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steposvetlana [31]
3 years ago
10

a deli offers a lunch special that comes with soup a sandwich and a drink the soup choices are chicken noodle or creamy potato t

he sandwich choices are ham turkey tuna or veggie and the drink choices are juice coffee tea how many different lunch specials are in the sample space
Mathematics
2 answers:
quester [9]3 years ago
5 0

Answer:

There are 24 different lunch specials in the sample space.

Step-by-step explanation:

Consider the provided information.

The choices for soup are chicken noodle or creamy potato.

The choices for sandwich are ham, turkey, tuna, or veggie.

The choices for drink are juice, coffee or tea.

A lunch menu consists of 2 different soups , 4 different sandwiches, and 3 different drinks.

Here, the order doesn't matter,

Suppose you are going to order a lunch, the number of ways you can select the soup is 2:

Now you are going to select the sandwich so the number of ways are:

<u>2</u> × <u>4</u>

You are going to select the drink so the number of ways are:

<u>2</u> × <u>4</u>× <u>3</u>

To find the number sample space for different lunch simply multiply all the numbers:

2 × 4× 3 = 24

Hence, there are 24 different lunch specials in the sample space.

Allushta [10]3 years ago
3 0
To do this, simply multiply each value of options together
Soup = 2 choices
Sandwich = 4 choices
Drink = 3 choices
2x4x3 = 24 lunch specials
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Answer:

cosФ = \frac{1}{\sqrt{65}} , sinФ = -\frac{8}{\sqrt{65}} , tanФ = -8, secФ = \sqrt{65} , cscФ = -\frac{\sqrt{65}}{8} , cotФ = -\frac{1}{8}

Step-by-step explanation:

If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:

  1. cosФ = \frac{x}{r}
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  3. tanФ = \frac{y}{x}
  4. secФ = \frac{r}{x}
  5. cscФ = \frac{r}{y}
  6. cotФ = \frac{x}{y}
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∵ Point (1, -8) lies on the terminal side of angle Ф in standard position

∵ x is positive and y is negative

→ That means the point lies on the 4th quadrant

∴ Angle Ф is on the 4th quadrant

∵ In the 4th quadrant cosФ and secФ only have positive values

∴ sinФ, secФ, tanФ, and cotФ have negative values

→ let us find r

∵ r = \sqrt{x^{2}+y^{2} }

∵ x = 1 and y = -8

∴ r = \sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}

→ Use the rules above to find the six trigonometric functions of Ф

∵ cosФ = \frac{x}{r}

∴ cosФ = \frac{1}{\sqrt{65}}

∵ sinФ = \frac{y}{r}

∴ sinФ = -\frac{8}{\sqrt{65}}

∵ tanФ = \frac{y}{x}

∴ tanФ = -\frac{8}{1} = -8

∵ secФ = \frac{r}{x}

∴ secФ = \frac{\sqrt{65}}{1} = \sqrt{65}

∵ cscФ = \frac{r}{y}

∴ cscФ = -\frac{\sqrt{65}}{8}

∵ cotФ = \frac{x}{y}

∴ cotФ = -\frac{1}{8}    

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