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2 years ago

Is the number 4.1234 rational

Mathematics

2 answers:

Rudiy272 years ago

8 0

Answer:

Yes

Step-by-step explanation:

A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0. Since 4.1234 is and integer or decimal above it is rational

SpyIntel [72]2 years ago

6 0

Yes, because it terminates and is able to be represented as a fraction

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For two events A and B show that P (A∩B) ≥ P (A)+P (B)−1.

nordsb [41]

Answer:

<h3>For two events A and B show that P (A∩B) ≥ P (A)+P (B)−1.</h3>

By De morgan's law

$(A\cap B)^{c}=A^{c}\cup B^{c}\\\\P((A\cap B)^{c})=P(A^{c}\cup B^{c})\leq P(A^{c})+P(B^{c}) \\\\1-P(A\cap B)\leq P(A^{c})+P(B^{c}) \\\\1-P(A\cap B)\leq 1-P(A)+1-P(B)\\\\-P(A\cap B)\leq 1-P(A)-P(B)\\\\P(A\cap B)\geq P(A)+P(B)-1$

which is Bonferroni’s inequality

<h3>Result 1: P (Ac) = 1 − P(A)</h3>

Proof

If S is universal set then

$A\cup A^{c}=S\\\\P(A\cup A^{c})=P(S)\\\\P(A)+P(A^{c})=1\\\\P(A^{c})=1-P(A)$

<h3>Result 2 : For any two events A and B, P (A∪B) = P (A)+P (B)−P (A∩B) and P(A) ≥ P(B)</h3>

Proof:

If S is a universal set then:

$A\cup(B\cap A^{c})=(A\cup B) \cap (A\cup A^{c})\\=(A\cup B) \cap S\\A\cup(B\cap A^{c})=(A\cup B)$

Which show A∪B can be expressed as union of two disjoint sets.

If A and (B∩Ac) are two disjoint sets then

$P(A\cup B) =P(A) + P(B\cap A^{c})---(1)\\$

B can be expressed as:

$B=B\cap(A\cup A^{c})\\$

If B is intersection of two disjoint sets then

$P(B)=P(B\cap(A)+P(B\cup A^{c})\\P(B\cup A^{c}=P(B)-P(B\cap A)$

Then (1) becomes

$P(A\cup B) =P(A) +P(B)-P(A\cap B)\\$

<h3>Result 3: For any two events A and B, P(A) = P(A ∩ B) + P (A ∩ Bc)</h3>

Proof:

If A and B are two disjoint sets then

$A=A\cap(B\cup B^{c})\\A=(A\cap B) \cup (A\cap B^{c})\\P(A)=P(A\cap B) + P(A\cap B^{c})\\$

<h3>Result 4: If B ⊂ A, then A∩B = B. Therefore P (A)−P (B) = P (A ∩ Bc) </h3>

Proof:

If B is subset of A then all elements of B lie in A so A ∩ B =B

$A =(A \cap B)\cup (A\cap B^{c}) = B \cup ( A\cap B^{c})$

where A and A ∩ Bc are disjoint.

$P(A)=P(B\cup ( A\cap B^{c}))\\\\P(A)=P(B)+P( A\cap B^{c})$

From axiom P(E)≥0

$P( A\cap B^{c})\geq 0\\\\P(A)-P(B)=P( A\cap B^{c})\\P(A)=P(B)+P(A\cap B^{c})\geq P(B)$

Therefore,

P(A)≥P(B)

8 0

2 years ago

What is x if 5x = 30?

horsena [70]

So 5x=30
then x= 30/5
and x=6

so the answer is last one !

6 0

3 years ago

Read 2 more answers

Find the domain and range of the exponential function h(x) = 125x.

kirill [66]

H(x) = 125^x

Domain: all the real numbers (from negative infinity to infinity)

Range: all the positive real numbers.

As x decreases 125^x decreases approaching to 0. The function will never reach the value 0 but will approximate to it as x goes to negative infinity. The rate of decreasing gets lower and lower, with a limit of zero, when x becomes more and more negative.

As x increases 125^x increases indefinetely and at an increasing rate. That means that the increase is accelerated (the bigger the value of x the bigger the rate of increasing).

4 0

2 years ago

WHOEVER EXPLAINS ALL THEIR WORK AND GOES THROW EAXH STEP WILL GET BRAINLEST THAT IS COMPLETELY FINISEHD. write the equation of t

neonofarm [45]

Answer:

$y = -3x+11$

Step-by-step explanation:

I accept your challenge!

First we know that a equation of the line is a linear equation, and its equation is:

$y = mx+b$

$m: \text{slope}\\b: \text{y-intercept}$

In this context, the slope, defined as the steepness of a line is characterized as the ratio of RISE (the difference in the y-coordinates, the vertical change) over the RUN (the difference in x-coordinates, the horizontal change).

$m=\frac{\text{change in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$