13. a) Since AC and AB are tangents to the circle, we know that two tangents that meet at an external point are equal.
Hence, AB = AC; so, AB = 40 ft.
13. b) (20 + r)² = 40² + r²
400 + 40r + r² = 1600 + r²
40r = 1200
r = 30
Hence, the diameter is 60 ft.
Given the table below comparing the marginal benefit Lucinda gets from
Kewpie dolls and Beanie Babies.
![\begin{tabular} {|p {2cm}|p {2cm}|p {2cm}|p {2cm}|} \multicolumn {4} {|c|} {Lucinda's Kewpie Doll and Beanie Baby Marginal Benefits}\\[1ex] \multicolumn {2} {|c|} {Kewpie Dolls}&\multicolumn {2} {|c|} {Beanie Babies}\\[1ex] 1&\$15.00&1&\$12.00\\ 2&\$12.00&2&\$10.00\\ 3&\$9.00&3&\$8.00\\ 4&\$6.00&4&\$6.00\\ 5&\$3.00&5&\$4.00\\ 6&\$0.00&6&\$2.00\\ \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cp%20%7B2cm%7D%7Cp%20%7B2cm%7D%7Cp%20%7B2cm%7D%7Cp%20%7B2cm%7D%7C%7D%0A%5Cmulticolumn%20%7B4%7D%20%7B%7Cc%7C%7D%20%7BLucinda%27s%20Kewpie%20Doll%20and%20Beanie%20Baby%20Marginal%20Benefits%7D%5C%5C%5B1ex%5D%0A%5Cmulticolumn%20%7B2%7D%20%7B%7Cc%7C%7D%20%7BKewpie%20Dolls%7D%26%5Cmulticolumn%20%7B2%7D%20%7B%7Cc%7C%7D%20%7BBeanie%20Babies%7D%5C%5C%5B1ex%5D%0A1%26%5C%2415.00%261%26%5C%2412.00%5C%5C%0A2%26%5C%2412.00%262%26%5C%2410.00%5C%5C%0A3%26%5C%249.00%263%26%5C%248.00%5C%5C%0A4%26%5C%246.00%264%26%5C%246.00%5C%5C%0A5%26%5C%243.00%265%26%5C%244.00%5C%5C%0A6%26%5C%240.00%266%26%5C%242.00%5C%5C%0A%5Cend%7Btabular%7D)
<span>If
lucinda has only $18 to spend and the price of kewpie dolls and the
price of beanie babies are both $6,
Lucinda will buy the combination for which marginal benefit is the same.
Therefore, Lucinda will buy </span><span>2 kewpie dolls and 1 beanie baby,</span><span>
if she were rational.</span>
Answer:

Step-by-step explanation:
Average life of electric bulbs = 300 hrs
standard deviation = 45
Total no of bulbs tested = 100
Probability that sample mean is less than 295 =?
Using Central Limit Theorem

From table of normal distribution:

- The coordinates of a point satisfies the equation of a line if the point lies on the line
- If a single point satisfies the equations of two lines, the point is on both lines, so the lines will intersect at that point.
- This means that each point where the two lines touch is a solution to the system of equations
- This means that if you substitute the x and y values of the point for x and y in the equations, both equations will be true
<h2>
Explanation:</h2>
You haven't given any option. However, I have tried to complete this question according to what we know about system of linear equations. Suppose you have the following system of two linear equations in two variables:

The fist equation is the blue one and the second equation is the red one. Both have been plotted in the first figure below. As you can see, (-3, -3) is the point of intersection and lies on both lines. So this point is a solution of the system of equation and we can also say that it touches both lines. On the other hand, if you substitute the x and y values of the point for x and y in the equations, both equations will be true, that is:

Also, you can have a system with infinitely many solutions as the following:

Here, every point that is solution of the first equation is solution of the second one. That is because both equations are basically the same. If we divide eq (2) by 2, then we get eq (1).
<h2>Learn more:</h2>
System of linear equations in real life problems: brainly.com/question/10412788
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