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3 years ago

14

Describe a way you can use graham crackers to demonstrate the division problem 3 divided by 1/4 . Include the result in your des

cription.

1 answer:

lesantik [10]3 years ago

5 0

You can take 3 graham crackers. Break each into 4 pieces. Then, you will have 12 pieces. So 3 divided by 1/4 = 12. Hope it helps! :)

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The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

natulia [17]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

P(a < X < b) = $\int_{a}^{b} \frac{2}{x^{3}} dx$ = $2\int_{a}^{b} x^{-3} dx$

= $2[ \frac{x^{-3+1} }{-3+1}]^{b}_a dx$ { Because $\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a$ }

= $2[ \frac{x^{-2} }{-2}]^{b}_a$ = $\frac{2}{-2} [ x^{-2} ]^{b}_a$

= $-1 [ b^{-2} - a^{-2} ]$ = $\frac{1}{a^{2} } - \frac{1}{b^{2} }$

a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }

Comparing with general probability we get,

P(1 < X < 5) = $\frac{1}{1^{2} } - \frac{1}{5^{2} }$ = $1 - \frac{1}{25}$ = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/ $8^{2}$ - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = $\frac{1}{6^{2} } - \frac{1}{10^{2} }$ = $\frac{1}{36} - \frac{1}{100 }$ = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

= $(\frac{1}{1^{2} } - \frac{1}{6^{2} })$ + (1/ $10^{2}$ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

⇒ P(1 < X < x) = 0.75

⇒ $\frac{1}{1^{2} } - \frac{1}{x^{2} }$ = 0.75

⇒ $\frac{1} {x^{2} }$ = 1 - 0.75 = 0.25

⇒ $x^{2}$ = $\frac{1}{0.25}$ ⇒ $x^{2}$ = 4 ⇒ x = $2$

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0

2 years ago

Can someone help me with this? its solving systems by substitution

yKpoI14uk [10]

Answer: x = 1 and y = 2

Given:
y = -3x + 5
5x - 4y = -3

Since we are given y, let’s sub it in the second equation.

5x - 4(-3x + 5) = -3
5x + 12x - 20 = -3
17x = 17
x = 1

After finding x, we can now find y.

5(1) - 4y = -3
-4y = -8
y = 2

Checking:

y = -3x + 5
2 = -3(1) + 5
2 = 2

5x - 4y = -3
5(1) - 4(2) = -3
-3 = -3

8 0

2 years ago

a 1 kg ball has 10 joules of kinetic energy and starts to roll up a hill how far up the hill will it be when it stops

AURORKA [14]

Answer:

<em>The ball will roll upto </em><em>1 m.</em>

Step-by-step explanation:

A 1 kg ball has 10 joules of kinetic energy and starts to roll up a hill.

As along the hill the ball rises up, it loses its kinetic energy. The kinetic energy is converted to potential energy.

According to the law of conservation of energy, the kinetic energy plus the potential energy equals a constant.

Here given kinetic energy as 10 J, so this energy will get converted to potential energy.

We know that, potential energy is

$P.E=m\cdot g\cdot h$

where,

m is the mass, g is the acceleration due to gravity and h is the height.

Putting the values,

$\Rightarrow 10=1\times 10\times h$

$\Rightarrow 10=10 h$

$\Rightarrow h=1\ m$

7 0

2 years ago

A certain type of bacteria doubles in population every 6 hours. There were approximately 100 bacteria at the beginning of the da

Zepler [3.9K]

Answer:

1600 after 24 hours

Step-by-step explanation:

100+100 = 200 after 6 hours

200+200 = 400 after 12 hours

400+400 = 800 after 18 hours

800+800 = 1600 after 24 hours

5 0

2 years ago

lung cancer kills about 3,000 people per day. if 90% of the deaths from luung cancer are attributted to smoking, what is the rat

defon

Answer:

2700!

Step-by-step explanation:

hope that helped <3

5 0

2 years ago