The expected value of a fair 6-sided die is 3.5.
Which of the following statements are true?
Choose all answers that apply:
А
3.5 is one of the possible outcomes of rolling a fair 6-sided die.
A fair 6-sided die is more likely to land on the number 4 than the number 6.
If you rolled a fair 6-sided die a large number of times, you should expect the average of the
numbers rolled to be about 3.5.

Given:

Consider the given expression is:

[tex]10n-\dfrac{1}{3}(9n-12)[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]10n-\dfrac{1}{3}(9n-12)[/tex]

Using distributive property, it can be written as:

[tex]=10n-\dfrac{1}{3}(9n)-\dfrac{1}{3}(-12)[/tex]

[tex]=10n-3n+4[/tex]

[tex]=7n+4[/tex]

Therefore, the correct option is A.

Answer:

x=76

Step-by-step explanation:

y+8=3y

-2y=-8

y=4

104*2=208

360-208=152

152/2=76

x=76

Answer:

100

Step-by-step explanation:

it gives you the formula for simple interest

Answer:

the 2nd and 3rd one I believe

Answer:

the last one- 4/24

Step-by-step explanation:

ive answered this question before and got it correct

Answer:

B. 14 ft

Step-by-step explanation:

I calculated it logically

Answer:

Step-by-step explanation:

Do you have any measurements?

1) 180-Angle 2 = Angle 1

3) Same as Angle 2

6) Same as Angle 2

Answer:

0.3425 = 34.25% probability it will be off probation in February 2020

Step-by-step explanation:

We have these desired outcomes:

Off probation in July 2019, with 0.25 probability, then continuing off in January, with 1 - 0.08 = 0.92 probability.

Still in probation in July 2019, with 1 - 0.25 = 0.75 probability, then coming off in January, with 0.15 probability.

What is the probability it will be off probation in February 2020?

[tex]p = 0.25*0.92 + 0.75*0.15 = 0.3425[/tex]

0.3425 = 34.25% probability it will be off probation in February 2020

Answer:

Yessir

Step-by-step explanation:

Answer:

POINTS HA

Step-by-step explanation:

Answer:

Can you add a picture if there are any?

Step-by-step explanation:

Answer: 55

Step-by-step explanation:

180 = 125 + x

x = 55

Answer:

This

Step-by-step explanation:

let x = rate of the slower plane (First plane!)

x+25 = rate of the faster plane (Second plane!)

The planes fly for 2 hours, where Distance = R*T

Distance between the planes = SUM of the distances.

R*T + R*T= 470 miles

2*x + 2*(x+25)=470

2x+2x + 50 = 470

4x+50=470

4x=420

x=105 mph First plane

x+25= 105+25=130 mph Second plane.

Answer:

4x+50=470

4x=420

x=105 mph First plane

x+25= 105+25=130 mph Second plane.

R^2

Step-by-step explanation:

Answer:

a) 0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they last more than 1,000 hours, or they do not. Components operate independently, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours.

So 1 - 0.1 = 0.9 probability of working for more, which means that [tex]p = 0.9[/tex]

a. exactly two of the four components last longer than 1000 hours.

This is P(X = 2) when [tex]n = 4[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{4,2}.(0.9)^{2}.(0.1)^{2} = 0.0486[/tex]

0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b. the subsystem operates longer than 1000 hours.

The subsystem has 8 components, which means that [tex]n = 8[/tex]

It will operate if at least 4 components are working correctly, so we want:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{8,0}.(0.9)^{0}.(0.1)^{8} \approx 0[/tex]

[tex]P(X = 1) = C_{8,1}.(0.9)^{1}.(0.1)^{7} \approx 0tex]

[tex]P(X = 2) = C_{8,2}.(0.9)^{2}.(0.1)^{6} \approx 0[/tex]

[tex]P(X = 3) = C_{8,3}.(0.9)^{3}.(0.1)^{5} = 0.0004[/tex]

Then

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0 + 0.0004 = 0.0004[/tex]

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0004 = 0.9996[/tex]

0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

Answer:

b.)36

Step-by-step explanation:

Formula for area of a trapezoid = [tex]\frac{a+b}{2} h[/tex]

where a and b = bases and h = height

The sign has the following dimensions

Base 1 = 6ft

base 2 = 12ft

height = 4ft

Using these dimensions we plug in the values into the formula

[tex]A=\frac{6+12}{2} 4\\6+12=18\\\frac{18}{2} =9\\9*4=36[/tex]

Hence the area of Mr. Wash's sign is 36 square feet.

Answer:

b) 36 sq ft.

Step-by-step explanation:

6 x 4 = 24 (multiply to find the square after splitting it)

12 - 6 = 6 x 4 = 24 / 2 = 12 (you divide by two because it's a triangle)

24 + 12 = 36

hope this helps :)

Answer:

hope it helps ya.

please give me brainliest

Answer:

48 years

Step-by-step explanation:

Let the ratio of their ages be

4:2:1

Sum up the numbers

4+2+1

= 7

Their total ages is 84

7/84

= 1/12

Therefore Jim age can be calculated as follows

= 12×4

= 48

Hence Jim is 48 years

Answer:

In (16.8+12=) 28.8 minutes the person will be left only with 2mg of dye in the body and be able to leave the doctor's office after being injected with 11 mg

Step-by-step explanation:

After 12 minutes, 7.75 milligrams of dye remain in your system.

