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3 years ago

HELP ME PLEASE Given that the universal set is all real numbers, write the complement of set A. Set A: {Irrational numbers}

Mathematics

1 answer:

jeka943 years ago

7 0

Answer: The complement is Q, the set of the rational numbers.

Step-by-step explanation:

Ok, here we can use the fact that the set of all the real numbers is equal to the union of the set of the rational numbers and the set of the irrational numbers. (Remember that Q, the rational numbers, also does include the set of the integer numbers))

Then, if the universal set is R, we have that the universal set is:

R = Q + I

Where Q = set of rational numbers and I = set of irrational numbers.

Then, the complement of the set A = I = irrational numbers, is equal to:

R - I = Q + I - I = Q

Then the set of the rational numbers is the complement of the set A.

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A sequence is defined by the recursive function f(n 1) = one-halff(n). if f(3) = 9 , what is f(1) ?

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Step-by-step explanation:

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4 years ago

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1 year ago

Construct a 95% prediction interval for y given x=-3.5, ^y= 2.097x - .552 and se= .976

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Answer:

95% Confidence interval for y

= (-9.804, -5.979)

Lower limit = -9.804

Upper limit = -5.979

Step-by-step explanation:

^y= 2.097x - 0.552

x = -3.5

Standard error = 0.976

Mathematically,

Confidence Interval = (Mean) ± (Margin of error)

Mean = 2.097x - 0.552 = (2.097×-3.5) - 0.552 = - 7.8915

(note that x=-3.5)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value for 95% confidence interval = 1.960

Standard Error of the mean = 0.976

95% Confidence Interval = (Mean) ± [(Critical value) × (standard Error of the mean)]

CI = -7.8915 ± (1.960 × 0.976)

CI = -7.8915 ± 1.91296

95% CI = (-9.80446, -5.97854)

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= (-9.804, -5.979)

Hope this Helps!!!

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3 years ago