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bogdanovich [222]
3 years ago
9

My son and I are stuck on this one. Can anyone give some insight to this problem? Thank you.

Mathematics
1 answer:
omeli [17]3 years ago
3 0

Answer:

I made is clear for you, now you may match each one

Step-by-step explanation:

f(1)= 11, f(n)= 3*f(n-1)

  • 11*3= 33, 33*3= 99, 99*3= 297, ...
  • 11, 33, 99, 297...

⊕ middle

f(1)= -18, f(n)= f(n-1)+21

  • -18+21= 3, 3+21= 24, 24+21= 45, ...
  • -18, 3, 24, 45, ...

f(1)= -18, f(n)= f(n-1) + 22

  • -18+22= 4, 4+22= 26, 26+22= 48, ...
  • -18, 4, 26, 48, ...

f(1)= -18, f(n)= 2*f(n-1)

  • -18*2= -36, -36*2= -72, -72*2= -144, ...
  • - 18, -36, -72, -144...

⊕ bottom

f(1)= -18, f(n)= 6*f(n-1)

  • -18*6= -108, -108*6= -648, -648*6= -3888, ...
  • - 18, - 108, - 648, -3888, ...

⊕ top

f(1)= 11, f(n)= f(n-1) + 22

  • 11+22= 33, 33+22= 55, 55+22= 77, ...
  • 11, 33, 55, 77, ...

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Is this true or false 276 times 13 = 276 times 7 + 276 times 6 = 1,932 + 1,656 and why?
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Step-by-step explanation:

13 = 6+7

276*13 = 276*(7+6)

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A pet store sells mice reptiles and birds
Vera_Pavlovna [14]

Answer:

P(A or B) represents the probability that a customer will buy either a mouse or a reptile at the pet store.  So, there is a 20%, or 1 out 5 chance that a customer will buy either one when they come in to purchase a pet.

Step-by-step explanation:

Probability represents the fraction of the desired number of outcomes over the total number of outcomes.  In the case of the pet store, their total outcomes can be the purchase of a mouse, reptile or bird.  We don't know how much of each animal they have, however, they tell us that the probability that a customer will buy either a mouse OR a reptile is 0.20.  This means that the probability of buying a mouse and the probability of buying a reptile are added together to equal 0.20 or 20% which is also 1/5.  

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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
If your starting salary is $40,000 and you  receive a 4.2% raise every year, how much  TOTAL money will you make in 15 years?
Oliga [24]
The first year, the amount is 40,000

the second year is 40000 + 4.2% of 40000, or 0.042 * 4000, so 40000+(0.042*4000)
common factoring that  we get 40000(1 + 0.042), or just 40000(1.042)

in short, the starting amount is 40000, and to get the next term's value you'd use the "common ratio" of 1.042, namely the multiplier of 1.042.

for the third year it'll be 40000(1.042) + (0.042 *40000(1.042) ), again, common factoring that

40000(1.042)(1 + 0.042) or 40000(1.042)(1.042) or 40000(1.042)²

therefore,

\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=40000\\
r=1.042\\
n=15
\end{cases}
\\\\\\
S_{15}=40000\left( \cfrac{1-1.042^{15}}{1-1.042} \right)\implies S_{15}\approx 40000\left( \cfrac{-0.8536}{-0.042} \right)
\\\\\\
S_{15}\approx 812951.42
5 0
3 years ago
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