# WHO EVER IS GUD AT MATHPLZ HELP ASAP

the 2nd one I think i mean I forget stuff but not math that much

## Related Questions

Melissa collects data on her college graduating class. She finds out that of her classmates, 60% are brunettes, 20% have blue eyes, and 5% are brunettes that have blue eyes. What is the probability that one of Melissa's classmates will be a brunette or have blue eyes

The probability that one of Melissa's classmates will be a brunette or have blue eyes is 0.75.

### What is probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, given that,

60% are brunettes,

i.e. P(A)=0.6

20% have blue eyes,

i.e. P(B)=0.2

and 5% are brunettes that have blue eyes

i.e. P(A∪B)=0.05

So. P(A∩B)=  P(A)+P(B)-P(A∪B)

=0.6+0.2-0.05

=0.75

Hence, the probability that one of Melissa's classmates will be a brunette or have blue eyes is 0.75.

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17

Step-by-step explanation:

The profit on a teddy bear can be found by using the function P(x) = - 2x2 + 35x - 99 where x is the price of the bear.Calculate the price that maximizes profit.

x=8.75

Step-by-step explanation:

The price x that maximizes profit is the maximum value of the function, and the maximum value of the function is located at a point where the first derivative of the function is equal to zero. The first derivative is:

Using P'(x)=0:

The minimum value of the function is also at a point where the first derivative of the function is equal to zero. To differentiate if x=8. is a minimum or a maximum obtain the second derivative and evaluate it at x=8.75 if the value P''(x)>0 x is minimum and if P''(x)<0 x is a maximum.

Evaluating at x=8.75:

Therefore, x=8.75 is the maximum value of the function and it is the price that maximizes profit.

triangle town wants to build a school that is equidistant from its three cities L,M, and N. Which construction correctly finds the best location of the school? A. Construction Y because point E is the incenter of triangleLMN B. Construction Y because point E is the circumcenter of triangleLMN C. Construction X because point C is the incenter of triangleLMN D. Construction X because point C is the circumcenter of triangleLMN

A

Step-by-step explanation:

Construction Y because point E is the circumcenter of Triangle LMN

The amount of time a passenger waits at an airport check-in counter is random variable with mean 10 minutes and standard deviation of 2 minutes. Suppose a random sample of 50 customers is observed. Calculate the probability that the average waiting time waiting in line for this sample is (a) less than 10 minutes (b) between 5 and 10 minutes

(a) less than 10 minutes

= 0.5

(b) between 5 and 10 minutes

= 0.5

Step-by-step explanation:

We solve the above question using z score formula. We given a random number of samples, z score formula :

z-score is z = (x-μ)/ Standard error where

x is the raw score

μ is the population mean

Standard error : σ/√n

σ is the population standard deviation

n = number of samples

(a) less than 10 minutes

x = 10 μ = 10, σ = 2 n = 50

z = 10 - 10/2/√50

z = 0 / 0.2828427125

z = 0

Using the z table to find the probability

P(z ≤ 0) = P(z < 0) = P(x = 10)

= 0.5

Therefore, the probability that the average waiting time waiting in line for this sample is less than 10 minutes = 0.5

(b) between 5 and 10 minutes

i) For 5 minutes

x = 5 μ = 10, σ = 2 n = 50

z = 5 - 10/2/√50

z = -5 / 0.2828427125

= -17.67767

P-value from Z-Table:

P(x<5) = 0

Using the z table to find the probability

P(z ≤ 0) = P(z = -17.67767) = P(x = 5)

= 0

ii) For 10 minutes

x = 10 μ = 10, σ = 2 n = 50

z = 10 - 10/2/√50

z = 0 / 0.2828427125

z = 0

Using the z table to find the probability

P(z ≤ 0) = P(z < 0) = P(x = 10)

= 0.5

Hence, the probability that the average waiting time waiting in line for this sample is between 5 and 10 minutes is

P(x = 10) - P(x = 5)

= 0.5 - 0

= 0.5

Every morning Jack flips a fair coin ten times. He does this for anentire year. LetXbe the number of days when all the flips come out the same way(all heads or all tails).(a) Give the exact expression for the probabilityP(X >1).(b) Is it appropriate to approximateXby a Poisson distribution

See the attached picture for detailed answer.

Step-by-step explanation:

See the attached picture for detailed answer.

The probability question from part (a) requires calculating the chance of getting all heads or all tails on multiple days in a year, which involves complex probability distributions. For part (b), using a Poisson distribution could be appropriate due to the rarity of the event and the high number of trials involved.

### Explanation:

The question pertains to the field of probability theory and involves calculating the probability of specific outcomes when flipping a fair coin. For part (a), Jack flips a coin ten times each morning for a year, counting the days (X) when all flips are identical (all heads or all tails). The exact expression for P(X > 1), the probability of more than one such day, requires several steps. First, we find the probability of a single day having all heads or all tails, then use that to calculate the probability for multiple days within the year. For part (b), whether it is appropriate to approximate X by a Poisson distribution depends on the rarity of the event in question and the number of trials. A Poisson distribution is typically used for rare events over many trials, which may apply here.

For part (a), the probability on any given day is the sum of the probabilities of all heads or all tails: 2*(0.5^10). Over a year (365 days), we need to calculate the probability distribution for this outcome occurring on multiple days. To find P(X > 1), we would need to use the binomial distribution and subtract the probability of the event not occurring at all (P(X=0)) and occurring exactly once (P(X=1)) from 1. However, this calculation can become quite complex due to the large number of trials.

For part (b), given the low probability of the event (all heads or all tails) and the high number of trials (365), a Poisson distribution may be an appropriate approximation. The mean (λ) for the Poisson distribution would be the expected number of times the event occurs in a year. Since the probability of all heads or all tails is low, it can be considered a rare event, and the Poisson distribution is often used for modeling such scenarios.

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Barker and Associates specialize in corporate law. They charge \$125 an hour for researching a case, \$80 an hour for consultations, and \$250 an hour for writing a brief. Last week one of the attorneys spent 8 hours consulting with her client, 12 hours researching the case, and 15 hours writing the brief. What was the weighted mean hourly charge for her legal services

Weighted mean hourly charge = \$168.28 (Approx)

Given:

Charge for research = \$125 per hour

Charge for consultations = \$80 per hour

Charge for writing a brief = \$250 per hour

Research work = 12 hour

Consultations = 8 hour

Writing = 15 hour

Computation:

Total hours = 12 + 8 + 15 = 35 hours

Total charge for researching = \$125 × 12 = \$1,500

Total charge for consulting = \$80 × 8 = \$640

Total charge for writing = \$250 × 15 = \$3,750

Total charge = \$5,890

Weighted mean hourly charge = 5890 / 35

Weighted mean hourly charge = \$168.28 (Approx)