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2 years ago

Alex can run 24 miles in 3 hours.what is his average speed in miles per hour?

Mathematics

2 answers:

djverab [1.8K]2 years ago

5 0

Answer:

8 mph

Step-by-step explanation:

24÷3=8

timurjin [86]2 years ago

3 0

Answer:

-89

Step-by-step explanation:

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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

Please help me thanks if u do

aniked [119]

Answer: a

Step-by-step explanation: look at the chart

3 0

3 years ago

GAS vs HYBRID

STALIN [3.7K]

Answer:

Electric vehicles (EVs) are becoming increasingly common, with many manufacturers currently offering models that plug in. Dozens more are expected to hit the market over the next few years.

Although sales of pure electric vehicles and plug-in hybrids account for less than 2 percent of U.S. light vehicle sales currently, there has been increasing interest from car shoppers. In 2010, just 1,919 EVs were sold in the U.S. In 2018, sales hit 233,411. But forecasts for how much of the U.S. auto market EVs could occupy range from 8 to 25 percent by 2025. Stephanie Brinley, an analyst at market research firm IHS Markit, says her prediction sits at the low end.

“If you look at EVs for 2021 and 2022, we’re really at the beginning of this market,” she says. “By 2025, EVs should be about 9 percent of the U.S. market. That’s a huge amount of growth from where we are right now

3 0

2 years ago

Solve for b. <br>4/3b+2=4-1/3b

Maksim231197 [3]

Answer:

b = $\frac{6}{5}$

Step-by-step explanation:

Multiply through by 3 to clear the fractions.

4b + 6 = 12 - b ( add b to both sides )

5b + 6 = 12 ( subtract 6 from both sides )

5b = 6 ( divide both sides by 5 )

b = $\frac{6}{5}$

4 0

3 years ago

Rita is the manager of the football team, and she has been assigned the task of painting a mascot in the middle of the field. Th

Alik [6]

Answer:

25 square yards

Step-by-step explanation:

We assume that "fits neatly" means "fills" so that the area of the painting is the same as the area of the square. Put the numbers in the formula and do the arithmetic.

A = (5 yd)² = 5² yd² = 25 yd²

4 0

3 years ago