As a result, the second table agrees with the formula y= 3x -3.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Here,
-3x - 3 = -6
y= 3x -3
Therefore, the second table matches the equation y= 3x -3.
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7. A five-person committee is to be selected from a group of 12 people. How many
different combinations are possible?
Answer: 792 Combinations
wendy has a monopoly in the retailing of motor homes. she can sell five per week at a price of $21,000 each. if she wants to sell six, she must charge $20,000 each. the marginal revenue of selling the sixth motor home is: -$5,000 -$1,000 $15,000 $20,000
She may sell five of them each week for $21,000. She needs to ask for $20,000 for each unit if she wants to sell six. The marginal revenue of selling the sixth motor home is -$5000. Here option A is the correct answer.
If demand is price inelastic, then raising the price will decrease income. If price increases elastic, lowering the price will boost earnings.
Demand is considered to be elastic if an increase in price results in a loss in overall income because the quantity required is significantly impacted by the price rise. Depending on whether they are requirements or wants, the marketplace. in other words, may have varying elasticities (accessories).
Thus, a fall in revenue because of a rise in price
= (20,000 - $21,000) × (5)
= -$5000
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A jar contains 5 red marbles numbered 1 to 5 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability that the marble is blue or even-numbered.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability of drawing an even-numbered blue marble.
= Number of even blue marble / Total number of marbles
The probability of drawing an even-numbered blue marble is 3/11.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of red marbles = 5
Number of blue marbles = 6
Number of even blue marbles = 3
Total number of marbles = 5 + 6 = 11
The probability of drawing an even-numbered blue marble.
= Number of even blue marble / Total number of marbles
= 3/11
Thus,
The probability of drawing an even-numbered blue marble is 3/11.
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As the X value of y=2x+80 the y value increases or decreases
Answer:
y value also increases
Step-by-step explanation:
As the X value (also known as the independent variable) of the equation y = 2x + 80 increases, the Y value (also known as the dependent variable) will also increase. This is because the coefficient of the X term (2) is positive, which means that for every increase in the X value, the Y value will also increase by an amount equal to twice the increase in the X value.
For example, if the X value increases from 2 to 3, the Y value will increase from 84 (which is calculated as 22 + 80) to 86 (which is calculated as 23 + 80). Similarly, if the X value increases from 3 to 4, the Y value will increase from 86 to 88, and so on.
What is - 8/15 - 3 4/5 mixed number in simplest form?
Answer:
–3 4/15
or
3 4/15
Step-by-step explanation:
A tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. At the start of a weekend, her win ratio is exactly 0.500. During the weekend, she plays four matches, winning three and losing one. At the end of the weekend, her win ratio is greater than 0.503. Find the largest number of matches she could have won before the weekend began.
is 107
is 164
is 840
cannot be determined from the given information
The number of tennis matches that she could have won before the weekend began is 0.
Before the weekend, the player had a win ratio of 0.500, which indicates that she had won exactly as many games as she had lost. Call this number x for now. She has so lost x matches in addition to the x matches she won before to the weekend.
She competes in three matches during the course of the weekend and loses one, bringing her overall win total (after the weekend) to x + 3 and her overall loss total (after the weekend) to x + 1. Consequently, her weekend victory ratio is
[tex]\frac{(x + 3)}{(x + 1)}[/tex]
= [tex]\frac{(3x + 3)}{(x + 1) }[/tex]
= [tex]\frac{3x }{x + 1 }[/tex]
= [tex]\frac{3}{\frac{1}{x+1} }[/tex]
given that this value is greater than 0.503,
Thus,
[tex]\frac{3}{\frac{1}{x+1} }[/tex] > 0.503
Simplifying,
[tex]\frac{3}{\frac{1}{x+1} }[/tex]> 0.503 - 1
= -0.497
Further,
[tex]\frac{3}{\frac{1}{x+1} }[/tex] > -0.497
[tex]\frac{3}{\frac{1}{x+1} }[/tex] is equivalent to 3x
This inequality can be written as
3x > -0.497
3x is positive, dividing on both sides by 3 we get
x > -0.497 / 3
Simplifying,
x > -0.166
The least value of x that meets this inequality is 0, as x, the number of matches won, must be a positive integer. Thus, the maximum number of games the player might have won prior to the start of the weekend is x = 0, and the response is 0.
