Assume that we have two events, A and B; that are mutually exclusive Assume further that we know P(A) = 0.30 and P(B) = 0.70. If an amount zero, enter "0". What is P(AnB)? What is P(AIB)? student in statistics argues that the concepts of mutually exclusive events and independent events are really the same_ and that if events are mutually exclusive they must be independent; Do You agree with this statement? Use the probability information in this problem to justify your answer. Select your answer because P(AIB) Select your answer P(A). What genera conclusion would You make about mutually exclusive and independent events given the results of this problem?

Answers

Answer 1

P(A∩B) = 0 (the probability of both events occurring is zero).

P(A|B) = 0.

No. The student's argument that mutually exclusive events are independent is incorrect.

How to find P(AnB) and P(AIB) of the event?

If events A and B are mutually exclusive, then by definition they cannot occur at the same time.

Thus, P(A∩B) = 0 (the probability of both events occurring is zero).

Since events A and B are mutually exclusive, they cannot be independent. In fact, if two events are mutually exclusive, it means that the occurrence of one event precludes the occurrence of the other event, so they are completely dependent on each other.

To calculate P(A|B), we can use the formula:

P(A|B) = P(A∩B) / P(B)

Since P(A∩B) = 0 and P(B) = 0.70, we have:

P(A|B) = 0 / 0.70 = 0

This means that if we know event B has occurred (i.e., P(B) > 0), then the probability of event A occurring (i.e., P(A|B)) is zero. Therefore, events A and B are not independent.

The student's argument that mutually exclusive events are independent is incorrect. Mutually exclusive events are by definition dependent events.

In general, the concept of mutually exclusive events and the concept of independent events are not the same. Mutually exclusive events are dependent events, while independent events are events that do not depend on each other.

In this problem, the fact that events A and B are mutually exclusive means that they are dependent events, and this is reflected in the probability calculation for P(A|B), which is zero. Therefore, we can conclude that mutually exclusive events are not independent events.

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Related Questions

Marcus has 19 blueberry muffins that he wants to share equally with his two
friends. How many blueberry muffins will Marcus and his two friends receive?

Answers

Answer: 6 and 1/3

Step-by-step explanation:

Assuming that sweet generous little Marcus here wants some muffins too, he has to share 19 blueberry muffins between 3 people (Marcus + friend 1 + friend 2.)

Most unfortunately, 19 isn't divisible by 3 to create a whole number (ie. a whole muffin).

Therefore you have 2 options:

Option 1:

19/3 = 6.333....

This means that each person will get 6 and 1/3 of a muffin

Option 2:

19/3 = 6 (and 1 remainder)

This means that each person will get 6 muffins each, but there will be a leftover muffin to feed the birds or something.

(I personally prefer option 2, but I think your teacher is looking for option 1.)

The fourth term in an arithmetic sequence is 3 and the tenth term is 18. If the first term is a1, which is an equation for the nth term of this sequence?

Answers

The equation for the nth term of this sequence is an = -4.5 + 2.5(n - 1)

How to determine the equation for the nth term of this sequence?

From the question, we have the following parameters that can be used in our computation:

a4 = 3

a10 = 18

An arithmetic sequence is represented as

an = a + (n - 1)d

Using the above as a guide, we have the following:

a + 3d = 3

a + 9d = 18

Subtract the equations

So, we have

6d = 15

Divide

d = 2.5

So, we have

a + 3 * 2.5 = 3

This gives

a = -4.5

So, the sequence is -4.5 + 2.5(n - 1)

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9. Liam ran 12 miles total over the weekend. He
ran 5.5 miles on Saturday. Which equation can
be used to find m, the number of miles he ran
on Sunday?
A. 12 + 5.5 = m
B. 5.5m= 12
C. m-5.5 = 12
D. 5.5+ m = 12

Answers

Answer:

x=6.5

Step-by-step explanation:

I'm not sure if it's correct

Ted made a nut mixture that contains 52%
peanuts by mixing together 9 kg of mixed
nuts that contain 20% peanuts and 16 kg
of a different brand of mixed nuts. The
second brand of mixed nuts contained
what percent peanuts?

Answers

Let's call the added amount of kg of mixed nuts that contain

40

%

peanuts

m

a

d

d

e

d

. If the new mixture contains

34

%

peanuts, then:

m

peanuts

m

total

=

0.34

The bag of

6

kg

already contained

0.3

6

=

1.8

kg

of peanuts. Furthermore,

40

%

of

m

added

will be peanuts. This means that:

m

peanuts

=

0.4

m

added

+

1.8

The total mass will be the original

6

kg

plus the added mass, so

m

total

=

m

added

+

6

.

