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mart [117]
3 years ago
12

The first difference of a sequence is 1, 4, 7, 10, 13…

Mathematics
1 answer:
Rama09 [41]3 years ago
8 0

Answer:

1) {4, 5, 9, 16, 26, 39}

2) {3, 4, 8, 15, 25, 38}

3) {3, 4, 8, 15, 25, 38}

Step-by-step explanation:

Hi!

Let's call the sequence {x₁, x₂, x₃, etc}

The information you have is the difference between to consecutive terms:

x_2-x_1= 1\\x_3-x_2= 4\\x_4-x_3= 7\\x_4-x_5= 10\\x_6-x_5= 13

1) Data: x₁=4, then to get x₂ you sum 1, and get x₂=5. Then to get x₃ you sum 4, and get x₃=9, and so on. Result:  {4, 5, 9, 16, 26, 39}

2) Data: x₁ + x₂ = 7. You know that x₂ = x₁ + 1. Then:

x_1+x_2 = x_1 +x_1 +1= 2x_1+1=7\\x_1=3\\x_2= x_1 +1 = 3+1=4

If you continue the same process as in 1), you get {3, 4, 8, 15, 25, 38}

3) Data: x₅ = 25. If you look at the result in 2), you see that x₅ = 25 there!

So the sequence in this case is the same as before {3, 4, 8, 15, 25, 38}

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Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 5 million dollars
GuDViN [60]

Answer:

Probability that a randomly selected firm will earn less than 100 million dollars is 0.8413.

Step-by-step explanation:

We are given that the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 5 million dollars. Also, incomes for the industry are distributed normally.

<em>Let X = incomes for the industry</em>

So, X ~ N(\mu=95,\sigma^{2}=5^{2})

Now, the z score probability distribution is given by;

         Z = \frac{X-\mu}{\sigma} ~ N(0,1)

where, \mu = mean income of firms in the industry = 95 million dollars

            \sigma = standard deviation = 5 million dollars

So, probability that a randomly selected firm will earn less than 100 million dollars is given by = P(X < 100 million dollars)

    P(X < 100) = P( \frac{X-\mu}{\sigma} < \frac{100-95}{5} ) = P(Z < 1) = 0.8413   {using z table]

                                                     

Therefore, probability that a randomly selected firm will earn less than 100 million dollars is 0.8413.

5 0
3 years ago
The flower shop makes bouquets with ten flowers in each bouquet.
denis-greek [22]
I agree with with the florist because when you divide 207 by 10 you will get 20.7. This means that the florist could make 20 bouquets but seven flowers would be left out.
Hope this helps and please mark brainliest!

3 0
2 years ago
What is the probability of getting a sum of 6, given that one die shows a 5? Question 1 options: 5/36 11/36 2/11 5/11
alisha [4.7K]

There are 11 ways a pair of dice can show a 5. Of those, 2 have a sum of 6.

Your probability is 2/11.

5 0
3 years ago
please help me answer these 3 questions correctly . u will get 30 pints if you do and the brainlest. please do not answer if you
stira [4]

Answer:

1

1

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Step-by-step explanation:

6 0
3 years ago
X divided by 3 equal -12
sammy [17]
The answer would be -36 because all i did is multiply -12 with 3 and you get -36.

hope this helped :)
7 0
3 years ago
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