Alicia walked 3 m east and then 6 m north. How far is she from the starting point?

The game is profitable since the payout is always less than what you earn.

Given that a fair game with 4 or more outcomes using a binomial situation presented in this lesson (simulated with a spinner or random number) and adjust the point values the  so cost of the 10 points will make the game profitable.

Let's discuss the Lucky 7 game

The game is played with the two fair dice rolls.

You put your money on either of 3 things: Above 7, Lucky 7 or below 7

The game below is designed in Excel:

Each cell formula to generate the game:

They are 36 possible outcomes.

7 is the most likely number coming up

6/36=1/6

of the time.

Thus the expected value of the bet is:

(5/12)x₂+(5/12)x₂+(1/6)x₃=26/12

Which, of course, can not make any sense. so, the good idea from the standpoint of the bank is to pay two times on only one of the two possibilities, not a seven, and to give the bet back on the 7. This then gives:

(5/12)x₂+(5/12)x₀+(1/6)x₁=12/12=1

Which is a perfectly fair game.

Of course, the bank wouldn't approve either, so we probably need more restrictions. The way 7 comes out is: 2 ways for each case, (1,5), (2,5), (3,4), then a constraint like not to pay on (5,1) would be added.

Then the 7 returns the money

4/36 = 1/9.

The new case then yields:

(5/12)x₂+(5/12)x₀+(1/9)x₁=34/36=17/18

This says that for every $18 handled in bets the bank expects to pay out $17.

Hence we can say that the game is profitable since the payout is always less than what you earn.

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Answer:

Step-by-step explanation:

255 people

Answer:

Vertex: (-2, 0)

Axis of symmetry: x = -2

Direction of opening: Upwards

Min: 0

Y-intercept: 4

Step-by-step explanation:

    Let us graph this line, and then pull out the details we need. See attached.

    What do all of these different things mean?

Vertex: This is where the graph intercepts the axis of symmetry (x = -2, see below) and is at point (-2, 0) for this graph.

Axis of Symmetry: This is the line that the graph is symmetrical across. The "center" of the graph. Here, it is x = -2.

Direction of Opening: The direction that the graph is going/opening towards. In this case, it is upwards.

Min: The minimum (in this case) value, the lowest y-coordinate. This is 0 here.

Y-intercept: The point at which the line intercepts the y-axis. This is 4 here.

Answer:

Step-by-step explanation:

Hi!

A is congruent to angle C. Because angle FCE is on the other side of the angle C which is equal to A, angle FCE has to equal A

The expressions equivalent to -0.5(1.7+1.7) are -0.5(1.7) - 0.5(1.7)

and 2(-0.5(1.7))

Given the expression below;

-0.5 (1.7 + 1.7)

According to the distributive law;

A(B+C) = AB + AC

Expand

-0.5(1.7) + (-0.5)(1.7)

-0.5(1.7) - 0.5(1.7)

2(-0.5(1.7))

Hence the expressions equivalent to -0.5(1.7+1.7) are -0.5(1.7) - 0.5(1.7)

and 2(-0.5(1.7))

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The number of people who are not Democrats , do not wear glasses, and don not like ice-cream by using sets are 155 people and the number of people who are democrats, not wearing glasses and do not like ice cream are 150 people.

Given total people of 1000 people, 595 democrats, 595 wearing glasses, 550 like ice cream, 395 of them are democrats who wear glasses,350 of them are democrats who like ice cream and 400 of them wear glasses as well as like ice cream ,250 of them are democrats as well as wear glasses and like ice cream.

We have to find the number of people who are not democrats , do not wear glasses ,do not like ice cream and the number of people who do not wear glasses and do not like ice cream.

let X shows the number of democrats and G be number of people who wear glasses and I be the number of people like ice cream.

So,

D=595, G=595 AND I=550

Now D∩G=395

D∩I=350

G∩I=400

so D∩G∩I=250

Formula will be :

D∪G∪I=D+G+I-(D∩G)-(G∩I)-(D∩G)+(D∩G∩I)

=595+595+550-(395+350+400)+250

=845

845 are either democrats or wear glasses as well as like ice cream.

So 1000-845=155

Number of people who are democrats, do not wear glasses and do not like ice cream=D-(D∩G)-(D∩I)+(D∩G∩I)

=595-(395+300)+250

=845-695

=150 people.

Hence the number of people who are not Democrats , do not wear glasses, and don not like ice-cream are 155 people and the number of people who are democrats, not wearing glasses and do not like ice cream are 150 people.

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Answer:

See Below

Step-by-step explanation:

Since they are lines, and if two lines have angles that are congruent, then it has to be perpendicular. Angles sum up to 180, and since they are equal, it is 90.

Using the binomial distribution, we have that:

A. The salesperson should expect 1.54 customers until he finds a customer that makes a purchase.

B. There is a 0.0279 = 2.79% probability that a salesperson helps 3 customers until he finds the first person to make a purchase.

The formula is:

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

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

The parameters are:

The expected number of trials until q successes are found is:

[tex]E(X) = \frac{q}{p}[/tex]

In this problem, the probability of a success is of p = 0.65, hence:

[tex]E(X) = \frac{1}{0.65} = 1.54[/tex]

The salesperson should expect 1.54 customers until he finds a customer that makes a purchase.

The probability is p = 0.65 multiplied by P(X = 0) when n = 3, hence:

0.65 x (0.35)³ = 0.0279.

There is a 0.0279 = 2.79% probability that a salesperson helps 3 customers until he finds the first person to make a purchase.

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The probability that a person will be entertained by either books or TV is 0.55

Express the given percentages as probabilities.

Let the probability of people being entertained by books be represented as

P(A)=0.36

Probability of people entertained by watching TV,

P(B)=0.32

Probability of people entertained by both books and TV,

P(A∩B)=0.13

P(A) + P(B) - P(A and B) is the formula for calculating the either/or probability for overlapping events. This formula is identical to the non-overlapping events, but we need to take the likelihood that the outcomes could occur simultaneously into account.

Thus, the probability of people being entertained by either books or TV is,

P(AUB)=P(A)+P(B)-P(A∩B)

           =0.36+0.32-0.13

           =0.68-0.13

          =0.55          

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Answer:

375

Step-by-step explanation:

Since they started at the same point and went in opposite directions, add the 2 distances.

162.5 + 212.5 = 375

a. x = 120°

b. x = 88°

c. x = 146°

Determining the value of x

A. We have that x and angle 80° as shown in the diagram is on a straight

Angles on a straight line = 180°

Then,

x + 80° = 180°

Make 'x' subject

x = 180° -  80°

x = 100°

B. From the diagram, we can see that 'x' at ∠BCD is alternate to ∠EDC which is 88°

It is important to note that alternate angles are equal

Then,

x =  88°

C. From the diagram, we can see that 'x' at CDE is on a straight line with ABC

Angles on a straight line are equal

Then,

x + 34° = 180°

Make 'x' subject of formula

x = 180° - 34°

x = 146°

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The total interest for 4 years with a principal amount of $500 and a rate of 2% is $40.

The formula for the simple interest is,

I = PTR

where

I is the interest, P is the principal amount, T is the period, and R is the rate of interest.

The given data is,

Kaitlin wants to save $500 in her savings account. I.e., P = $500

For 4 years i.e., T = 4 years and the rate R = 2%  i.e., R = 0.02

Then,

the total interest for 4 years with no more deposits is

I = PTR

 = $500 × 4 × 0.02

 = $40

Therefore, the total interest that Kaitlin will earn for 4 years is $40.

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Answer:

-4

Step-by-step explanation:

Hence, the area of base is [tex]x^2 - 2x - 9[/tex]

Division in maths is breaking a number into equal parts and finding out how many equal parts can be made.

The volume of a rectangular prism is,

        Volume = Area x Height

Substituting the given expressions,

[tex]x^3 + 2x^2 - 17x - 36 = Area x (x + 4)[/tex]

Area = [tex](x^3 + 2x^2 - 17x - 36) / (x + 4)[/tex]

Now, let's use synthetic division,

-4 |    1    2    -17   -36

----    __-4___8___36

        1    -2     -9     0

The expression for the area is [tex]x^2 - 2x - 9[/tex]

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The system of inequalities represents the number of color copies, x, and grayscale copies, y, that julissa can print to meet her goal is;

x + y ≥ 8

x + y ≥ 84x + 2y ≤ 25

let

x + y ≥ 8

4x + 2y ≤ 25

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The value of y if the perimeter of the figure is 5y is 15meters.

The perimeter of a polygon is the sum of the length of the whole sides.

Therefore,

perimeter = y + 2y + 30

perimeter = 5y

Hence,

5y = 3y + 30

5y - 3y = 30

2y = 30

divide both sides by 2

2y / 2 = 30 / 2

y = 15

Therefore, the value of y is 15m.

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The probability of not winning of united is [tex]\frac{2}{5}[/tex] .

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given that the probability of winning of united is [tex]P(A)=\frac{3}{5}[/tex] .

Usually, we take the total probability is 1

So, the probability of not winning of united is [tex]1-\frac{3}{5}[/tex]

                                                                        [tex]=\frac{5-3}{5}\\=\frac{2}{5}[/tex]

Therefore, the probability of not winning of united is [tex]\frac{2}{5}[/tex] .

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The final amount of the compound interest after 6 years would be $ 294, 122, 500

The formula for the final amount is given as;

[tex]A = P( 1 + \frac{r}{n}) ^n^t[/tex]

Where

A = final amount

P = principal interest

r = interest rate

n = number of times

t = time of periods

We have,

A = [tex]2500[/tex] [tex]( 1 + \frac{6}{1}) ^1^*^6[/tex]

A = [tex]2500 ( 7)^6[/tex]

A = [tex]2500[/tex] × [tex]117, 649[/tex]

A =$ [tex]294, 122, 500[/tex]

Thus, the final amount of the compound interest after 6 years would be $ 294, 122, 500

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Answer:

OC

Step-by-step explanation:

4×3=12m

5+1=6n

4÷1=4

The Pythagorean theorem is [tex]a^2+b^2=c^2[/tex], where a and b are two legs of a right triangle and c is the hypotenuse (the longest side).

We're given a triangle with the following:

We can plug these values into the Pythagorean theorem as a, b and c:

[tex]a^2+b^2=c^2\\2^2+b^2=6^2[/tex]

Now, isolate b:

[tex]b^2=6^2-2^2\\b=\sqrt{6^2-2^2}\\b=\sqrt{36-4}\\b=\sqrt{32}[/tex]

[tex]b=\sqrt{32}[/tex]

[tex]\huge\boxed{10}[/tex]

[tex]\sqrt{100}[/tex] means that you are looking for the number that, when multiplied by itself, produces [tex]100[/tex]. That number is [tex]10[/tex], because [tex]10\cdot10=100[/tex], meaning that [tex]\sqrt{100}=10[/tex].

The largest possible volume of the box is x²y

It is important to note that the given figure is a rectangle

Area of the box is given as 100 square feet

Formula for volume of a rectangle

Volume = length × width × height

Length = x

Width = x

Height = y

Substitute the values in the formula

We have;

Volume = x × x × y

Volume = x²y

Thus, the largest possible volume of the box is x²y

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Answer:

the Slope: 11

the y-intercept: (0, - 8) x        y

                                     0       -8

                                     1         3

Step-by-step explanation:

Answer:

[tex]y=\frac{11}{8}x+\frac{1}{2}[/tex]

It will take the company 20.3 years to have a financial worth of $11.4

The estimate of profit is given as;

Profit = $0.6 million per year

This means that the engineers based their estimate per year

Hence, the unit of time is year

To do this, we make use of any variable of our choice.

In this case, we let x represents the variable of the amount of time.

In (a), we have:

Profit = $0.6 million per year

So, the expected financial status is 0.6x

This is the amount taken as loan by the engineers.

So, the financial status at the beginning is 1.8

Using the expressions above, we have the yearly worth to be:

y = 0.6x - 1.8

When the financial status is $11.4 million, we have:

0.6x - 1.8 = 11.4

Evaluate the like terms

0.6x = 12.2

Divide both sides by 0.6

x = 20.3

Hence, it will take the company 20.3 years to have a financial worth of $11.4

See attachment for the graph of y = 0.6x - 1.8

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You can by 42 combinations of items from the store

The given parameters are:

Envelop = 7

Stamp = 6

The number of combination is:

Combination = Envelop * Stamp

So, we have:

Combination = 7 * 6

Evaluate

Combination = 42

Hence, you can by 42 combinations of items from the store

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Answer:

QR=17

Step-by-step explanation:

[tex](12)(x-2)=(3)(3x-1)\\12x-24=9x-3\\3x-24=-3\\3x=21\\x=7[/tex]                

 [tex]x=7\\\\QR=12+x-2\\=12+(7)-2\\QR=17[/tex]

Answer:

dan is 24

I had to redo this one

The age of Margo and Dan will be 32 years and 24 years, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Margo is 8 years older than her brother Dan. The sum of their ages is 56.

Let M be the age of Margo and D be the age of Dan. Then the equations are written as,

M = D + 8               ...1

M + D = 56            ...2

From equations 1 and 2, then we have

D + 8 + D = 56

2D + 8 = 56

2D = 56 - 8

2D = 48

D = 48 / 2

D = 24 years

Then the age of Margo will be given as,

M + 24 = 56

M = 56 - 24

M = 32 years

The age of Margo and Dan will be 32 years and 24 years, respectively.

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Answer:

y + 1/2 = 3(x - 2)

Step-by-step explanation:

We have to think about this question in point-slope form, which is a form that explicitly gives us the slope of the line and a single point that it passes through. Point-slope form looks like this: y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point that the line goes through. We are given that the line goes through (2, -1/2) which means x1 = 2 and y1 = (-1/2). We are also given that the slope is 3. We can plug these quantities into the equation to solve:

y - (-1/2) = 3(x - 2) OR y + 1/2 = 3(x - 2)

The equation of the line is y + 1/2 = 3(x - 2).

The correct option is (3).

The slope of a line indicates its direction and steepness. Finding the slope of lines in a coordinate plane can help predict whether the lines are parallel, perpendicular, or have no relationship at all without actually using a compass.

As per the given data:

We have to find out the equation of the line that passes through (2, -1/2) and has a slope of 3.

As we know a point at the slope of the line, we can use the point slope form:

[tex]y - y_1 = m(x-x_1)[/tex] , where m is the slope and [tex](x_1, y_1)[/tex] is the point through which the line passes.

y - (-1/2) = 3(x - 2)

y + 1/2 = 3(x - 2)

The equation of the line is y + 1/2 = 3(x - 2).

Hence, The equation of the line is y + 1/2 = 3(x - 2).

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