This gives us the following equation.

0.4

m

added

+

1.8

m

added

+

6

=

0.34

Multiply both sides with

m

added

+

6

.

0.4

m

added

+

1.8

=

0.34

(

m

added

+

6

)

Multiply out the brackets.

0.4

m

added

+

1.8

=

0.34

m

added

+

2.04

Subtract

0.34

m

added

from both sides.

0.04

m

added

+

1.8

=

2.04

Subtract

1.8

from both sides.

0.06

m

added

=

0.24

Divide both sides by

0.06

.

m

added

=

4

Therefore, Jenny must add

4

kg

.

I NEED HELP ON THIS ASAP!!

Answers

The solution of both inequalities is (-1, 2).

What is Inequality?

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have the inequalities

x+ y >1.........(1)

-x+ y <3.........(2)

The graph for x+ y >1 is shown by the red shaded region.

and, the graph for -x+ y <3  is shown by the blue shaded region.

Also , the Inequality intersect at (-1, 2) which shows the solution of both inequalities.

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A car travels at an average speed of 80 km/h for 2 hours. What distance does the car travel? c) A car travels a distance of 330 km at an average speed of ​

Answers

its 450 just did it on my own test at school

I need help on this please

Answers

The values a and b should be replaced to rewrite the given expression as (x + a)(x - b).

What is a quadratic function?

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

c represents the constant.

Next, we would solve the above quadratic function by using the factorization method;

x² + x - 72 = 0

x² - 8x + 9x - 72 = 0

x(x - 8) + 9(x - 8) = 0

(x + 9)(x - 8) = 0

(x + 9)(x - 8) = (x + a)(x - b).

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The sides of a triangle measure 32 inches, 22 inches, and 19 inches. What is the area of the triangle? Round intermediate results to 3 decimal places and the final answer to 1 decimal place. The area of the triangle is?

Answers

The area of the given triangle is approximately 204.2 square inches.

What is a Triangle?

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

To calculate the area of a triangle with given side lengths, we can use Heron's formula:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle (half of the perimeter), and a, b, and c are the lengths of the sides.

In this case, the lengths of the sides are a=32, b=22, and c=19. Therefore, the semi-perimeter is:

s = (a + b + c) / 2 = (32 + 22 + 19) / 2 = 36.5

Now we can plug in these values into the formula and simplify:

Area = √(36.5(36.5-32)(36.5-22)(36.5-19)) ≈ 204.16

Rounding this to 1 decimal place, the area of the triangle is approximately 204.2 square inches.

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Which statement is true about this equation??
y = 2^x + 4
A.
It represents neither a relation nor a function.
B.
It represents a relation only.
C.
It represents a function only.
D.
It represents both a relation and a function.

Answers

Answer: The correct answer is C. It represents a function only.

A function is a special type of relation where each input value is associated with only one output value. In other words, for every x in the domain of the function, there is only one corresponding y in the range.

In this equation, y = 2^x + 4, for every value of x, there is a unique corresponding value of y. So, it satisfies the requirement of a function and represents a function only.

Step-by-step explanation:

Answer:

D. It represents both a relation and a function

Hope this helps!

Step-by-step explanation:

All functions are relations, but not all relations are functions. The equation given is an Exponential function.

The diameter of a circle is 18 millimeters. What is the circle's circumference?

Answers

Answer:

he circumference of the circle is approximately 56.52 millimeters.

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.

Substituting the given value of the diameter, we get:

C = πd = π(18) = 56.52 mm (rounded to two decimal places)

Therefore, the circumference of the circle is approximately 56.52 millimeters.

If the tire height is 5.2 in. and the rim diameter is 17 in., what is the tire diameter?

Answers

Answer:

Circumference = (3.14)(15) = 47.1 in

Step-by-step explanation:

Assuming the tire is a typical radial tire, the tire diameter can be calculated as follows:

First, convert the rim diameter from inches to centimeters, since tire measurements are typically given in metric units:

17 inches = 43.18 cm

Next, convert the tire height from inches to centimeters:

5.2 inches = 13.21 cm

The tire diameter is then calculated as follows:

Tire diameter = 2 x (tire height) + rim diameter

Tire diameter = 2 x 13.21 cm + 43.18 cm

Tire diameter = 69.6 cm

Therefore, the tire diameter is approximately 69.6 cm.

what function is equivalent to y = 3x(x+2)^2+7?

