Perform the following sequence of transformations on the polygon ABCDEFGHIJKLMNOPQRSTUVWXYZ on the coordinate plane. Rotate 180degree clockwise about the origin
Then translate horizontally 2 units to the left and vertically 3 units down
What are the coordinates of A”?
Answers
The new coordinates are A′(2, -2) B′(0, -4) C′(3, -6)
We are given that;
The graph
Now,
The original coordinates of ∆ABC are:
A(3, 4) B(5, 2) C(7, 5)
After applying the translation rule, we get:
A(3 - 1, 4 - 2) = A(2, 2) B(5 - 1, 2 - 2) = B(4, 0) C(7 - 1, 5 - 2) = C(6, 3)
Step 2: Apply the rotation rule to each translated vertex
To rotate a point 90° clockwise about the origin, we need to use this formula:
(x, y) → (y, -x)
we can rotate each translated vertex:
A(2, 2) → (2, -2) B(4, 0) → (0, -4) C(6, 3) → (3, -6)
Step 3: Write the new coordinates of each rotated vertex using prime notation
The prime notation indicates that these are the new coordinates after the transformation. We use A′ for the image of A, B′ for the image of B, and C′ for the image of C.
Therefore, by transformation the answer will be A′(2, -2) B′(0, -4) C′(3, -6).
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Related Questions
Which graph shows the solution to the system of linear equations? y equals negative one fourth times x plus 1 y = −2x − 1 a coordinate grid with one line that passes through the points 0 comma 1 and 4 comma 0 and another line that passes through the points 0 comma negative 1 and 1 comma negative 3 a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma 0 and another line that passes through the points 0 comma negative 3 and 1 comma negative 5 a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma negative 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 5 a coordinate grid with one line that passes through the points 0 comma 1 and 4 comma negative 2 and another line that passes through the points 0 comma negative 2 and 1 comma negative 5
Answers
Answer:
Step-by-step explanation:
The system of linear equations is:
y = -1/4 x + 1
y = -2x - 1
To find the solution to the system, we need to find the point where the two lines intersect. We can do this by graphing the two lines and finding their point of intersection, or by solving the system of equations algebraically.
Using the second method, we can substitute the first equation into the second equation for y:
-1/4 x + 1 = -2x - 1
Simplifying and solving for x, we get:
15/8 x = 2
x = 16/15
Substituting this value of x into the first equation to solve for y, we get:
y = -1/4 (16/15) + 1
y = 19/15
So the solution to the system is (16/15, 19/15).
Looking at the graphs, we can see that only the first option has a point of intersection that matches the solution we found algebraically. Therefore, the graph that shows the solution to the system of linear equations is a coordinate grid with one line that passes through the points 0,1 and 4,0 and another line that passes through the points 0,-1 and 1,-3.
What is the inverse of function g(x) = -x-2/x+4 ? G^-1(x)=
Answers
Answer:
Step-by-step explanation:
what is the most general solution ψ of the time-independent schrödinger equation?
Answers
This solution is unique for each quantum system and provides a complete description of the system's stationary states.
The most general solution ψ of the time-independent Schrödinger equation is a mathematical function that describes the wave-like behavior of a quantum system in a stationary state.
This solution is obtained by solving the Schrödinger equation, which is a fundamental equation in quantum mechanics that relates the energy of a system to its wave function.
The wave function ψ is a complex-valued function that gives the probability density of finding a particle in a given region of space. The most general solution ψ is a linear combination of wave functions that satisfy the Schrödinger equation for a given potential energy function.
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A rectangular park is 75 yards wide and 110 yards long.give the length and width of another rectangular park that has the same perimeter but a larger area.
Answers
Answer: Thus, the width of the second park is 92.5 yards, and its length is also 92.5 yards.
Step-by-step explanation: The perimeter of the first rectangular park is:
P = 2L + 2W
P = 2(110 yds) + 2(75 yds)
P = 220 yds + 150 yds
P = 370 yds
Since the second rectangular park has the same perimeter as the first, its perimeter is also 370 yards. Let's call its width "x" and its length "y".
