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3 years ago

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A restaurant offers 6 choices of appetizer, 8 choices of main meal, and 5 choices of dessert. A customer can choose to eat just

one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible meals does the restaurant offer?

1 answer:

rodikova [14]3 years ago

4 0

Step-by-step explanation:

For one course:

6+8+5=

Two courses with appetizers and main meals (* means times)

6*8

Two courses with appetizers and dessert

6*5

Two courses with main meals and dessert

8*5

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The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day.

valina [46]

Answer:

A sample of 179 is needed.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.85}{2} = 0.075$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.075 = 0.925$ , so Z = 1.44.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

A previous study found that for an average family the variance is 1.69 gallon?

This means that $\sigma = \sqrt{1.69} = 1.3$

If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water?

A sample of n is needed, and n is found for M = 0.14. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.14 = 1.44\frac{1.3}{\sqrt{n}}$

$0.14\sqrt{n} = 1.44*1.3$

$\sqrt{n} = \frac{1.44*1.3}{0.14}$

$(\sqrt{n})^2 = (\frac{1.44*1.3}{0.14})^2$

$n = 178.8$

Rounding up

A sample of 179 is needed.

7 0

3 years ago

Suppose that F is an inverse square force field below, where c is a constant.

Andre45 [30]

Answer:

Forces in our Universe

Step-by-step explanation:

a)

First of all we have,

$F(r) = \frac{cr}{|r|^{3} }$

and,

$r = xi+yj+zk$

We need to define a function that allows us to find said change based on r, so one of the functions that shows that change is,

$f(r) = - c /|r|$

That is,

$\nabla f = F$

For this case F is a conservative field and the line integral is independent of the path. Thus, defining $P_{1} = (x_{1}, y_{1}, z_{1})$ and $P_{2} = (x_{2}, y_{2}, z_{2})$ . So the amount of work on the movement of the object from P1 to P2 is,

$W=\int\limits_c {F} \, dr$

$W= f(P_{1}-P_{2})$

$W= \frac{c}{(x_{2}^2+ y_{2}^2+ z_{2}^2)^{1/2} } -\frac{c}{(x_{1}^2+ y_{1}^2+ z_{1}^2)^{1/2}}$

$W= c(\frac{1}{d1}-\frac{1}{d2} )$

2) The gravitational force field is given by,

$F(r) =-\frac{mMGr}{ |r|^3}$

The maximum distance from the earth to the sun is $1.52*10 ^ 8$ km and the minimum distance is $1.47*10 ^ 8$ km. The mass values of the bodies are given by m = $5.97*10 ^ {24}$ kg, M = $1.99 *19 ^ {30}$ kg and the constant G is $6.67 * 10 ^{ -11 }$ $\frac{Nm ^ 2}{kg^2}$

In this way we raise the problem like this,

$c= -mMG$

$W= -mMG (\frac{1}{1.52*10 ^ 8} -\frac{1}{1.47*10 ^ 8} )$

$W= -(5.95*10^{24})(1.99*10^{30})(6.67*10^{-11})(-2.2377*10^{-10})$

$W \approx 1.77*10^{35}}J$

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2 years ago

Solve for X using either sine, cosine, or tangent

vovikov84 [41]

Answer:

•12.12

•56.92

Step-by-step explanation:

•Sin 30° = x ÷ 14√3

x=14√3 *Sin30

x=7√3

x=12.12

•Tan30°=6√3÷x

x=6√30 ÷Tan 30

x=18√10

x=56.92

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3 years ago

Express 24 as a fraction of 60

seraphim [82]

Answer:

24/60 = 2/5

Step-by-step explanation:

24/60

Divide both the numerator and denominator by a common factor, 6

4/10

Divide both the numerator and denominator by a common factor, 2

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3 years ago

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Rewrite the expression that is equivalent to x^2/3.<br> -pasagot po please-.-

EastWind [94]

Answer:

$\sqrt[3]{x^{2}}$

Step-by-step explanation:

$x^{2/3} = \sqrt[3]{x^{2}}$

5 0

2 years ago