math nation section 7

Answer and Step-by-step explanation: This function is a probability density function of a random variable X:

[tex]f(x)=\frac{3(8x-x^{2})}{256}[/tex]

and to calculate probabilities, we will have to integrate it:

[tex]P(X<x)=\int\limits^x_0 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]

Solving:

[tex]P(X<x)=\frac{3}{256}(4x^{2}-\frac{x^{3}}{3} )[/tex]

Then:

a. P(X < 5)

[tex]P(X<5)=\int\limits^5_0 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]

[tex]P(X<5)=\frac{3}{256}(100-\frac{125}{3} )[/tex]

[tex]P(X<5)=\frac{3}{256}(\frac{300-125}{3} )[/tex]

[tex]P(X<5)=\frac{175}{256}[/tex]

P(X < 5) = 0.683

b. P(X < 9)

Since density function's upper limit is 8, probability of x < 9 is 100% or 1.

So, P(X < 9) = 1

c. P(5 < X < 7)

[tex]P(5<X<7)=\int\limits^7_5 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]

[tex]P(5<X<7)=\frac{3}{256}[4(7)^{2}-\frac{7^{3}}{3}-4(5)^{2}+\frac{5^{3}}{3}][/tex]

[tex]P(5<X<7)=\frac{3}{256}[96-\frac{218}{3} ][/tex]

[tex]P(5<X<7)=\frac{70}{256}[/tex]

P(5 < X < 7) = 0.273

d. P(X > 3)

[tex]P(X>3)=\int\limits^8_3 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]

[tex]P(X>3)=\frac{3}{256}[256-\frac{512}{3}-36+9 ][/tex]

[tex]P(X>3)=\frac{3}{256}(229-\frac{512}{3} )[/tex]

[tex]P(X>3)=\frac{175}{256}[/tex]

P (X > 3) = 0.683

e. P(X < x) = 0.95

[tex]0.95=\int\limits^x_0 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]

[tex]\frac{3}{256}[\frac{12x^{2}-x^{3}}{3} ] =0.95[/tex]

[tex]\frac{12x^{2}-x^{3}}{256}=0.95[/tex]

[tex]12x^{2}-x^{3}=243.2[/tex]

[tex]-x^{3}+12x^{2}-243.2=0[/tex]

Solving this cubic equation, we have three values for x:

x₁ = -3.909

x₂ = 8.992

x₃ = 6.917

The value of x will the one between 0 and 8, which are the limits of the function. So, value of x which gives a probability of 0.95 is x = 6.917.

Answer:

Your answer is 5009.2

Upvote it. Welcome

Answer:

5009,206

Step-by-step explanation:

Hope this helped!

Answer:

3.53

Step-by-step explanation:

I checked it using a calculator. :)

AB=8.7 cm. Work out the length of BC. ... 1. Adi. Diagram NOT accurately drawn. POR is a triangle. Angle Q = 90° ... Give your answer correct to 1 decimal place. ton o. Ady ... Ad. POR is a right-angled triangle. PR = 12 cm. OR = 4.5 cm. Angle PRO = 90°. ... AB= 7 cm. BC = 12 cm. Angle BAD= 65°. Calculate the length of AC.

Answer:

Step-by-step explanation:

let n= number, the quotient of a number and 4 is

n/4

Answer:

X = log(0.96)(0.85)

Step-by-step explanation:

Given that on an island, the deer population has been decreasing by 4% per year and the current population is 792 deer, assuming that the deer population continues to decrease by 4% per year, to determine the number of years it will take for the deer population to decrease from 792 deer to 674 deer the following calculation must be performed:

792 x 0.96 ^ X = 674

X = 3.95

So, rounded to whole numbers, it will take 4 years for the deer population to drop to 674.

