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Kruka [31]
3 years ago
5

Charity is ordering a sundae at a restaurant, and the server tells her that she can have up to five toppings: chocolate chips, b

utterscotch sauce, strawberries, a cherry, and hot fudge. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Charity gets just chocolate chips and a cherry? Express your answer as a fraction or a decimal number rounded to four decimal places.
Mathematics
1 answer:
Nataliya [291]3 years ago
6 0

Answer:

1/31 = 0.0323 probability that Charity gets just chocolate chips and a cherry.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Number of subsets in a set of n elements:

The number of subsets in a set of n elements, including the empty set, is given by:

2^{n}

Up to five toppings:

Up to five toppings means that the total number of possibilities is:

T = 2^{5} - 1 = 32 - 1 = 31

We subtract one to disconsider the option with no toppings.

What is the probability that Charity gets just chocolate chips and a cherry?

Chocolate chips and cherry is 1 subset, so D = 1

The probability is:

p = \frac{D}{T} = \frac{1}{31} = 0.0323

1/31 = 0.0323 probability that Charity gets just chocolate chips and a cherry.

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En una panadería se elaboraron 140 panes diarios, el 25% son conchas, 10% cortadillos, 40% donas y 25% bolillos. Cada pieza de p
torisob [31]

Answer:

Se obtuvo $ 448 de ganancia por la venta de donas.

Se obtuvo $ 280 de ganancia por la venta de bolillos.

Step-by-step explanation:

1) <em>¿Cuanta ganancia se obtuvo en la venta de donas?</em>

La ganancia es el producto del porcentaje producido de donas, expresado como razón, el precio unitario de la dona y el total producido de panes. Es decir:

C = \frac{40\,donas}{100\,panes}\times (140\,panes)\times \left(8\,\frac{USD}{dona} \right)

C = 448\,USD

Se obtuvo $ 448 de ganancia por la venta de donas.

2) <em>¿Cuanta ganancia se obtuvo en la venta de bolillos?</em>

La ganancia es el producto del porcentaje producido de bolillos, expresado como razón, el precio unitario del bolillo y el total producido de panes. Es decir:

C = \frac{25\,bolillos}{100\,panes}\times (140\,panes)\times \left(8\,\frac{USD}{bolillo}\right)

C = 280\,USD

Se obtuvo $ 280 de ganancia por la venta de bolillos.

3 0
3 years ago
Find the equation of a line in slope intercept form that is perpendicular to the line y = 2x + 6 through the point (10,4)
dalvyx [7]

The equation of the straight line is y = -1/6(x - 10) + 4

<h3>How to determine the line equation?</h3>

The equation is given as:

y = 2x + 6

Linear equations are represented as:

y = mx + c

Where:

Slope = m

So, we have:

m = 6

The slopes of perpendicular lines are represented as:

n = -1/m

So, we have:

n = -1/6

The equation is then represented as:

y = n(x - x1) + y1

This gives

y = -1/6(x - 10) + 4

Hence, the equation of the straight line is y = -1/6(x - 10) + 4

Read more about linear equations at:

brainly.com/question/14323743

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6 0
2 years ago
Solve the triangle given that a=19 b=16, c=11.
kirill [66]

Answer:

The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.

Step-by-step explanation:

From statement we know all sides of the triangle (a, b, c), but all angles are unknown (A, B, C). (Please notice that angles with upper case letters represent the angle opposite to the side with the same letter but in lower case) From Geometry it is given that sum of internal angles of triangles equal 180º, we can obtain the missing information by using Law of Cosine twice and this property mentioned above.

If we know that a = 19, b = 16 and c = 11, then the missing angles are, respectively:

Angle A

a^{2} = b^{2}+c^{2}-2\cdot b\cdot c \cdot \cos A (1)

A = \cos^{-1}\left(\frac{b^{2}+c^{2}-a^{2}}{2\cdot b\cdot c} \right)

A = \cos^{-1}\left[\frac{16^{2}+11^{2}-19^{2}}{2\cdot (16)\cdot (11)} \right]

A \approx 87.395^{\circ}

Angle B

b^{2} = a^{2}+c^{2}-2\cdot a\cdot c \cdot \cos B (2)

B = \cos^{-1}\left(\frac{a^{2}+c^{2}-b^{2}}{2\cdot a\cdot c} \right)

B = \cos^{-1}\left[\frac{19^{2}+11^{2}-16^{2}}{2\cdot (19)\cdot (11)} \right]

B\approx 57.271^{\circ}

Angle C

C = 180^{\circ}-A-B

C = 180^{\circ}-87.395^{\circ}-57.271^{\circ}

C = 35.334^{\circ}

The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.

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Answer:

1500

Step-by-step explanation:

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