Answer: D) 
Step-by-step explanation:
From the given table we can see that this is not representing a linear function as the rate of change is not constant.
So it can be exponential growth function 
, where A is the initial amount , b is the multiplicative rate of growth and n is the time period in weeks.
Now here at n=1 , f(n)=8
Therefore, A=8
Now, for n=2
By substitute the values of A and b in the above equation, we get the equation
Therefore, the function best shows the relationship between n and f(n) is
, where n is the number of weeks.
The coordinates of B and C are solutions to the system of inequalities because both are true to the two inequalities. A is not a solution to the system of inequalities because it is only true to “y is less than or equal to 2x”.
Answer:
a. 0.0368
b. 0.99992131
c. 0.2039
d. 0.0048
e. 0.6533
Step-by-step explanation:
Let the probability of obtaining a head be p = 65% = 13/20 = 0.65. The probability of not obtaining a head is q = 1 - p = 1 -13/20 = 7/20 = 0.35
Since this is a binomial probability, we use a binomial probability.
a. The probability of obtaining 11 heads is ¹²C₁₁p¹¹q¹ = 12 × (0.65)¹¹(0.35) = 0.0368
b. Probability of 2 or more heads P(x ≥ 2) is
P(x ≥ 2) = 1 - P(x ≤ 1)
Now P(x ≤ 1) = P(0) + P(1)
= ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹
= (0.65)⁰(0.35)¹² + 12(0.65)¹(0.35)¹¹
= 0.000003379 + 0.00007531
= 0.0007869
P(x ≥ 2) = 1 - P(x ≤ 1)
= 1 - 0.00007869
= 0.99992131
c. The probability of obtaining 7 heads is ¹²C₇p⁷q⁵ = 792(0.65)⁷(0.35)⁵ = 0.2039
d. The probability of obtaining 7 heads is ¹²C₉q⁹p³ = 220(0.65)³(0.35)⁹ = 0.0048
e. Probability of 8 heads or less P(x ≤ 8) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰ + ¹²C₃p³q⁹ + ¹²C₄p⁴q⁸ + ¹²C₅p⁵q⁷ + ¹²C₆p⁶q⁶ + ¹²C₇p⁷q⁵ + ¹²C₈p⁸q⁴
= = ¹²C₀(0.65)⁰(0.35)¹² + ¹²C₁(0.65)¹(0.35)¹¹ + ¹²C₂(0.65)²(0.35)¹⁰ + ¹²C₃(0.65)³(0.35)⁹ + ¹²C₄(0.65)⁴(0.35)⁸ + ¹²C₅(0.65)⁵(0.35)⁷ + ¹²C₆(0.65)⁶(0.35)⁶ + ¹²C₇(0.65)⁷(0.35)⁵ + ¹²C₈(0.65)⁸(0.35)⁴
= 0.000003379 + 0.00007531 + 0.0007692 + 0.004762 + 0.01990 + 0.05912 + 0.1281 + 0.2039 + 0.2367
= 0.6533
Answer:
The probability of getting an a in both courses is 1.27
Step-by-step explanation:
Probability of getting A in Math, P(M) = 0.6
5
Probability of getting A in Science, P(S) = 0.62
Required probability of getting A in both courses, P(M and S)
= P(M) + P(S)
= 0.65 + 0.62
= 1.27
Answer:
The probability of the flavor of the second cookie is always going to be dependent on the first one eaten.
Step-by-step explanation:
Since the number of the type of cookies left depends on the first cookie taken out.
This is better explained with an example:
- Probability Miguel eats a chocolate cookie is 4/10. The probability he eats a chocolate or butter cookie after that is <u>3/9</u> and <u>6/9</u> respectively. This is because there are now only 3 chocolate cookies left and still 6 butter cookies left.
- In another case, Miguel gets a butter cookie on the first try with the probability of 6/10. The cookies left are now 4 chocolate and 5 butter cookies. The probability of the next cookie being chocolate or butter is now <u>4/9</u> and <u>5/9</u> respectively.
The two scenarios give us different probabilities for the second cookie. This means that the probability of the second cookie depends on the first cookie eaten.
