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Answer:
The answer to your question is below
Step-by-step explanation:
Number 9.
To find x use the law of sines
sin x / 8 = sin 95 / 12
Solve for sin x
sin x = 8 sin 95 / 12
sin x = 0.664
x = 41.6°
Number 10
To find x use law of cosines
x² = 6² + 8² - 2(6)(8)cos100
x² = 36 + 64 - 96(-0.174)
x² = 100 + 16.67
x² = 116.67
x = 10.80
Answer:
The ratio of the circumference of a circle to its diameter is approximately 3.14.
Using the normal distribution, it is found that there is a 0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:

- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
.
The probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters is <u>one subtracted by the p-value of Z when X = 4</u>, hence:


Z = 1.71
Z = 1.71 has a p-value of 0.9564.
1 - 0.9564 = 0.0436.
0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
More can be learned about the normal distribution at brainly.com/question/24663213
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When competing the square, you want to have

at the end, and using the fact that the x term and coefficient are really

, we see that the third option is the most efficient way to start