Answer:
(1, 14)
Step-by-step explanation:
If you substitute the 14 in;
14 = 12x+2
-2 -2
12 = 12x
/12 /12
1 = x
Answer:
The expected value for the random variable is 14.16.
Step-by-step explanation:
We are given the following data below;
Z P(Z) 
9 0.16 1.44
12 0.25 3
15 0.36 5.4
18 0.17 3.06
21 <u> 0.06 </u> <u> 1.26 </u>
Total <u> 1 </u> <u> 14.16 </u>
Now, the expected value for the random variable Z is given by;
E(Z) =
= 
= 14.16.
Ok for this problem, there are 2 equations representing hall A and hall B
hall A: y=76x+862 where x=number of dinners and y=total cost
hall B: y=75x+894 for the same variables
To find where the 2 meet, simply substitute one equation into the other, creating: 76x+862=75x+894
Solving this, we find that x=32, so at 32 guests, the cost would be the same
For part 2, put the answer for part 1 into either equation from the start, so y=76(32)+862, or y=3294
And we already found that x=32, which represents the # of guests
The circumference of a circle can be found using the equation: c = 2<span>πr, where c=circumference and r=radius.
The radius of the circle is also equal to half the diameter: r = </span>

, where r=radius and d=diameter.
Plug the equation for the radius of the circle into the equation for the circumference of the circle and simplify to get an equation that relates circumference and diameter:

Now solve that equation for π (aka isolate π) to get the ratio of the circumference to the diameter:

You know that the diameter,

, so plug that into your ratio to get your answer. Remember that dividing by a fraction is equal to multiplying by the inverse of that fraction (aka the fraction flipped):
Your answer is B) <span>
3C/2 = π. </span>