Then, we have:
2x + 2y = 370
Simplifying this equation, we get:
x + y = 185
The area of the second park is:
A = xy
To find the dimensions of the second park with the largest area, we need to maximize this expression subject to the constraint x + y = 185.
One way to do this is to use the method of Lagrange multipliers. However, in this case, we can use a simpler approach based on the fact that the area of a rectangle is maximized when its sides are equal. Therefore, we can set x = y = 185/2 = 92.5.
There are 68 phones in an office building.
How many unique connections between two of these phones can be made?
Responses
Answers
2278
lthe correct answer is the second option. 2278
Factor completely 18x3y3 − 6x2y. A. 6x2(3xy3 − y) B. 6y(3x3y2 − x2)
C. 6x2y(3xy2 − 1) D. 6xy(3x2y2 − x)
Answers
The simplified factor of the given expression 18x³y³ − 6x²y is given by option C. 6x²y(3xy² − 1).
Expression is equal to,
18x³y³ − 6x²y
Factor out the greatest common factor of the two terms 18x³y³ and 6x²y.
Greatest common factor of 18 and 6 is 6.
Greatest common factor of x³y³ and x²y is equal to x²y.
using both results we have,
Greatest common factor ( 18x³y³ and 6x²y ) = 6x²y
Now take out the greatest common factor and simplify the expression, we get,
= 18x³y³ − 6x²y
= 6x²y(3xy² − 1)
Therefore, the simplified factor form of the expression is option C. 6x²y(3xy² − 1).
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The above question is incomplete, the complete question is:
Write the simplified factor form completely for the expression.
18x³y³ − 6x²y.
A. 6x²(3xy³ − y)
B. 6y(3x³y² − x²)
C. 6x²y(3xy² − 1)
D. 6xy(3x²y² − x)
what line passes through (3,-1) and is perpendicular to x+4y=10
Answers
The equation of a line passing through (3, -1) and is perpendicular to x+4y=10 is y = 4x - 13.
Given that a line is passing through (3, -1) and is perpendicular to x+4y=10,
We need to find the equation of the line,
The slope-intercept of a line is, y = mx+c, where m is the slope.
Converting the given line into its slope-intercept form =
x + 4y = 10
4y = -x + 10
y = -x/4 + 5/2
Therefore, the slope is -1/4.
We know that the slopes of two perpendicular lines are negative reciprocal of each other.
So, the slope of the asked line is 4.
Therefore, the equation in form of c is =
y = 4x+c
To find c put x = 3, y = -1 in the equation above,
-1 = 4(3) + c
-1 = 12 + c
c = -13
Now, the equation is y = 4x - 13.
Hence the equation of a line passing through (3, -1) and is perpendicular to x+4y=10 is y = 4x - 13.
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2. Similar triangles are
are
8
10
-5: Find the value of x.
shown.
shown. Solve for the variable.
x5
Answers
Based on the corresponding sides, the calculated value of x in the similar triangles is x = 7.5
Finding the value of x in the similar trianglesFrom the question, we have the following parameters that can be used in our computation:
The similar triangles
As a general rule, the corresponding sides of similar triangles are in proportions
Using the ratio of corresponding sides, we have
x : 10 = 6 : 8
Express as fraction
This gives
x/10 = 6/8
Multiply both sides by 10
x = 60/8
Divide
x = 7.5
Hence, the value of x in the similar triangles is x = 7.5
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a sampling technique where the sample is split into mutually exclusive groups proportionate to the population and then simple random sampling is employed within those groups, is called....... a. systematic sampling b. stratified sampling c. convenience sampling d. expert sampling
Answers
Stratified sampling is a technique where the sample is split into exclusive groups proportional to the population and then simple random sampling is employed within those groups. So, option B is correct.
This sampling technique involves dividing the population statistics into smaller subgroups on certain given characteristics and then selecting a random sample of solution from each stratum based on the requirement.
This technique is best suitable when the type of population is heterogeneous with respect to characteristics of interest. This sampling uses Proportionate sampling which takes an equal stratum with population size. The output of data is identical to the entire population size.
