suppose the integers from 1 to 25 are arranged in consecutive order. How many different pairs of integers may be selected if there are at least four integers between the selected integers?

The expected value of the game in which 5 dice (6-sided) are rolled simultaneously is -0.2094.

Supposing that the considered random variable is discrete, we get:

Mean =  [tex]E(X) =[/tex] [tex]\sum_{\forall x_i} f(x_i)x_i[/tex]

Here,   [tex]x_i; \: \: i = 1,2, ... ,[/tex] n is its n data values and [tex]f(x_i)[/tex]is the probability of  [tex]X = x_i[/tex]

Suppose you play a game in which 5 dice (6-sided) are rolled simultaneously.

Let Y is the amount of money player won. The value of X can be,

[tex]Y=2,4,6,8,1000,-5[/tex]

Binomial distributions consists of n independent Bernoulli trials. Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

The expected value and variance of X are:

[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]

Put the values as 5 trials for each time 4 appears.

[tex]P(X =0) = \: ^5C_1(\dfrac{1}{6})^0(1-\dfrac{1}{6})^{5-0}=0.4018 \:\\P(X =1) = \: ^5C_1(\dfrac{1}{6})^1(1-\dfrac{1}{6})^{5-1}=0.402\\P(X =2) = \: ^5C_2(\dfrac{1}{6})^2(1-\dfrac{1}{6})^{5-2}=0.162\\P(X =3) = \: ^5C_3(\dfrac{1}{6})^3(1-\dfrac{1}{6})^{5-3}=0.032\\P(X =4) = \: ^5C_4(\dfrac{1}{6})^4(1-\dfrac{1}{6})^{5-4}=0.0032\\P(X =5) = \: ^5C_5(\dfrac{1}{6})^5(1-\dfrac{1}{6})^{5-5}=0.00013\\[/tex]

The probability of loosing $5 equal probability of 0 success.

[tex]P(Y=-5)=P(x=0)[/tex]

Similarly, for probability of getting profit are,

[tex]P(Y=2)=P(x=1)\\P(Y=4)=P(x=2)\\P(Y=6)=P(x=3)\\P(Y=8)=P(x=4)\\P(Y=1000)=P(x=5)[/tex]

Expected value of game,

[tex]E(Y)=\sum y .P(Y=y)\\E(Y)=-5.P(X=0)+2.P(X=1)+4.P(X=2)+6.P(X=3)+8.P(X=4)+1000.P(X=5)\\E(Y)=-0.2094[/tex]

Thus, the expected value of the game in which 5 dice (6-sided) are rolled simultaneously is -0.2094.

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Answer:

The height of the building is about 553.4 feet.

Step-by-step explanation:

tan (3°) = h/2

h = 2 tan (3°) = .10481 miles = 553.4 feet

Using the box plot, it is found that:

It is a plot that focuses the interquartile range of the population, that is, it gives:

In this problem, the box plot starts at 5, hence the least amount of snowfall in any of the cities was of 5 inches.

The data was most concentraded in the third quarter, betwen 35 and 40, as it is the smallest quarter in the graph.

The data was most spread out in the second quarter, betwen 13 and 35, as it is the greater quarter in the graph.

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Answer:

a) 5

b) 35 - 40 this is the smallest part in the purple bar

c) 13 - 35, this is the biggest part of the purple bar

Step-by-step explanation:

(this is off my test!)

By looking at the plot, you can see where everything is, and since it asks how you know, there you go.

Answer:

It always happens because you asked the question

Step-by-step explanation:

[tex]~~~~10x+7\geq 67\\\\\implies 10x \geq 67 -7\\\\\implies 10x \geq 60\\\\\implies x \geq \dfrac{60}{10}\\\\\implies x \geq 6[/tex]

Answer:

x = 165, y = 15

Step-by-step explanation:

1. Well, what does supplementary mean? - The angles add up to 180°.

2. Let's form an equation: x + y = 180°

3. Let's say x is the larger angle and y is the smaller angle.

4. Let's form another equation: x = 150 + y

5. Put the two equations next to each other:

x + y = 180

x = 150 + y

6. We know what x is equaled to, so let's plug it into the first equation!

150 + y + y = 180

150 + 2y = 180

-150           -150

2y = 30

y = 15

7. Now, we know what y is, let's find x!

x + 15 = 180

   -15     -15

x = 165

The measure of both angles are  15 degrees and 165 degrees.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle

Given that the two angles are supplementary.

we know that supplementary angles are the angles whose sum is added to 180 degrees.

Let the smaller angle is x.

The larger angle is 150∘ larger than the smaller angle.

y=x+150

Now add both the angles which makes 180 degrees

x+x+150=180

2x+150=180

Subtract 150 on both sides

2x=30

Divide both sides by 2

x=15

So the smaller angle is 15 and the larger angle is 165 degrees

Hence,  the measure of both angles are  15 degrees and 165 degrees.

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Answer:  [tex]E \ge 31[/tex]

Reason:

"at least 31 points" means "31 or more".

So either E = 31 or E > 31 (meaning Embiid scored 31 points or he scored more than 31 points).

Choice A looks like the closest match assuming the inequality sign is [tex]\ge[/tex]

Saying E > 31 instead of [tex]E \ge 31[/tex] would be false because it leaves out the case E = 31.

