Answer:
The probability mass of X is 0.03
Step-by-step explanation:
If we set the winning requirement of your heads and my tails then the occurring possibility of both is 1/2 or 0.5.
Hence let us make a graph and use the figures to calculate the all the probabilities of you getting a heads.
Where X represents the number of dollars won during the flip of the coin, probability of heads represent the chances of occurrence of the value and of winning the dollars.
The probability of winning start to drop as the winning amount increases.
X 0 1 2 3 4 5
Probability of Heads 0 0.50 0.25 0.13 0.06 0.03
Refer to the diagram below.
Because ray NP bisects ∠MNQ, therefore
∠MNP = ∠PNQ = 2x + 1.
Therefore
∠MNQ = 2*∠PNQ = 2(2x + 1) = 4x + 2.
Because ∠MNQ is given as x² - 10, therefore
x² - 10 = 4x + 2
x² - 4x - 12 = 0
(x + 2 )(x - 6) = 0
x = -2, or x = 6
When x = -2,
∠MNQ = 4*(-2) + 2 = -6°
This answer is not acceptablle, therefore x = -2 should be rejected.
When x = 6,
∠MNQ = 4*6 + 2 = 26°
Answer: x = 6, and ∠MNQ = 26°
Given:

To find:
The highest and lowest scores Sam could have made in the tournament.
Solution:
We have,


It can be written as

Add 288 on both sides.

and 
and 
Therefore, the highest and lowest scores Sam could have made in the tournament are 290 and 286 respectively.
Answer:
The average rate of change is 1.275
Step-by-step explanation:
The average rate of change of f(x) from x=a to x=b is given by:

The money Terry invested is modeled by the function
where x represents number of days.
The average rate of change from day 2 to day 10 is given by:

The average rate of change becomes:


Answer:

Step-by-step explanation:
Given: Maria spent $2388 for natural gas, last year.
Maria chooses to use balance billing process to pay this year´s gas bill.
Balance billing is a billing practice, where provider bill you the difference between total cost and allowed amount. It can be paid partially or monthly. It generally in practice for medical billing as healthcare bill are generated for difference between total cost and amount which is paid through insurance.
Now, lets find out monthly bill paid by Maria.
We know there are 12 months in a year.
∴ Monthly payment= 
∴Maria will pay $199 monthly as her gas bill this year.