Round 6.7086 to the nearest thousandth.

A. Describe the connection of the pattern of outcomes to Pascal’s triangle.

pychu [463]

Answer:

The answer to the question is;

A. The pattern of outcomes of 0 heads, 1 head, 2 heads ... n heads when arranged in the Pascal's triangle is given by the row of the triangles with the lowest at the edges and highest outcome in the middle potion of the rows in the Pascal's triangle.

B. The number of total possible outcomes in a row n is 2ⁿ.

Step-by-step explanation:

To solve the question, we note that.

Pascal's triangle is an important sequence of numbers formed by starting with 1 at the top of the triangle followed by 1s on the outer edges of the triangle and the numbers directly below two adjacent numbers is the sum of the two adjacent numbers.

In probability theory, such as in throwing a coin, Pascal's triangle indicates the number of possible heads obtained when n number of coins is thrown, that is, 0 heads, 1 head 2 heads etc. as follows

Number of coins Possible head outcome Total outcome

0 coin 1 1

1 coin 1 1 2

2 coins 1 2 1 4

3 coins 1 3 3 1 8

4 coins 1 4 6 4 1 16

The above triangle means that when

0 coin is flipped, the number of 0 heads is 1

1 coin is flipped, the number of 0 heads is 1 (T) and 1 head is 1 (H)

2 coins are flipped, the number of 0 heads is 1, (TT), 1 head is 2 (TH), (HT) and 2 heads is 1 (HH)

3 coins are flipped 0 heads = 1 (TTT), 1 head = 3, (TTH), (THT), (HTT), the number of 2 heads = 3, (HHT), (HTH), (TTH) and the number of 3 heads = 1, (HHH).

B. The pattern in the number of total possible outcomes is

1, 2, 4, 8, 16 which is =2 raised to the power of the number of coin tossed for a particular row as follows

Number of coin tossed = 0 = 2⁰ = 1 = Total possible outcome

Number of coin tossed = 1 = 2¹ = 2 = Total possible outcomes

Number of coin tossed = 2 = 2² = 4 = Total possible outcomes

Number of coin tossed = 3 = 2³ = 8 = Total possible outcomes

Number of coin tossed = 4 = 2⁴ = 16 = Total possible outcomes

Therefore total number of possible outcome = 2ⁿ where n = number of coins tossed.

6 0

3 years ago

3. A box contains 7 Green balls, 5 Red balls, and 3 Blue balls. A ball is randomly selected and its color is noted. Then it is r

ziro4ka [17]

Answer:

a. 7/45

b. 1/15

Step-by-step explanation:

15 total balls

a. Selecting 1 Blue ball and 1 Green ball

3/15 * 7/15 = 21/225 = 7/45

b. Selecting 1 Red ball and 1 blue ball

5/15 * 3/15 = 15/225 = 1/15

6 0

3 years ago

A nursery has two hundred 7-gallon palm trees to sell, consisting of coconut palm trees, saw palmetto palm trees and christmas p

motikmotik

Total number of trees available to be sold = 200

Selling price of coconut palm trees sell (Pco)= $75 each

Selling price of saw palmetto palm trees sell (Pp) = $45 each

Selling price of christmas palm trees (Pch) = $30 each

Number of saw palmetto palm trees (Np) = 3 × Number of christmas palm trees (Nch)

Let number of coconut palm trees be Nco

Total price paid by developer for all the palm trees = 12,300

So Total number of trees = Nco + Np + Nch

⇒ 200 = Nco + 3×Nch + Nch

⇒ 200 = Nco + 4Nch ................ (i)

Total selling price of trees = Sco × Nco + Sp × Np + Sch × Nch

⇒ 12,300 = 75×Nco + 45×Np + 30×Nch

Dividing above equation by 5

⇒ 2,460 = 15Nco + 9Np + 6Nch

Substituting Np = 3Nch in the above equation

⇒ 2,460 = 15Nco + 9 (3Nch) + 6Nch

⇒ 2,460 = 15Nco + 33Nch ................ (ii)

Mutiply (i) with 15 and subtract from (ii)

⇒ 2,460 - 3,000 = 15Nco + 33Nch - 15Nco - 60Nch

⇒ -540 = 33Nch - 60Nch

⇒ -540 = 27Nch

⇒ Nch=20

If Nch = 20, Np = 3×20 = 60

Since Nco + Np + Nch = 200

⇒ Nco = 200 - (80)

⇒ Nco = 120

Hence, the developer purchased 120 coconut palm trees, 20 christmas palm trees and 60 saw palmetto palm trees.

6 0

4 years ago

the highest recorded temperature in hawaii is 100 degrees F. The highest recorded temperature in colorado is 18 degrees higher t

PolarNik [594]

Answer:

The highest recorded temperature in colorado is 118 degrees F.

Step-by-step explanation:

We have to model this problem initially.

I am going to call the highest recorded temperature in Colorado x.

The highest recorded temperature in hawaii is 100 degrees F. The highest recorded temperature in colorado is 18 degrees higher than that of hawaii.

This means that x is 18 added to 100. So

$x = 100 + 18$

$x = 118$

The highest recorded temperature in colorado is 118 degrees F.

6 0

3 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

3 years ago