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3 years ago

[Statistics and Probability] How to find if something is mutually exclusive given a sample space?

Mathematics

1 answer:

Anastasy [175]3 years ago

6 0

Also, not being mutually exclusive could be proven by showing there are values in the intersection: A ∩ B

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Tower one, a cube with a hexagonal prism measures 15.6cm. Tower two, a cube with a cylinder measures 18.3cm. Tower 3, a hexagona

lina2011 [118]

Answer:

$Tower 4 = 23.9cm$

Step-by-step explanation:

Given

Tower one = 15.6 cm

Tower two = 18.3 cm

Tower 3 = 13.9 cm.

Required:

Height of the 4th tower

Represent a cube by X; a cylinder by Y and a hexagonal prism by Z

Tower one, a cube with a hexagonal prism = X + Z = 15.6

Tower two, a cube with a cylinder = X + Y = 18.3

Tower 3, a hexagonal prism with a cylinder = Z + Y = 13.9

$X + Z = 15.6$ ----- Equation 1

$X + Y = 18.3$ ----- Equation 2

$Z + Y = 13.9$ ----- Equation 3

Subtract equation 1 from 2

$(X + Y = 18.3) - (X + Z = 15.6)$

$X - X + Y - Z = 18.3 -15.6$

$Y - Z = 18.3 -15.6$

$Y - Z = 2.7$ ---- Equation 4

Add Equation 4 to Equation 3

$(Y - Z = 2.7) + (Z + Y = 13.9)$

$Y + Y - Z + Z = 2.7+ 13.9$

$2Y = 2.7+ 13.9$

$2Y = 16.6$

Divide both sides by 2

$\frac{2Y}{2} = \frac{16.6}{2}$

$Y = \frac{16.6}{2}$

$Y = 8.3cm$

Substitute $Y = 8.3cm$ in Equation 2 and 3

$X + Y = 18.3$ ----- Equation 2

$X + 8.3 = 18.3$

Subtract 8.3 from both sides

$X + 8.3 - 8.3 = 18.3 - 8.3$

$X = 18.3 - 8.3$

$X = 10cm$

$Z + Y = 13.9$ ----- Equation 3

$Z + 8.3 = 13.9$

Subtract 8.3 from both sides

$Z + 8.3 - 8.3 = 13.9 - 8.3$

$Z = 13.9 - 8.3$

$Z = 5.6cm$

So, we have that

$X = 10cm$

$Y = 8.3cm$

$Z = 5.6cm$

The question states that the 4th tower is made up of the three shapes;

This implies that;

$Tower 4 = X + Y + Z$

$Tower 4 = 10cm + 8.3cm + 5.6cm$

$Tower 4 = 23.9cm$

The height of the 4th tower is 23.9cm

8 0

3 years ago

I need help with this

Pachacha [2.7K]

Answer:8a-28b+15c

Step-by-step explanation:

3 0

3 years ago

Jocelyn boils 24 eggs. From experience, she knows that the shell of any given egg has a 0.04 probability of cracking during the

Varvara68 [4.7K]

Probability of an egg coming out of the boiling process with a cracked shell:
$1-(1-0.04)^{24} = 0.6246$

4 0

2 years ago

Read 2 more answers

Simplify.[2 × (10 + 5)] - 5

N76 [4]

2(10+5)−5 =(2)(15)−5 =30−5 =25 C is the answer.

4 0

4 years ago

Read 2 more answers

The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 73.7 m

Schach [20]

Answer:

A) 90.32%

B) 90.11%

C) 81.546 miles per hour

D)77.93%

Step-by-step explanation:

Given data:

speed = 73.7 miles/hour

standard deviation = 4.77 miles /hour

a) $P(X< 80) = P(z< \frac{80 - 73.7}{4.77}$

= P (z< 1.31)

= 0.90320 = 90.32%

b) $P(60 < X< 80) = P(\frac{60 - 73.7}{4.77} < z< \frac{80 - 73.7}{4.77})$

= P (-2.872< z< 1.31)

= P (z<1.31) - P(z<-2.87)

= 0.90320 - 0.00205

= 0.90115 = 90.11%

c) P(X <X) = 0.95

z = 1.645

$\frac{x - 73.7}{4.77} = 1.645$

x = 81.546 miles per hour

$d)P(X< 70) = P(z> \frac{70 - 73.7}{4.77})$

= P (z> -0.775)

= 0. 0.7793 = 77.93%

4 0

3 years ago