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valina [46]
2 years ago
15

For the dinner special at a restaurant, the customer must choose an appetizer, a salad, an entree, a side dish, and a dessert. H

ere are the items to choose from. Choice Possible items Appetizer Chicken strips, Shrimp cocktail, Buffalo wings, Potato skins Salad Garden, Caesar Entree T-bone steak, Pot roast, Lamb Side dish Corn, Rice, French fries, Baked potato, Pinto beans Dessert Chocolate cake, Brownies, Ice cream, Apple pie How many dinner specials are possible
Mathematics
1 answer:
Ostrovityanka [42]2 years ago
3 0

Answer:

The number of possible dinner specials are 4368.

Step-by-step explanation:

The number of dinner specials = 5

They include appetizer, a salad, an entree, a side dish, and a dessert.

Possible items to choose from = 16.

They are 1. Appetizer Chicken strips, 2. Shrimp cocktail, 3. Buffalo wings, 4. Potato skins, 5. Salad Garden, 6. Caesar Entree T-bone steak, 7. Pot roast, 8. Lamb Side dish Corn, 9. Rice, 10. French fries, 11. Baked potato, 12. Pinto beans, 13. Dessert Chocolate cake, 14. Brownies, 15. Ice cream, 16. Apple pie

This is a combination problem requiring a combination solution with the following formula and steps:

C (n, r) =? C (n, r) = ?

n choose r

n (objects) =  16

r (sample) =  5

C (n, r) =? C (n, r) = ?

C (n, r) =C (14,5) C (n, r) =C (16,5)

=16! (5! (16−5)!) =16! (5! (16−5)!)

= 4368

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Does 4/6 have equal parts
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6 0
2 years ago
The price of an item yesterday was $60. Today, the price fell to $42. Find the percentage decrease.
oksian1 [2.3K]

Answer:

-30% or 30% decrease

Step-by-step explanation:

What's percentage decrease?

  • Percent decrease is the difference between the initial value and new value, indicating a loss of value.
  • The formula to find percent decrease is \frac{NV-IV}{IV} * 100, where NV = new value and IV = initial value.

How do we solve this problem?

  • We know that the original value was $60, so that represents IV. Also, now that the price is $42, it represents NV.
  • Now, we plug in the values!
  • \frac{42-60}{60} * 100
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Therefore, the answer is 30% decrease.

6 0
2 years ago
Graphing polynomial functions?
Leni [432]

NOTES:

Degree: the largest exponent in the polynomial

End Behavior:

  • Coefficient is POSITIVE, then right side goes to POSITIVE infinity
  • Coefficient is NEGATIVE, then right side goes to NEGATIVE infinity
  • Degree is EVEN, then left side is SAME direction as right side
  • Degree is ODD, then left side is OPPOSITE direction as right side

Multiplicity (M): the exponent of the zero. <em>e.g. (x - 3)²  has a multiplicity of 2</em>

Relative max/min: the y-value of the vertices.  

  1. Find the axis of symmetry <em>(the midpoint of two neighboring zeros)</em>
  2. Plug the x-value from 1 (above) into the given equation to find the y-value. <em>(which is the max/min)</em>
  3. Repeat 1 and 2 (above) for each pair of neighboring zeros.

Rate of Change: slope between the two given points.

********************************************************************************************

1. f(x) = (x-1)²(x + 6)

a) Degree = 3

b) end behavior:

  • Coefficient is positive so right side goes to positive infinity
  • Degree is odd so left side goes to negative infinity

c) (x - 1)²(x + 6) = 0

   x - 1 = 0                     x + 6 = 0

       x = 1 (M=2)                   x = -6 (M=1)

d) The midpoint between 1 and -6 is -3.5, so axis of symmetry is at x = -3.5

y = (-3.5 - 1)²(-3.5 + 6)

  =  (-4.5)²(2.5)

  = 50.625

50.625 is the relative max

e) see attachment #1

f) The interval at which the graph increases is: (-∞, -3.5)U(1, ∞)

g) The interval at which the graph decreases is: (-3.5, 1)

h) f(-1) = (-1 - 1)²(-1 + 6)

          = (-2)²(5)

          = 20

    f(0) = (0 - 1)²(0 + 6)

          = (-1)²(6)

          = 6

Find the slope between (-1, 20) and (0, 6)

m = \frac{20-6}{-1-0}

   = \frac{14}{-1}

   = -14

********************************************************************************************

2.    y = x³+3x²-10x

         = x(x² + 3x - 10)      

         = x(x + 5)(x - 2)

a) Degree = 3

b) end behavior:

   Coefficient is positive so right side goes to positive infinity

   Degree is odd so left side goes to negative infinity

c) x(x + 5)(x - 2) = 0

   x = 0                     x + 5 = 0                     x - 2 = 0

   x = 0 (M=1)                   x = -5 (M=1)                x = 2 (M=1)

d) The midpoint between -5 and 0 is -2.5, so axis of symmetry is at x = -2.5

y = -2.5(-2.5 + 5)(-2.5 - 2)

  =  -2.5(2.5)(-4.5)

  = 28.125

28.125 is the relative max

The midpoint between 0 and 2 is 1, so axis of symmetry is at x = 1

y = 1(1 + 5)(1 - 2)

  =  1(6)(-1)

  = -6

-6 is the relative min

e) see attachment #2

f) The interval at which the graph increases is: (-∞, -2.5)U(1, ∞)

g) The interval at which the graph decreases is: (-2.5, 1)

h) f(-1) = -1(-1 + 5)(-1 - 2)

********************************************************************************************

3. y = -x(x + 2)(x - 7)(x - 3)

a) Degree = 4

b) end behavior:

   Coefficient is negative so right side goes to negative infinity

   Degree is even so left side goes to negative infinity

c)  -x(x + 2)(x - 7)(x - 3) = 0

  -x = 0                     x + 2 = 0                     x - 7 = 0             x - 3 = 0

   x = 0 (M=1)                 x = -2 (M=1)                x = 7 (M=1)          x = 3 (M=1)

d) The midpoint between -2 and 0 is -1, so axis of symmetry is at x = -1

y = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)

  =  1(1)(-8)(-4)

  = 32

32 is a relative max

The midpoint between 0 and 3 is 1.5, so axis of symmetry is at x = 1.5

y = -(1.5)(1.5 + 2)(1.5 - 7)(1.5 - 3)

  =  -1.5(3.5)(-5.5)(-1.5)

  = -43.3125

-43.3125 is the relative min

The midpoint between 3 and 7 is 5, so axis of symmetry is at x = 5

y = -(5)(5 + 2)(5 - 7)(5 - 3)

  =  -5(7)(-2)(2)

  = 140

140 is the relative max

e) see attachment #3

f) The interval at which the graph increases is: (-∞, -1)U(1.5, 5)

g) The interval at which the graph decreases is: (-1, 1.5)U(5, ∞)

h) f(-1) = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)

          = 1(1)(-8)(-4)

          = 32

    f(0) = -(0)(0 + 2)(0 - 7)(0 - 3)

          = 0

Find the slope between (-1, 32) and (0, 0)

m = \frac{32-0}{-1-0}

   = \frac{32}{-1}

   = -32



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NemiM [27]

Step-by-step explanation:

5x5

because 5^2 equals the area

4 0
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