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3 years ago

What is 8 out of 50 as a percentage?

Mathematics

2 answers:

ANTONII [103]3 years ago

7 0

8 % 50=16

Hope it helps

Anni [7]3 years ago

3 0

8 % 50 = 16

Good Lessons

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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

Chang is estimating the volume of his bathtub the actual volume of his bathtub is 37 gal chang’s estimate is 31 gal find the abs

stepladder [879]

<h3>The absolute error is 6</h3><h3>The percent error is 16.22 %</h3>

<em><u>Solution:</u></em>

Given that,

Actual volume of his bathtub is 37 gal

Estimate is 31 gal

<em><u>Find the absolute error</u></em>

Absolute Error = | Measured Value - Actual Value |

Absolute Error = | 31 - 37 |

Absolute Error = 6

<em><u>Find the percent error</u></em>

$Percent\ error = \frac{\text{estimate - actual}}{actual} \times 100$

Substituting we get,

$percent\ error = \frac{31-37}{37} \times 100\\\\percent\ error = \frac{-6}{37} \times 100\\\\percent\ error = -16.22$

Negative sign means percent decrease

Thus percent error is 16.22 %

5 0

2 years ago

Find the area of the triangle.

Archy [21]

Answer:

Area= 80 in square

Step-by-step explanation:

h=8

b=20

formula= b*h/2

so, 8*20/2

Area= 80 in square

7 0

2 years ago

Write 7x10x10x10x10 with an exponent

polet [3.4K]

Answer:

7x10^4

Step-by-step explanation:

Please add the thanks and rate me please

6 0

3 years ago

Read 2 more answers

What is the overlap of Data Set 1 and Data Set 2?

Dima020 [189]

<h3>Answer: A) high</h3>

Explanation:

Each set spans from 3 to 7 as the min and max. Since we're dealing with the same endpoints, we have perfect overlap.

4 0

2 years ago