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Answer:
164
Step-by-step explanation:
Let n be the number of matches she won, and m be the number of matches she played. Then, n/m = 1/2 and (n + 3) / (m + 4) > 0.503. By the first equation, 2n = m. Substituting m = 2n into the second equation/inequality, we get (n + 3) / (2n + 4) > 0.503. Because n cannot be negative in this context, we can multiply both sides by (2n + 4). We get n + 3 > 0.503 (2n + 4). Distributing the right-hand side, we get n + 3 > 1.006n + 2.012. Solving this inequality gives us 0.006n < 0.988, or n < 164.666667. n must be a whole number, so the greatest n you can achieve is 164.
On an actual test, you can also check using answer choices if given them. 164 gives around 0.50301, so it is 164, or cannot be determined. Then it is a 50/50 guess, and 164 is most likely the correct answer, which in this case, is the correct answer.
i need help with this 2 answers
(Oops forgot pic)
The angle measures in this problem are given as follows:
7 - m < ADC = 82º.
8 - m < ADC = 44º.
How to obtain the angle measures?In item 7, the angle measure is found obtained the angle addition postulate, meaning that the measures are obtained as follows:
m<ADB = m < BDC + m < ADC.
Then the equation to find the value of x is obtained as follows:
144 = 7x + 34 + 9x + 46
16x = 64
x = 64/16
x = 4.
Then the angle ADC is obtained as follows:
m < ADC = 9(4) + 46 = 82º.
In item 8, the bisection means that the two angle measures are equal, hence the value of x is obtained as follows:
7x - 19 = 9x - 37
2x = 18
x = 18/2
x = 9.
m < ADC = 9(9) - 37 = 44º.
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If you choose a group of four tiles, what is the probability you get four tiles that are each worth one point? Write your answer as a decimal with three decimal places (0.XXX), not as a percent.
The probability to choose a group of four tiles with each tile worth one point is 0.200.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Let there are total 25 tiles.
From this 20 tiles having one point each and 5 tiles having more than one point.
We have to choose a group of four tiles with each tile worth one point.
So,
probability = 4/20 = 0.200
Hence, the probability to choose a group of four tiles with each tile worth one point is 0.200.
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Write a number in each blank to make the statements true.
Each paper clip can be traded for three matches.
Each pencil can be traded for six paper clips.
Therefore, one pencil is worth
matches.
Five paper clips are worth
matches.
Three pencils and four paper clips together are equal in value to
matches.
Two pencils and nine matches together are equal in value to
paper clips.
Answer:
greater than
Paperclip = 3 matches
Pencil = 6 paperclips
22×3 = 66
66×3 = 198
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Show another place along the x-axis where You can situate the wave generator between the two fixed endpoints to produce a standing wave (other than the already employed cases of x = L/2 and x = L/3 ) Use sketch to show this position and the resultant mode: Explain why this location would work:
The (two-way) wave equation is a second-order partial differential equation describing waves, including traveling and standing waves; the latter can be considered as linear superpositions of waves traveling in opposite directions.
This article mostly focuses on the scalar wave equation describing waves in scalars by scalar functions u = u (x1, x2, ..., xn; t) of a time variable t (a variable representing time) and one or more spatial variables x₁, x₂, ..., xₙ (variables representing a position in a space under discussion) while there are vector wave equations describing waves in vectors such as waves for electrical field, magnetic field, and magnetic vector potential and elastic waves. By comparison with vector wave equations, the scalar wave equation can be seen as a special case of the vector wave equations; in the Cartesian coordinate system, the scalar wave equation is the equation to be satisfied by each component (for each coordinate axis, such as the x-component for the x-axis) of a vector wave without sources of waves in the considered domain (i.e., a space and time). For example, in the Cartesian coordinate system, for Eₓ , Eₐ and Eₙ the representation of an electric vector field wave E in the absence of wave sources, each coordinate axis component
Ei ( i = x , a , n) must satisfy the scalar wave equation. Other scalar wave equation solutions u are for physical quantities in scalars such as pressure in a liquid or gas, or the displacement, along some specific direction, of particles of a vibrating solid away from their resting (equilibrium) positions.
