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leva [86]
2 years ago
7

Are the following triangles similar, Explain your answer​

Mathematics
1 answer:
Pie2 years ago
3 0
Yes the have the same 78° angle . The smaller one should be able to fit inside the larger one.
You might be interested in
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
The nicotine content in a single cigarette of a particular brand has a distribution with mean 0.4 mg and standard deviation 0.1
a_sh-v [17]

Answer:

Step-by-step explanation:

For this case we can define the random variable of interest as: "The nicotine content in a single cigarette " and for this case we know the following parameters:

\mu = 0.4, \sigma = 0.1

And for this case we select a sample size of n =100 and we want to find the following probability:

P(\bar X

And for this case we can use the z score formula given by:

z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

z= \frac{0.38-0.4}{\frac{0.1}{\sqrt{100}}}= -2

And we can find the required probability with the normal standard table and we got:

P(z

8 0
3 years ago
16. Solve for the angle x.<br> cos(¹/2x) = ¹/2
Basile [38]

Answer:

We know that ,

\rightarrow \tt \cos( \frac{\pi}{3} )  =  \frac{1}{2}

So ,

\:  \rightarrow \tt \cos( \frac{1}{2}x )    =  \cos( \frac{\pi}{3} )  \\  \\   \rightarrow \tt \frac{1}{2}.x =  \frac{\pi}{3}  \\  \\ \rightarrow \tt x =  \frac{2\pi}{3}

we can add 2 pi to it since there will be no change in the value

Also,

\: \rightarrow \tt  \cos( \frac{14\pi}{6} )  =  \frac{1}{2}  \\  \\  \\ \rightarrow \tt \frac{1}{2}  x =  \frac{14\pi}{6}  \\  \\ \rightarrow \tt x =  \frac{7\pi}{3}

Answer : Option B

6 0
2 years ago
PLEASE HELP ME!!! THE RIGHT ANSWER WILL GET THE BRAINIEST!
Lina20 [59]

Answer:

\sf D) \quad s=8 \frac{1}{4}t

Step-by-step explanation:

  • t  = time (in hours) → this is the independent variable
  • s = total area cleaned (in square feet) → this is the dependent variable (as the number of square feet cleaned depends on the number of hours worked)

Therefore, if the rate of cleaning is 8 1/4 square feet per hour, the relationship between s and t is:

\sf s=8 \frac{1}{4}t

8 0
2 years ago
Three increased by the quotient of six and a number
GuDViN [60]

"Increased" means to add.

"Quotient" is a total of a division problem.

"A number" means the unknown.

This is our problem: 3 + 6 / N

8 0
2 years ago
Read 2 more answers
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