1.3, 1 1/3, 1.34
The decimal version of 1 1/3 is 1.333 (so on)
so 1.3 is less than 1.333 and 1.333 is less than 1.34
1.3<1.333<1.34
Answer:
C. x = 3, y = 2
Step-by-step explanation:
If both triangles are congruent by the HL Theorem, then their hypotenuse and a corresponding leg would be equal to each other.
Thus:
x + 3 = 3y (eqn. 1) => equal hypotenuse
Also,
x = y + 1 (eqn. 2) => equal legs
✔️Substitute x = y + 1 into eqn. 1 to find y.
x + 3 = 3y (eqn. 1)
(y + 1) + 3 = 3y
y + 1 + 3 = 3y
y + 4 = 3y
y + 4 - y = 3y - y
4 = 2y
Divide both sides by 2
4/2 = 2y/2
2 = y
y = 2
✔️ Substitute y = 2 into eqn. 2 to find x.
x = y + 1 (eqn. 2)
x = 2 + 1
x = 3
6.75%
1 penny = 50% chance of tail
50% x 50% x 50% x 50%= 6.75%
Using the hypergeometric distribution, it is found that there is a 0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.
In this problem, the bulbs are chosen without replacement, hence the <em>hypergeometric distribution</em> is used to solve this question.
<h3>What is the hypergeometric distribution formula?</h3>
The formula is:


The parameters are:
- x is the number of successes.
- N is the size of the population.
- n is the size of the sample.
- k is the total number of desired outcomes.
In this problem:
- There are 12 bulbs, hence N = 12.
- 3 are defective, hence k = 3.
The third defective bulb is the fifth bulb if:
- Two of the first 4 bulbs are defective, which is P(X = 2) when n = 4.
- The fifth is defective, with probability of 1/8, as of the eight remaining bulbs, one will be defective.
Hence:


0.2182 x 1/8 = 0.0273.
0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.
More can be learned about the hypergeometric distribution at brainly.com/question/24826394