Answer:
(a) 120 choices
(b) 110 choices
Step-by-step explanation:
The number of ways in which we can select k element from a group n elements is given by:
So, the number of ways in which a student can select the 7 questions from the 10 questions is calculated as:
Then each student have 120 possible choices.
On the other hand, if a student must answer at least 3 of the first 5 questions, we have the following cases:
1. A student select 3 questions from the first 5 questions and 4 questions from the last 5 questions. It means that the number of choices is given by:
2. A student select 4 questions from the first 5 questions and 3 questions from the last 5 questions. It means that the number of choices is given by:
3. A student select 5 questions from the first 5 questions and 2 questions from the last 5 questions. It means that the number of choices is given by:
So, if a student must answer at least 3 of the first 5 questions, he/she have 110 choices. It is calculated as:
50 + 50 + 10 = 110
Answer:
a. Present value of a lump sum =
PV = FV / ( 1 + i )ⁿ
b. Present value of an annuity =
P = PMT x ((1 – (1 / (1 + r)⁻ⁿ )) / r)
Step-by-step explanation:
a. Present Value of a Lump sum =
PV = FV / ( 1 + i )ⁿ
Where variables in the formula are explained as follows
PV = Present Value of the given amount today
FV = Future Value of the given amount
i = Discount rate
n = Number of periods
b. Present value of an annuity is given as:
P = PMT x ((1 – (1 / (1 + r)⁻ⁿ)) / r)
The variables in the equation are explained as the follows:
P = the present value of annuity
PMT = Payment per period or the amount in each annuity payment
r = the interest or discount rate
n = total number of periods or the number of payments left to receive
Beth's speed was 60 mph.
<h3>
What is speed?</h3>
- The speed (commonly referred to as v) of an object in everyday use and kinematics is the magnitude of the change in its position over time or the magnitude of the change in its position per unit of time; it is thus a scalar quantity.
- The distance traveled by an object in a time interval is divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.
- Velocity is not the same as speed.
To find what was Beth's speed:
Beth's data:
- time = 2 hrs; rate = r mph; distance = r×t = 2r miles
Tim's data:
- time = 1 hr; rate = r-6 mph; distance = r-6 miles
Equation:
- distance + distance = 174 miles
So,
- 2r + r - 6 = 174
- 3r - 6 = 174
- 3r = 180
- r = 60 mph (Beth's rate)
- r-6 = 54 mph (Tims's rate)
Therefore, Beth's speed was 60 mph.
Know more about speed here:
brainly.com/question/4931057
#SPJ4
Answer:
1. 60%
2. 70
3. 8%
Step-by-step explanation:
I attached pictures to show my work (sorry if they’re a bit messy)!
Answer:
84 different lineups are possible
Step-by-step explanation:
The order in which the songs are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
6 musics from a set of 9. So
84 different lineups are possible
