Answer:
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Explanation:
The figure attached shows the <em>Venn diagram </em>for the given sets.
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<em><u>a) What is the probability that the number chosen is a multiple of 3 given that it is a factor of 24?</u></em>
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From the whole numbers 1 to 15, the multiples of 3 that are factors of 24 are in the intersection of the two sets: 3, 6, and 12.
There are a total of 7 multiples of 24, from 1 to 15.
Then, there are 3 multiples of 3 out of 7 factors of 24, and the probability that the number chosen is a multiple of 3 given that is a factor of 24 is:
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<em><u>b) What is the probability that the number chosen is a factor of 24 given that it is a multiple of 3?</u></em>
The factors of 24 that are multiples of 3 are, again, 3, 6, and 12. Thus, 3 numbers.
The multiples of 3 are 3, 6, 9, 12, and 15: 5 numbers.
Then, the probability that the number chosen is a factor of 24 given that is a multiple of 3 is:
Answer:
That would be sina.
Step-by-step explanation:
sin(a+b) = sinacosb + cosasinb
sin(a-b) = sinacosb - cosasinb
Adding we get sin(a+b) + sin(a-b) = 2sinaccosb
so sinacosb = 1/2sin(a+b) + sin(a-b)
Answer:
455 or 680, depending
Step-by-step explanation:
If we assume the three choices are different, then there are ...
15C3 = 15·14·13/(3·2·1) = 35·13 = 455
ways to make the pizza.
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If two or three of the topping choices can be the same, then there are an additional ...
2(15C2) +15C1 = 2·105 +15 = 225
ways to make the pizza, for a total of ...
455 + 225 = 680
different types of pizza.
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There is a factor of 2 attached to the number of choices of 2 toppings, because you can have double anchovies and tomato, or double tomato and anchovies, for example, when your choice of two toppings is anchovies and tomato.
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nCk = n!/(k!(n-k)!)
H (t) = - 16t ^ 2 + 16t + 480
For this case, the first thing to do is to match the polynomial to zero to find the roots.
We have then:
0 = -16t ^ 2 + 16t + 480
From here, we obtain the following roots of the polynomial:
t1 = -5
t2 = 6
We ignore the negative root because the time is always greater than zero.
Answer:
it takes Rose to hit the water about
t = 6 seconds
Total internal energy increases by 1760 J
Step-by-step explanation:
The kinetic energy of an object is the energy possessed by the object due to its motion.
It is calculated as
where
m is the mass of the object
v is its speed
For the hammer in this problem:
m = 2.50 kg
v = 65.0 m/s
So its kinetic energy is
Then the problem says that 1/3 of the hammer's kinetic energy is converted into internal energy: therefore, the total internal energy increases by
Learn more about kinetic energy:
brainly.com/question/6536722
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