Identify the zeros if the quadratic function.
2 answers:
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Answer:
The amount invested at 3% is 300 &
The amount invested at 2% is 100.
Step-by-step explanation:
Total yearly interest for the two accounts is: $11
Let x be the amount invested at 3%
& y be the amount invested at 2%
From the question we can get 2 equations as;
x = 3y --------------------------Equation 1
0.03x + 0.02y = 11 ----------Equation 2
Substitute for x in Equation 2 we get;
0.03 (3y) + 0.02y = 11
0.09y + 0.02y = 11
0.11y = 11
Divide the above equation by 0.11, we get;
y =
y = 100
Let us substitute the value of y in Equation 1 we get;
x = 3(100)
x = 300
Now to check our answer let us put in the simple interest formula. If we get the sum of the two interests equal to 11 then our answers are correct:
0.03 x 300 + 0.02 x 100
= 9 + 2
= 11
Hence the amount invested at 3% is 300 and the amount invested at 2% is 100.
Answer:
a) P ( 3 ≤X≤ 5 ) = 0.02619
b) E(X) = 1
Step-by-step explanation:
Given:
- The CDF of a random variable X = { 0 , 1 , 2 , 3 , .... } is given as:
Find:
a.Calculate the probability that 3 ≤X≤ 5
b) Find the expected value of X, E(X), using the fact that. (Hint: You will have to evaluate an infinite sum, but that will be easy to do if you notice that
Solution:
- The CDF gives the probability of (X < x) for any value of x. So to compute the P ( 3 ≤X≤ 5 ) we will set the limits.
- The Expected Value can be determined by sum to infinity of CDF:
E(X) = Σ ( 1 - F(X) )
E(X) = Limit n->∞ [1 - 1 / ( n + 2 ) ]
E(X) = 1