This is a problem in "binomial probability." Either the archer hits his target or he does not. This experiment is performed 5 times (so that n=5), and the probability that the archer will hit the target is 0.7 (so that p=0.7).
We need to find the binomial probability that x=3 when the possible outcomes are {0, 1, 2, 3, 4, 5}.
You could use a table of binomial probabilities to evaluate the following:
P(5, 0.7, 3).
Alternatively, you could use a TI-83 or TI-84 calculator and its built-in "binompdf( " function.
I evaluated binompdf(5,0.7,3) and obtained the result 0.309.
Answer:
2
Step-by-step explanation:
Using the law of cosines and sines, the measure of angle B is: 38.4°.
<h3>What is the Law of Cosines and Sines?</h3>
Law of cosines is: c = √[a² + b² ﹣ 2ab(cos C)]
Law of sines is: sin A/a = sin B/b = sin C/c
Use the law of cosines to find c:
c = √[12² + 18² ﹣ 2(12)(18)(cos 117)]
c ≈ 25.8
Use the law of sines to find angle B:
sin B/b = sin C/c
sin B/18 = sin 117/25.8
sin B = (sin 117 × 18)/25.8
sin B = 0.6216
B = sin^(-1)(0.6216)
B = 38.4°
Learn more about the law of cosines on:
brainly.com/question/23720007
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<h2>
Hello!</h2>
The answer is:
The third option:
2.7 times as much.
<h2>
Why?</h2>
To calculate how many more juice will the new can hold, we need to calculate the old can volume to the new can volume.
So, calculating we have:
Old can:
Since the cans have a right cylinder shape, we can calculate their volume using the following formula:

Where,

We are given the old can dimensions:

So, calculating the volume, we have:

We have that the volume of the old can is:

New can:
We are given the new can dimensions, the diameter is increased but the height is the same, so:

Calculating we have:

Now, dividing the volume of the new can by the old can volume to know how many times more juice will the new can hold, we have:

Hence, we have that the new can hold 2.7 more juice than the old can, so, the answer is the third option:
2.7 times as much.
Have a nice day!