Answers

The function equivalent to y = [tex]3x(x+2)^2+7[/tex] is [tex]y = 3x^3[/tex]+[tex]12x^2[/tex] + 12x + 7.

Which function is equivalent functionally?

Functionally equivalent refers to when a design, material, practice, method, technique, procedure, or component serves the same purpose and offers the same or better utility as is needed by the rule.

When we add the parenthesis to the expression, we get:

[tex]y = 3x(x^2 + 4x + 4) + 7[/tex]

If we simplify, we get:

[tex]y = 3x^3 + 12x^2 + 12x + 7[/tex]

As a result, y = 3x(x+2)2+7 is identical to y = 3x3 + 12x2 + 12x + 7.

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Please help. what is an equation of the line best fit. This is urgent

Answers

a. The line of the best fit is ŷ = -8.55485X + 118.39451.

b. The value of the correlation coefficient is  -0.8619.

What is the line of best fit?

A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

Sum of X = 117.4

Sum of Y = 298

Mean X = 10.6727

Mean Y = 27.0909

The sum of squares (SSX) = 0.8618

The sum of products (SP) = -7.3727

Regression Equation = ŷ = bX + a

b = SP/SSX = -7.37/0.86 = -8.55485

a = MY - bMX = 27.09 - (-8.55*10.67) = 118.39451

ŷ = -8.55485X + 118.39451

X Values

∑ = 117.4

Mean = 10.673

∑(X - Mx)² = SSx = 0.862

Y Values

∑ = 298

Mean = 27.091

∑(Y - My)² = SSy = 84.909

X and Y Combined

N = 11

∑(X - Mx)(Y - My) = -7.373

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -7.373 / √((0.862)(84.909)) = -0.8619

Therefore, the line of the best fit is ŷ = -8.55485X + 118.39451

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If a vertex of a triangle is (7,-2) and the midpoints of two
sides are (3.5, -0.5) and. (3,1) find the other vertices of
the triangle.

Answers

The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).

What is a triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

Let's call the vertex we know A, and the midpoints of the other two sides B and C, respectively.

Using the midpoint formula, we can find the coordinates of the other two vertices, which are the endpoints of the sides that have B and C as midpoints

Coordinates of B:

x-coordinate: (7 + 3.5)/2 = 5.25

y-coordinate: (-2 - 0.5)/2 = -1.25

So, B is (5.25, -1.25)

Coordinates of C:

x-coordinate: (7 + 3) / 2 = 5

y-coordinate: (-2 + 1)/2 = -0.5

So, C is (5, -0.5)

Therefore, The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).

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Order the following numbers from least to greatest: 3√2 , √3 − 1, √19 + 1, 6,
2√10 ÷ 5 and √14
can anyone help me with this answer please.

Answers

The order from least to greatest would be as follows:

√3 - 1 < 2√10 ÷ 5 < √14 < 3√2 < √19 + 1 < 6

How did we get the value?

To order the numbers, we need to first simplify and evaluate each expression.

1. √3 - 1 = 1.73205080757 - 1 = 0.73205080757

2. 2√10 ÷ 5 = 1.265

3. √14 = 3.74166

4. 3√2 = 4.243

5. √19 + 1 = 5.359

6. 6 is simply 6

Therefore, the correct answer is as given above. It could then be concluded that the order from least to greatest is:

0.73205080757 < 1.265 < 3.74166 < 4.243 < 5.359 < 6

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based on the data in the table, what is the probability that a randomly selected persons favorite restaurant is a deli?

Answer choices
8/25
2/5
1/10
9/50

Answers

The probability that a randomly selected persons favorite restaurant is a deli is 9/50

How to determine the probability

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table, we have

Total = 100

Deli = 18

So, the probability is

P = Deli/Total

Substitute the known values in the above equation, so, we have the following representation

P = 18/100

Simplify

P = 9/50

Hence, the probability is (d) 9/50

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This graph represents the amount of milk in a bottle in the fridge. Tell a story of the amount of milk in the bottle.

Answers

The milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Thus, option (a) is correct.

What is passage?

The term “passage” refers to the explanation and description of a sentence in relation to a topic. The passage aimed to describe those details related to the theme of the story. The different passage is to justify to the different things as to clarify. The passage is to define the important terms.

The milk bottle sat on the central shelf, as mentioned in the passage. The artifact is a completely empty milk bottle. The section gives information regarding signs. The passage was Sig's refrigerator, which had been opened. A milk bottle sat on the middle shelf, its cap missing and no milk inside.

