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3 years ago

8

Paul is buying lunch from a fast-food restaurant. He has 5 sandwiches, 7 sides, and 10 drinks to choose from. If Paul doesn’t wa

nt two of the sandwiches, how many possibilities for lunch can he have?

1 answer:

34kurt3 years ago

8 0

Answer:

He has 5 sandwiches, 7 sides, and 10 drinks to choose from

Step-by-step explanation:

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Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

<u>ANSWER</u>

${r}^{2} = 4 \cos2\theta$

<u>EXPLANATION</u>

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

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

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

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The polar equation then becomes:

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3 years ago

Here is a list of the normal monthly precipitation (in inches) for January for 20 different U.S. cities. 4.0, 1.0, 1.5, 1.6, 2.0

shutvik [7]

Answer:

minimum value = 1.0 , the lower quartile = 2.3, the middle value = 3.5.

the upper quartile = 3.95, the maximum value = 7.3.

Step-by-step explanation:

Five Number Summary of any data consists basically of 5 data sets.

1) The minimum Value

2)The first (lower) quartile

3) The middle value (Median)

4) The third (upper) quartile

5)The maximum value

Now, the given data is 4.0, 1.0, 1.5, 1.6, 2.0, 2.2, 2.4, 2.7, 3.4, 3.4, 3.5, 3.6, 3.6, 3.7, 3.7, 3.9, 4.1, 5.8, 4.1, 7.3

Arrange it in the ascending order,

1.0, 1.5, 1.6, 2.0, 2.2, 2.4, 2.7, 3.4, 3.4, 3.5, 3.6, 3.6, 3.7, 3.7, 3.9, 4.0, 4.1, 4.1, 5.8, 7.3

Here,

1) The minimum Value is 1.0

2)The first (lower) quartile is 2.3.

3) The middle value (Median) is 3.5.

4) The third (upper) quartile is 3.95.

5)The maximum value is 7.3.

7 0

3 years ago