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Alika [10]
3 years ago
7

Suppose you are ordering a calzone from D.P. Dough. You want 4 distinct toppings, chosen from their list of 8 vegetarian topping

s. How many choices do you have for your calzone
Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
6 0

Answer:

1680

Step-by-step explanation:

Number of distinct Toppings wanted = 4

Total number of vegetarian topping = 8

To choose 4 distinct toppings from a total of 8

Using permutation :

nPr : n! (n - r)!

8P4 = 8! / 4!

8P4 = (8*7*6*5)

8P4 = 1680

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P(<br> b.=15/16,p(a and <br> b.=3/4 find p(a
Bess [88]
And or both means we multiply the given probability situations that are mutually exclusive and exhaustive - they cannot occur at the same time.

let P(a)=x

then: P(b) * P(a) =3/4

         15/16 * x = 3/4

          15x/16 = 3/4
therefore x= 3/4 *16/15
          x = 4/5
P(a) = 4/5

hope it's clear

6 0
3 years ago
1. Derive the half-angle formulas from the double
lilavasa [31]

1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

<h3>How to apply trigonometry on deriving formulas and transforming points</h3>

1) The following <em>trigonometric</em> formulae are used to derive the <em>half-angle</em> formulas:

sin² θ / 2 + cos² θ / 2 = 1                      (1)

cos θ = cos² (θ / 2) - sin² (θ / 2)           (2)

First, we derive the formula for the sine of a <em>half</em> angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a <em>half</em> angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a <em>half</em> angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in <em>rectangular</em> form to <em>polar</em> form are obtained by <em>trigonometric</em> functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in <em>polar</em> form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in <em>rectangular</em> form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the <em>linear</em> function y = 5 · x - 8, we proceed to use the following <em>substitution</em> formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

To learn more on trigonometric expressions: brainly.com/question/14746686

#SPJ1

4 0
2 years ago
A bage contains 5 blue marbles, 3 red marbles, and 2 yellow marbles. You select a marble at radom. What is p(yellow)
vodomira [7]
Total marbles = 5 + 3 + 2 = 10
Total yellow marbles = 2
P(yellow)  = 2/10 = 1/5

Answer: 1/5
7 0
3 years ago
AACB = ADCE. If<br> AC = 5 and BC = 7<br> CD = [ ? ).<br> PLS HELP LOL PLS
FromTheMoon [43]

Answer:

CD = 5

Step-by-step explanation:

AC = 5

BC = 7

∆ACB ≅ ∆DCE, therefore,

AC = CD,

BC = CE, and,

AB = DE

Thus,

AC = CD = 5

CD = 5

6 0
2 years ago
Complete the square to transform the quadratic equation into the form
faltersainse [42]

The square of a binomial is written like

(x\pm a)^2 = x^2\pm 2ax + a^2

In your case, you have 2ax=-8x, which implies a=-4

So, we want to write

(x-4)^2 = x^2-8x+16

But our left hand side is

x^2-8x-10

If we add 26 to both sides, we have

x^2 - 8x - 10 +26 = 18+26 \iff x^2-8x+16=44 \iff (x-4)^2=44

7 0
3 years ago
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