Answer:
∠4 and ∠3
∠4 and ∠5
∠3 and ∠6
Step-by-step explanation:
A pair of angles is said to be supplementary when the 2 angles add up to give 180°.
Two right angles add up to give 180°. Also, if we have two angles on a straight line, their sum = 180°, according to the linear pair property.
Thus, since m< 3 is given as 90°, m<4 = 90°.
m<4 + m<3 = 180°.
Therefore, <4 and <3 are supplementary.
<4 and <5, <3 and <6 are both linear pairs, therefore they are also supplementary.
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
Answer:
y²+5y+4=y²+4y+y+4=y(y+4)+1(y+4)=
<u>(y+4)(y+1)</u>
6 + (-4) —> 6 - 4 = 2
(-8) + (-14) —> (-8 + (-14)) —> -(8+ 14) —> -(22) = -22
(-12) + 5 —> (-12 + 5) —> -(12-5) —> -(7) = -7
Answer:
c(4) = -76
Step-by-step explanation:
c(x) x=4 so plug 4 in for x
-5(4)² + (4)
Do parentheses first so... 4² = 16
-5(16) + 4
-5(16) = -80
-80+4 = -76
c(4) = -76