Complete the square so that the left side of x2 + 8x − 3 = 0 becomes a binomial squared. (x +___)2 = __

On a certain route, an airline carries 7000 passengers per month, each paying $30. A market survey indicates that for each $

KengaRu [80]

Answer:

The ticket price that maximizes revenue is $50.

The maximum monthly revenue is $250,000.

Step-by-step explanation:

We have to write a function that describes the revenue of the airline.

We know one point of this function: when the price is $30, the amount of passengers is 7000.

We also know that for an increase of $1 in the ticket price, the amount of passengers will decrease by 100.

Then, we can write the revenue as the multiplication of price and passengers:

$R=p\cdot N=(30+x)(7000-x)$

where x is the variation in the price of the ticket.

Then, if we derive R in function of x, and equal to 0, we will have the value of x that maximizes the revenue.

$R(x)=(30+x)(7000-100x)=30\cdot7000-30\cdot100x+7000x-100x^2\\\\R(x)=-100x^2+(7000-3000)x+210000\\\\R(x)=-100x^2+4000x+210000\\\\\\\dfrac{dR}{dx}=100(-2x)+4000=0\\\\\\200x=4000\\\\x=4000/200=20$

We know that the increment in price (from the $30 level) that maximizes the revenue is $20, so the price should be:

$p=30+x=30+20=50$

The maximum monthly revenue is:

$R(x)=(30+x)(7000-100x)\\\\R(20)=(30+20)(7000-100\cdot20)\\\\R(20)=50\cdot5000\\\\R(20)=250000$

3 0

2 years ago

Mandy begins cycling west at 30 miles per hour at 11a.M. If Liz leaves from same point 20 minutes later bicycling west at 36 mph

RoseWind [281]

The answer is 1:00 PM

8 0

1 year ago

Ralph is paid twice per month. His work offers a flexible-spending account to be used for medical expenses. This plan allows Ral

slava [35]

In this question, we're assuming Ralph had 0 in his saving funds to start with.

The glasses cost 1200 dollars.

There are 12 months in a year.

Each month, Ralph is given his check two times, that means that Ralph receives his check 2(12), or 24, times per year.

Divide 1200 (the cost of the glasses) by 24 (the amount of times Ralph is given his check)

1200 / 24
Divide both numerator and denominator by 12
100 / 2
Simplify
50

Ralph should have put 50 dollars per pay check to pay for the glasses.

A is your answer.

Have an awesome day! :)

6 0

2 years ago

Suppose that 4% of the 2 million high school students who take the SAT each year receive special accommodations because of docum

dangina [55]

Answer:

a. 0.0122

b. 0.294

c. 0.2818

d. 30.671%

e. 2.01 hours

Step-by-step explanation:

Given

Let X represents the number of students that receive special accommodation

P(X) = 4%

P(X) = 0.04

Let S = Sample Size = 30

Let Y be a selected numbers of Sample Size

Y ≈ Bin (30,0.04)

a. The probability that 1 candidate received special accommodation

P(Y = 1) = (30,1)

= (0.04)¹ * (1 - 0.04)^(30 - 1)

= 0.04 * 0.96^29

= 0.012244068467946074580191760542164986632531806368667873050624

P(Y=1) = 0.0122 --- Approximated

b. The probability that at least 1 received a special accommodation is given by:

This means P(Y≥1)

But P(Y=0) + P(Y≥1) = 1

P(Y≥1) = 1 - P(Y=0)

Calculating P(Y=0)

P(Y=0) = (0.04)° * (1 - 0.04)^(30 - 0)

= 1 * 0.96^36

= 0.293857643230705789924602253011959679180763352848028953214976

= 0.294 --- Approximated

c.

The probability that at least 2 received a special accommodation is given by:

P (Y≥2) = 1 -P(Y=0) - P(Y=1)

= 0.294 - 0.0122

= 0.2818

d. The probability that the number among the 15 who received a special accommodation is within 2 standard deviations of the number you would expect to be accommodated?

First, we calculate the standard deviation

SD = √npq

n = 15

p = 0.04

q = 1 - 0.04 = 0.96

SD = √(15 * 0.04 * 0.96)

SD = 0.758946638440411

SD = 0.759

Mean =np = 15 * 0.04 = 0.6

The interval that is two standard deviations away from .6 is [0, 2.55] which means that we want the probability that either 0, 1 , or 2 students among the 20 students received a special accommodation.

P(Y≤2)

P(0) + P(1) + P(2)

=.

P(0) + P(1) = 0.0122 + 0.294

Calculating P(2)

P(2) = (0.04)² * (1 - 0.04)^(30 - 2(

P(2) = 0.00051

So,

P(0) +P(1) + P(2). = 0.0122 + 0.294 + 0.00051

= 0.30671

Thus it 30.671% probable that 0, 1, or 2 students received accommodation.

e.

The expected value from d) is .6

The average time is [.6(4.5) + 19.2(3)]/30 = 2.01 hours

8 0

2 years ago

Diana sold 336 muffins at the bake sale.Bob sold 287 muffins.Bob estimates that he sold 50 fewer muffins than Diana.how did he e

malfutka [58]

Step-by-step explanation:

Since we have given that

Number of muffins Diana sold at the bake sale = 336

Number of muffins Bob sold at the bake sale = 287

Now, here we are using the method of estimation i.e. rounding the integers to nearest ones.

By estimation, we get

Number of muffins Diana sold at the bake sale = 340

Number of muffins Bob sold at the bake sale = 290

So,

Difference between them is given by

$340-290\\=50$

Hence, Bob sold 50 fewer muffins than Diana.

3 0

1 year ago

Read 2 more answers

Complete the square so that the left side of x2 + 8x − 3 = 0 becomes a binomial squared. (x +___)2 = ___

Complete the square so that the left side of x2 + 8x − 3 = 0 becomes a binomial squared. (x +_)2 = _