Andy has a cube edge length 8 cm He paints

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Question:- Andy has a cube edge length 8 cm. He paints the outside of the cube red and then divides the cube into smaller cubes, each of edge length 1 cm. Andy randomly chooses one of the unit cubes and rolls it on a table. If the cube lands so that an unpainted face is on the bottom, touching the table, What is the probability that the entire cube is unpainted ?

Solution:-  Total number of cube of 1 cm making from a large cube of 8 cm = 8³ = 512

Number of unpainted cube = 6³ = 216

Number of cube having three face painted = 8

Number of cube having 2 painted face = 72

Number of cube having one painted face = 6(6×6) = 216

A= three painted face

B = Two painted face

C=  one painted face

D =  no painted face

Z = unpainted face on the table

P(A) = 8/512

P(B) = 72/512

p(C) =  216/512

P(D) = 216/512

P(Z/A) = 3/6

P(Z/B) = 4/6

P(Z/C) = 5/6

P(Z/D) = 6/6

P(Z) = P(A)×P(Z/A) + P(B)×P(Z/B) + P(C)×p(Z/C) + P(D)×P(Z/D)

P(Z) = 8/512 × 3/6 + 272/512 × 4/6 + 216/512 ×5/6 + 6/6 × 216/512

⇒ P(Z) = 7/8

P(No face painted/touching face are unpainted) = \dfrac{P(\text{unpainted cube})}{P(Z)}

= \dfrac{216/512}{7/8}

=\dfrac{27}{56}

Question 3:- A restaurant sells three sizes of drinks: small for $1.20, medium for $1.30 and large for $1.80. Each person at a table of ten ordered one drink, for a total cost of $14.90, before sales tax. How many people ordered a large drink ?

Solution:- See full solution

Question 2:- The length of a rectangle is three times its width. A new rectangle is created by decreasing the length of the original rectangle by 9 feet and increasing its width by 4 feet. The area of the new rectangle is the same as the area of the original rectangle. What is the perimeter of the new rectanle ?

Solution:- See full solution

Question 1:- A streaming video service offers its customers two plans. The first plan has a $ 24 registration fee, a fixed monthly rate of $5 and a charge of $0.75 for each video download. The second plan has a $15 registration fee, a fixed monthly rate of $3 and a charge of $1.50 for each vedio download. For how many download would the two plans cost the same for a year of service ?

Solution:- See full solution

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