Answer:

$428

Step-by-step explanation:

you can do 72*24= the 2 year period and then you get 1728

you then do 1728-1300 and you will get $428 more

I'm not sure for my awnser but I thing 30

Answer:

Stay after school more often with your math teacher or come early to school to practice math or to see what your stuggling at.

Answer:

the answer is in the picture

Answer:

sure I'll help u with this as this question required to have a and asuch a being used to review with an associate with you in the comment of the item that you used in the comment is the only one that was a good one to review the product and details about the refund

Answer:The answer to this oroblem would be -7

Step-by-step explanation:We can see this by when f(x) is 0 right next to it is -7

The value of the other solution for f(x)=0 is -7. This is obtained by taking the general form of the quadratic equation f(x)=y.

In the table, x values range from -8 to 1

So, we can write using the general form f(x)=y for these values

For x=-8, f(-8)=-2.75

x=-7, f(-7)=0

x=-6, f(-6)=2.25

x=-5, f(-5)=4

x=-4, f(-4)=5.25

x=-3, f(-3)=6

x=-2, f(-2)=6.25

x=-1, f(-1)=6

x=0, f(0)=5.25

x=1, f(1)=4

And 3 is one of the solution to f(x)=0.

It is given that f(x)=0 when x=3

Thus,

f(3)=0

From the table,

f(-7)=0

So, the other solution for the function f(x)=0 is -7.

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Answer:

139

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

First of all substitute the values to where ever you see their corresponding variables to make them multiply.

x = 9

y = 3

z = 2

so we get

8x as 8(9),

7z as 7(2)

2y as 2(3)

then the it's will be

8(9) - 7(2) + 2(3)

which is

72 - 14 + 6

finally we get

64

Answer:

The greatest prime number less than 50 is 47

Answer:

A = $2,779.16

Step-by-step explanation:

A = $2,779.16

A = P + I where

P (principal) = $1,778.00

I (interest) = $1,001.16

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 1,778.00(1 + 0.03/2)^(2)(15)

A = 1,778.00(1 + 0.015)^(30)

A = $2,779.16

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $1,778.00 at a rate of 3% per year compounded 2 times per year over 15 years is $2,779.16.

Answer:

b = 10 mm

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex]bh ( b is the base and h the height )

given A = 30 and h = 6 , then

[tex]\frac{1}{2}[/tex]b × 6 = 30 , that is

3b = 30 ( divide both sides by 3 )

b = 10

Answer:

tanB =40/9

Step-by-step explanation:

tan B = opposite/adjacent

where the opposite is 40 and the adjacent is 9

therefore, tanB =40/9

box one
box three
box four

box two is incorrect because 0.80/100 x 400 is 3.2
and we are looking for the common denominator of 320 :)

how do i know the common denominator is 320? it's is 80% of 400!

i hope this helps

Answer:

first box, second box and third box.

Step-by-step explanation:

This is because they shared the same answer which is 320.

hope it helps =)

The worth of the boat of Maya which goes for 15% deprication this year at the end of the first year of purchase, with the considered purchase price, is $15,589

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Deprecated price = Initial price- amount of deprication

We have:

Initial price = $18,340

And the amount of deprication = 15% of $18,340

= [tex]\dfrac{18340}{100} \times 15 = 2751 \: \rm dollars[/tex]

(as deprication on first year was by 15% of the original price, and we want to know the deprication for the first year only)

Thus, we get:

Depricated price of Maya's boat = $18,340 - $2,751 = $15,589

Thus, the worth of the boat of Maya which goes for 15% deprication this year at the end of the first year of purchase, with the considered purchase price, is $15,589

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Answer:

The median is 45

Step-by-step explanation:

The median is also referred to as "the middle" value, so you want to take all the values in order and find the middle number. that will be the median. It's the same either box plots.

A quicker way to find it with box plot is to look at the line inside the of the box (line is not always in center of box) on the plot. that is where you'll find the median on questions like these.

hope this helps! :)

Answer:

Step-by-step explanation:

To solve this inequality, you have to isolate the term of x from one side of the equation.

-9<x-4<9

First, add by 4 from both sides.

x-4+4>-9+4

Solve.

-9+4=-5

Add by 4 from both sides.

x-4+4<9+4

Solve.

Add the numbers from left to right.

9+4=13

x<13

I hope this helps. Let me know if you have any questions.

Answer:

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean

Step-by-step explanation:

i dont know if i am correct tho, please like if i am correct

Answer:

1.5x1.5t=9

Step-by-step explanation:

because i am learning this topic

Answer:

D

Step-by-step explanation:

We want to find the values of x such that:

[tex]\displaystyle -x^2 + 7x + 5 = 0[/tex]

We can use the quadratic formula. Recall that:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = -1, b = 7, and c = 5. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} x & = \frac{-(7)\pm\sqrt{(7)^2-4(-1)(5)}}{2(-1)}\\ \\ & = \frac{-7\pm\sqrt{49+20}}{-2} \\ \\ & = \frac{-7\pm\sqrt{69}}{-2}\end{aligned}[/tex]

In conclusion, the answer is D.