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plss tell me someone understands this
Answers
The temperature of a bowl of soup left out on the kitchen counter is modeled by the following table, where x is the time in minutes.
A table Time in minutes ranges as 5, 10, 20, 30, 45, 60, 80 and temperature in Fahrenheit ranges from 139.503, 109.047, 83.158, 75.361, 72.556, 72.092, 72.008 respectively.
Which statement is true about the temperature of the soup over time?
A.
As time increases, the temperature of the soup approaches 80 °F.
B.
As time increases, the temperature of the soup approaches 70 °F.
C.
As time increases, the temperature of the soup approaches 0 °F.
D.
As time increases, the temperature of the soup approaches 72 °F.
Answers
The statement is true about the temperature of the soup over time is
As time increases, the temperature of the soup approaches 72 °F.
We have,
Time in min 5 10 20 30 45 60 80
temperature 139.503, 109.047, 83.158, 75.361, 72.556, 72.092, 72.008
(in Fahrenheit)
Here from the table we can see that the time in increasing and the temperature is dropping till 72.008 F.
A. As time increases, the temperature of the soup approaches 80 °F.
False
B. As time increases, the temperature of the soup approaches 70 °F.
False
C. As time increases, the temperature of the soup approaches 0 °F.
False
D. As time increases, the temperature of the soup approaches 72 °F.
True
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Use the following chart to explain how the interest rate affects the total cost of the loan.
Answers
The higher the principal, the higher the total cost of the loan.
Given that;
the following chart to explain how the interest rate affects the total cost of the loan.
Now, In a part of the mortgage payment is dedicated to repayment of the principal balance.
And, explain that Loans are structured so the amount of principal returned to the borrower starts low and increases with each mortgage payment.
Then, The payments in the first years are applied more to interest than principal, while the payments are in the final years.
In our mortgage $100,000, The principal is $100,000.
This happens because the interest rate attached affects larger First figures will more than smaller ones.
6.47% of $5,000 is $323.5 which is less than = 10.8% of $5,000 which is $540 .
now,(calculating the cost of a loan is more this shows the effect as well).
When compounded over time, this is difference will be even more and thus shows that larger principals cause larger total costs.
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help me asap pls and thank you
Answers
The probability of drawing 1 red marble and 1 blue marble from the given boxes is 2/7.
The probability of drawing 1 red marble and 1 blue marble from the given boxes can be calculated using the concept of probability and sample space. The probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. The sample space can be defined as the set of all possible outcomes.
Given, a box contains 4 white marbles and 3 red marbles. A second box has 3 white marbles and 6 blue marbles. If one marble is drawn from each box, the probability that 1 red marble and 1 blue marble will be drawn can be calculated as follows:
The total number of possible outcomes is given by the product of the number of marbles in each box:
Total number of possible outcomes = 7 × 9 = 63
The number of favorable outcomes can be calculated by considering all possible cases where one red marble is drawn from the first box and one blue marble is drawn from the second box.
The number of ways to draw one red marble from the first box = 3
The number of ways to draw one blue marble from the second box = 6
Therefore, the number of favorable outcomes = 3 × 6 = 18
Hence, the probability of drawing 1 red marble and 1 blue marble can be given as follows:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 18/63
The probability of drawing 1 red marble and 1 blue marble from the given boxes is 2/7.
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complete question:
a box contains 4 white marbles and 3 red marbles. a second box has 3 white marbles and 6 blue marbles. if one marble is drawn from each box, what is the probability that 1 red marble and 1 blue marblle will be drawn
a recent survey found that 81% of senior adults wear glasses for driving. in a group of 20 senior adults, how like that no more than 16 wear glasses for driving? 37% 58.8% 63% 41.2%
Answers
The answer is approximately 45.82%, which is closest to 41.2% which is calculated using the binomial distribution formula.