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10x-8y=4
20x-16y=8
Please help me solve this
A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. At the end of the questionnaire is an (optional) invitation to donate money to the organization. Which of the following statements about this survey is true?
A) The survey results are invalid because it’s impossible to word questions about politics without creating bias.
B) The survey results are invalid because only surveys conducted by phone are free from bias.
C) The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money.
D) The survey results will overestimate support for this political action committee in the entire population because people more likely to respond if they are prepared to donate money.
E) Since the survey was sent to randomly-selected households, it should be free of bias.
(c) The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that askes for money.
What is politics?
Politics is a category of activities that are related to group decision-making or other types of power dynamics between people, such as the allocation of resources or status. Political science is the name of the area of social science that focuses on politics and governance.
EXPLANATION: This type of sampling will yield biased result, because in addition to asking to reply for the survey queries regarding importance of a variety of economic and social issues facing the country, at the end request for donation.
(c) The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that askes for money
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help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
344
Step-by-step explanation:
6 percent of 530 is 31.8
530-31.8=498.2 or 498
6 percent of 498=29.88
498-30=468
6 percent of 468=28.08
468-28=440
6 percent of 440=26
440-26=414
6 percent of 414=24.84
414-25=389
6 percent of 389=23.34
389-23=366
6 percent of 366=21.96
366-22=344
Thus, our answer is 344
There are 8 people participating in a focus group for a new software product related to the health system, 3 of them are software engineers, 2 of them are nurses, 1 of them is a doctor, and the remanining 2 people are technicians. In how many ways they can be seated in a row so that no two software engineers are together? Show all your work to get credit
In 480 ways people can be seated in a row so that no two software engineers are together.
We have given that there are 8 people participating in a focus group, 3 of them are software engineers, 2 of them are nurses, 1 is doctor and 2 are technicians.
So the 3 software engineers can sit in 3! ways,
2 nurses can sit in 2! ways,
doctor can sit in 1! way and
2 technicians can sit in 2! ways.
We have to find that how many ways they can sit such that no two software can sit together.
So we first place 5 people in a row and software engineers has to sit between them so no two software engineers are to be sited together.
We get that in 6 places they can sit in 6C3 ways
i.e 6C3 = 20 (by formula of combination)
Therefore total ways are,
6 × 2 × 1 ×2 × 20 = 480.
Hence in 480 ways people can be seated in a row so that no two engineers are together.
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Determine a series of transformations that would map Figure H onto Figure I.
Answer:
reflection across the line y=x
Step-by-step explanation: the point (-2,1) would turn into (1,-2) which the other figure shows
8. Jim hopes a park will be built within 5 miles of his
house. If a park is built at the coordinates (3, 7),
does that meet Jim's criteria? Explain.
No, he wanted a park developed within 5 miles of his residence, yet this park is 8.30 miles away.
What is coordinate?The horizontal and vertical distances from the two reference axes are used to define the location of a point on a coordinate plane. The x-value and y-value are often denoted as (x,y). To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate. The distance between two points is known as the x-coordinate, or abscissa, while the distance between two points is known as the y-coordinate, or ordinate.
Here,
let the house be (0,0).
coordinate of park=(3,7)
distance=√3²+7²
=√21+49
=√69
=8.30 miles.
No, He wanted a park to be built within 5 miles of his house while this park is 8.30 miles from his house.
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based on the survey data and calculated expected values, what is the value of the chi-square (\chi^2) test statistic, using the following formula? \chi^{2}
The value of chi-square statistic is;
In the contingency table, "O" stands for the observed value, "E" for the predicted value, and "I" for the "ith" position.
