Which equation represents the line with slope 1/4 that passes through (-4, 8)?

In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 11% of voters a

Radda [10]

Answer:

a) 0.0214 = 2.14% probability that none of the people are Independent.

b) 0.8516 = 85.16% probability that fewer than 6 are Independent.

c) 0.8914 = 89.14% probability that more than 2 people are Independent.

Step-by-step explanation:

For each people, there are only two possible outcomes. Either they are independent, or they are not. For each person asked, the probability of them being Independent voters is the same. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

It is believed that 11% of voters are Independent.

This means that $p = 0.11$

A survey asked 33 people to identify themselves as Democrat, Republican, or Independent.

This means that $n = 33$

A. What is the probability that none of the people are Independent?

This is P(X = 0). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

0.0214 = 2.14% probability that none of the people are Independent.

B. What is the probability that fewer than 6 are Independent?

This is

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

$P(X = 1) = C_{33,1}.(0.11)^{1}.(0.89)^{32} = 0.0872$

$P(X = 2) = C_{33,2}.(0.11)^{2}.(0.89)^{31} = 0.1724$

$P(X = 3) = C_{33,3}.(0.11)^{3}.(0.89)^{30} = 0.2202$

$P(X = 4) = C_{33,4}.(0.11)^{4}.(0.89)^{29} = 0.2041$

$P(X = 5) = C_{33,5}.(0.11)^{5}.(0.89)^{28} = 0.1463$

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0214 + 0.0872 + 0.1724 + 0.2202 + 0.2041 + 0.1463 = 0.8516$

0.8516 = 85.16% probability that fewer than 6 are Independent.

C. What is the probability that more than 2 people are Independent?

This is:

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

$P(X = 1) = C_{33,1}.(0.11)^{1}.(0.89)^{32} = 0.0872$

$P(X < 2) = 0.0214 + 0.0872 = 0.1086$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1086 = 0.8914$

0.8914 = 89.14% probability that more than 2 people are Independent.

8 0

2 years ago

Beth is writing out the steps using the "Shortest Route Algorithm". She just finished writing out all

JulijaS [17]

Answer:

ACBD; 7

Step-by-step Explanation:

The Route Algorigtm finds the short route that is efficient, in order to find the solution following pathways.

From the pictures from the complete question,

STEP #1, there exist, three routes, which are:

AB

AC,

and AD.

*AB is not viable because of the negative distance, so it can be removed .

* the AC distance is 3,and AD distance is 8. Therefore, AC can be selected and circled.is because of AC efficiency is high compare to AD.

*from selected AC, the possible routes are ACB; 3 and ACE; 6. which are route shown in #2

* ACB is circled, because it's more shorter than ACE

*The possible routes are ACBE; 8 and ACBD; 7. which are route shown in #3 . Therefore, route ACBD is circled because it's more shorter.

From the analysis of the algorithm, the route ACBD route is the shortest and the most efficient

5 0

3 years ago

The length of a rectangle is 4 centimeters less than twice it’s width. The perimeter of the rectangle is 34vm. What are the dime

IrinaVladis [17]

l = 2w - 4

Because we're solving for 2l + 2w, that can be simplified to

2(2w - 4) + 2w = 34

4w - 8 + 2w = 34

6w - 8 = 34

6w = 42

w = 7

Knowing this, we can input w:

2(7) + 2l = 34

14 + 2L = 34

2l = 20

l = 10

L = 10, W = 7, Option C

5 0

3 years ago

Read 2 more answers

PLEASE HELP! 50 POINTS

s2008m [1.1K]

Answer:

x = 45

Step-by-step explanation:

→ Add all the angles together

x + 2x + 3x + 90 = 360

→ Simplify

6x + 90 = 360

→ Minus 90 from both

6x = 270

→ Divide by 6

x = 45

8 0

2 years ago

Read 2 more answers

Box A has a volume of 48 cubic meters. Box B is similar to Box A. To create Box B, Box A's dimensions were doubled. What is the

Serggg [28]

Answer: 96m3

Step-by-step explanation:

multiply 48 by two

6 0

1 year ago