To solve this problem, we can use the binomial distribution formula, which is:
[tex]P(X ≤ k) = Σ^n_i=0 (n choose i) p^i (1-p)^(n-i)[/tex]
Where:
X= number of senior adults who wear glasses for driving
k= maximum number of senior adults who wear glasses for driving that we're interested in (in this case, 16)
total number of senior adults in the group (in this case, 20)
p =probability that a senior adult wears glasses for driving (in this case, 0.81)
We want to find P(X ≤ 16), which represents the probability that no more than 16 senior adults wear glasses for driving.
Using the formula above, we get:
[tex]P(X ≤ 16) = Σ^20_i=0 (20 choose i) 0.81^i (1-0.81)^(20-i)[/tex]
Calculating this sum exactly can be quite tedious, but we can use a normal approximation to get an estimate.
Utilizing the mean (np = 20*0.81 = 16.2) and the standard deviation (sqrt(np(1-p)) = 1.94) of the binomial dissemination, able to surmise the likelihood utilizing the ordinary dissemination as taken after:
P(X ≤ 16) ≈ P(Z ≤ (16 - 16.2)/1.94)
Where Z =standard normal random variable.
Using a standard normal distribution table or a calculator, we can find that:
P(Z ≤ (16 - 16.2)/1.94) ≈ P(Z ≤ -0.103)
≈ 0.4582
hence, the answer is approximately 45.82%, which is closest to 41.2%.
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Let the vector
�
v have an initial point at
(
7
,
−
6
)
(7,−6) and a terminal point at
(
6
,
−
3
)
(6,−3). Determine the components of vector
�. V
Answers
The components of the vector with initial point (7,−6) and a terminal point at (6,−3) are:
(6, -6) to (3, -6)(7, -6) to (6, -6)How to find the components of the vectorThe components of a vector are the vectors that makes up the resultant as described in the problem to have starting point (7,−6) and terminal point (6,−3).
This can be gotten by plotting these points and getting the coordinates of the points that makes the initial point and the terminal point the hypotenuse of the triangle
From the graph, the coordinates are:
component 1: (6, -6) to (3, -6)
component 2: (7, -6) to (6, -6)
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Ethan rolls a number cube with sides numbered 1 through 6. If he rolls the number cube 150 times, how many times would he expect to roll a 5 or a 6?
Answers
Answer:
Do 1:6 150x =6x5
Step-by-step explanation:
it wouuld be 2/6*150=50
help plssss i neeed this done
Answers
The complete answers are:
If c=√a+b² and u=√a+b² then, c must equal u.If two triangles have the same side lengths, then the triangles are congruent.ΔSTU was drawn to include a right angle at angle U.If two triangles are congruent, then the corresponding parts of the triangles are also congruent.A right triangle is defined as a triangle that has a right angle. This description fits triangle ABC, so triangle ABC is a right triangle.What are right angles and congruent angles?Right angles are angles that are equal to 90 degrees.
A triangle that includes a right angle is known as a right-angled triangle.
Congruent angles are angles that are equal in size or measure. For example, the right angles in two or more right-angled triangles are congruent.
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PLS HELP FAST! 10 POINTS
Answers
The median of a data set is the middle number. To find this value, you'll need to order your data set from smallest to largest and then cross off values equally from each end until you reach the middle. In the case there are two numbers in the middle, you will find the mean/average of those two numbers.
7, 9, 11, 14, 18, 20, 30, 35
9, 11, 14, 18, 20, 30
11, 14, 18, 20
14, 18
Average of 14 and 18 = 16
Answer: C. 16
Hope this helps!
The graph below show the proportional relationship between the number of cops of milk and the number of cups of strawberry juice in a recipe of homemade strawberry milk
Answers
where's thw graph? what we have to show?
For the parallelogram, if m∠2= 5x - 23 and m∠4= 3x - 5, find the m∠1.
Answers
The measure of m∠1 is equal to 158 degrees.
What is a parallelogram?In Mathematics, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.
In this context, we can reasonably infer and logically deduce that this parallelogram has both pairs of opposite sides being parallel to each other and the opposite angles (vertical angles) are equal and congruent:
m∠1 = m∠3
m∠2 = m∠4
5x - 23 = 3x - 5
5x - 3x = 23 - 5
2x = 18
x = 9.
m∠2 = 5(9) - 23 = 22°
m∠1 + m∠2 + m∠3 + m∠4 = 360
2(m∠1) + 2(22) = 360
m∠1 = (360 - 44)/2
m∠1 = 158°
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pls help with a detailed explanation!