Given,
Chi- Square test;-
A statistical technique called the chi-square test is used to compare actual outcomes with predictions. The goal of this test is to establish whether a discrepancy between observed and expected data is the result of chance or a correlation between the variables you are researching.
We have to find the value of chi- square statistic;
The chi-squared statistic is a single figure that indicates the degree to which the counts you saw deviate from the counts you would anticipate if there were no association at all in the population. If I is the "ith" position in the contingency table, "O" is the observed value, "E" is the anticipated value, and "O" is the observed value.
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The matrices below show how many juniors and seniors at Phoenix High School participated in various programs. They participated as an Office Aide (O), a Media Aide (M), and in Work Based Learning Program (W), over a three-year period. Which of the programs has had the most students in it over the ? How many did it have?
the program with the most students over the three-year period is the Office Aide program, with a total number of 10 students participating
Junior Year Senior Year
O 3 7
M 4 6
W 5 4
The program with the most students over the three-year period is the Office Aide program, with a total of 10 students participating.
1. We can start by looking at the matrices to see how many students participated in each program.
2. For the Office Aide program, there were 3 juniors and 7 seniors, for a total of 10 students.
3. For the Media Aide program, there were 4 juniors and 6 seniors, for a total of 10 students.
4. For the Work Based Learning Program, there were 5 juniors and 4 seniors, for a total of 9 students.
5. Therefore, the program with the most students over the three-year period is the Office Aide program, with a total number of 10 students participating.
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How did you transform the given equation into it's Standard form?
The standard form of such an equation is Ax + By + C = 0 or Ax + By = C.
What is standard form of an equation ?
The standard form of such an equation is Ax + By + C = 0 or Ax + By = C.
If you rewrite this equation in a different way, you'll obtain y by itself on the left side, it then forms y = mx +b.
An assertion of equality between two expressions containing variables and/or numbers is called an equation.
In essence, equations are questions, and attempts to discover systematic answers to those questions have spurred the development of mathematics.
Linear equations can be written in three different ways: point-slope form, standard form, and slope-intercept form.
General Procedure:
Equation in slope intercept form has the basic structure
y = mx + b
y - mx = (mx - mx ) + b
y - mx = b
y - mx - b = b - b
y - mx - b = 0
-mx + y - b = 0−mx+y−b=0
If m is an integer, then B will equal 1.
-A/Bx + y - b = 0−
x+y−b=0
-Ax + By - Bb = 0−Ax+By−Bb=0
-Ax + By - C = 0−Ax+By−C=0
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A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one half gallon of water is needed, and for every 5 scoops of mix, one and one fourth gallons of water are needed.
Part A: Find the constant of proportionality. Show every step of your work.
Part B: Write an equation that represents the relationship. Show every step of your work.
Part C: Describe how you would graph the relationship. Use complete sentences.
Part D: How many gallons of water are needed for 12 scoops of drink mix?
Answer:
A. 1/4 gal/scoop
B. w = 1/4s
C. line through the origin with slope 1/4; s-, w- axes labeled "scoops" and "gallons"
D. 3 gallons
Step-by-step explanation:
Given 2 scoops of powdered drink mix needs 1/2 gallon of water, you want (A) the constant of proportionality, (B) the equation for the relationship, (C) a description of the graph, (D) gallons for 12 scoops.
Proportional relationshipA proportional relationship between gallons of water (w) and scoops of drink mix (s) can be written as ...
w = ks
where k is the constant of proportionality.
A Proportionality constantSolving the equation for k, we get ...
k = w/s
Using the given values, we find k to be ...
k = (1/2 gal)/(2 scoops) = 1/4 gal/scoop
The constant of proportionality is 1/4 gallon per scoop.
B EquationWe show the equation in part A. Filling in the value of k gives ...
w = 1/4s . . . . . . . where s is number of scoops, and w is gallons of water
C GraphThe attached shows a graph. A line starts at the origin with slope 1/4; s-, w- axes are labeled "scoops" and "gallons". The practical domain is s ≥ 0, so no part of the graph is in the 3rd quadrant.
