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3 years ago

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A catering service offers 11 appetizers, 12 main courses, and 8 desserts. A customer is to select 9 appetizers, 2 main courses,

and 3 desserts for a banquet. In how many ways can this be done?

1 answer:

Blizzard [7]3 years ago

3 0

Answer: 203,280

Step-by-step explanation:

Given: A catering service offers 11 appetizers, 12 main courses, and 8 desserts.

Number of combinations of choosing r things out of n = $^nC_r=\dfrac{n!}{r!(n-r)!}$

A customer is to select 9 appetizers, 2 main courses, and 3 desserts for a banquet.

Total number of ways to do this: $^{11}C_9\times ^{12}C_2\times^{8}C_3$

$=\dfrac{11!}{9!2!}\times\dfrac{12!}{2!10!}\times\dfrac{8!}{3!5!}\\\\=\dfrac{11\times10}{2}\times\dfrac{12\times11}{2}\times\dfrac{8\times7\times6}{3\times2}\\\\= 203280$

hence , this can be done in 203,280 ways.

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Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

$y = - \frac{ 1 }{10} {x}^{2} + \frac{5}{2}$

Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

${r}^{2} = {x}^{2} + {y}^{2}$

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

Or

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

$\sqrt{ {x}^{2} + {y}^{2} }=5 - y$

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

$y = - \frac{ {x}^{2} }{10} + \frac{5}{2}$

This is a parabola (0,2.5) and turns upside down.

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3 years ago

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Nata [24]

Answer:

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Step-by-step explanation:

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3 years ago

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The distribution of a sample of the outside diameters of PVC pipes approximates a normal distribution. The mean is 14.0 inches,

lakkis [162]

Answer:

A. 13.9 and 14.1 inches

See explanation below.

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".

Solution to the problem

Let X the random variable that represent the outside diameters of a population, and for this case we know the distribution for X is given by:

$X \sim N(14,0.1)$

Where $\mu=14$ and $\sigma=0.1$

If we want the middle 68% of the data we need to have on the tails 16% on each one

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.84$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.16 of the area on the left and 0.84 of the area on the right it's z=-0.994. On this case P(Z<-0.994)=0.16 and P(z>-0.994)=0.84

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.994$

And if we solve for a we got

$a=14 -0.994*0.1=13.9$

And since the distribution is symmetrical for the upper limit we can use z = 0.994 and we have:

$z=0.994$

And if we solve for a we got

$a=14 +0.994*0.1=14.1$

So the correct answer for this case would be:

A. 13.9 and 14.1 inches

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3 years ago

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Veseljchak [2.6K]

if / means absolute value, then the answer is -3. The absolute value of 3 is 3, then you take the negative value of it, which is -3.

Btw, the absolute sign is ||, not //.

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3 years ago