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3 years ago

×=3y,×-3y=0 substitution step by step please

Mathematics

1 answer:

krek1111 [17]3 years ago

6 0

Answer:

Step-by-step explanation:

x = 3y.......(1)

x - 3y = 0 ....(2)

Substituting x in (1) into (2)

3y - 3y = 0

No solutions

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Delicious Candy markets a two-pound box of assorted chocolates. Because of imperfec- tions in the candy making equipment, the ac

saveliy_v [14]

Answer:

The required probability is 0.533.

Step-by-step explanation:

Consider the provided information.

The actual weight of the chocolate has a uniform distribution ranging from 31 to 32.5 ounces.

Let x is the random variable for the actual weight of chocolate.

According to PDF function.

$P(a\leq x\leq b)=\int\limits^b_a {f(x)} \, dx$

Where $f(x)=\left\{\begin{matrix}\frac{1}{b-a} & a$

It is given that ranging from 31 to 32.5 ounces.

Substitute a=31 and b=32.5 in above function.

$f(x)=\left\{\begin{matrix}\frac{1}{32.5-31} & 31$

$f(x)=\left\{\begin{matrix}\frac{1}{1.5} & 31$

We need to find the probability that a box weighs less than 31.8 ounces

Now according to PDF:

$P(x$

Hence, the required probability is 0.533.

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4 years ago

Yosin bought car for 4500

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Answer:

10%

Step-by-step explanation:

450 is 10% of 4500

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3 years ago

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.08

kvv77 [185]

Answer:

a) 44.93% probability that there are no surface flaws in an auto's interior

b) 0.03% probability that none of the 10 cars has any surface flaws

c) 0.44% probability that at most 1 car has any surface flaws

Step-by-step explanation:

To solve this question, we need to understand the Poisson and the binomial probability distributions.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Poisson distribution with a mean of 0.08 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.

So $\mu = 10*0.08 = 0.8$

(a) What is the probability that there are no surface flaws in an auto's interior?

Single car, so Poisson distribution. This is P(X = 0).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.8}*(0.8)^{0}}{(0)!} = 0.4493$

44.93% probability that there are no surface flaws in an auto's interior

(b) If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?

For each car, there is a $p = 0.4493$ probability of having no surface flaws. 10 cars, so n = 10. This is P(X = 10), binomial, since there are multiple cars and each of them has the same probability of not having a surface defect.