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2 years ago

In the picture lines AB and CD are parallel. Find the measures of the following angles. Explain your reasoning.

Mathematics

1 answer:

hichkok12 [17]2 years ago

5 0

Answer/Step-by-step explanation:

1. <ABC and <BCD are alternate interior angles. Alternate interior angles are equal, therefore, since m<ABC = 38°, then m<BCD = 38°

2. m<ECF = m<BCD (corresponding angles)

m<ECF = 38° (substitution)

3. m<DCF + m<ECF = 180° (linear pair)

m<DCF + 38° = 180° (substitution)

m<DCF = 180° - 38° (Subtraction property of equality)

m<DCF = 142°

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Based on probability and if it is appropriate for a decision to be left up to chance, choose every situation that is both statis

svet-max [94.6K]

The situations that are both statistically fair and morally fair are Situation 2, Situation 3 and Situation 5

<h3>How to categorize the situations?</h3>

For a situation to be fair, the probability of every outcome must be equal.

We can now analyze each option using the above highlight

Situation 1

Alphabets = 26
Probability of vowel = 5/26
Probability of consonant = 21/26

The probabilities of vowels and consonant are not equal.

Hence, this situation is not fair

Situation 2

People = 4

P(Each) = 1/4

The probability of each participant is equal in the above scenario i.e. 1/4

Hence, this situation is fair

Situation 3

People = 5
P(Each) = 1/5

The probability of each cousin is equal in the above scenario i.e. 1/5

Hence, this situation is fair

Situation 4

Numbers = 5 i.e. 2 to 6
P(Prime) = 3/5
P(Composite) = 4/6

The probabilities of prime and composite numbers are not equal.

Hence, this situation is not fair

Situation 5

Roommates = 5
Cards = 5
Aces = 4
P(Each) = 1/5

All probabilities are equal in the above scenario i.e. 1/5

Hence, this situation is fair

Read more about probability at:

brainly.com/question/251701

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4 0

2 years ago

The clubhouse has a water tank from which hikers fill their water jugs before walking the trail. The tank is a 5-gallon cylindri

Ghella [55]

After Alex fill's the jug, the remaining volume of water will be 4 gallons
1 gallon is equivalent to 231 cubic inches
The volume of a cylinder is given by
V = πr²h
4 x 231 = π x 4² x h
h = 181.4 inches or 15.1 feet

6 0

3 years ago

Read 2 more answers

Find the value of x. Round to the nearest tenth.

Nezavi [6.7K]

Answer:

x ≈ 55.6

Step-by-step explanation:

Using the sine ratio in the right triangle

sin20° = $\frac{opposite}{hypotenuse}$ = $\frac{19}{x}$ ( multiply both sides by x )

x × sin20° = 19 ( divide both sides by sin20° )

x = $\frac{19}{sin20}$ ≈ 55.6 ( to the nearest tenth )

7 0

2 years ago

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if

topjm [15]

Answer:

a) The expected value is $\frac{-1}{15}$

b) The variance is $\frac{49}{45}$

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is $\binom{10}{2}$ .

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is $\binom{5}{2}$ . Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is $\binom{5}{1}\cdot \binom{5}{1}$ . So, we define the following probabilities.