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2 years ago

if the second term of a geometric series is 48 and its fifth term is 6 then find the sum of its first term 6 terms

Mathematics

1 answer:

aev [14]2 years ago

6 0

Answer:

The answer is 189.

Step-by-step explanation:

This geometric sequence is actually just a division of 2 for every term downwards. Therefore, we can see the first term is $48 \cdot 2$ which is 96. Hence, we can work our way down from there:

List:

First term: 96

Second term: 48

Third term: 24

Fourth term: 12

Fifth term: 6

Sixth term: 3

Now, all we have to do is to add all the first 6 terms together to get:

$96 + 48 + 24 + 12 + 6 + 3$

$= 189$

The answer is 189.

Hope this helped!

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HELPP PLEASE

umka21 [38]

Answer:

27.5 mm

Step-by-step explanation:

The game piece has the shape of two identical square pyramids attached at their bases. Given that the perimeters of the square bases are 80 millimeters, and the slant height of each pyramid is 17 millimeters.

Let the side length of each of the side of the base of the pyramid be b, hence:

perimeter = 4b

80 = 4b

b = 20 mm. half of the side length = b/2 = 20 / 2 = 10 mm

The slant height (l) = 17 mm, Let h be the height of one of the pyramid, hence, using Pythagoras theorem:

(b/2)² + h² = l²

17² = 10² + h²

h² = 17² - 10² = 189

h = √189

h = 13.75 mm

The length of the game piece = 2 * h = 2 * 13.75 = 27.5 mm.

6 0

3 years ago

Are 35:40 and 21:24 equivalent?

andrew-mc [135]

Answer:

yes

Step-by-step explanation:

35:40=0.875

21:24=0.875

3 0

2 years ago

Read 2 more answers

Determine whether there is a difference between the two data sets that is not apparent from a comparison of the measures of cent

Iteru [2.4K]

Answer:

It seems the question is incomplete as the two data sets implied from the question are not visible.

However, two data sets having identical measures of center have a difference.

Step-by-step explanation:

Let's consider these two data sets:

2, 2, 3, 5, 6, 6 and 1, 1, 1, 1, 1, 19

Both were contrived.

The most reliable among the measures of center is the mean. The mean of each is calculated by summing the data and dividing by the number of elements. In both sets, the mean is 4.

The data in the first set seem to be concentrated around the mean indeed. But for the second data set, one of them, 19, is obviously very far from the others and the mean. We need another measure to describe this: standard deviation.

Its formula is:

$\rho=\sqrt{\dfrac{\sum (x-\overline{x})^2}{n}}$

$x$ represents each data, $\overline{x}$ is the mean and $n$ is the number of items. $x-\overline{x}$ is the deviation from the mean of each data item.

For the first data set, $\rho=\sqrt{6}=2.45$

For the second data set,

$\rho=\sqrt{45}=6.71$

The low value of $\rho$ for the first set indicates that the items are all closer to the mean than for the second set.

Variance is the square of the standard deviation. It could also be used.

7 0

2 years ago

Find the mean and variance of the following data 52,34,64,49,55,26,38,63

BlackZzzverrR [31]

Answer:

Mean = 47,625

Variance, ignoring the commas = 157

Explanation:

The mean is quite simple: is the mid value of an amount (m') of numbers.

Examples:

Mean of 2, 4: 2 + 4/2 = 3

Mean of 5, 6 and 8: 1+6+8/3 = 15/3 = 5

Generalizing: M' = An + Bn-1 + Cn-2 +... + Y1/ n

So, for the enunciated, we have:

M = 52 + 34 + 64 + 49 + 55 + 26 + 38 + 63/8

M = 47,625

Variance is quite harder.

The mathematics definition is also quite harder:

∑n, i=1 (Xi - X')²/n

Traduction: the sum of the difference of the square of the dispersion measures by the arithmetic mean of them, divided by the number of observed terms is the square of the standard deviation, that is, the variance.

Don't worry, you don't need to understand that. I'll do the question, then you will see in practice what that means.

First, we need the mean of the observerd terms. We already have done that.

M = 47,625.

Next, we will do the the difference of the square of the dispersion measures by the arithmetic mean of them. Which are:

A.52 - 47,625 = (4,375)²

B.34 - 47,625 = (-13,625)² - Because of a value like that, you know see why

C.64 - 47,625 = (16,375)²

D.49 - 47,625 = (1,375)²

E.55 - 47,625 = (7,375)²

F.26 - 47,625 = (-21,625)² - we need to square everything: because a negati

G.38 - 47,625 = (-9,625)² - ve result doest not help in the statisc.

K.63 - 47,625 = (15,375)²

I am using a calculator, but really with that, I'll aproximately the values. If you need a accurate measure, just square them all the way.

A = 16 D = 1 G = 100

B = 169 E = 49 K = 225

C = 256 F = 441

The last part is the sum of the difference of the square of the dispersion measures by the arithmetic mean of them, dividing them by the number of observations.

16 + 169 + 256 + 1 + 49 + 441 + 100 + 225/ 8 = 157,125

8 is the number of observations.

___________________________

But why we do the variance? The variance serves to us for know how much the mean is precise.

So, the lower is the variance, the better is the mean.

Take a look on this example:

Imagine three persons, A, B and C.

They are in pub, talking about how much they receive. A gets, per month, 1000US$, b 2000 and C 3000US$.

So, their mean are 3000US$.

Now imagine that Bill Gates joins the group. And Bill, last month, got 100 milion US$.

Now the mean will be almost 25 milions of dollars. So, she is VERY far from the reality of the major part of the group. And is in there that cames the variance. Looking to the variance, we will see that there is a big discrepancy for each observed term.

5 0

2 years ago

4x + x - 3-9 + 4x = 6 ??

Nookie1986 [14]

Answer:

$x=2$

Step-by-step explanation:

-------------------------

Given:

$4x+x-3-9+4x=6$

---------->>>>

Combine like terms.

$9x-12=6$

---------->>>>

Add 12 to both sides.

$9x=18$

---------->>>>

Divide both sides by 9.

$x=2$

-------------------------

Hope this is helpful.

8 0

2 years ago

if the second term of a geometric series is 48 and its fifth term is 6 then find the sum of its first term 6 terms​

if the second term of a geometric series is 48 and its fifth term is 6 then find the sum of its first term 6 terms