_{0.025,\ 24}=2.0639$

95% Confidence interval for population mean:

$3.54\ \pm\ (2.0639)\dfrac{0.20}{\sqrt{25}}$

$=3.54\ \pm\ (2.0639)\dfrac{0.20}{5}$

$=3.54\ \pm\ (2.0639)(0.04)$

$=3.54\ \pm\ 0.082556$

$=(3.54- 0.082556,\ 3.54+ 0.082556 )=(3.457444,\ 3.622556)\approx(3.46,\ 3.62)$

Hence, the 95% two-sided confidence interval for the mean glass thickness = (3.46, 3.62)

7 0

4 years ago