Two points are chosen randomly and independently from the interval [0, 1] according to a uniform distribution. Show that the expected distance between the two points is 1/3.

Answer: 2

Step-by-step explanation:

3/5 of 30 = 18(AL)

2/6 of 30 = 10 (ML)

18+10 = 28 (AL+ ML)

the remainder

30-28 = 2 (CL)

Answer:

(g o h)(t) = -4t² - 16t + 3

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

g(t) = -4t + 3

h(t) = -t² + 4t

(g o h)(t) = g(h(t))

Step 2: Find

And we have our final answer!

Answer:

There are 16 winning tickets and 64 losing tickets

Step-by-step explanation:

Total no of tickets in a bag = 80

The ratio of winning tickets to losing tickets is 2:8.

Let there are 2x winning tickets and 8x losing tickets.

ATQ,

2x+8x=80

10x=80

x = 8

Winning tickets = 2x = 2(8) = 16

Losing tickets = 8x = 8(8) = 64

Hence, there are 16 winning tickets and 64 losing tickets.

There's probably a more efficient way to do it, but the following method works.

First, note that

x² - x - 2 = (x + 1) (x - 2)

Now use synthetic division to divide

a x⁴ + b x³ - x² + 2x + 3

by the two factors above.

Division by x + 1 :

-1   |   a           b               -1                   2                3

…   |               -a          a - b      -a + b + 1      a - b - 3

= = = = = = = = = = = = = = = = = = = = = = = = = = = = =

…   |   a      b - a     a - b - 1      -a + b + 3           a - b

which is to say,

(a x⁴ + b x³ - x² + 2x + 3) / (x + 1)

= a x³ + (b - a) x² + (a - b - 1) x + (-a + b + 3) + (a - b) / (x + 1)

Division by x - 2 :

2   |    a        b - a           a - b - 1          -a + b + 3

…   |                 2a          2a + 2b       6a + 2b - 2

= = = = = = = = = = = = = = = = = = = = = = = = = = =

…   |    a       a + b        3a + b - 1       5a + 3b + 1

meaning,

(a x³ + (b - a) x² + (a - b - 1) x + (-a + b + 3)) / (x - 2)

= a x² + (a + b) x + (3a + b - 1) + (5a + 3b + 1) / (x - 2)

Putting everything together, we have

(a x⁴ + b x³ - x² + 2x + 3) / (x² - x - 2)

= a x² + (a + b) x + (3a + b - 1) + (5a + 3b + 1) / (x - 2) + (a - b) / (x² - x - 2)

Combine the remainder terms:

(5a + 3b + 1) / (x - 2) + (a - b) / (x² - x - 2)

= ((5a + 3b + 1) x + (6a + 2b + 1)) / (x² - x - 2)

We're given that the remainder is 3x + 5, so

5a + 3b + 1 = 3

6a + 2b + 1 = 5

Solve this system for a and b :

5a + 3b = 2

6a + 2b = 4

5a + 3b = 2

3a + b = 2

5a + 3b = 2

-9a - 3b = -6

(5a + 3b) + (-9a - 3b) = 2 + (-6)

-4a = -4

a = 1

5 • 1 + 3b = 2

3b = -3

b = -1

Answer:

After solving the pair of simultaneous equations we get x=5 and y=1. Solution Set = {5,1}

Step-by-step explanation:

We need to solve the pair of simultaneous equations

[tex]0.6x-4y=-1\\0.8x-3.5y=0.5[/tex]

We can solve using substitution method.

Let:

[tex]0.6x-4y=-1--eq(1)\\0.8x-3.5y=0.5--eq(2)[/tex]

Find value of x from eq(1) and put it in eq(2)

[tex]From \ eq(1):\\0.6x-4y=-1\\0.6x=-1+4y\\x=\frac{-1+4y}{0.6}[/tex]

Putting in equation 2

[tex]0.8x -3.5y =0.5\\0.8(\frac{-1+4y}{0.6})-3.5y=0.5\\1.33(-1+4y)-3.5y=0.5\\-1.33+5.32y-3.5y=0.5\\-1.33+1.82y=0.5\\1.82y=0.5+1.33\\1.82y=1.83\\y=\frac{1.83}{1.82}\\y=1.00[/tex]

So, we get value of y= 1.00

Now finding value of x by putting value of y in eq(1)

[tex]x=\frac{-1+4y}{0.6}\\x= \frac{-1+4(1.00)}{0.6}\\x=\frac{3}{0.6}\\x=5[/tex]

We get value of x = 5

So, After solving the pair of simultaneous equations we get x=5 and y=1. Solution Set = {5,1}

Answer:

x = -4

Step-by-step explanation:

Equation of the Line

It can be written in the slope-intercept form as:

y = mx + b

Where m is the slope of the line and b is the y-intercept.

For horizontal lines, m=0. For slanted lines, m can have any real value.

Vertical lines have an infinite slope and the above equation cannot be used.

Vertical lines have a fixed value for x, thus the equation is:

x = h

If the vertical line goes through the point (-4,1), then its equation is:

x = -4

Answer:

g= 11.5

Step-by-step explanation:

32+3g = 4g+20.5

11.5+3g = 4g

11.5 = 1g

11.5 = g

Answer: -13 x -13 = 169

Step-by-step explanation: you have to multiply -13 two times  and a negative time a negative equals a positive

Answer:

44

Step-by-step explanation:

6 times 3 is 18 so.. 18 minus 69 would be -36 plus 12 is a positive 1 times 14 would be 14 minus 7 would be 7 7 times 27 would 38 plus 7 would be  45 minus one would be 44

Answer:

-186

Step-by-step explanation:

6x3-69+12x4-7(27)+7-1

18-69+48-189+7-1

-51+48-189+7-1

-3-189+7-1

-192+7-1

-185-1

-186

Answer: -26 i think srry if im wrong

Step-by-step explanation:

Answer:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

Step-by-step explanation:

Answer:

654

Step-by-step explanation:

Answer:

$222.08

Step-by-step explanation:

To find the original price, divide 193.21 by 0.87:

193.21/0.87

= 222.08

So, the non-markup price was $222.08

Answer:

4

Step-by-step explanation:

The answer would be D

Answer:

1,2,3

Step-by-step explanation:

you cant let them be equal its an inequality

Answer:

[tex]Probability = 0.30[/tex]

Step-by-step explanation:

Given

Represent Black with B and White with W

[tex]B = 14[/tex]

[tex]W = 6[/tex]

Required

Probability of the second selection being white

This means that: The first selection could be white or black but the second must be white.

