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3 years ago

What type of number is -12.123 repeating?

Mathematics

2 answers:

AleksAgata [21]3 years ago

8 0

Answer:

Step-by-step explanation:

A: a whole number is a positive number (not including 0) that does not have anything after the decimal.

B: an integer is 0, all the + and all the minus numbers that have nothing after the decimal.

D: an irrational number has an unending decimal like pi.

C: has a terminating decimal and is minus. It is C, rational.

sashaice [31]3 years ago

3 0

Answer:

C. Rational

Step-by-step explanation:

While this number technically has no end, it repeats. This puts it in a special case.

First, lets look at the decimal portion and ignore the integer with it.

When looking at $0.123123123123$ ..., we can convert this into the fraction $\frac{123}{999}$

Now, we can multiply -12 by the denominator and add them together to get

$-12*\frac{999}{999} =-\frac{11988}{999} \\-\frac{11988}{999}-\frac{123}{999} =-\frac{12111}{999}$

As this number can be written as a fraction, it is a rational number.

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3 years ago

In a random sample of 150 customers of a high-speed Internetprovider, 63 said that their service had been interrupted one ormore

erastovalidia [21]

Answer:

a) The 95% confidence interval would be given by (0.341;0.499)

b) The 99% confidence interval would be given by (0.316;0.524)

c) n=335

d)n=649

Step-by-step explanation:

1) Notation and definitions

$X_{IS}=63$ number of high speed internet users that had been interrupted one or more times in the past month.

$n=150$ random sample taken

$\hat p_{IS}=\frac{63}{150}=0.42$ estimated proportion of high speed internet users that had been interrupted one or more times in the past month.

$p_{IS}$ true population proportion of high speed internet users that had been interrupted one or more times in the past month.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

1) Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.42 - 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.341$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.499$

The 95% confidence interval would be given by (0.341;0.499)

2) Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by: