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3 years ago

What does it mean to say that a function is linear?

Mathematics

1 answer:

abruzzese [7]3 years ago

7 0

A function is linear if:

B. The function can be described by an equation of the form y = mx + b.

C. The function has a constant rate of change.

D. The function has a straight-line graph.

A function is said to be linear if it is a straight line graph and it can be represented by the equation:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

A linear function has a constant rate of change (either increasing or decreasing).

Find out more at: brainly.com/question/21835898

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At a new exhibit in the museum of science, people are asked to choose between 90 or 120 random draws from a machine. The machine

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There is a probability of P₉₀=0.09853 of winning the prize with a 90-balls sample.

There is a probability of P₁₂₀=0.0853 of winning the prize with a 120-balls sample.

Step-by-step explanation:

In this problem, the balls that are removed are then replaced in the total, so the probability of obtaining a green ball is constant and is equal to:

$P_g=\frac{93}{93+65}= 0.5886$

This type of sampling should be analyzed with the binomial distribution, but given the sample size, it is convenient to use the approximation to a normal distribution.

The parameters of the normal distribution are:

$\mu=P_g*n=0.5886*90=52.9746\\\\\sigma=\sqrt{np(1-p)}=\sqrt{90*0.5886*(1-0.5886)} =4.6684$

To win the prize it is needed at least 65% of green balls in the sample, which means there have to be at least 59 green balls in the sample:

$0.65*90=58.5$

To calculate the probability of getting 59 or more green balls, we have to calculate the z-value

$z=\frac{x-\mu}{\sigma}=\frac{59-52.9746}{4.6684}= 1.29$

Then, the probability can be look up with the z-value in a normal distribution table:

$P(X \geq 59)=P(z\geq 1.29)=0.09853$

There is a probability of P=0.09853 of winning the prize with a 90-balls sample.

When the sample is of 120 balls, we have to recalculate the parameters.

Normal distribution

$\mu=P_g*n=0.5886*120=70.6320\\\\\sigma=\sqrt{np(1-p)}=\sqrt{120*0.5886*(1-0.5886)} =5.3905$

To win the prize it is needed at least 65% of green balls in the sample, which means there have to be at least 78 green balls in the sample:

$0.65*120=78$

To calculate the probability of getting 78 or more green balls, we have to calculate the z-value

$z=\frac{x-\mu}{\sigma}=\frac{78-70.6320}{5.3905}=1.37$

Then, the probability can be look up with the z-value in a normal distribution table:

$P(X \geq 78 )=P(z\geq 1.37)=0.0853$

There is a probability of P=0.0853 of winning the prize with a 120-balls sample.

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3 years ago