If Talia and Yoshi redesign their spinner to have 14
sections instead of 16 sections, would they likely have
more or fewer winners? Explain why.

For this first case with 16 sections asuming that only one section is the winning part the probability of win is given by:

And when we reduce the sections to 14 then the probability of win for any given section is given by:

So then we can see that the probability of win increase if we reduce the number of sections so then we would expected more winners if we reduce the sections from 16 to 14

Step-by-step explanation:

For this first case with 16 sections asuming that only one section is the winning part the probability of win is given by:

And when we reduce the sections to 14 then the probability of win for any given section is given by:

So then we can see that the probability of win increase if we reduce the number of sections so then we would expected more winners if we reduce the sections from 16 to 14

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

the answer is:

the lateral area is equal to

to find the lateral area of the square pyramid, first we need to find the perimeter of the base, and then, find the lateral area using the following formulas:

where,

s, is the base length

slant height, is the height of a the side of the pyramid

we are given:

now, calculating the perimeter of the base, we have:

then, calculating the lateral area:

hence, we have that the lateral area is equal to

have a nice day!