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2 years ago

What is the difference between decimal and binary numbering systems give examples of when you would use each?

Mathematics

1 answer:

vaieri [72.5K]2 years ago

6 0

The difference between decimal and binary system are-

The base-10 system, often known as the decimal system, is the oldest and most widely used system of numbers.
The binary number system, often known as base 2, is used by computers.

<h3>What is decimal system?</h3>

Our daily use of numbers is based on a decimal number system, which uses 10 digits. A number system in mathematics is thought of as the use of digits or symbols to represent numbers.

The binary number system, the decimal number system, the octal number system, and the hexadecimal number system are the four primary varieties of the number system.
Given that it was challenging to multiply & divide big numbers by hand in earlier civilizations, this decimal system system is sometimes called as the Hindu-Arabic and Arabic number system.

<h3>What is binary system?</h3>

The base-2 number system is the binary system. That implies that it solely use the digits 0 and 1. The 1 one location is moved to its left into the 2s place when adding one to one, and a 0 is placed in the ones place, yielding the number 10. In such a base-10 system, 10 thus = 10. 10 = 2 in the base-2 system.

The place values in a base-2 system begin with ones and progress to twos, fours, then eights as one move to its left.
This is due to the base-2 system's foundation in powers of two.
A bit is the term for each binary digit.

Therefore, a binary number system only employs two different digits(0 and 1), whereas decimal number system includes ten different digits (ranging from 0 to 9).

To know more about decimal system, here

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Step-by-step explanation:

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3 years ago

The National Transportation Safety Board publishes statistics on the number of automobile crashes that people in various age gro

ra1l [238]

Answer:

a) Null hypothesis: $p\leq 0.12$

Alternative hypothesis: $p > 0.12$

b) $z_{\alpha}=1.64$

c) $z=\frac{0.134 -0.12}{\sqrt{\frac{0.12(1-0.12)}{1000}}}=1.362$

d) $p_v =P(z>1.362)=0.0866$

e) For this case since the statistic is lower than the critical value and the p value higher than the significance level we have enough evidence to FAIL to reject the null hypothesis so then we don't have information to conclude that the true proportion is higher than 0.12

Step-by-step explanation:

Information given

n=1000 represent the random sample selected

X=134 represent the number of young drivers ages 18 – 24 that had an accident

$\hat p=\frac{134}{1000}=0.134$ estimated proportion of young drivers ages 18 – 24 that had an accident

$p_o=0.12$ is the value that we want to verify

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic

$p_v{/tex} represent the p valuePart aWe want to verify if the population proportion of young drivers, ages 18 – 24, having accidents is greater than 12%: Null hypothesis:[tex]p\leq 0.12$

Alternative hypothesis: $p > 0.12$

The statistic would be given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Part b

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.05 of the area in the right and we got:

$z_{\alpha}=1.64$

Part c

For this case the statistic would be given by:

$z=\frac{0.134 -0.12}{\sqrt{\frac{0.12(1-0.12)}{1000}}}=1.362$

Part d

The p value can be calculated with the following probability:

$p_v =P(z>1.362)=0.0866$

Part e

For this case since the statistic is lower than the critical value and the p value higher than the significance level we have enough evidence to FAIL to reject the null hypothesis so then we don't have information to conclude that the true proportion is higher than 0.12

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