Question 2

One dozen students each drop a brass tack six times from a height of six inches onto a level hard surface. They record the numbe

pshichka [43]

Experimental Probability = 2/3

To find the experimental probability that the tack lands point-up for student 4, we can use the following equation

$\frac{Point-up}{Attempts}\\\frac{4}{6} or\frac{2}{3}$

If this helped you a Brainliest would be appreciated!

8 0

3 years ago

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

What is the height of the tv and is it square inches or inches ??

fiasKO [112]

To find the height of the TV you first need to realize that the question is giving you dimensions for a triangle.

Every triangle has a hypotenuse and two sides. To find the hypotenuse you square both sides, add them, and then square root. So to find one of the sides you get the hypotenuse, square it, and subtract the square length of the given side.

The equation is 25^2-20^2.
Which if simplified is 625-400, the then solution is going to be 225.
You next will square root 225, 225^(1/2). Which your answer should be 15 inches for the missing side length.

7 0

3 years ago

Read 2 more answers

Kendra is participating in a fundraiser walk-a-thon she walks 4 miles in 60 minutes how many minutes will it take to walk 7 mile

Lemur [1.5K]

Answer:

105 min

Step-by-step explanation:

60 minutes ÷ 4 miles= 15 minutes per mile

15min per mile x 7 miles = 105 minutes

8 0

3 years ago

Please help me with my work

vaieri [72.5K]

,so first split them into separate shapes (refer to pic) then calculate each one
I started with the triangle
8×6=48 and 48÷2=24 so the triangles area its 24
next the rectangle
12×8=96
and I did the triangle shape cut out of the square
4×3=12 12÷2=6 so its area is 6
and the squares area is 8×8=64
but u need to subtract 6 from 64 because that area is missing
then you get 64-6=58
then add all the areas
58+24+96 to get your answer of 178m

8 0

3 years ago