The one on the bottom asap! 6th grade math pre-ap

Two people are to be selected from a group of five employees: Jane, Jan, Jack, John and Joe.

AlexFokin [52]

Answer:

a) 10

b) $\frac{4}{10}$

c) $\frac{6}{10}$

d) 20

Step-by-step explanation:

Hi,

There are two ways of solving counting problems:

1. Combination: It is used when order does not matter.

2. Permutation: It is used when order does matter.

a)

We use combination, order doesn't matter.

There are five total members, we need to select two.

n = 5 and r = 2

$5C2 = 10$

b)

We are fixing one seat for Jack. Hence only four people are left, any one of them can take the other seat.

n = 4 and r = 1

$4C1 = 4$

There are 4 possibilities where Jack will be selected from a total of 10 possibilities (as calculated in part a. )

$\frac{4}{10}$ is the total probability of selection.

c)

To select Jack or Jane, means having one seat fixed for either of them.

$2C1 = 2$

To select any one the other three members, the possibilities are:

$3C1 = 3$

In the rules of probability, and = multiplication; or = addition.

Here, we are considering an "AND" situation.

$2$ × $3$ $= 6$ are the total instances of having Jack or Jane on one seat out of a total of 10 possibilities (as calculated in part a)

The probability then changes to $\frac{6}{10}$

d)

Here we use Permutation since order does matter.

There are 5 people and 2 are to be selected.

n = 5 ; r = 2

$5P2 = 20$

Formula:

Combination: $\frac{n!}{(n-k)! k!}$

Permutation: $\frac{n!}{(n-k)!}$

7 0

4 years ago

Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the

Alexxandr [17]

Answer:

Step-by-step explanation:

The table can be computed as:

Advertising Expenses ($ million) Number of companies

25 up to 35 4

35 up to 45 19

45 up to 55 27

55 up to 65 16

65 up to 75 9

TOTAL 75

Let's find the probabilities first:

$P(25 - 35) = P \Big(\dfrac{25-50.93}{10.80}$

For 35 up to 45

$P(35 - 45) = P \Big(\dfrac{35-50.93}{10.80}$

For 45 up to 55

$P(45 - 55) = P \Big(\dfrac{45-50.93}{10.80}$

For 55 up to 65

$P(55 - 65) = P \Big(\dfrac{55-50.93}{10.80}$

For 65 up to 75

$P(65 - 75) = P \Big(\dfrac{65-50.93}{10.80}$

Chi-Square Table can be computed as follows:

Expense No of Probabilities(P) Expe $(O-E)^2$ $\dfrac{(O-E)^2}{E}$

compa cted E (n*p)

nies (O)

25-35 4 0.0612 75*0.0612 = 4.59 0.3481 0.0758

35-45 19 0.2218 75*0.2218 = 16.635 5.5932 0.3362

45-55 27 0.3568 75*0.3568 = 26.76 0.0576 0.021

55-65 16 0.2552 75*0.2552 = 19.14 9.8596 0.5151

65-75 9 0.0839 75*0.0839 = 6.2925 7.331 1.1650

$\sum \dfrac{(O-E)^2}{E}= 2.0492$

Using the Chi-square formula:

$X^2 = \dfrac{(O-E)^2}{E} \\ \\ Chi-square \ X^2 = 2.0942$

Null hypothesis:

$H_o: \text{The population of advertising expenses follows a normal distribution}$

Alternative hypothesis:

$H_a: \text{The population of advertising expenses does not follows a normal distribution}$

Assume that:

$\alpha = 0.02$

degree of freedom:

= n-1

= 5 -1

= 4

Critical value from $X^2 = 11.667$

Decision rule: To reject $H_o \ if \ X^2$ test statistics is greater than $X^2$ tabulated.

Conclusion: Since $X^2 = 2.0942$ is less than critical value 11.667. Then we fail to reject $H_o$

6 0

3 years ago

I need help with finding the correct way of doing the order of operations.

igor_vitrenko [27]

I hope this helps you

6+4.10-5

6+40-5

46-5

41

8 0

4 years ago

Read 2 more answers

1. What is the value of the expression 8^–2? a. -16 b. 1/64 c.1/16 d.64

AnnyKZ [126]

Your answer is
B. 1/64

8 0

4 years ago

Read 2 more answers

HELP PLZ WILL MARK YOU BRAINLIEST

pentagon [3]

Answer: 12

Step-by-step explanation:

If you look at K to M its the same length as M to J which would be 12

Hope this helped

4 0

3 years ago