Virtual Nerd™: How Do You Use a Tree Diagram to Count the Number of Outcomes in a Sample Space?

PLEASE HELP!! URGENT!! i will mark brainliest if its right!! In the figure below, ∠DEC ≅ ∠DCE, ∠B ≅ ∠F, and DF ≅ BD. Point C is

zvonat [6]

Answer:

See below.

Step-by-step explanation:

This is how you prove it.

<B and <F are given as congruent.

This is 1 pair of congruent angles for triangles ABC and GFE.

<DEC and <DCE are given as congruent.

Using vertical angles and substitution of transitivity of congruence of angles, show that angles ACB and GEF are congruent.

This is 1 pair of congruent angles for triangles ABC and GFE.

Now you need another side to do either AAS or ASA.

Look at triangle DCE. Using the fact that angles DEC and DCE are congruent, opposite sides are congruent, so segments DC and DE are congruent. You are told segments DF and BD are congruent. Using segment addition postulate and substitution, show that segments CB and EF are congruent.

Now you have 1 pair of included sides congruent ABC and GFE.

Now using ASA, you prove triangles ABC and GFE congruent.

7 0

2 years ago

Two angles are supplementary if the sum of their measures is 180. If one angle’s measure is 45 more than 3 times the other angle

faust18 [17]

Assuming the two angles are supplementary, the angle measuring x is equal to 33.75, and the angle measuring 3x+45 is equal to 146.25.

Step-by-step explanation:

x+(3x+45)=4x+45=180

4x+45=180

-45 -45

4x=135

÷3 ÷3

x=33.75

3x+45=146.25

7 0

2 years ago

The number and frequency of Atlantic hurricanes annually from 1940 through 2007 is shown here:

klio [65]

Answer:

The probability table is shown below.

A Poisson distribution can be used to approximate the model of the number of hurricanes each season.

Step-by-step explanation:

(a)

The formula to compute the probability of an event E is:

$P(E)=\frac{Favorable\ no.\ of\ frequencies}{Total\ NO.\ of\ frequencies}$

Use this formula to compute the probabilities of 0 - 8 hurricanes each season.

The table for the probabilities is shown below.

(b)

Compute the mean number of hurricanes per season as follows:

$E(X)=\frac{\sum x f_{x}}{\sum f_{x}}=\frac{176}{68}= 2.5882\approx2.59$

If the variable X follows a Poisson distribution with parameter λ = 7.56 then the probability function is:

$P(X=x)=\frac{e^{-2.59}(2.59)^{x}}{x!} ;\ x=0, 1, 2,...$

Compute the probability of X = 0 as follows:

$P(X=0)=\frac{e^{-2.59}(2.59)^{0}}{0!} =\frac{0.075\times1}{1}=0.075$

Compute the probability of X = 1 as follows:

$\neq P(X=1)=\frac{e^{-2.59}(2.59)^{1}}{1!} =\frac{0.075\times7.56}{1}=0.1943$

Compute the probabilities for the rest of the values of X in the similar way.

The probabilities are shown in the table.

On comparing the two probability tables, it can be seen that the Poisson distribution can be used to approximate the distribution of the number of hurricanes each season. This is because for every value of X the Poisson probability is approximately equal to the empirical probability.

5 0

3 years ago

Jane has $7 and her sister had $2. Their parents have each of them an equal amount of money. Then, Jane had twice as much money

Tems11 [23]

Answer:

Then, Jane had twice as much money as her sister. How much money did their parents give each of them?

Let x = amt given to them

Solve this equation for x

7 + x = 2(2 + x) Jane had $7 and her sister had $2.

Their parents gave them each equal amount of money

4 0

3 years ago

What are the slope and the y-intercept of the linear function that is represented by the equation 8x - 2y = 5?

ivann1987 [24]

Y=mx+b is the formula you need to get it in
start with the equation 8x-2y=5
so we want to get y by itself and everything else on the right side of the equation. to do this first subtract -8x from the left side and put it on the right side. this step would look like this:
8x-2y=5
-8x-2y=5 -> -2y=5-8x
-------------

next take and divide -2 from both sides of the equation. this would look like this:
-2y= 5 -8x
÷-2y=÷-2÷-2 -> y= -5/2 +4x
-------------------
so your new equation is y=4x-5/2 y=mx+b tells you the slope and y-intercept. m=slope and b=y-intercept. so in this case 4 is your slope and -5/2 is your y-int

6 0

2 years ago

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