Which ratio is greater? 4:3 or 7:9. (Show necessary steps and calculations for your answer)

Mathematics

2 answers:

scoundrel [369]3 years ago

8 0

Answer:

4 : 3 > 7 : 9

Step-by-step explanation:

In order to compare two ratios or fractions, we make their denominators equal and then equate their numerators.

$4 : 3 = \frac{4}{3} = \frac{4 \times 3}{3 \times 3} = \frac{12}{9} \\ \\ 7 : 9 = \frac{7}{9} \\ \\ \because \: 12 > 7 \\ \\ \therefore \: \frac{4}{3} > \frac{7}{9} \\ \\ \implies \: 4 : 3 > 7 : 9$

stiks02 [169]3 years ago

7 0

4:3

= 4/3

= 1.333333...

7:9

= 7/9

= 0.777777...

4:3 is greater than 7:9

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Question Help When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select

horrorfan [7]

Answer:

The probability is $P(X \le 2 ) = 0.9072$

The company will accept 90.72% of the shipment and will reject $(100 -90.72) = 9.2\%$ of the shipment , so many of the shipment are rejected

Step-by-step explanation:

From the question we are told that

The sample size is n = 36

The proportion that did not meet the requirement is $p = 0.03$

Generally the probability that the whole shipment is accepted is equivalent to the probability that there is at most 2 batteries that do not meet the requirement , this is mathematically represented as

$P(X \le 2 ) = [ P(X = 0 ) + P(X = 1 ) + P(X = 0)]$

=> $P(X \le 2 ) = [ [^{n}C_0 * (p)^{0} *(1-p)^{n-0} ] + [^{n}C_1 * (p)^{1} *(1-p)^{n-1} ] + [^{n}C_2 * (p)^{2} *(1-p)^{n-2} ]]$

Here C stands for Combination (so we will be making the combination function in our calculators )

=> $P(X \le 2 ) = [ [^{36}C_0 * (0.03)^{0} *(1-0.03)^{36-0} ] + [^{36}C_1 * (0.03)^{1} *(1-0.03)^{36-1} ] + [^{36}C_2 * (0.03)^{2} *(1-0.03)^{36-2} ]]$