**Answer:**

12 tiles will fit

**Step-by-step explanation:**

1/2 foot is 6 inch

6 inch times 12 is 6ft

**Answer:**

Radius of the convergence is R =

and,

The Interval of convergence is

**Step-by-step explanation:**

Given function : Σ(21x)^k

Now,

Using the ratio test, we have

R =

or

R =

or

R =

now,

for convergence R|x| < 1

Therefore,

< 1

or

and,

Radius of the convergence is R =

and,

The Interval of convergence is

**Answer:**

**hello your question is incomplete, the missing part of the question is attached below**

answer :

1) β1 = 0.25

β2 = 4.85

2) 40.55 + 0.25 ( math score ) + 4.85 ( hours )

**Step-by-step explanation:**

<u>1) The estimate for β1 and β2 </u>

From the attached excel result the estimates are ;

β1 = 0.25 : This shows the change in the mean value of the final score in relation to the change in math score while the time is kept constant

β2 = 4.85 : This represents the change in the mean value of the final score in relation to the change in time while the math score is held constant

<u>2) sample regression equation</u>

The Final sample regression equation = 40.55 + 0.25 ( math score ) + 4.85 ( hours )

Answer:

-$13.5

Step-by-step explanation:

Let x be a random variable of a count of player gain.

- We are told that if the die shows 3, the player wins $45.

- there is a charge of $9 to play the game

If he wins, he gains; 45 - 9 = $36

If he looses, he has a net gain which is a loss = -$9

Thus, the x-values are; (36, -9)

Probability of getting a 3 which is a win is P(X) = 1/6 since there are 6 numbers on the dice and probability of getting any other number is P(X) = 5/6

Thus;

E(X) = Σ(x•P(X)) = (1/6)(36) + (5/6)(-9)

E(X) = (1/6)(36 - (5 × 9))

E(X) = (1/6)(36 - 45)

E(X) = -9/6 = -3/2

E(X) = -3/2

This represents -3/2 of $9 = -(3/2) × 9 = - 27/2 = -$13.5