Exhibit 5-3 The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number of
1 answer:
Answer:
0.55 is the probability that Lions will score less than 3 goals.
Step-by-step explanation:
We are given the following in the question:
Number of goals(x): 0 1 2 3 4
Probability: 0.05 0.15 0.35 0.30 0.25
We have to find the probability that Lions will score less than 3 goals.
0.55 is the probability that Lions will score less than 3 goals.
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Answer:
<em>y = - cos ( </em><em> x + </em>
<em> ) </em>
Step-by-step explanation:
y = A cos ( Bx + C) + D
Vertical shift D = 0
A = - 1
Compression / Stretching B
Period of given function is
Period of cos x is 2π
=
⇒ B =
Horizontal shift is C ÷ B
Horizontal shift of given function is
= C ÷
⇒ C =
So, the equation of given function is
<em>y = - cos ( </em><em> x + </em>
<em> ) </em>
To solve this we are going to use the future value of annuity ordinary formula: ![FV=P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3DP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bkt%7D%20-1%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where
is the future value
is the periodic payment
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the number of payments per year
is the number of years
We know for our problem that
and 
. To convert the interest rate to decimal form, we are going to divide the rate by 100%:
Since the deposit is made semiannually, it is made 2 times per year, so
.
Since the type of the annuity is ordinary, payments are made at the end of each period, and we know that we have 2 periods, so
.
Lets replace the values in our formula:
![FV=6200[ \frac{(1+ \frac{0.06}{2} )^{(2)(5)} -1}{ \frac{0.06}{2} } ]](https://tex.z-dn.net/?f=FV%3D6200%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.06%7D%7B2%7D%20%29%5E%7B%282%29%285%29%7D%20-1%7D%7B%20%5Cfrac%7B0.06%7D%7B2%7D%20%7D%20%5D)
We can conclude that the correct answer is <span>$71,076.06</span>
where
We know for our problem that
Since the deposit is made semiannually, it is made 2 times per year, so
Since the type of the annuity is ordinary, payments are made at the end of each period, and we know that we have 2 periods, so
Lets replace the values in our formula:
We can conclude that the correct answer is <span>$71,076.06</span>