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mash [69]
3 years ago
5

What are the first 3 terms in. t(n)=-2n+7

Mathematics
1 answer:
seropon [69]3 years ago
5 0

Answer:

The first 3 terms of the sequence t(n)=-2n+7 are:

5, 3, 1

Step-by-step explanation:

Given the sequence

t(n)=-2n+7

Here n represents any term number in the sequence

Determining the first term

substitute n = 1 in the sequence to determine the first term

t(n)=-2n+7

t(1)=-2(1)+7

t(1)=-2+7

t(1) = 5

Determining the 2nd term

substitute n = 2 in the sequence to determine the 2nd term

t(n)=-2n+7

t(2) = -2(2) + 7

t(2) = -4 + 7

t(2) = 3

Determining the 3rd term

substitute n = 3 in the sequence to determine the 3rd term

t(n)=-2n+7

t(3) = -2(3) + 7

t(3) = -6 + 7

t(3) = 1

Therefore, the first 3 terms of the sequence t(n)=-2n+7 are:

5, 3, 1

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Use the recursive relationship to complete the next two rows of Pascal's triangle. Row 5: 1 _ _ _ _ 1 Row 6: 1 _ _ _ _ _ 1
frosja888 [35]

Answer:

      1  <u> 5 </u>  <u>10 </u>  <u>10</u>   <u>5</u>   1           Row 5

   1   <u>6</u>   <u>15</u>  <u>20</u>  <u>15</u>   <u>6</u>    1       Row 6

Recursive relationship:

Each row has number of positions = row number + 1. The Row 0 is always 1.

The first and last number in each row is 1, the number in the second position and the penultimate corresponds to the number of the row.  The middle numbers correspond to the sum of the two numbers in the top row. The resulting number from the addition is located in the middle of the numbers added in the next row.

Step-by-step explanation:

The pascal's triangle

* Row 0  =  1

* Row 1 = 1  1

                   1                          Row 0

                1    1                       Row 1

Since there are only two positions, the first and last are 1.

*Row 2 = 1  _ 1

                   1                          Row 0

                1    1                       Row 1

              1   2   1                     Row 2

2 is the sum of 1 + 1 and we place it in the next row between the added numbers 1 and 1.

* Row 3 = 1 _  _    1

                  1                          Row 0

                1    1                       Row 1

              1   <u>2</u>  <u>1 </u>                    Row 2

            1   3   <u>3</u>  1                   Row 3

1 + 2 = 3  (the row number and the and adding the numbers from the previous row)

* Row 4 = 1 _  _    _   1

                  1                          Row 0

                1    1                       Row 1

              1   2   1                     Row 2

            1   <u>3</u><u> </u>  <u>3</u>  1                   Row 3

         1   4   <u>6</u>   4   1                Row 4

1 + 3 = 4  (the row number)

3 +3 = 6

* Row 5 = 1 _  _   _  _   1

                  1                          Row 0

                1    1                       Row 1

              1   2   1                     Row 2

            1   3   3  1                   Row 3

         1   4   6  4   1                Row 4

     1   5   10   10   5   1           Row 5

1 + 4 = 5

4 + 6 = 10

* Row 6 = <u>1</u>  _  _ _  _  _   <u>1</u>

                  1                          Row 0

                1    1                       Row 1

              1   2   1                     Row 2

            1   3   3  1                   Row 3

         1   4   6   4   1                Row 4

     1   5   <u>10</u> <u> 10 </u>  5   1           Row 5

   1   6   15  <u>20</u>  15   6   1        Row 6

1 + 5 = 6

5 + 10 = 15

10 + 10 = 20

3 0
3 years ago
Bob rolls a fair six-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime numb
hammer [34]

Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

According to the statement

we have given that the Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal.

and we have to find that the expected value of the difference between the number of days.

So, the total number of days in a year is 365 days.

Chance to get a prime number on a die = 3/6

Chance to get a prime number on a die = 1/2.

and chances to get a composite number = 2/6

chances to get a composite number = 1/3

and chances to get a 1 on a die = 1/6.

Then the expected value =

so, expected value = 365(1/6) + 365(1/3) + 365(1/2)

then after calculating

Expected value = 1+2+1

then the value become is 4

and by this way he eat 171 days sweet cereal and other days he eat unsweetened.

So, Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

Learn more about Expected value here brainly.com/question/15858152

#SPJ4

3 0
2 years ago
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