As a result, the milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Therefore, option (a) is correct.

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You want to save up to buy a car. You currently have $500 saved and are going to work this summer cleaning house for your grandma. She will pay you $50 every time you clean her house. Write an equation for this situation. Make sure you define your variables. (How many times will you need to clean her house to have $4,500 for the car you want to buy?
I need answer by 2/25/2023

Answers

80 times, the house should be cleaned to buy the car.

Equation for the amount is y = 50t + 500

What is linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

Given,

Amount in the savings = $500

Amount to get the car = $4500

Grandma pays $50 for every time after cleaning

then, after t times, the amount will be

y = 50 t + 500

here, y is the total amount after working

t is number of times of cleaning the house

For $4500

4500 = 50t + 500

50t = 4500 - 500

50t = 4000

t = 4000/50

t = 80

Hence, we have to clean the house 80 times to have $4500.

equation for the amount is y = 50t + 500

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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answers

Answer:

A. 2 + x = 5

B x + 1 = 4

E -5 + x = -2

Step-by-step explanation:

2 + 3 = 5

3 + 1 + 4

-5 + 3 + -2

if this correct mark me as brainliest please

You start driving west for 3 miles, turn right, and drive north for another 2 miles. At the end of driving, what is your straight line distance from your starting point?

Answers

Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

[tex]L^{2}[/tex]=[tex]3^{2}[/tex]+[tex]2^{2}[/tex]=9+4=13

L=[tex]\sqrt{13}[/tex]

drop-down menu.
An experiment is conducted in which a bead is randomly drawn from a bag, the color is recorded, and then the bead is replaced.
The results of the experiment are given in the table below.
Color
Red
Orange
Yellow
Green
Blue
Purple
Frequency
17
12
10
13
8
5
Which of the following lists would most likely have produced the given experimental results?
Color
List A
List B
Red
33
31
Orange
27
24
Yellow
22
18
Green
30
34
Blue
18
19
Purple
12
5
For the list selected above, what is the theoretical probability of selecting a red bead?
Using the experimental results, if 156 beads are drawn from a bag and returned, which color would have a frequency closest
to 24?

Answers

The theoretical probability of selecting a red bead is 0.28.

What is the probability?

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that,

Color                     Frequency

Red                               17

Orange                         12

Yellow                          10

Green                           9

Blue                              8

Purple                           5

Color                      List A                      List B

Red                           33                            31

Orange                     27                            24

Yellow                       22                           18

Green                        30                           34

Blue                           18                            19

Purple                        12                            5

Probability of selecting a red bead = 17/61

= 0.28

Orange color would have a frequency closest to 24.

Therefore, the theoretical probability of selecting a red bead is 0.28.

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How does the formula for the sample mean differ from the formula for the Population mean?

Answers

The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).

The sample mean is the average value for a set of observations which is derived from a population. While the population mean is the average value for the entire set of observation belonging to a particular study of interest.

The set of observation belonging to a population is denoted by 'N' ; while the sample size is denoted as 'n' :

The mean formula is written thus :

Population mean = Σx / N

Sample mean = Σx / n

Where, x = set of values.

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Need help???!!!! Please

Answers

-5 and 2. -5x2=-10 and -5+2 is -3.

Answer:

+5&-2

Step-by-step explanation:

Copy each statement. Insert , -, x, + or division symbol to make each statement true.
27 3 5 2 = 19
81 11 8 4 1 = 60

Answers

The Complete statement are:

1. 27/3 + 5 x 2

2. 81 + 1 - 8 x 4 x 1 = 60

What are Arithmetic Operations?

Combining operands with a single arithmetic operator specifies an arithmetic operation. The  ADD, SUBTRACT, DIVIDE, and MULTIPLY can also be used to specify arithmetic operations.

Given:

we have to apply the operation to make

27 3 5 2 = 19

81 11 8 4 1 = 60

so, first 27 3 5 2 = 19

1. 27/ 3 = 9

2. 5 x 2= 10

3. 9+ 10 = 19

For second,

1.81 + 11 = 92

2. 8 x 4 x 1 = 32

3. 92-32 = 60

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2x + 3y = 12
2x - y = 4

Answers

Answer:

The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)

Step-by-step explanation:

Please help please now help ASAP

Answers

Answer:

2

Step-by-step explanation:

Which graph represents data points that have no correlation?

