Atool box contains 12 bolts and 10 nuts. if a handyman grabs 8 items randomly, what is the probability that he gets four bolts and four nuts? (the answer is rounded to three decimal places). (a) 0.225 (b) 0.275 (c) 0.325 (d) 0.375 (e) 0.425 ia on ib nin

(c) 0.325

Step-by-step explanation:

Given,

The number of bolts = 12,

Numbers of nuts = 10,

Total items = 12 + 10 = 22

Thus, the number of ways of choosing 8 items out of 22 items = C(22,8)

Now, the number of ways of choosing 4 bolts and 4 nuts = C(12, 4) × C(10, 4)

Hence, the probability of getting four bolts and four nuts

Therefore, option (c) is correct.

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204