X+y+z=6, xy+yz+zx=9 prove (x-1) +(y-2)²+(z-3)⁴<88

The function p(x) = -2(x-9)2 + 100 used to determine the profit on T-shirts sold for x dollars. What would the profit from sales

Elden [556K]

Answer:

$28.

Step-by-step explanation:

p(x) = -2(x - 9)^2 + 100

If the prices (x) = 15 dollars we work out the profit by substituting x = 15 in the above formula:

p(15) = -2(15 - 9)^2 + 100

= -2 * 6^2 + 100

= $28.

5 0

2 years ago

Read 2 more answers

Jackie collects data from two different companies each company have for employees the data is listed in the table below which of

Crazy boy [7]

•one of the salary amounts in company B is potentially an outlier.
• the median salaries of both companies are greater than 31000
•the mean salary at company B is greater than company A's

7 0

2 years ago

Read 2 more answers

A brewery produces cans of beer that are supposed to contain exactly 12 ounces. But owing to the inevitable variation in the fil

MArishka [77]

Answer:

$T \sim N (\mu = 6*12=72 , \sigma= \sqrt{6} *0.3=0.735)$

$P(T \leq 72) = P(Z< \frac{72-72}{0.735}) = P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solutio to the problem

Let X the random variable that represent the amount of beer in each can of a population, and for this case we know the distribution for X is given by:

$X \sim N(12,0.3)$

Where $\mu=12$ and $\sigma=0.3$

For this case we select 6 cans and we are interested in the probability that the total would be less or equal than 72 ounces. So we need to find a distribution for the total.

The definition of sample mean is given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n} = \frac{T}{n}$

If we solve for the total T we got:

$T= n \bar X$

For this case then the expected value and variance are given by:

$E(T) = n E(\bar X) =n \mu$

$Var(T) = n^2 Var(\bar X)= n^2 \frac{\sigma^2}{n}= n \sigma^2$

And the deviation is just:

$Sd(T) = \sqrt{n} \sigma$

So then the distribution for the total would be also normal and given by:

$T \sim N (\mu = 6*12=72 , \sigma= \sqrt{6} *0.3=0.735)$

And we want this probability:

$P(T\leq 72)$

And we can use the z score formula given by:

$z = \frac{x-\mu}{\sigma}$

$P(T \leq 72) = P(Z< \frac{72-72}{0.735}) = P(Z$

6 0

2 years ago

Emily is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Emily will earn $

Hitman42 [59]

Answer:

(6,2)

Step-by-step explanation:

Variable Definitions:

x= the number of commercials

y= the number of movies

Each commercial earns Emily $50, so x commercials would earn her 50x dollars in royalties. Each movie earns Emily $150, so y movies would earn her 150y dollars in royalties. Therefore, the total royalties 50x+150y equals $600:

50x+150y=600

Since Emily's songs were played on 3 times as many commercials as movies, if we multiply 3 by the number of movies, we will get the number of commercials, meaning x equals 3y.

x=3y

Write System of Equations:

50x+150y=600

x=3y

Solve for y in each equation:

1) 50x+150y=600

150y=−50x+600

y=-1/3x+4

2) x=3y

y=1/3x

The x variable represents the number of commercials and the yy variable represents the number of movies. Since the lines intersect at the point (6,2) we can say:

Emily's songs were played on 6 commercials and 2 movies.

4 0

2 years ago

Your grandparents send you a check for $150 for your birthday. You deposit the check into your savings account which has a balan

NNADVOKAT [17]

313.75 I believe that is the correct answer or som

4 0

2 years ago

X+y+z=6, xy+yz+zx=9 prove (x-1) +(y-2)²+(z-3)⁴<88 ​

X+y+z=6, xy+yz+zx=9 prove (x-1) +(y-2)²+(z-3)⁴<88