D 12 scoopsThe equation tells you that 12 scoops will require ...
w = 1/4·12 = 3 . . . . gallons
3 gallons of water are needed for 12 scoops of drink mix.
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Find the volume of a right circular cone that has a height of 4.5 ft and a base with a diameter of 19 ft.
Answer:135.375[tex]\pi[/tex] ft³
Step-by-step explanation:
The formula for the volume of a right circular cone is [tex]\frac{1}{3}[/tex][tex]\pi[/tex]r²h.
We are given height, and we can find r by dividing diameter by 2, which is 9.5 ft.
Plugging these values into the equation give us [tex]\frac{1}{3} \pi (9.5)^{2} (4.5)[/tex].
This equation equals 135.375[tex]\pi[/tex] ft³
Can someone please help me asap, This is overdue and i need to get it done and im very confused... !! ILL GIVE BRAINLIST !!
Answer:
Below
Step-by-step explanation:
At B ( 40 mins) and D (30 mins) he is not moving....visiting .
The width of A is the time it took to get to first house = 20 mins
The width of C is t the time to get to second house = 60 to 70 = 10 mins
Riding toward home at C and E ( the distance...the y-value....is getting less)
He is fastest where the line has greatest slope...where it is steepest = C
He was away from home the width of the graph = 115 mins
Notice
-4x plus what results in 5x?
Answer: 9x
Step-by-step explanation:
-4x+y=5x
solve for x
y=9x
Which of the following are true concerning this diagram? You may assume that the lines are parallel.
The solution is
a) ∠1 ≅ ∠5 by Corresponding Angles
b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles
c) ∠6 ≅ ∠4 by Alternate Interior Angles
d) ∠2 ≅ ∠8 by Alternate Exterior Angles
What are Parallel Lines Cut by Transversal?
Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
From the figure , we can see that
The Corresponding angles are
Angle 1 and Angle 5
Angle 2 and Angle 6
Angle 4 and Angle 8
Angle 3 and Angle 7
The Alternate Interior angles are
Angle 4 and Angle 6
Angle 3 and Angle 5
The Co-Interior angles are
Angle 4 and Angle 5
Angle 3 and Angle 6
The Alternate exterior angles are
Angle 1 and Angle 7
Angle 2 and Angle 8
Hence , the angles from the figure that are true are
a) ∠1 ≅ ∠5 by Corresponding Angles
b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles
c) ∠6 ≅ ∠4 by Alternate Interior Angles
d) ∠2 ≅ ∠8 by Alternate Exterior Angles
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Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. The better deal is:
Multiple Choice
Four Rivers because she will earn about $6,442 more.
Four Rivers because she will earn about $6,523 more.
Four Rivers because she will earn about $4,000 more.
Four Rivers because she will earn about $20,000 more.
Jane must therefore deposit her savings in the four rivers bank.
What is compound interest?Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.
As per the data provided in the question,
Rate, r = 12%
After five years, the total amount, if Jane had saved at Mystic Bank,if Jane had saved at Mystic Bank would be:
[tex]A = P(1+\frac{r}{100} )^n[/tex]
For compounded quarterly,
n = 5 × 4
n = 20
A = 40000(1 + 12/(4 × 100))²⁰
A = 72244.44 (i)
If Jane placed her savings with the Four Rivers, then,
A = 40000(1 + 14/(2 × 100))¹⁰
A = 40000 × 1.9671
A = 78686.054 (ii)
Therefore, it is evident that case (ii) is higher than case (i). Jane must therefore deposit her savings in the four rivers bank.
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CAN SOMEONE HELP ME WITH ALGEBRA 2?
The solution set is for the given inequality is (-∞, -2.25]
How to solve the inequality?Here we want to solve the following inequality:
-11 - 8k ≥ 23 - (7 - 4k)
To solve this, we need to isolate the variable k in one side of the equation.
