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Mariulka [41]
2 years ago
15

Olivia has enter a buffet line in which he chooses one kind of meat two kinds of vegatables and one dessert if the order of the

food items are not important how many different meals can she choose meat: duck beef chicken mutton Vegatables: baked beams corn potatoes tomatoes spinach lettuce dessert brownies chocalate cake ice cream and vanilla pudding
Mathematics
1 answer:
masya89 [10]2 years ago
4 0

Using the Fundamental Counting Theorem, it is found that she can choose 180 different meals.

<h3>What is the Fundamental Counting Theorem?</h3>

It is a theorem that states that if there are n things, each with n_1, n_2, \cdots, n_n ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n_1 \times n_2 \times \cdots \times n_n

In this problem:

  • For the meat, there are 3 outcomes, hence n_1 = 3.
  • For the two vegetables, 2 are taken from a set of 6, hence, applying the combination formula, n_2 = C_{6,2} = \frac{6!}{2!4!} = 15.
  • For the dessert, there are 4 outcomes, hence n_3 = 4.

Then:

N = n_1n_2n_3 = 3(15)(4) = 180

She can choose 180 different meals.

To learn more about the Fundamental Counting Theorem, you can take a look at brainly.com/question/24314866

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goldfiish [28.3K]

\angle1\cong\angle2 corresponding angles, therefore

m∠1 = m∠2 → m∠2 = 130°

\angle2\cong\angle3 vertical angles, therefore

m∠2 = m∠3 → m∠3 = 130°


If ∠1 and ∠2 are complementary, then m∠1 + m∠2 = 90°.

If ∠2 and ∠3 are complementary, then m∠2 + m∠3 = 90°

Therfore

m\angle1 + m\angle2 = m\angle2 + m\angle3\qquad|\text{subtract}\ m\angle2\ \text{ from both sides}\\\\m\angle1 = m\angle3\to\angle1\cong\angle3

5 0
3 years ago
Simplify the expression 5(n+3)+4n
Xelga [282]

Answer:

9n + 15

Step-by-step explanation:5XN + 5X3  +  4N = 5n + 15 + 4n = 9n + 15

6 0
3 years ago
I have no clue how to do this!!!
lara31 [8.8K]
Step One
Find z
All triangles have 180 degrees. No exceptions.
z + 47 + 90 = 180      combine like terms on the left.
z + 137 = 180            subtract 137 from both sides
z =  180 - 137        
z = 43 degrees.

Step Two
Use the sine function to find y
Sin(43) = opposite side / hypotenuse
opposite side = 35 

sin(43) = 35 / hypotenuse
hypotenuse = 35 / sin(43)
y = 35/0.6820
y = 51.32 

Solve using cos(x)
Note this problem could have been done in a shorter way.
Cos(47) = adjacent / hypotenuse.
hypotenuse = adjacent / cos(47)
y = 35 / cos(47)
y = 35 / 0.6820
y = 51.32 Both answers agree. It is a good thing to know how to do this question both ways.
5 0
3 years ago
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bagirrra123 [75]

Answer:

Option B:

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H_a: \mu \neq 22.1

Classification:

The hypothesis test is Two-tailed.

Step-by-step explanation:

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This means that the null hypothesis is that the mean is of 22.1 months, that is:

H_0: \mu = 22.1

A hypothesis test is to be performed to determine whether the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 22.1 months.

At the alternate hypothesis, we test if this mean is different of 22.1, that is:

H_a: \mu \neq 22.1

Which means that the answer is given by option b).

Which of the following is the correct classification of the hypothesis test?

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Where’s the data?................
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