Answers

Answer:

bottom-right

Step-by-step explanation:

the points on the graph are scattered and have no correlation whereas the others all remain in a relatively similar shape

Is he right explain if no explain as well and this is my last question I need to answer for my test Thank you.

Answers

Scott's statement that (13g + 1) + (-2 - 5g) and 8/3(3g + 9/8) are equivalent is wrong

How to determine if he is right or not

From the question, we have the following parameters that can be used in our computation:

(13g + 1) + (-2 - 5g)

Remove the brackets

So, we have

13g + 1 - 2 - 5g

Evaluate the like terms

8g - 1

When factorized, we have

8/3(3g - 3/8)

This is not the same as Scott's expression

Hence, Scott is incorrect

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For the points P and Q do the following.
(a) Find the distance d(P,Q).
(b) Find the coordinates of the midpoint M of the segment PQ.
P (3√2,5√3), Q(√2,-√3)

Answers

The solution is, the distance = √116.

What is distance?

The distance between two points is the length of the line joining the two points.

Formula: distance= √(x_2-x_1)²+(y_2-y_1)²

here, we have,

given that,

P (3√2,5√3), Q(√2,-√3)

so,  the distance d(P,Q).

by using the formula we get,

the distance = √108 + 8

                     = √116

Hence, The solution is, the distance = √116.

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Write an equation in slope-intercept form for the line that passes through each pair of points.
(-7, -3) (-3, 5)

Answers

The equation of line passes through the points (- 7, -3) and (-3, 5) will be;

⇒ y = 2x + 11

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 7, -3) and (-3, 5).

Now,

Since, The equation of line passes through the points (- 7, -3) and (-3, 5).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - (-3)) / (-3 - (-7))

m = 8 / 4

m = 2

Thus, The equation of line with slope 2 is,

⇒ y - (-3) = 2 (x - (-7))

⇒ y + 3 = 2 (x + 7)

⇒ y + 3 = 2x + 14

⇒ y = 2x + 14 - 3

⇒ y = 2x + 11

Therefore, The equation of line passes through the points (- 7, -3) and

(-3, 5) will be;

⇒ y = 2x + 11

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What is the ICD-10 for primary hyperparathyroidism? Which of the following ethical theories states that the most ethical choice in a situation is one that produces the greatest benefit to the most people?a. Deontological theoryb. Moral relativism theoryc. Casuist ethical theoryd. Utilitarian ethical theory methods of preventing denial of service attack determine whether the number described is a statistic or a parameter. in a survery of hospital employees, feel that they are overworked. write balanced dissociation equations to represent the dissolving of the following solution in water: fecl3 Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation. The correlation value he calculates is only 0.05. What does Bob conclude? Bob gives up on his research because r=.05 means there is no relationship of any kind between bedrooms and selling price. Bob continues his research because even though there is no linear relationship here, there could be a different relationship. TREES From point A,the angle of elevation to the top of a pine tree is 42.From point B,on the same side of the tree, the angle of elevation to the top of the tree is 50.If point Aand point Bare located 12feet apart and are both at ground level, what is the approximate height of the tree to the nearest foot? fill in the blank. the ___performs all arithmetic operations (for example, addition and subtraction) and all logic operations (such as sorting and comparing numbers). (please use acronym) multiple choice question. can somebody help me here the geometric distribution arises as the distribution of the number of times we flip a coin until it comes up heads. consider now the distribution of the number of flips until the -th head appears, where each coin flip comes up heads independently with probability . this is known as the negative binomial distribution, and we also write . find . hint: here counts the number of flips including the flip with the -th head. mark the correct expression for , below. suppose that the bureau of labor statistics predicts that the number of jobs for dental hygienists will grow faster than most occupations while the number of jobs for bookbinders will decline. this change in the labor market could lead to:________ Please help with my homework :) What is the definition of social loafing in psychology? How do trees transport nutrients to the leaves? a fixed crystalline structure.Choose matching term1The change in the viscosity of a melt is directly proportional to the change in2What does grain size generally indicate about the cooling of a melt?3A mineral, as geologists understand the term, is a naturally occurring solid substance with a definable chemical composition and4Rank each lava type according to the relative distance it can generally travel from a volcano vent before solidifying. What are the items required for DNA replication? Suggest two measurable plant traits that could affect relative fitness and explain them briefly: who were gary ridgway spouse According to Genesis 37:26-27, which of Joseph's brothers pleaded that Joseph's blood not be shed and that his life be spared? calculate the specific heat of brass from your data. show your work and record your answer below. include units. the specific heat of water is cwater