Math 1314 lab module 2

The third number amounts to 180. To explain, let the third number equal 9x where x is an integer. The prime factorization of 48 is 2*2*2*2*3, while 264 equals 2*2*2*3*11. Then, 9x can be rewritten as 3*3*x, leading to 2*2*2*2*3*3*11*x equaling 7920y for some integer y. Thus, 1584x equals 7920y which simplifies to x = 7920y / 1584 = 5y. With the GCD being 12, x must include 4 as a factor. Since x is a multiple of 5, one possibility is 20, making y equal to 4. Hence, if x = 20, the third number becomes 9*20 = 180, which can be confirmed.

Answer:

220 items must be sold to achieve break-even.

Step-by-step explanation:

550 + 3.00x = 5.50x

550 = 2.50x

220 = x

The formula , where r! is defined as 1*2*3*...r

provides the total number of combinations for forming groups of r items from a collection of n items.

For instance, with 10 items, there are C(10,6) possible ways to create groups of 6 from these 10 objects.

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Choosing 4 individuals from a total of 12 can be accomplished in:

many different ways.

All unique groupings of 4 individuals, including the husband and wife pair, can be computed as C(10, 2) ways, since we only consider the potential selections of 2 from 10 individuals to form a group of 4.

Consequently, the probability that both the husband and wife are selected is 45/495=0.09


Part 2)

The chance that one gets selected while the other does not =

P(husband selected, wife not selected) + P(wife selected, husband not selected)

These two scenarios are precisely equal, so it suffices to compute one.


Let's analyze the scenario: husband chosen, wife not selected.

Assuming the husband is selected, we need to determine the possible formations of 3 from the 11 total excluding the wife=10 individuals.

This results in:

Hence,

P(husband selected, wife not selected)=120/495=0.24

Thus, the overall probability that one is picked while the other is not =

P(husband selected, wife not selected) + P(wife selected, husband not selected) =

0.24+0.24=0.48

Result:

A) 0.09

B) 0.48

To tackle this issue, we need to utilize the t statistic. This requires calculating the t score first and then consulting standard distribution tables to find the corresponding p value based on the obtained t score.

 

The formula for calculating the t score is:

t = (x – μ) / (σ / sqrt(n))

 

Where,

x = sample mean = 40

n = number of sample subjects = 16

s = standard deviation = 20

μ = Population Mean = 30

 

Plugging in the known values:

t = (40 – 30) / (20 / sqrt 16)

t = 10 / 5

t = 2

 

Utilizing the standard distribution tables and calculating the degrees of freedom, which is n – 1 = 15, we then find:

p = 0.032

Revenue = price * quantity of backpacks
quantity of backpacks = -2p + 50

For p = 9: -2(9) + 50 = -18 + 50 = 32
thus, revenue = 9 * 32 = 288

For p = 12: -2(12) + 50 = -24 + 50 = 26
therefore, revenue = 12 * 26 = 312

For p = 12.50: -2(12.50) + 50 = -25 + 50 = 25
thus, revenue = 12.50 * 25 = 312.50   MAXIMIZES REVENUE

For p = 15: -2(15) + 50 = -30 + 50 = 20
so, revenue = 15 * 20 = 300