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4 years ago

Assemble the proof by dragging tiles to the statements and reasons columns

Mathematics

2 answers:

Elena L [17]4 years ago

5 0

Answer:

Step-by-step explanation:

Given: ∠2 and ∠4 are vertical angles.

To prove: ∠2≅∠4

Proof:

Statement Reason

1. m∠2+m∠3=180° ∠2 and ∠3 form a linear pair

2. m∠3+m∠4=180° ∠3 and ∠4 form a linear pair

3. From statement 1 and 2, m∠2=m∠4

and they are vertical angles. lines m and n intersect at p

Therefore, ∠2≅∠4

Hence proved.

mestny [16]4 years ago

3 0

Answer: 1) <2 and <4 are vert. angles=given

2)lines m and n intersect at P=def. of vertical angles

3)<2 and <3 are a linear pair=def. of a linear pair

4)m<2 + m<3=180 = angles addition postulate

5)<3 and <4 are a linear pair =def. of a linear pair

6)m<3 + m<4=180 = angle addition postulate

7)m<2+m<3=m<3+m<4 = substitution property

8)m<2=m<4 = subtraction property

9)<2=<4 = definition of = angles

Step-by-step explanation:

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Luden [163]

Answer:

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3 years ago

1. write an algebraic expression for the phrase three times the sum of B and F.

Nezavi [6.7K]

The sum of b and f is b+f

Three times this sum is 3(b+f)

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3 years ago

If 400 bricks measuring 81" by 31" are required to build a wall 42 ft. high, how long is the wall

musickatia [10]

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3 years ago

Miss larner had a bowl of jolly ranchers sitting on her desk. One day sean decided to grab a handful of the candies and took 1/3

soldier1979 [14.2K]

Answer: 36 candies were in the bowl when the day started

Step-by-step explanation:

Let x represent the number of candies in the bowl initially.

One day sean decided to grab a handful of the candies and took 1/3 of the candies. This means that Sean took x/3 candies. Number of candies left would be x - x/3 = 2x/3.

Since he decided to return 4 of them, the remaining number of candies would be

2x/3 + 4 = (2x + 12)/3

Tracy also helped herself and took 1/4 of the candies in the bowl. This means that she took

1/4(2x + 12)/3 = (2x + 12)/12

The number of candies left would be (2x + 12)/3 - (2x + 12)/12

= 4(2x + 12) - (2x + 12)/12 = (8x + 48 - 2x - 12)/12 = (10x - 36)/12

Since she put down 3, the number remaining would be

(10x - 36)/12 + 3 = (10x - 36 + 36)/12 = 10x/12

Eugene grabbed 1/2 of the candies in the bowl. This means that he took

1/2 × (10x)/12 = (10x)/24

The amount remaining is

(10x)/12 - (10x)/24 = [2(10x) - 10x)]/24

= [20x - 10x]/24 = 10x/24

He put those two back. It means that amount left would be

(10x)/24 + 2

At the end of the day, there are 17 candies left. This means that

10x/24 + 2 = 17

10x/24 = 17 - 2 = 15

10x = 24×15 = 360

x = 360/10 = 36

4 0

3 years ago

About 3% of children in the United States are allergic to peanuts. Choose three children at random and let the random variable X

Charra [1.4K]

Answer:

0.029991 = 2.9991% conditional probability that exactly two of the children will be allergic to peanuts, given that at least one of the three children suffers from this allergy

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they are allergic to peanuts, or they are not. The probability of a children being allergic to peanut butter is independent of other children. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

3% of children in the United States are allergic to peanuts.

So $p = 0.03$

Three children:

So n = 3,

The probabilities are:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{3,0}.(0.03)^{0}.(0.97)^{3} = 0.912673$

$P(X = 1) = C_{3,1}.(0.03)^{1}.(0.97)^{2} = 0.084681$

$P(X = 2) = C_{3,2}.(0.03)^{2}.(0.97)^{1} = 0.002619$

$P(X = 3) = C_{3,3}.(0.03)^{3}.(0.97)^{0} = 0.000027$

What is the conditional probability that exactly two of the children will be allergic to peanuts, given that at least one of the three children suffers from this allergy?

This is

$p = \frac{P(X = 2)}{P(X \geq 1)}$

In which

$P(X \geq 1) = 0.084681 + 0.002619 + 0.000027 = 0.087327$

$P(X = 2) = 0.002619$

$p = \frac{0.002619}{0.087327} = 0.03$

0.029991 = 2.9991% conditional probability that exactly two of the children will be allergic to peanuts, given that at least one of the three children suffers from this allergy

8 0

4 years ago