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vodka [1.7K]
2 years ago
8

Application of Geometric Series

Mathematics
1 answer:
Gnoma [55]2 years ago
6 0

Answer:

  7.2224

Step-by-step explanation:

The value of the summation is given by the formula ...

  Sn = (a1)(1 -r^n)/(1 -r) . . . . . where a1 is the first of n terms, and r is the common ratio.

Your sum has first term and ratio ...

  a1 = 2(0.6) . . . . . summation term for n=1

  r = 0.6

So the sum is ...

  \displaystyle \sum_{n=1}^4{2(0.6^n)}=2(0.6)\dfrac{1-0.6^4}{1-0.6}=\dfrac{1.2}{0.4}(0.8704) = 2.6112

Then the value of the entire given expression is ...

  \displaystyle 2+2\sum_{n=1}^4{}2(0.6^n)=2+2(2.6112)=\boxed{7.2224}

_____

A calculator can help you find the value.

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A game costs $39.00. But the new special edition version is going to be $56.94. What is the increased percent?
astraxan [27]

Answer:

46%

Step-by-step explanation:

<u>Step 1:  Make an expression</u>

<u />39.00 * x = 56.94

39x = 56.94

<u>Step 2:  Divide both sides by 39</u>

<u />39x / 39 = 56.94 / 39

x = 1.46

<u>Step 3:  Find the percent</u>

<u />1.46 - 1 -> Gives us the increased percent

0.46 * 100

46%

Answer:  46%

8 0
3 years ago
How to do the problem
SpyIntel [72]
The top and sides of the cylinder have an area of pr^2+2prh, but the pr^2 of the top is also removed from the cube which has an area of 6s^2.

A=6s^2+2prh

A=6*36+2p4*1

A=216+8p in^2

A≈241.13 in^2 (to nearest one-hundredth)

Note that I did not include the area of the cylinder that touches the cube...
3 0
3 years ago
The perimeter of a rectangular field is 380 yards. The length is 70 yards. Find the dimensions.
lawyer [7]
380-140 is 240 and 240 divided by 2 is 120 and that's the width, 120
4 0
3 years ago
10. A random sample of 10 fibers is taken from a collection of 92 fibers that consists of 43 fibers of polymer A, 17 fibers of p
vazorg [7]

Answer:

0.1150 = 11.50% probability that the sample does not contain any fibers of polymer B

Step-by-step explanation:

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

Fibers are chosen without replacement, which means that we use the hypergeometric distribution.

92 fibers means that N = 92

Sample of 10 means that n = 10

No polymeter B which means that x = 0

17 fibers of polymeter B which means that k = 17

a. What is the probability that the sample does not contain any fibers of polymer B

This is P(X = 0).

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 0) = h(0,92,10,17) = \frac{C_{17,0}*C_{75,10}}{C_{92,10}} = 0.1150

0.1150 = 11.50% probability that the sample does not contain any fibers of polymer B

4 0
2 years ago
What is the value of x in the figure shown?
Leona [35]

Answer:

x=66

Step-by-step explanation:

Hey There

So if you didn't know the exterior angle is equal to the sum of two opposite interior angles (38 and x)

so to find x we subtract 38 from 180

104-38=66

so x = 66

7 0
3 years ago
Read 2 more answers
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