Nate is watching a baseball game. So far, 15 batters have gotten a hit and 5 batters have not. Out of the next 4 batters, how many should Nate expect to get a hit, given the past data?

3 batters

Step-by-step explanation:

For the past data, we have observed that:

15 batters have gotten a hit

5 batters have not

The total of batters that we have observed is

n = 15 + 5 = 20

Therefore, this means that based on the observed data, the probability that a batter gets a hit is:

where

n(h) = 15 is the number of batters that got a hit

After that, we want to know how many batters we will expect to get a hit in the next 4 batters. We can write it as:

And since

p(hit) = 0.75

We find:

So, we expect 3 batters to get a hit in the next 4.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

2 x t divided by n

step-by-step explanation: