According to the normal distribution and the central limit theorem the ballot measure is greater than 0.50.
The term called normal distribution is defined as a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.
Here we know that t a random sample of 500 voters from one region, region a, of the city and the ballot measure in region a is 0.47.
Here we have to find the mean and the standard deviation are calculated as,
=> mean = 0.47
=> Standard deviation = √0.47(1-0.47)/500
When we simplify this then we get,
=> Standard deviation = 0.0223
By using the Central Limit Theorem the probability is calculated as,
=> Z = (0.5 - 0.47) / 0.0223
=> Z = 1.34
When we use the z table, then we get the p - value as 0.9099
Then the probability is calculated as,
=> P = 1 - 0.9099
=> P = 0.0901
Hence 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
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The expression 16t-3t is not equivalent to 3t-16t because the negative sign belongs to the term _____
The expression 16t-3t is not equivalent to 3t-16t because the negative sign belongs to the term 3t
For t = 2, 16t - 3t is equal to 26 and 3t - 16t is equal to -26
We know that an expression is nothing but a mathematical sentence with a minimum of two numbers or variables and at least one algebraic operation.
Also, if two expressions are equivalent expression , then the two expressions must have the same value when we substitute the same values for the variables.
Here we have been given two mathemtical expressions:
16t - 3t and 3t - 16t
For t = 2,
16(2) - 3(2)
= 32 - 6
= 26
and 3(2) - 16(2)
= 6 - 32
= -26
This means, 16t - 3t ≠ 3t - 16t
We can oberve that 16t - 3t = -(-16 + 3t)
= -(3t - 16)
This means, 16t-3t is not equivalent to 3t-16t because the negative sign belongs to the term 3t
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A ship is on its maiden voyage to the mystery island. According to the map, it has to travel
99 miles to the north and then, 20 miles to the west to reach the island. Find the shortest
route that leads to the mystery island.
Answer:
I also need help
Step-by-step explanation:
A ship is on its maiden voyage to the mystery island. According to the map, it has to travel
99 miles to the north and then, 20 miles to the west to reach the island. Find the shortest
route that leads to the mystery island.
Answer:
20 miles
Step-by-step explanation:
would you rather go 99 miles or 20 miles
The polling results show the ratio of votes for Candidate A to Candidate B.
Candidate A Candidate B
12 20
18 30
27 45
36 ?
At this rate, if Candidate A received 36 votes, how many votes did Candidate B receive?
36
50
60
72
If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes. (third option)
How many votes did Candidate B receive?The first step is to determine the relationship between the number of votes of Candidate A and B. This can be determined by expressing the number of votes in its simplest form.
12 : 20 in its simplest form is 3 : 5
18 : 30 in its simplest form is 3 : 5
27 : 45 in its simplest form is 3 : 5
Now, determine the factor second factor of 36 if the first factor is 3.
36 / 3 = 12
Now multiply 12 by 5: 12 x 5 = 60
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the garden clud at central middle school is planting a flower bed. a scale drawing of the flower is shown. the scale 1 in. :2 ft
If the plant is n inches then,
the actual plant = 2n feet.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Given:
The garden club at central middle school is planting a flower bed.
A scale drawing of the flower is shown.
The scale 1 in:2 ft
The scale factor,
the model = 1 inch
Then the actual plant = 2 feet.
If the plant is n inches then,
the actual plant = 2n feet.
Therefore, If the plant is n inches then, the actual plant = 2n feet.
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Simplify the radical expression completely:
Square root of 48x^2y^5z
The radical expression completely:
Square root of [tex]48x^2y^5z[/tex] is 4[tex]xy^2[/tex] × sqrt(3y)
Now, According to the question:
Factor 48 into its prime factors
48 = 24 × 3
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
16 = [tex]2^4[/tex]
Factors which will remain inside the root are :
3 = 3
To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
4 = [tex]2^2[/tex]
At the end of this step the partly simplified SQRT looks like this:
4 × sqrt[tex](3x^2y^5)[/tex]z
Rules for simplifying variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt[tex](x^8)=x^4[/tex]
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or < (-2) , examples:
(4.1)[tex]sqrt(x^5)=x^2sqrt(x)[/tex]
(4.2) sqrt(x-7)=x-3sqrt(x-1)
Applying these rules to our case we find out that
SQRT[tex](x^2y^5) = xy^2[/tex]SQRT(y)
Simplified root:
4[tex]xy^2[/tex] × sqrt(3y)
Hence, the radical expression completely:
Square root of [tex]48x^2y^5z[/tex] is 4[tex]xy^2[/tex] × sqrt(3y)
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We placed a 2 kg textbook and a 4kg textbook at least 2cm away from each other. After a while we moved the two textbooks so now they are 8 cm away from each other. Explain which textbook has a larger gravitational pull and how do the different distances affect it?
Book 2 with 4 kg weight has the higher gravitational pull and the pull decreases with increase in distance.
What is Meant by Gravitational Force?In Physics, the gravitational force is one of the types of forces. It is a force that attracts any two objects with mass. The gravitational force is also known as the attractive force, as it always pulls the masses of two objects together. Newton’s gravitational law states that every object in the universe is pulled by other objects. The other types of forces are electromagnetic force, strong force, weak force, and so on. The formula to calculate the gravitational force is given by Gravitational Force = (Gravitational Constant × Mass of first object × Mass of the second object) / (Distance between the centre of two bodies)².
Given here:
Book 1 has 2 kg textbook and Book 2 weighs 4 kg.
In the first case The gravitational pull when they were 2 cm apart is
F₁= Gm₁m₂ / 2cm
=0.00000133486 N
While if the two books are 8 cm apart we have
F₂= Gm₁m₂ / 8
=0.0000000834288 N
clearly the gravitational pull decreases with the increase in distance.
And owing to Book 2's higher weight it has the superior gravitational pull.
Hence, Book 2 with 4 kg weight has the higher gravitational pull and the pull decreases with increase in distance.
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Parallel lines e and f are cut by transversal b.
Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 18) degrees. At the intersection of lines b and f, the top right angle is (4 x minus 14) degrees and the bottom right angle is y degrees.
What is the value of y?
Using the congruency of the top-right angles, it is found that the value of y is of 130.
What are parallel lines ?
Parallel lines can be defined as the lines which are equi distant from each other and they never intersect.
When two parallel lines are cut by a transversal, the top-right angles are congruent, that is, they have the same measure.
In this question, their measures are of (2x + 18)º and (4x - 14)º. Thus, with this, we can find x:
4x-14 = 2x+18
4x-2x = 18+14
2x = 32
x = 32/2
x = 16
Thus, the measure of the top right angles is given by, in degrees:
4x-14 = 4*16 - 14 = 64 - 14 = 50
The top-right and the bottom-right angles are supplementary, that is, the sum of their measures is 180º.
The measure of the top-right angle is of 50º.
The measure of the bottom-right angle is of y.
Thus:
y + 50 = 180
y = 180 - 50
y = 130
Hence, The value of y is of 130.
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11. Is the triangle a right triangle? Explain. 6 8 12
Answer:
Step-by-step explanation:
35368
Scott has a blue front of the new deck his building with dimension 7.5” x 4.5”. The actual deck will have dimensions 20’ x 12’. What is the scale
The scale of the drawing is given as follows:
1 : 4.5.
How to obtain the scale of the drawing?The scale of the drawing is obtained applying the proportions in the context of this problem.
The scale is defined as the division of the drawn length by the actual length.
The lengths are given as follows:
Drawn length: 20 inches.Actual length: 7.5 feet = 7.5 x 12 = 90 inches.90/20 = 4.5, hence the scale of the drawing is given as follows:
1 : 4.5.
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HELP!! ASAP! 60 POINTS
This diagram shows right triangular prism UVWXYZ.
What is the volume of UVWXYZ? If necessary, round your answer to the nearest tenth.
In the diagram which shows right triangular prism UVWXYZ, the volume of UVWXYZ can be expressed in nearest tenth as 750 cm^3.
How can the the volume of UVWXYZbe calculated?The concept that will be used here is volume. In mathematics, 'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3
√ (12.5^2 -7.5^2) =10 cm
The volume can be calculated as : (1/2 * 7.5 * 10 *20
=750 cm^3
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One bank account pays 6% interest and another pays 12%. If $6,000 was invested for a year and the interest earned was $540, how much was invested at 6%?
Answer:
360
Step-by-step explanation:
0.06x6000=360 also that 6% equal 6/100 wich is 0.06
one of the five quadratics below has a repeated root. (the other four have distinct roots.) what is the repeated root? \begin{align*}
Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.
Quadratics representing repeated roots has discriminant equals to zero.
Standard quadratic equation is:
ax² + bx + c = 0
Discriminant 'D' = b² - 4ac
option a. -x²+ 18x + 81
Discriminant
'D' = 18² - 4(-1)(81)
= 324 + 324
= 648
D>0 has distinct roots.
option b. 3x²- 3x - 168
Discriminant
'D' = (-3)² - 4(-3)(-168)
= 9 - 2016
= -2007
D< 0 has distinct roots.
option c. x²- 4x - 4
Discriminant
'D' = (-4)² - 4(1)(-4)
= 16 + 16
= 32
D>0 has distinct roots.
option d. 25x²- 30x + 9
Discriminant
'D' = (-30)² - 4(25)(9)
= 900 - 900
= 0
D = 0 has repeated roots.
Repeated roots are:
x = ( -b ±√D ) / 2a
= [-(-30)±√0 ]/ 2(25)
= 30/ 50
= 3/5.
option e. x² - 14x + 24
Discriminant
'D' = (-14)² - 4(1)(24)
= 196 - 96
= 100
D>0 has distinct roots.
Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.
The above question is incomplete, the complete question is:
One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?
a. -x²+ 18x + 81
b. 3x² - 3x - 168
c. x² - 4x - 4
d. 25x² - 30x + 9
e. x² - 14x + 24
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assume your favorite football team has two games left to finish the season. the outcome of each game can be win, lose, or tie. the number of possible outcomes is
The possible outcomes are the sample space of the game
The number of possible outcomes in the game is 3
Now, According to the question:
In the domain of Statistics, the number of possible outcomes for a given event help in determining the overall size of the universe of outcomes. From such a universe, one can ascertain the probability or likelihood of desirable outcomes in terms of percentage or fraction.
How to determine the possible outcomes
The number of games is given as:
n = 2 i.e. 2 games to finish the season
In each game, the soccer team can either win, lose or tie.
So, we have the outcome of each game to be:
Outcome = {Win, Lose, Tie}
Count the outcomes
Count = 3
Hence, the number of possible outcomes in the game is 3.
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The given question is incomplete , complete question is:
Assume your favorite football team has two games left to finish the season. the outcome of each game can be win, lose, or tie. the number of possible outcomes is in the game ____
PLEASE ANSWER QUICK,
Answer:
C=5Q
Step-by-step explanation:
what term is used to describe this type of survey in which the people surveyed consist of those who decided to respond? what is wrong with this type of sampling method
Part A: The respondents in the population are a voluntary response sample.
Part B: The responses may not reflect the opinions of the general population
The total number of internet users in those is 1072 people.
The percentage of the total number of people that chose to respond is 38%
We can note that this survey does not compel the population to respond to the survey. These responses are given by the voluntary respondents.
Another point is that a voluntary response sample is a sample that consists of participants who are interested to participate in a sample group voluntarily.
In this type of survey, the people who are supposed to decide to provide voluntary responses to the survey are called voluntary response samples.
The percentage of those that chose to respond to this survey which is 38% is less than half of the total population. This result shows that the responses may not reflect the opinions of the general population.
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A pizza company charges $60 for 12 pizzas.
v) Create a table from 60=12m
The required table would be:
Quantity (x) Price (y)
12 $60
What is the slope-intercept form?
The slope-intercept form of a linear equation is y = mx + b, where x and y are variables, m is the slope of the line (also known as the "rate of change" or "rise over run"), and b is the y-intercept (the point where the line crosses the y-axis). The slope-intercept form is so called because it gives the slope of the line and the y-intercept in one equation
Here is the table you requested:
Quantity (x) Price (y)
12 $60
This table shows the relationship between the quantity of pizzas ordered (x) and the price (y) for a pizza company that charges $60 for 12 pizzas. The equation y = mx + b can be used to represent the relationship, where m is the unit price and b is the y-intercept. In this case, m = 5 and b = 0.
Hence, the required table would be:
Quantity (x) Price (y)
12 $60
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The sides of AFGH are FG = 6x + 7, GH = 8x - 5, and FH = 10x - 11. If the perimeter of AFGH,
is 87, list the angles in order from largest to smallest.
Answer: Since AFGH is a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. We can use this property, known as the triangle inequality theorem, to determine the angles of AFGH in order from largest to smallest.
We are given that the perimeter of AFGH is 87, so we know that:
FG + GH + FH = 87
6x + 7 + 8x - 5 + 10x - 11 = 87
24x + 1 = 87
24x = 86
x = 3.5
Now that we know that x = 3.5, we can use the given lengths of the sides to find the values of the sides:
FG = 6x + 7 = 6(3.5) + 7 = 23
GH = 8x - 5 = 8(3.5) - 5 = 25
FH = 10x - 11 = 10(3.5) - 11 = 29
We can now use these values to determine the angles of AFGH in order from largest to smallest.
We can use the triangle inequality theorem to determine that:
FH>FG+GH
29>23+25
Therefore, the angle that is opposite to side FH is the largest angle in the triangle, and the angles opposite to FG and GH are the smaller angles.
So, the angles in the triangle AFGH are ordered from largest to smallest:
The angle opposite to side FH, angle A, is the largest.
The angles opposite to side FG and GH are the smaller angles.
Step-by-step explanation:
A rectangle has an area of 15 square millimeters. The width of the rectangle is 3 millimeters.
Answer:
5 millimeters
Step-by-step explanation:
15 = 3x
5 = x
what number is an integer
An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z or blackboard bold \mathbb {Z}.
below are two diagrams, one represents 2+5=7 the other represents 5x2=, determind the equation that matches up with each diagram then label the length of each diagram
The first diagram is the equation represented by 5 . 2 = 10 and the second diagram is the one with the equation represented by 2 + 5 = 7.
What are Tape Diagrams?Tape diagrams are diagrams which are used to understand about the relationship between quantities and also they describe how those relationships has been described by operations.
Given are two tape diagrams.
First take the equation 2 + 5 = 7.
This means that 2 is just added to 5 to get 7.
One part contains 2 and the other part contains 5.
Length of it is 7.
Consider the second equation 5 × 2 = 10.
5 × 2 actually means that 5 is added to itself two times or 2 is added to itself five times.
Either 5 + 5 = 10 or 2 + 2 + 2 + 2 + 2 = 10
We have a diagram with 5 equal parts of 2.
Length is 10.
Hence the length of the first diagram is 10 and the length of second diagram is 7.
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7-5p+3q when
�
=
1
p=1p, equals, 1 and
�
=
7
q=7q, equals, 7
The solution to the equation is 23
How to determine the solution to the expression?From the question, we have the following parameters that can be used to solve the question
7 - 5p + 3q
Also, we have the following values
p = 1 and q = 7
Substitute the know values in the given expression, so we have the following representation
7 - 5(1) + 3(7)
Evaluate the products
This gives
7 - 5 + 21
Evaluate the like terms
23
Hence the solution is 23
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g) 25+ [14 - {8+ (13-4)}]
Answer: 22
Step-by-step explanation:
25+ [14 - {8+ (13-4)}]
= 25 + [14 - {8 + 9 }]
= 25 + [14 - 17]
= 25 - 3
= 22
PartA :Using a computer software a correlation coefficient of r=0. 51 was calculated. Based on the scatter plot is that an accurate value fir this data?Why or why not?
PartB: instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a casual relationship for pumpkins picked on the farm
Part A) According to the the scatter plot r = 0.01 is not an accurate value for this data
Part B) We have to describe a scenery where a variable is the cause of the number of strawberries picked.
The term scatter plot in math is known as a horizontal and a vertical axis in the attempt to show how much one variable is affected by another
As we all know that the correlation coefficients r and it measure the strength of the correlation of two variables and they can have values from - 1 to 1.
Here we have know that r = - 1 is a perfect negative correlation and the points will adjust perfectly to a line with negative slope.
Where as r = + 1 is a perfect positive correlation and the points will adjust perfectly to a line with positive slope.
Where as r = 0 means that the variables are not correlated at all.
Hence the calculated value of r = 0.01 is not accurate for t his scatter plot.
As we all know that the causal relationship means that the explanatory variable is the cause of the dependent variable.
Therefore here we know we have to find a reasonable variable that can be the cause of the number of strawberries picked.
As the amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.
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A sales representative's orders for May were less than her April orders, which amounted to $51,120. (a) How much were the sales rep's orders in May? (b) By what amount did her orders decrease?
As per the unitary method,
(a) The amount earned by the sales rep's orders in May is $42 600
(b) The amount did her orders decrease is $8520
in math the term unitary method is known as the process of how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.
Here we have given that a sales representative’s orders for May were 16 2/3% less than her April orders, which amounted to $51 120.
By using the unitary method as we all know that the May order is decreased, then it can be calculated as,
=> 51120 – 16 2/3% of $51120
When we simplify this one then we get,
=> 51120 – 1/6 × 51120 = 51120 – 8520
Therefore the earning is $42 600
Similarly, through the calculation we have identified that the decreased amount is $8520.
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Suppose Randy has 1/4 of a round cake and 1/4 of a square cake. Are the wholes the same? Does the sum 1/4 + 1/4= 2/4 make sense in this situation? Explain
Randy's cake situation will be better solved in the following manner:
a) If the area of a round cake and a square cake are different then the quarter portion will be different.
b) Though as a concept 1/4 + 1/4 = 2/4, it is not actually true in this case. If the area of different cakes are different then the quarters will also be different.
Measuring a particular region or patch of a figure is its area. Area is significant in contemporary mathematics. Area is crucial in geometry and calculus, but it also plays a role in the definition of determinants in linear algebra and is a fundamental characteristic of surfaces in differential geometry.
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1. Jake is reading a book for a class assignment. He creates a plan to read the book over an 8 day
period. Use the table below to create a graph of this accounts. Y
Day's
0
2
4
6
8
Pages
Read
0
54
108
162
216
a. What does x represent?
b. What does y represent?
c. Describe the slope of the line.
What does it represent?
d.what is the slope?
The analysis of the data in the table, which is a linear relationship between the pages Jake reads to the number of days is as follows;
1. Please find attached the graph of the data in the table created with MS Excel
a. The variable x represents the number of days Jake reads the book
b. The variable y represents the number of pages Jake reads
c. The slope is the rate of change of the pages Jake reads to the number of days he has been reading the book
d. The slope is 27 pages per day
What is a linear relationship?A linear relationship is a relationship that has a straight line graph when plotted on the coordinate plane.
1. The data in the table are presented as follows;
Days[tex]{}[/tex] Pages Read
0[tex]{}[/tex] 0
2[tex]{}[/tex] 54
4[tex]{}[/tex] 108
6[tex]{}[/tex] 162
8[tex]{}[/tex] 216
Please find attached the graph created with the above data in the table for the Days and the number of Pages Jake read, created with MS Excel.
a. The input variable is normally represented by x, while the output variable is normally represented by y.
The input variable, which is the variable that determines or indicates the number of pages Jake reads is the number of days, therefore;
The value of x represents the number of days
b. The output variable obtained from the input variable which is the number of days is the number of books Jake reads, therefore;
The output variable, y, represents the number of books Jake reads
c. The slope is the rate of change of the number of pages Jake reads per unit time. Therefore, the slope represents the number of pages Jake reads per day.
d. The graph of the data in the table indicates that the relationship is a straight line relationship,the slope can therefore be obtained using two points as follows;
Slope, m = (108 - 0)/(4 - 0) = 27
The slope of the line is 27 pages per day
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James has 20$ to pay for a movie ticket and candy. Each box of candy cost 2$, the movie ticket cost 12$. Write and equation that can be used to determine how many boxes of candy, c, James can buy
Answer:
4 candy boxes
Step-by-step explanation:
2$ one candy box
then 20-12=8 then
left 8$ now,2$=1 candy box 8$=8÷2
Ans will be 4
Answer:
2c + 12 = 20. Simplified to 2c = 8
Step-by-step explanation:
We can start with a Template
Y = Xc + C
Y being the total
X being candy price
c bring candy boxes, as stated
C being ticket price
Plugging those in we get
20 = 2c + 12
Since you bought the ticket with your $20, we can subtract the ticket price from both sides, giving you
8 = 2c or 2c = 8
a bowl contains 7 blue chips and 3 white chips. two chips are to be drawn successively at random and without replacement. what is the probability of the first chip is white and the second chip is blue?
The probability of drawing a white chip first and a blue chip second is 1/5.
To find the probability of drawing a white chip first and a blue chip second, we can use the formula for conditional probability.
Conditional probability is the probability of an event occurring given that another event has already occurred. It is represented by the notation P(A|B), where A is the event of interest and B is the event that has already occurred.
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
This formula expresses the probability of event A occurring given that event B has occurred, as a ratio of the probability of the two events occurring together and the probability of event B occurring alone.
Where A is the event of drawing a white chip first and B is the event of drawing a blue chip second.
We know that the probability of drawing a white chip first is 3/10 (since there are 3 white chips out of a total of 10 chips in the bowl), so P(A) = 3/10.
Once a white chip has been drawn, there are 9 chips left in the bowl, with 6 of them being blue. This means that the probability of drawing a blue chip second given that a white chip has already been drawn is 6/9, so P(B|A) = 6/9.
By multiplying these two probabilities together, we get:
P(A and B) = (3/10) * (6/9) = (3/10) * (2/3) = 6/30 = 1/5
Therefore, the probability of drawing a white chip first and a blue chip second is 1/5.
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HELP PLEASE!!!!
What happens if you graph y=f(f^-1(x))? Explain.
How do you write 90% as a fraction
Answer:
9/10
Step-by-step explanation:
90/100
is 9/10 simplified
Answer:
it 9/10 becuse nvm
Step-by-step explanation: