A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles. (4 points)
Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.
show all work
insert picture of the tree diagram pls

The cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add  [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from  [tex]C_{i}[/tex]-1 to  [tex]c_{n}+1[/tex] and from  [tex]c_{n}+1[/tex] to  [tex]C_{i}[/tex]. Place  [tex]c_{n}+1[/tex] between  [tex]C_{i}[/tex]−1 and  [tex]C_{i}[/tex] to get the desired path.

Mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n. By generalizing this in form of a principle which we would use to prove any mathematical statement is 'Principle of Mathematical Induction'.

The question says that between any two cities X and Y, either there’s an

one-way road from X to Y or from Y to X, but not both. Then show that

there is a path from some city A which visits all the cities exactly once.

This problem is very similar to the Football league problem #7 in Homework 1. This problem can be modeled as a directed graph in which cities

are represented as vertices and there’s an edge from vertices X to Y if

there’s a road from cities X to Y. And then, our goal is to find a path

in this graph which visits every vertex in the graph.

The rest of the solution is very similar to the argument in Problem 7 of

homework 1. We use induction of number of cities, say n.

As a base case, if n = 2, there are only two cities X and Y and the path

is simply the edge between X and Y.

For induction hypothesis, assume that the statement is true for any set

of n cities. That is’ for any set of n cities, we can find a path which visits

all the cities exactly once.

Let’s prove the statement for n + 1 cities. Leave out n + 1 th city (say,

[tex]c_{n}+1[/tex]) and for the remaining n cities, by induction hypothesis, we can find a path which visits all these n cities exactly once. Let us label the cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add  [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from  [tex]C_{i}[/tex]-1 to  [tex]c_{n}+1[/tex] and from  [tex]c_{n}+1[/tex] to  [tex]C_{i}[/tex]. Place  [tex]c_{n}+1[/tex] between  [tex]C_{i}[/tex]−1 and  [tex]C_{i}[/tex] to get the desired path.

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Using linear function concepts, it is found that the volume of each marble is of 0.05 liters.

A linear function is modeled by:

y = mx + b

In which:

The linear function that gives the volume of water, when n marbles are inserted into the tank, is given by:

w = 32 - 0.05n

The slope of -0.05 means that for each marble inserted, there are 0.05 liters less for water, hence the volume of each marble is of 0.05 liters.

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Answer:

.05 liters

Step-by-step explanation:

Answer:

[tex]T_{23}=-153[/tex]

Step-by-step explanation:

[tex]T_{23}=a+(n-1)d\\[/tex]

[tex]=a+(23-1)d=a+22d[/tex]

Now [tex]a=-21[/tex] and

[tex]d=-27-(-21)\\=-6[/tex]

So [tex]T_{23}==21+((22)6\times-1)[/tex]

[tex]=-153[/tex]

Answer:

B. [tex]2^{-14}*5^{10}[/tex].

Step-by-step explanation:

Use the power of a power property.

[tex](2^{-7}*5^{5} )^{2}[/tex]

Multiply all the exponents in the parenthesis by 2.

[tex](2^{-7}*5^{5} )^{2}=(2^{-14}*5^{10} )[/tex]

The answer is B. [tex]2^{-14}*5^{10}[/tex].

Hope this helps!

Answer:

this graph has an x-intercept values of -1 and 2

Answer:

Answer:The chocolate are 0.0042 lighter than the stated on the label

For the males' data, we can logically deduce the following data elements:

Mathematically, the male IQR can be calculated by using this formula:

IQR = Q₃ - Q₁

IQR = 14 - 2

Male IQR = 12.

Next, we would find the difference between the median values:

Note: The median of male's data is equal to 10 while median of female's data is equal to 18.

Difference, d = 18 - 10

Difference, d = 8.

The male's data has an outlier probably due to sampling technique used while the female's data doesn't have an outlier. Thus, the median would be a better measure of center for the male's data and the mean being a better measure of center for the female's data.

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Answer: s

Step-by-step explanation:

Answer:

option D

Step-by-step explanation:

[tex]\sf 5\dfrac{3}{6}=\dfrac{33}{6}\\\\2\dfrac{1}{3}=\dfrac{7}{3}[/tex]

LCM of  6 , 3 = 6

[tex]\sf \dfrac{33}{6}-\dfrac{7}{3}=\dfrac{33}{6}-\dfrac{7*2}{3*2}\\[/tex]

           [tex]\sf =\dfrac{33}{6}-\dfrac{14}{6}\\\\=\dfrac{33-14}{6}\\\\= \dfrac{19*3}{6*3=\dfrac{57}{18}}\\\\=3\dfrac{3}{18}[/tex]

The extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.

In the question, we are given a graph showing the bird population of a large lake and are asked the reason for the extreme drop between November and December most likely represent.

Birds migrate in order to shift from low-resource regions to high-resource areas or vice versa. The two main items sought after are food and places to build nests.

Thus, the fall in the graph for the number of birds between November and December represents the migration pattern of birds, in search of new resources.

Hence, the extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.

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Answer: A reflection of the migratory nature of the birds at the lake.

Answer:

the 50th percentile = 66

The 25th percentile = 35

The 75th percentile = 85

Step-by-step explanation:

 We have 11 numbers ,so we are dealing with an odd set of values.

Also ,we notice that the numbers are already in order.

then

the 50th percentile of the set  27, 34, 35, 48, 48, 66, 75, 85, 85, 96, 99

is the 6 number in the list [ 6 = (11+1)/2 ]

Which is 66.

The 25th percentile (the median) of the set 27, 34, 35, 48, 48

is the 3rd number [ 3 = (5+1/)2 ]

Which is 35.

The 75th percentile (the median) of the set 75, 85, 85, 96, 99

is the 3rd number [ 3 = (5+1/)2 ]

Which is 85.

Answer: 14.353 or 18.647

Step-by-step explanation:

Hi.

Subtracting:

16.5 - 2.147 = 14.353

Adding:

16.5 + 2.147 = 18.647

Answer:

[tex]\{x=\frac{19-\sqrt{409} }{2}\ , \ x=\frac{19+\sqrt{409} }{2}\}[/tex]

Step-by-step explanation:

x² = 19x + 12

⇔ x² - 19x - 12 = 0

Calculating the discriminant :

b² - 4ac = (-19)² - 4×1×(-12) = 409

The discriminant is positive ,then the equation has two solutions.

[tex]x=\frac{19-\sqrt{409} }{2} \ \ or\ \ x=\frac{19+\sqrt{409} }{2}[/tex]

Answer:

C. Radius or diameter must be known.

Step-by-step explanation:

The radius or diameter must be known so you can use the formula.

Hope this helps!

The bag that has more fruits is the second bag, because the ratio is greater.

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

Number of fruits in the first bag : (3/8) x 60 = 22.50

Number of fruits in the second bag :(7/17) x 60 = 24.71

Here is the complete question:

Tamika has two bags of trail mix. Each has a combination of 60 pieces of fruit and nuts. Ratio of fruit to nuts in the first bag:3 5 Ratio of fruit to nuts in the second bag:7 10 Which bag has more fruit? Use the ratios to justify your answer. The first bag, because the ratio is greater. The first bag, because the ratio is smaller. The second bag, because the ratio is greater. The second bag, because the ratio is smaller.

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The probability of rolling an odd number is 9/19.

According to the statement

Total number of possible outcomes = 38

Odd numbered of outcomes = 18

Now we find the probability

Probability = possible outcomes / total outcomes

Probability = 18/38

Probability = 9/19

So, The probability of rolling an odd number is 9/19.

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The value of the probability P(A and B) is 0.12

The given parameters are

P(A) = 0.40

P(B) = 0.30

Given that the events are independent events;, we have:

P(A and B) = P(A) * P(B)

So, we have:

P(A and B) = 0.40 * 0.30

Evaluate

P(A and B) = 0.12

Hence, the value of the probability P(A and B) is 0.12

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In the right angled triangle ACD shown with isosceles triangle ABC and ADC, AB = AC = AD

An equation is an expression that shows the relationship between two or more numbers and variables.

A triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, equilateral and scalene.

In the diagram shown:

AB = AC = AD

In the right angled triangle ACD shown with isosceles triangle ABC and ADC, AB = AC = AD

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The value of X is 2/3 and -3/2.

According to the statement

we have given equation is 6x^2+5x-6 =0

and we have to find x by the factorization.

Factorization defines the the operation of resolving a quantity into factors.

So, by factorization method the equation is written as

6x^2+5x-6 =0

After forming factors the equation becomes

6x^2+9x-4x-6 =0

3x(2x+3) -2(2x+3) =0

By taking common

(3x-2) (2x+3) = 0

Now equate values equal to 0. and after that the output will get in the form of value of X.

Here the value of x is 2/3 and -3/2

So, the value of X is 2/3 and -3/2.

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The probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15

For given question,

A research center poll showed that 85 percent of people believe that it is morally wrong to not report all income on tax returns.

so, the probability that someone have this belief is P = 0.85

We know that in probability,

p = 1 - q

where;

p is probability of success

q is probability of failure.

Thus the probability that someone does not have this​ belief would be,

= 1 - P

= 1 - 0.85

= 0.15

Therefore, the probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15

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The solution set of the inequality is x ≤ - 4. The graph of inequality is shown below and the points x = - 4, x = - 12, x = - 42 are part of the solution set.

In this question we must use algebraic axioms and theorems to solve an inequality and graph the solution set with the help of a graphing tool. Now we proceed to present the procedure to solve for x:

7 - 2 · x ≥ 15

7 - 15 ≥ 2 · x

2 · x ≤ - 8

x ≤ - 4

Now we present the graph of the inequality. The points x = - 4, x = - 12, x = - 42 are part of the solution set.

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Answer:

6

Step-by-step explanation:

[tex]\frac{y}{2} =x^{2} -7[/tex]

[tex]\frac{a}{2} =2^{2} -7[/tex]

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

[tex]a=-6[/tex]

[tex]\frac{b}{2} =1^{2} -7[/tex]

[tex]\frac{b}{2} =-6[/tex]

[tex]b=-12[/tex]

From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.

[tex]-6=2m+b[/tex]        

[tex]-12=m+b[/tex]

[tex]-24=2m+2b[/tex]

[tex]18=-b[/tex]

[tex]b=-18[/tex]

[tex]-12=m-18[/tex]

[tex]m=6[/tex]

Therefore, the slope of line l is 6.

Answer:

slope = 6

Step-by-step explanation:

substitute the given points into the equation of the curve to find a and b

(2, a )

[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )

a = - 6

then point (2, a ) = (2, - 6 )

(1, b )

[tex]\frac{b}{2}[/tex] = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )

b = - 12

then point (1, b ) = (1, - 12 )

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )

m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6

Answer:

1.11

Step-by-step explanation:

The value of the directrix is -5/4.

According to the statement

we have given that the equation of parabola is y2 = 5x. And we have to find that the which equation represents the directrix.

We know that the general equation of parabola is

(y - k)2 = 4a(x - h)  -(1)

and given parabola equation is

y2 = 5x.  -(2)

After comparing the both equations we get k=0 and h=0

And the formula to find the directrix is

x = h - a

Substitute the values of h and a in it then

x = 0-5/4

x = -5/4.

Here the directrix is -5/4.

So, The value of the directrix is -5/4.

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The inference that can be made from the dot plot is the range of each round is the same.

A dot plot is a graph that shows the frequency of a number using dots. The greater the number of dots above a number, the greater its frequency.

Range is the difference between the largest number and smallest number.

Range of round 1 = 8 - 5 = 3

Range of round 2 = 9 - 6 = 3

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The perimeter of the mat is 4m and the area of the mat is [tex]m^{2}[/tex].

The complete length of a square's boundary is referred to as its perimeter. To get the perimeter of a square, we must add all of its sides.

Perimeter of square = sum of the length  of all 4 sides.

In the question side of the mat is m.

Perimeter of the mat = m + m + m + m

                                   = 4m.

Therefore, the perimeter of the mat is 4m.
What is the area of the square?

The total number of unit squares in a square's shape is used to calculate its area.

Area = (Side x Side)

Since, side of the mat is m.

Area of the mat = m x m

                           = [tex]m^{2}[/tex]

Therefore, the area of the mat is [tex]m^{2}[/tex].

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Answer:

52 degrees

Step-by-step explanation:

Really easy, i learned it this summer

1. 180-128=52

2. 3=52 cus  alternate interior angles

The true statements are:

If two planes are said to have intersect each other, the intersection will be regarded as a line.

Hence, looking at the image attached, you will see that Points C, D, and A are noncollinear and the line containing points F and G is on plane R.

Note that when a line and a plane are said to intersect each other , the intersection will be a single point, or say a line. So Points A, B, and D are on both planes.

Therefore, option 1, 2, 4 and 5 are correct.

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Answer: option 1 , 2 , 4 , 5

Step-by-step explanation: edge 2022

Mike brought $15 and Hallie brought $45 to the movie

There are many ways to define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

The value of the variable that makes the equation a true statement is the solution to the equation.

We have to find how much money Mike and Hallie brought to the movie.

Let the money Brought by Mike be $ m and by Hallie be $ h.

Mike and hallie are going to a movie. together they bring $60 in cash

m + h = $ 60.............(1)

Hallie brings three times as much cash as mike does

h = 3 m.......... (2)

Pur the value of h from equation (2) in equation (1)

m + 3 m = $ 60

4 m = $ 60

m = $ 60/4

m = $ 15

put this value of m in equation (2)

h = 3(15)

h = $ 45

Hence we created a system of equations that models the information given in this problem and Mike brought $15 and Hallie brought $45 to the movie

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Answer: A.  2x + 30 = 90

Step-by-step explanation:

You want to choose answer A because you know that together the section of 2x and the section of 30 equal 90 degrees (we know this because the other side shows the right angle which equals 90 degrees).

The equation 2x + 30 = 90 will be used to determine x so option (A) will be correct.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.

Given an angle with two participants, one is 2x and another one is 30°.

Now if we look right-hand side angle it is a right-angle i.e. 90°.

Since the complete angle above a straight line is 180°

So,

2x + 30 + 90° = 180°

2x + 30 = 90

Hence "The equation 2x + 30 = 90 will be used to determine x".

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