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3 years ago

Given: ABC, DE || AC

Mathematics

1 answer:

777dan777 [17]3 years ago

7 0

Answer:

1. ∠BDE ≅ ∠ BAC Corresponding Angles Postulate

∠BED ≅ ∠BCA

2. BA = BD + DA

BC = BE + EC Segment Addition Postulate

3. BD + DA / BD = BE + EC / BE Substitutional property equality

Step-by-step explanation:

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Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

crimeas [40]

Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c) $P(X = 2)$ is unusual, $P(X = 0)$ is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

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

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

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

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

And $\pi$ is the probability of X happening.

A number of sucesses $x$ is considered unusually low if $P(X \leq x) \leq 0.05$ and unusually high if $P(X \geq x) \geq 0.05$

In this problem, we have that:

Two cans are randomly chosen, so $n = 2$

Two out of 18 cans are filled with diet coke, so $\pi = \frac{2}{18} = 0.11$

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

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

$P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121$

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

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

$P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921$

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that $P(X = 2)$ is unusual, since $P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05$

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

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

$P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958$

There is a 19.58% probability that exactly one is diet and exactly one is regular.

8 0

3 years ago

traveling at 60 miles per hour how many minutes rounded to the nearest whole number does it take to drive 125 miles from San Die

Gre4nikov [31]

<span>125/65=1.92 hours=115.2min=115min i hope this helps u happy halloween</span>

4 0

3 years ago

Can you guys help me with this one please

PilotLPTM [1.2K]

Answer:

1 to 100,000

Step-by-step explanation:

1 km is equivalent to 100,000 cm.

3 0

3 years ago

Please help?!’ answerr

Ugo [173]

Answer:

The choice Draw 2

Step-by-step explanation:

$3(8 - 4x) < 6(x - 5) \\ 24 - 12x < 6x - 30 \\ 24- 12x + 12x < 6x + 12x - 30 \\ 24 < 18x - 30 \\ 24 + 30 < 18x - 30 + 30 \\ 54 < 18x \\ 54 \div 18 < 18x \div 18 \\ 3 < x \\ x > 3$

I hope I helped you^_^

6 0

3 years ago

One third of the opposite of a number is less than 12. Write and inequality.

fenix001 [56]

X= a number

The opposite of a number is its negative opposite. It's the additive inverses of a number. The additive inverse of 4 is -4. It will always equal zero when added together.

Inequality:
1/3(-x) < 12

Hope this helps! :)

3 0

3 years ago