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3 years ago

Find the L.C.M of the given pair of numbers using the prime factors method. 70 and 84

Mathematics

2 answers:

Allisa [31]3 years ago

5 0

2| 70,84

2|35,42

3|35,21

5|35,7

.|5,7

LCM=2×2×3×5×5×7=2100

Snowcat [4.5K]3 years ago

5 0

Answer:

420

Step-by-step explanation:

Prime Number: a whole number greater than 1 that cannot be made by multiplying other whole numbers

First prime numbers: 2, 3, 5, 7, 11, 13, 17, ...

Prime Factorization: prime numbers that multiply together to make the original number.

LCM = least common multiple: smallest positive number that is a multiple of two or more numbers

Start by finding the prime factorization of each number.

Start with the smallest prime number: 2

70 ÷ 2 = 35

35 is not divisible by 2 or 3, but is divisible by 5:

35 ÷ 5 = 7

7 is a prime number, so cannot be divided any further

So 70 = 2 × 5 × 7

Start with the smallest prime number: 2

84 ÷ 2 = 42

Again divide by 2:

42 ÷ 2 = 21

Now divide by 3:

21 ÷ 3 = 7

So 84 = 2 × 2 × 3 × 7

Write each number as a product of primes, matching primes vertically when possible

84 = 2 × 2 × 3 × 7

70 = 2 × 5 × 7

Now bring down the primes in each column. The LCM is the product of these factors.

LCM = 2 × 2 × 3 × 5 × 7 = 420

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Which describes how to find the solution to 3p < 14?

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Answer:

A. divide both sides by 3

Step-by-step explanation:

3p < 14

We want to isolate p, so we divide both sides by 3

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3 years ago

A machine, when working properly, produces 5% or less defective items. Whenever the machine produces significantly greater than

vovikov84 [41]

Answer:

The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.

Step-by-step explanation:

A machine, when working properly, produces 5% or less defective items.

This means that the null hypothesis is:

$H_0: p \leq 0.05$

Test if the percentage of defective items produced by this machine is greater than 5%.

This means that the alternate hypothesis is:

$H_a: p > 0.05$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.05 is tested at the null hypothesis:

This means that $\mu = 0.05, \sigma = \sqrt{0.05*0.95}$

A random sample of 300 items taken from the production line contained 27 defective items.

This means that $n = 300, X = \frac{27}{300} = 0.09$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.09 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{300}}}$

$z = 3.18$

Pvalue of the test:

Testing if the mean is greater than a value, which means that the pvalue of the test is 1 subtracted by the pvalue of Z = 3.18, which is the probability of a finding a sample proportion of 0.09 or higher.

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3 years ago

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You get 75, but it is not whole.
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8 0

3 years ago

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Nana76 [90]

Answer:

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Step-by-step explanation:

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3 years ago

Find the L.C.M of the given pair of numbers using the prime factors method. 70 and 84​

Find the L.C.M of the given pair of numbers using the prime factors method. 70 and 84