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3 years ago

How could you use the Distributive Property to rewrite the expression −(8 + 12)?

Mathematics

2 answers:

guajiro [1.7K]3 years ago

8 0

Answer:

-20

Step-by-step explanation:

-8-12=-20

bogdanovich [222]3 years ago

6 0

The answer is this number -20

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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

3 years ago

Pls write the steps u did

frez [133]

When two parallel lines are intersected by a transversal, the same-side exterior angles are supplementary. That means that their sum is 180.

Using that logic, if the two roads were parallel, then the sum of their same-side exterior angles will add up to 180. Yet their same-side exterior angles add up to 170 (130 + 40 = 170), hence they can't be parallel.

See the drawing attached below.

Using supplmenatry angles (two angles whose sum of measures add up to 180 or a straight line), we can say that:

m<DIE + m<HID = 18

40 + m<HID = 180

m<HID = 140

Similarly:

m<BHC + m<CHI = 180

130 + m<CHI = 180

m<CHI = 50

Using verticle angles therome, (when two lines intersect, the angles opposite to eachother are congruent, or have the same measure), we can say that:

m<DIE = m<GIH = 40

m<GIE = m<HID = 140

m<CHI = m<AHB = 50

m<BHC = m<AHI = 130

5 0

3 years ago

Construction This section of a concrete skateboard ramp has the shape of a triangular prism. Find the volume

irina [24]

Answer:

volume = 73.3ft³

value = $194.4

Step-by-step explanation:

volume of prism = (½bh)l

=(½×4×4)×9.2

=73.6ft³

value of concrete

1ft³ : $4.00

73 .6ft³ : X

X : (73.6ft³ × $4.00) ÷ 1ft³

X : $294.4

7 0

2 years ago

Brainliest to the correct answer :)

frozen [14]

Answer:

Assume that the formula is true for the (k+1)term

Step-by-step explanation:

I learned this in class a couple weeks ago in intermediate algebra

7 0

2 years ago

What is the answer to this please

Alex_Xolod [135]

Domain: x≤5 (notice the closed dot on the right and the arrow on the left)
Range: y≤2 (notice the closed dot on the right and the arrow on the left)

The arrow means it keeps going infinitely. The closed dot means it stops there but is inclusive of that value.

3 0

3 years ago