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3 years ago

Find a formula for the sequence 3, 9/4, 27/7, 81/10,... in sigma notation

Mathematics

1 answer:

Juliette [100K]3 years ago

4 0

9514 1404 393

Answer:

$\displaystyle S_n=\sum_{k=1}^n{\frac{3^k}{3k-2}}$

Step-by-step explanation:

The sequence terms appear to have numerators that are powers of 3, and denominators that are a linear (arithmetic) sequence with a first term of 1 and a common difference of 3.

numerator: 3^x

denominator: 1 +3(n -1) = 3n-2

Then the sum of n terms of the sequence can be described by ...

$\displaystyle \boxed{S_n=\sum_{k=1}^n{\frac{3^k}{3k-2}}}$

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A boat is traveling at an average speed of 15 meters per second. How many kilometers per second is the boat traveling

damaskus [11]

$15 \frac{m}{s} \to 15\frac{10^{-3} km}{s} \to\boxed{0.015 \frac{km}{s}}$

8 0

3 years ago

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Write an absolute value equation to satisfy the given solution set shown on a number line.

aivan3 [116]

Answer: IX - 4I ≤ 4

Step-by-step explanation:

In the numer line we can see that our possible values of x are in the range:

0 ≤ x ≤ 8

And we want to find an absolute value equation such that this set is the set of possible solutions.

An example can be:

IX - 4I ≤ 4

To construct this, we first find the midpoint M of our set, in this case is 4.

Then we write:

Ix - MI ≤ IMI

Notice that i am using the minor and equal sign, this is because the black dots means that the values x = 0 and x = 8 are included, if the dots were empty dots, it would be an open set and we should use the < > signs.

8 0

3 years ago

100 PTS

Digiron [165]

Answer:

69 yards

Step-by-step explanation:

Perimeter = 2(length + width)

300 = 2(81 + width)

150 = 81 + width

width = 69

7 0

3 years ago

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Pls do it for me thank you so much

Bond [772]

Answer:

(a) Attached to this response.

(b)

(i) 0 cups = 0.275

(ii) 4 cups = 0.125

(iii) 8 cups = 0.025

Step-by-step explanation:

(a) The frequency and relative frequency table has been attached to this response.

i. The first column, labelled x, is the number of cups of coffee consumed per day.

ii. The second column, labelled f, is the number of people that consumed x cups of coffee per day. It is found by counting the number of occurrences (i.e frequency) of the numbers of the first column, x, in the given data.

For example, 0 in first column appears 11 times in the given data. Also, 5 in the first column appears 4 times in the given data.

iii. The third column, labelled r, is the relative relative frequency of the number of cups of coffee. It is calculated by dividing the frequency of the cups of coffee by the total number of people that consumed it. As shown on the table, it is calculated by dividing the each of the values on the second column by the sum of the values on that same column (second column).

For example, the relative frequency of 2 cups of coffee is given by:

r = 7 ÷ 40 = 0.175

Also, the relative frequency of 4 cups of coffee is given by;

r = 5 ÷ 40 = 0.125

(b) The probability (Pₓ) that a randomly selected person consumed x cups of coffee is given by;

Pₓ = frequency of x ÷ total frequency

This is also the relative frequency of x

Therefore,

(i) The probability (P₀) that a randomly selected person consumed 0 cups of coffee is given by;

the relative frequency of 0 = 0.275

(ii) The probability (P₄) that a randomly selected person consumed 4 cups of coffee is given by;

the relative frequency of 4 = 0.125

(iii) The probability (P₈) that a randomly selected person consumed 8 cups of coffee is given by;

the relative frequency of 8 = 0.025

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5 0

3 years ago

5. The measure of an intercepted arc is 86, and the measure of the inscribed angle creating the intercepted arc is 3x +

Nonamiya [84]

Answer:

Th correct option is D. 13

Therefore the value of x is 13.

Step-by-step explanation:

Given:

measure of an intercepted arc = 86°

Center Angle = 86°

measure of the inscribed angle creating the intercepted arc= (3x+4)°

Angle Inscribed in arc = (3x+4)°

To Find:

value of x = ?

Solution:

Inscribed Angle Theorem:

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

$\textrm{Angle Inscribed in arc}=\dfrac{1}{2}\textrm{Center Angle}$

Substituting the values we get

$3x+4=\dfrac{1}{2}86=43\\\\3x=39\\\\x=\dfrac{39}{3}=13\\\\x=13$

Therefore the value of x is 13.

4 0

3 years ago

Find a formula for the sequence 3, 9/4, 27/7, 81/10,... in sigma notation​

Find a formula for the sequence 3, 9/4, 27/7, 81/10,... in sigma notation