First we can expand the right side so we get:
-11 - 8k ≥ 23 - (7 - 4k)
-11 - 8k ≥ 23 - 7 + 4k
Group like terms:
-11 - 23 + 7 ≥ 4k + 8k
-34 + 7 ≥ 12k
-27 ≥ 12k
-27/12 ≥ k
-2.25 ≥ k
Then the solution is the set of all values smaller than or equal to -2.25, then the solution set is (-∞, -2.25]
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What is the rate of change of the function y = \frac{5}{4}x+1y=
4
5
x+1?
Rate of change of y =[tex]\frac{5}{4}x +1[/tex] is 5/4.
What is rate of change?The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.
Given that the expression, y =[tex]\frac{5}{4}x +1[/tex] .
To find the rate of change,
first we make the equation in standard form.
Slope intercept form ;
(y₂ - y₁) =m (x₂ -x₁) + c
Comparing the expression to the standard form;
Here, x intercepts: ( -4/5 , 0) and y intercepts: (0,1)
Rate of change = (y₂ - y₁) / (x₂ -x₁)
Rate of change = 5/4
Therefore, rate of change of y = is 5/4.
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Determine whether the following statement is sometimes, always, or
never true.
The range of an even function is (-∞o, max], where max is the
maximum of the function.
It is occasionally accurate to say that the range of an even function is (-∞o, max), where max is the function's maximum.
what is range ?the range of variation that is conceivable or the boundaries between it: pricing for various grades of steel; a variety of designs. a thing's operation or action's reach or extent: accessible to the eye. a projectile's range is how far a weapon can or will shoot it.
here the explanation
We can say that our range is any real number value between -infinity and infinity, or (,), if our range is any real number value. The range is all real numbers, but we can express this more succinctly by using the symbol R.
a position where the value of a function is highest. It is an absolute maximum if the value is larger than or equal to all other function values.
It is occasionally accurate to say that the range of an even function is (-∞o, max), where max is the function's maximum.
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The probability that a store sells all of their
ground hamburger for the week is 0.75. The
probability that the store sells all of it's steak for
the week is 0.68. The probability that the stores
sells all of both of the meats for the week is 0.62.
Given this information, are events A and B
dependent or independent?
Events A and B dependent as occurrence of one event does not affect the chances of the occurrence of the other event.
What is Probability?Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.
To understand this branch, it is extremely important to know its most basic definitions, such as the formula for calculating probabilities in equiprobable sample spaces, probability of the union of two events, probability of the complementary event, etc.
Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).
Since we have given that;
A be the event that a store sells all of their ground hamburger for the week
P(A)=0.75
B be the event that that the store sells all of it's steak for the week is
P(B)=0.68
The probability that the store sells all of both of the meats for the week is 0.62.
P(A|B)=0.62
but for A and B to be independent ,
P(A).P(B)= P(A and B)
0.75×0.68=0.51
but,
[tex]P(A|B) = \frac{P(AnB)}{P(B)}[/tex]
P(AnB) = 0.62 x 0.68
P(AnB) = 0.4216
So, P(A∩B) does not satisfy the condition.
Hence, A and B are not independent events.
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A recent report indicated that 90 percent of adults in a certain region actively try to include vegetables in their diet. A simulation was conducted that consisted of 50 trials with a population parameter of 0.9. Each trial consisted of a sample size of 10. The number of successes out of 10 was recorded, where success represented an adult trying to include vegetables in the diet.
Five possible simulation results are shown. Which simulation is the best match to the one described?
tallest on nine all focused on the right side
On dot plot we take no. of successes out of 10. Hence it having 0 to 10 numbering.
What is dot plots in statistics?
For relatively small data sets with values falling into a handful of discrete bins, a dot plot, also known as a dot chart, is a sort of straightforward histogram-like display used in statistics.
To create a dot plot, count the data points that fall into each bin and then draw a stack of dots that is that many dots high for each bin.
Because we conduct 50 trials, dot plot should have 50 points, one point per each trial.
On X axis, we take no. of successes out of 10. Hence it having 0 to 10 numbering.
Learn more about dot plots
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