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4 years ago

What is the solution of 7+m<2 or m+1>2

1 answer:

3 0

$7+m\ \textless \ 2$

$m\ \textless \ 2-7$ $Subtract \ 7 \ from \ both \ sides$

$m\ \textless \ -5$

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$m+1\ \textgreater \ 2$

$
m\ \textgreater \ 2-1
 
$ <span> $Subtract \ 1 \ from \ both \ sides$
</span>
$m\ \textgreater \ 1$

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4 years ago

A cone has a radius of 5 inches and a height of 18 inches.

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4 years ago

At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .51.

satela [25.4K]

Answer:

$P(x\geq 7)=0.1886$

Step-by-step explanation:

The variable x, that said the number of customer that will order a nonalcoholic beverage in a sample of n customers follows a binomial distribution. Because we have n identical and independent events with a probability p of success and (1-p) of fail.

So, the probability that x customers will order a nonalcoholic beverage is:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}$

Where n is the size of the sample and p is the probability that a customer order a nonalcoholic beverage, so replacing the values, we get:

$P(x)=\frac{10!}{x!(10-x)!}*0.51^{x}*(1-0.51)^{10-x}$

Now, the probability that at least 7 will order a nonalcoholic beverage is equal to:

$P(x\geq 7)=P(7)+P(8)+P(9)+P(10)$

Where:

$P(7)=\frac{10!}{7!(10-7)!}*0.51^{7}*(1-0.51)^{10-7}=0.1267\\P(8)=\frac{10!}{8!(10-8)!}*0.51^{8}*(1-0.51)^{10-8}=0.0494\\P(9)=\frac{10!}{9!(10-9)!}*0.51^{9}*(1-0.51)^{10-9}=0.0114\\P(10)=\frac{10!}{10!(10-10)!}*0.51^{10}*(1-0.51)^{10-10}=0.0011$

So, $P(x\geq 7)$ is equal to:

$P(x\geq 7)=0.1267+0.0494+0.0114+0.0011\\P(x\geq 7)=0.1886$

Finally, the probability that in a sample of 10 customers, at least 7 will order a nonalcoholic beverage is equal to 0.1886

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3 years ago