This means that 11- 7.75= 3.25 milligrams of dye are used up in 12 minutes

7.75-2= 5.75 milligrams still needs to be used up

         Dye           Minutes

         3.25             12

          5.75             x

x= 12*5.75/3.25

x= 16.8 minutes

5.75 mg will be used up in 16.8 minutes

In (16.8+12=) 28.8 minutes the person will be left only with 2mg of dye in the body and be able to leave the doctor's office.

Answer:

B 18.38

Step-by-step explanation:

log4x = 2.1

logx/log4 = 2.1

logx = log(4) x 2.1

logx = 1.2643

x = antilog(1.2643)

x = 18.38 (to 2 d.p)

Answer:

X=18.38

Step-by-step explanation:

Answer: 720 ways

Step-by-step explanation:

Given

Leroy wants to teach his puppy 6 new tricks

Considering each trick is different from other

The first trick can be taught in 6 different ways

After learning the first trick, there are 5 tricks remaining which can be taught in 5 different ways

Similarly, for the remaining tricks, it is 4, 3, 2, and 1 way

So, the total number of ways is [tex]6\times 5\times 4\times 3\times 2\times 1=720\ \text{Ways}[/tex]

Answer:

20x^2 +19xy+3y^2

Step-by-step explanation:

See Image below :)

9514 1404 393

Answer:

  20x² +19xy +3y²

Step-by-step explanation:

Use the distributive property.

  (4x +3y)(5x +y)

  = 4x(5x +y) +3y(5x +y)

  = 20x² +4xy +15xy +3y²

Collect terms.

  = 20x² +19xy +3y²

Answer:

the ans is 21 hope it may help u

Step-by-step explanation:

g = 6

x=6

x= 3x + 3

x = 3 × 6 +3

x = 18 + 3

x= 21

Answer:

If a = 5 and b = 3, then that means 2a - 3b + 3a = 16

Step-by-step explanation:

2a - 3b + 3a

(2×5) - (3×3) + (3×5)

10 - 9 + 15 = 16

Answer:

[tex]E(Y)=\frac{1}{25}[/tex]

Step-by-step explanation:

Let's start defining the random variables for this exercise :

[tex]X_{1}:[/tex] '' The proportion of the particulates that are removed by the first pass ''

[tex]X_{2}:[/tex] '' The proportion of what remains after the first pass that is removed by the second pass ''

[tex]Y:[/tex] '' The proportion of the original particulates that remain in the sample after two passes ''

We know the relation between the random variables :

[tex]Y=(1-X_{1})(1-X_{2})[/tex]

We also assume that [tex]X_{1}[/tex] and [tex]X_{2}[/tex] are independent random variables with common pdf.

The probability density function for both variables is [tex]f(x)=4x^{3}[/tex] for [tex]0<x<1[/tex] and [tex]f(x)=0[/tex] otherwise.

The first step to solve this exercise is to find the expected value for [tex]X_{1}[/tex] and [tex]X_{2}[/tex].

Because the variables have the same pdf we write :

[tex]E(X_{1})= E(X_{2})=E(X)[/tex]

Using the pdf to calculate the expected value we write :

[tex]E(X)=\int\limits^a_b {xf(x)} \, dx[/tex]

Where [tex]a=[/tex] ∞ and [tex]b=[/tex] - ∞ (because we integrate in the whole range of the random variable). In this case, we will integrate between [tex]0[/tex] and [tex]1[/tex] ⇒

Using the pdf we calculate the expected value :

[tex]E(X)=\int\limits^1_0 {x4x^{3}} \, dx=\int\limits^1_0 {4x^{4}} \, dx=\frac{4}{5}[/tex]

⇒ [tex]E(X)=E(X_{1})=E(X_{2})=\frac{4}{5}[/tex]

Now we need to use some expected value properties in the expression of [tex]Y[/tex] ⇒

[tex]Y=(1-X_{1})(1-X_{2})[/tex] ⇒

[tex]Y=1-X_{2}-X_{1}+X_{1}X_{2}[/tex]

Applying the expected value properties (linearity and expected value of a constant) ⇒

[tex]E(Y)=E(1)-E(X_{2})-E(X_{1})+E(X_{1}X_{2})[/tex]

Using that [tex]X_{1}[/tex] and [tex]X_{2}[/tex] have the same expected value [tex]E(X)[/tex] and given that [tex]X_{1}[/tex] and [tex]X_{2}[/tex] are independent random variables we can write [tex]E(X_{1}X_{2})=E(X_{1})E(X_{2})[/tex]   ⇒

[tex]E(Y)=E(1)-E(X)-E(X)+E(X_{1})E(X_{2})[/tex] ⇒

[tex]E(Y)=E(1)-2E(X)+[E(X)]^{2}[/tex]

Using the value of [tex]E(X)[/tex] calculated :

[tex]E(Y)=1-2(\frac{4}{5})+(\frac{4}{5})^{2}=\frac{1}{25}[/tex]

[tex]E(Y)=\frac{1}{25}[/tex]

We find that the expected value of the variable [tex]Y[/tex] is [tex]E(Y)=\frac{1}{25}[/tex]

Answer:

Step-by-step explanation:

x^1/3( x^1/2 + 2x^2)

x^(1/2 + 1/3) + 2x^(2 + 1/3)

x^(5/6) + 2x^(7/3)

Answer:

Step-by-step explanation:

answer= 1

5 x 2 - 3^2

1. First simplify exponents

= that is nine

2. Then Do 5 x 2- 9

5 x 2=10

10-9

= 1