This probability would be represented as thus:

[tex]Probability = (P(W)\ and\ P(W))\ or\ (P(B)\ and\ P(W))[/tex]

And it is calculated as:

[tex]Probability = (\frac{n(W)}{Total} * \frac{n(W)-1}{Total - 1}) + (\frac{n(B)}{Total} * \frac{n(W)}{Total - 1})[/tex]

Notice that, the second selection has total -1 has its denominator. This is so because, the first selection was made without replacement

So, the formula becomes

[tex]Probability = (\frac{6}{20} * \frac{6-1}{20- 1}) + (\frac{14}{20} * \frac{6}{20- 1})[/tex]

[tex]Probability = (\frac{6}{20} * \frac{5}{19}) + (\frac{14}{20} * \frac{6}{19})[/tex]

[tex]Probability = \frac{30}{380}+ \frac{84}{380}[/tex]

[tex]Probability = \frac{30 + 84}{380}[/tex]

[tex]Probability = \frac{114}{380}[/tex]

[tex]Probability = 0.30[/tex]

The probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is 0.33.

Given :

The formula given below can be used in order to determine the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball.

[tex]\rm P = \left(\dfrac{n(W)}{Total}\times \dfrac{n(W)-1}{Total-1}\right)+ \left(\dfrac{n(B)}{Total}\times \dfrac{n(W)}{Total-1}\right)[/tex]

Now, substitute the values of known terms in the above formula.

[tex]\rm P = \left(\dfrac{6}{20}\times \dfrac{6-1}{20-1}\right)+ \left(\dfrac{14}{20}\times \dfrac{6}{20-1}\right)[/tex]

Simplify the above expression.

[tex]\rm P = \dfrac{30}{380}+\dfrac{84}{380}[/tex]

[tex]\rm P =\dfrac{114}{380}[/tex]

P = 0.33

So, the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is 0.33.

Therefore, the correct option is a).

For more information, refer to the link given below:

https://brainly.com/question/23044118

Answer:

45

Step-by-step explanation:

Answer:

3x 4x and -5 so

3x+4x-5 is the answer

Answer:

4/5

Step-by-step explanation:

Okay, I'm pretty sure about this one! I might be wrong but:

If the number is prime and LESS than 13 (so it can't be 13 either), it's either 2, 3, 5, 7, or 11. Those are 5 numbers in all, and 4 of those are odd. So the fraction would be 4/5!

I might have done this wrong, but I hope it helps!! Have a nice day c:

Answer:

The correct option is a. 65 to 89.

Step-by-step explanation:

According to the Empirical Rule in a normal distribution with mean µ and standard-deviation σ, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be broken into three parts:

• 68% data falls within 1 standard deviation of the mean. That is P (µ-σ≤X≤ µ+σ) = 0.68.

• 95% data falls within 2 standard deviations of the mean. That is P (µ-2σ≤X≤ µ+2σ) = 0.95.

• 99.7% data falls within 3 standard deviations of the mean. That is P (µ-3σ≤X≤ µ+3σ) = 0.997.

The information provided is:

[tex]\mu=77\\\sigma = 6[/tex]

Use the Empirical rule to compute the middle 95% of the distribution as follows:

[tex]P(\mu-2\sigma\leq X\leq \mu+2\sigma)=0.95\\\\\mu-2\sigma=77-(2\times 6)=65\\\\\mu+2\sigma=77+(2\times 6)=89\\\\\Rightarrow P(65\leq X\leq 89)=0.95[/tex]

Thus, the correct option is a. 65 to 89.

Answer:

2x+9=-17

Step-by-step explanation:

hopefully this helps :)

Answer: I’m not sure what the number is but it’s a negative number, probably somewhere around 26. Take 9 from it and you will get 17.

Step-by-step explanation:

Answer:

one pencil cost  $0.15

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

5.004493

Step-by-step explanation:

Answer:

2.27 kg is about 5 pounds.

Step-by-step explanation:

1 kilogram = 2.2 pounds

So, we have to multiply 2.2 by the amount of kilograms, which in this case, is 2.27.

2.27 x 2.2 = 4.994 or 5 when rounded to the nearest whole number.

Therefore, 2.27 kg = 5 lbs

Hope this helps! :)

Answer:

Answer- 432

Step-by-step explanation:

a= 3

b=4

c=12

(2(12) + (3)(4))12

(24 + 12)12

288 +144 = 432

Answer:

2 goes to a type of ratio that compares two different kinds of quantities or numbers

Step-by-step explanation:

a type of ratio that compares two different kinds of quantities or numbers

Answer:

65 mins

Step-by-step explanation:

I well help anyone because I’m a hero and I well always be one thanks to all of you

Answer:

g= -4 is correct answer

Answer:

6.66666666667

Step-by-step explanation:

Answer: 6.66

Step-by-step explanation: because you have to divide 24/3.6

Answer:

6/10

Step-by-step explanation:

The answer is A

Answer:

b

Step-by-step explanation: