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lidiya [134]
3 years ago
6

Perpendicular line for 7 x + 5 y equals -1

Mathematics
1 answer:
Leya [2.2K]3 years ago
6 0
7x + 5y = -1 
get: y = mx + c
firstly, subtract 7x from both sides:
5y = -7x -1
divide both sides by 5:
y = (-7x -1)/5:
y= -7x/5 -1/5
therefore the slope, m  = -7/5 in the formula y = mx + c
perpendicular test m1 .m2 = -1
m1 = -7/5, substitute in formula:
(-7/5) x m2 = -1
m2 = -1 /(-7/5) which equals [ invert and multiply] -1 x -5/7 = 5/7
perpendicular slope m2 = 5/7 
new line y=mx +c is:
y = 5/7 x -1/5  

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Of the following three statements, choose the best option and write a viable argument showing how it is reflected by the cost fu
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A viable argument showing how it is reflected by the Cost Function for Wichita’s factory is; The cost of production per unit of item produced is 1$ as long as total units produced is less than 2500. If more than 2500 units are produced than the cost per unit actually comes down to 0.8$per unit.

<h3>How to Interpret Cost Functions?</h3>

From the given options, the best statement is;

The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.

A cost function is a formula used to predict the cost that will be experienced at a certain activity level. Thus, the cost function for the best option is;

The cost of production per unit of item produced is 1$ as long as total units produced is less than 2500. If more than 2500 units are produced than the cost per unit actually comes down to 0.8$per unit.

The missing options are;

___ The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.

___ The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.

___ Overtime wages were required to produce at levels above 25,000 units.

Read more about Cost Functions at; brainly.com/question/14038368

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An insurance company has 25,000 automobile policy holders. If the yearly claim of a policy holder is a random variable with mean
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Answer:

P(T>8300000)=1-P(T

Step-by-step explanation:

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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

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".  

Data given

n = 25000 represent the automobile policy holders

\mu= 320 represent the population mean

\sigma =540 represent the population standard deviation

Let T the variable that represent the total of interest on this case. We can assume that the random variable for an individual policy holder is given by:

X\sim N(\mu = 540, \sigma=540)

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

Solution to the problem

First we need to find the distribution for the random variable T like this:

\bar X = \frac{\sum_{i=1}^n x_i}{n}

And the total T is given by:

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

We can find the expected value, variance and deviation for this random variable like this:

E(T)= n E(\bar X) = n \mu = 25000*320=8000000

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Sd(T)=\sqrt{7290000000}=85381.497

And we are interested on this probability:

P(T>8300000)

And we can use the Z score formula given by:

Z=\frac{T-E(T)}{\sigma_T}

P(T>8300000)=1-P(T

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