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OverLord2011 [107]
2 years ago
11

Judith’s parents invest money into a bank account to save up for college. The formula () = ,(.) can be used to find out how much

their investment is worth after t years. a. How much was their initial investment? b. What was the interest rate the investment earned each year? c. How much money would be in the account after 18 years?
Mathematics
1 answer:
Semenov [28]2 years ago
6 0

Answer:

c. How much money would be in the account after 18 years?

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A pen company averages 1.2 defective pens per carton produced (200 pens). The number of defects per carton is Poisson distribute
nlexa [21]

Answer:

a. P(x = 0 | λ = 1.2) = 0.301

b. P(x ≥ 8 | λ = 1.2) = 0.000

c. P(x > 5 | λ = 1.2) = 0.002

Step-by-step explanation:

If the number of defects per carton is Poisson distributed, with parameter 1.2 pens/carton, we can model the probability of k defects as:

P(k)=\frac{\lambda^{k}e^{-\lambda}}{k!}= \frac{1.2^{k}\cdot e^{-1.2}}{k!}

a. What is the probability of selecting a carton and finding no defective pens?

This happens for k=0, so the probability is:

P(0)=\frac{1.2^{0}\cdot e^{-1.2}}{0!}=e^{-1.2}=0.301

b. What is the probability of finding eight or more defective pens in a carton?

This can be calculated as one minus the probablity of having 7 or less defective pens.

P(k\geq8)=1-P(k

P(0)=1.2^{0} \cdot e^{-1.2}/0!=1*0.3012/1=0.301\\\\P(1)=1.2^{1} \cdot e^{-1.2}/1!=1*0.3012/1=0.361\\\\P(2)=1.2^{2} \cdot e^{-1.2}/2!=1*0.3012/2=0.217\\\\P(3)=1.2^{3} \cdot e^{-1.2}/3!=2*0.3012/6=0.087\\\\P(4)=1.2^{4} \cdot e^{-1.2}/4!=2*0.3012/24=0.026\\\\P(5)=1.2^{5} \cdot e^{-1.2}/5!=2*0.3012/120=0.006\\\\P(6)=1.2^{6} \cdot e^{-1.2}/6!=3*0.3012/720=0.001\\\\P(7)=1.2^{7} \cdot e^{-1.2}/7!=4*0.3012/5040=0\\\\

P(k

c. Suppose a purchaser of these pens will quit buying from the company if a carton contains more than five defective pens. What is the probability that a carton contains more than five defective pens?

We can calculate this as we did the previous question, but for k=5.

P(k>5)=1-P(k\leq5)=1-\sum_{k=0}^5P(k)\\\\P(k>5)=1-(0.301+0.361+0.217+0.087+0.026+0.006)\\\\P(k>5)=1-0.998=0.002

5 0
3 years ago
The ratio of the number of Sam's CDs to the number of Alice's CD's is 7 to 8. Sam has 84 CDS.
Alex

Answer:

180 CDs

Step-by-step explanation:

So if Sam has 84 CDs, and the ratio from Sam to Alice is 7:8, we can do 84/7=12 so each number is equal to 12. Then we add up 7 and 8 and get 15, so we do 15*12 and we get 180.

7 0
2 years ago
Factoring polynomials
-Dominant- [34]
1. x(2x^2-x+4)
2.-3(y-1)(y+2)
3.-(11w^2+18w-1)

7 0
3 years ago
Last questions on this quiz (I always get confused on finding the x value)
zimovet [89]
For the first one, we know that is a right angle. right angles are 90 degrees. if we subtract 90 - 49 that equals 41. so the second value needs to equal 41. since we have a 3 there already, we are going to subtract 41-3, which is 38. x = 38
3 0
3 years ago
B 5 3 a 4 What is the length of the hypotenuse of this triangle? 3 units 5 units 4 units​
Lunna [17]

Answer:

5 units

Step-by-step explanation:

The hypotenuse is always the longest segment on a triangle. If the lengths of the sides of this triangle are 3 units, 4 units, and 5 units, the hypotenuse will be 5 units. You can use the pythagorean theorem to check.

a^2+b^2=c^2

If you substitute the variable with the lengths of the legs in ascending order, you will get 3^2+4^2=5^2. Simplifying the equation, you will get 9+16=25, or 25=25. Thus, proving the equation.

Hope this helped! :)

6 0
3 years ago
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