Answer:

Step-by-step explanation:

[tex]V=Ar^t\\ \\ V=17300((100-7)/100)^t\\ V=17300(0.93)^{(y-2006)}\\ V(2011)=17300(0.93)^{(2012-2006)}=\$ 11192.29[/tex]

Answer:

Should be $11.25

Step-by-step explanation:

Since 25% is 1/4 you can just divide 45 by 4.

45/4 = 11.25

Answer: 33.75. 25% of 45 is 11.25. So 45-11.25=33.75

Step-by-step explanation:

Answer:I think it’s 1/5 but if u have another attemp and it’s wrong somehow do 1/3

Step-by-step explanation:

Answer:

3/4 or 1/3

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

El número de personas que vieron solo A = n (A) = 17

El número de personas que vieron solo B = n (B) = 17

El número de personas que vieron solo C = n (C) = 23

El número de personas que vieron A y B = n (A ∩ B) = 6

El número de personas que vieron A y C = n (A ∩ C) = 8

El número de personas que vieron B y C = n (B ∩ C) = 10

El número de personas que vieron las tres películas = n (A ∩ B ∩ C) = 2

1) Número de estudiantes que han visto dos películas = n (A ∩ B) + n (A ∩ C) + n (B ∩ C) = 6 + 8 + 10 = 24

2)

n (A∩ B '∩ C') = n (A) -n (A ∩ B) -n (A ∩ C) -n (A ∩ B ∩ C) = 17-8-6-2 = 1

n (A'∩ B ∩ C ') = n (B) -n (A ∩ B) -n (B ∩ C) -n (A ∩ B ∩ C) = 17-6-10-2 = 1

n (A'∩ B '∩ C) = norte (C) -n (UNA ∩ C) -n (B ∩ C) -n (UNA ∩ B ∩ C) = 23-8-10-2 = 3

estudiantes que no han visto = 55 - n (A∩ B '∩ C') -n (A'∩ B ∩ C ') - n (A'∩ B ∩ C') - n (A ∩ B) -n ( B ∩ C) -n (UNA ∩ C) -n (A∩ B ∩ C) = 55-1-1-3-6-8-10-2 = 24

3)

número de alumnos que no han visto =

4)

número de estudiantes que vieron solo A = n (A∩ B '∩ C') = 1

Answer:

3)x=−9  and x=4

4)x=−12  and x=−5

5)x=8  and x=14

6)x=−7  and x=3

7)x=-1 2/3 and x = 1/4

8)x=2/5

Step-by-step explanation:

Hope this helps

Answer:

A - treatments

Step-by-step explanation:

We are told the 100 participants were required to drive under 1 of the 3 conditions below which are;

- no texting while driving.

- sending five text messages while driving

- sending 10 text messages while driving

In experimental a research, these 3 conditions are referred to as treatments because they are used to derive an experimental result.

Answer:8 y sobran 4

Step-by-step explanation:

8entre  4

Answer:

1.5

Step-by-step explanation:

Answer:

Radius: 3.5

Diameter: 7

i might be wrong tho im sorry !!

The answer:

Radius = 3.5cm

Diameter = 7cm

Answer:

7 hours 30 minutes

Step-by-step explanation:

Jane clocks into work at 7:30 and goes to lunch at 11:30. (4 hours)

4 hours so far.

takes 1 hour break and returns for 12:30.

She finishes at 4. Time from 12:30 to 4 is (3h30)

3h30 + 4 = 7h30m

Check yourself ^

Answer:

ok so.. whats the question?

Step-by-step explanation:

Answer:

y = 1/3x + 14

Step-by-step explanation:

The REASON THAT IS AN SLOPE INTERCEPT FORM IS BECAUSE IT IS ALREADY IN SLOPE INTERCEPT FORM.

Answer:

the answer is 1027.91159

Answer:

its the second one bc if u multiply 8.34 times 5305 it equals to 44243.7 the diameter of the pool was jus to throw u off it was unneeded information.

Step-by-step explanation:

Answer:

(x−1)(x−2)

Step-by-step explanation: