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3 years ago

{(-3, 7.5) , (-2, 10) , (-1, 12.5)} arithmetic or geomatic

Mathematics

1 answer:

marysya [2.9K]3 years ago

4 0

Answer:

arithmetic

Step-by-step explanation:

The points fall on a straight line. They won't do that for a geometric sequence.

___

Normally the terms of either sort of sequence are numbered with counting numbers: 1, 2, 3, .... Your x-values are negative, so are obviously not term numbers of a sequence. The differences of x-values are 1, and the differences of y-values are 2.5, so we know the x- and y-values are linearly related. That relationship can be expressed in point-slope form by ...

y = 2.5(x +1) +12.5

which can be simplified to

y = 2.5x +15

The arithmetic sequence with first term 17.5 and common difference 2.5 would be described by this same equation.

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4 years ago

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Answer:

A. P=0.4013

B. P=0.9884

C. P=0.3222

Step-by-step explanation:

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The probability is p=0.05 for scrap and p=0.05+0.15=0.20 for degraded or scrap.

The probability of having k scrap gears in the sample is:

$P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{10}{k} 0.05^{k} 0.95^{10-k}\\\\\\$

The probability that one or more is scrap can be calculated as 100% less the probability that no one is scrap:

$P(x\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{10}{0} p^{0}(1-p)^{10}=1*1*0.5987=0.5987\\\\\\P(x\geq1)=1-0.5987=0.4013$

The probability that 8 or more are not scrap is equal to the probability of having 2 or less that are scrap:

$P(x\leq2)=P(x=0)+P(x=1)+P(x=2)\\\\\\P(x=0) = \dbinom{10}{0} p^{0}(1-p)^{10}=1*1*0.5987=0.5987\\\\\\P(x=1) = \dbinom{10}{1} p^{1}(1-p)^{9}=10*0.05*0.6302=0.3151\\\\\\P(x=2) = \dbinom{10}{2} p^{2}(1-p)^{8}=45*0.0025*0.6634=0.0746\\\\\\P(x\leq2)=0.5987+0.3151+0.0746=0.9884$

The probability that more than two are degraded or scrap (p=0.2) is calculated as:

$P(x>2)=1-P(x\leq2)=1-(P(x=0)+P(x=1)+P(x=2))\\\\\\P(x=0) = \dbinom{10}{0} p^{0}(1-p)^{10}=1*1*0.1074=0.1074\\\\\\P(x=1) = \dbinom{10}{1} p^{1}(1-p)^{9}=10*0.2*0.1342=0.2684\\\\\\P(x=2) = \dbinom{10}{2} p^{2}(1-p)^{8}=45*0.04*0.1678=0.3020\\\\\\P(x>2)=1-(0.1074+0.2684+0.3020)=1-0.6778=0.3222$

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3 years ago