All categories

2 years ago

Write the condition under which the hcf of the given algebraic expression is 1

Mathematics

1 answer:

solong [7]2 years ago

6 0

Answer:

A HCF is the highest common factor between 2 or more numbers. because every number times 1 is equal to itself, every 2 numbers have a common factor of 1.

HCF between 2 numbers a,b or expressions such that a and b are not equal to 0 , will never be 0 , because of the simple fact that anything times 0 is equal to 0 , and we stated that a,b isn’t equal to 0 , so that’s a contradiction.

Since you stated that there is no common factor bigger or lower than 1 between the 2 numbers (which means that the two numbers are equal to each other and equal to 1 or 0 , think about it yourself a little bit) that means that the only factor is 1 when the two numbers are not 1 , and 0 or anything if the two numbers are 0 , because again, every number times 0 is equal to 0 .

So finally, there is not HCF if the two numbers stated are both 0 , and the only other possibility is for them to be 1 , and in this case, the HCF will be 1 .

You might be interested in

In proof testing of circuit boards, the probability that any particular diode will fail is . Suppose a circuit board contains di

ira [324]

Complete Question

In proof testing of circuit boards, the probability that any particular diode will fail is 0.01.

Suppose a circuit board contains 200 diodes. How many diodes would you expect to fail, and what is the standard deviation of the number that are expected to fail? What is the (approximate) probability that at least four diodes will fail on a randomly selected board?If five boards are shipped to a particular customer, how likely is it that at least four of them will work properly? (A board works properly only if all its diodes work)

Answer:

The number of diode expected to fail is

$\mu =2$

The standard deviation is

$\sigma = 1.407$

The probability that at least four diodes will fail on a randomly selected board is

$P(X \ge 4) = 0.1419$

Step-by-step explanation:

Generally the testing follows a binomial distribution because

1 The number of trials is finite

2 There is only two outcomes( which (a) A diode fail (b) a diode does not fail)

3 The each individual trial is independent of each other.

4 The chances of success is constant for every trial

From the question we are told that

The probability that a diode will fail is $p = 0.01$

The sample size is n = 200

Generally the number of diode expected to fail is mathematically represented as

$\mu = n * p$

=> $\mu = 200 * 0.01$

=> $\mu =2$

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{ np * (1 - p)}$

=> $\sigma = \sqrt{ 200* 0.01 * (1 - 0.01 )}$

=> $\sigma = 1.407$

Generally the probability that at least 4 diode will fail is mathematically represented as

$P(X \ge 4) = 1 - P(X < 4 )$

Generally

$P(X < 4 ) = P(X = 0 ) + P(X = 1) + P(X = 2) + P(X = 3)$

=> $P(X < 4 ) = ^nC_0 p^0 * (1-p)^{n-0} +^nC_1 p^1 * (1-p)^{n-1}+^nC_2 p^2 * (1-p)^{n-2}+ ^nC_3 p^3 * (1-p)^{n-3}$

=> $P(X < 4 ) = ^{200}C_0 p^0 * (1-0.01)^{200-0} +^{200}C_1 (0.01)^1 * (1-0.01)^{200-1}+^{200}C_2 (0.01)^2 * (1-0.01)^{200-2}+ ^{200}C_3 (0.01)^3 * (1-0.01)^{200-3}$

=> $P(X < 4 ) = 0.134 + 0.2707 + 0.2727 + 0.1814$

=> $P(X$

$P(X \ge 4) = 1 -0.8581)$

=> $P(X \ge 4) = 0.1419$

3 0

3 years ago

What is 8,794 , 17,117 , and 20,655 rounded to the nearest thousand.

maks197457 [2]

9000, 17 000, and 21 000

7 0

4 years ago

Read 2 more answers

Help me please! I don't know how to do this. Merci!

Kaylis [27]

Answer:

The next term is

Step-by-step explanation:

The sequence is going down by 5 so you divide -250 by 5 and you get -50

3 0

3 years ago

Read 2 more answers

SOMEONE PLZ HELP I HAVE TO TURN THIS IS BY 12:00

jeka57 [31]

So what you do is make a fraction with the conversation between miles and km with km on the bottom to cancel out the units and multiply the fraction by the amount of km

5km (.62miles/1km) = 3.1 miles

4 0

3 years ago

Simplify the following fraction 12/15 answers:<br> 2/3<br> 12/15<br> 4/5<br> 3/4

Semmy [17]

Answer:

4/5

find a common factor that can divide evenly into 12 and 15 in this case its 3

12÷3=4

15÷3=5

so therefore the answer is 4/5.

I hope this helps!

7 0

3 years ago

Read 2 more answers

Write the condition under which the hcf of the given algebraic expression is 1​

Write the condition under which the hcf of the given algebraic expression is 1