Answers
x is an integer. Prove that (3x - 1)² - 2x(4x + 2) + 24 is a square number.
Answers
Answer:
Step-by-step explanation:
=9x^2 -6x +1 -8x^2 -4x +24
=x^2 -10x +25
=(x-5)^2
when x is an integer,
(x-5)^2 is a square number because you can put any integer as X.
the double number line shows that faye can sort 150150150 recyclable items in 333 minutes. 003333time (minutes)00150150150150items a double number line with 6 equally spaced tick marks. the line labeled time, minutes, reads from left to right: 0, two unlabeled tick marks, 3, two unlabeled tick marks. the line labeled items, reads from left to right: 0, two unlabeled tick marks, 150, two unlabeled tick marks. based on the ratio shown in the double number line, how many recyclable items can faye sort in 444 minutes?
Answers
Faye can sort 22,200 recyclable items in 444 minutes, based on the ratio shown in the double number line.
To determine how many recyclable items Faye can sort in 444 minutes, we need to use the ratio shown in the double number line. We can do this by finding the slope of the line, which is the ratio of the change in items to the change in time.
To find the slope, we start at the point (0,0) on the number line and move to the point (150,3). The change in items is 150 - 0 = 150, and the change in time is 3 - 0 = 3. Therefore, the slope is:
slope = change in items / change in time
slope = 150 / 3
slope = 50
This means that Faye can sort 50 recyclable items in one minute. To find out how many items she can sort in 444 minutes, we simply multiply the number of minutes by the rate of 50 items per minute:
items sorted = rate x time
items sorted = 50 x 444
items sorted = 22,200
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Look at the figure below. Select TWO equations that represent angle relationships in the figure. A 7x−9=6x+14 B 7x−9=5x−10+33 C 6x+14=33+180−(7x−9) D 33+(5x−10)+(7x−9)=180
Answers
Answer:
C and D both represent angle relationships in the figure.
C represents the relationship between the angles labeled x, y, and z. We know that the sum of the angles in a triangle is 180 degrees, so we can set 6x+14 (angle x), 33 (angle y), and 180-(7x-9) (angle z) equal to 180 and solve for x.
D represents the relationship between the angles labeled w, x, y, and z. We know that the sum of the angles in a quadrilateral is 360 degrees, so we can set 33+(5x-10)+(7x-9)+w equal to 360 and solve for x.
at the forrester manufacturing company, one repair technician has been assigned the responsibility of maintaining four machines. for each machine, the probability distribution of the running time before a breakdown is exponential, with a mean of 8 hours. the repair time also has an exponential distribution, with a mean of 4 hours. (a) find the probability distribution of the number of machines not running, and the mean of this distribution. (b) what is the expected fraction of time that the repair technician will be busy?
Answers
(a) The probability distribution of the number of machines not running, and the mean of this distribution is 0.899.
(b)The expected fraction of time that the repair technician will be busy is 88.9% of the time.
(a) Let X be the number of machines not running. At that point, X can take on values 0, 1, 2, 3, or 4. We will discover the likelihood conveyance of X as takes after:
P(X = 0) = P(all machines are running) = [tex]e^(-84)^4[/tex]/4! = 0.302
P(X = 1) = P(one machine isn't running) = (4)([tex]e^(-84)^3[/tex]/3!) = 0.393
P(X = 2) = P(two machines are not running) = (6)([tex]e^(-84)^2[/tex]/2!) = 0.236
P(X = 3) = P(three machines are not running) = (4)([tex]e^(-84)^1[/tex]/1!) = 0.067
P(X = 4) = P(all machines are not running) = [tex]e^(-8*4)^0[/tex]/0! = 0.002
The cruel(mean) of this dispersion is E(X) = (0)(0.302) + (1)(0.393) + (2)(0.236) + (3)(0.067) + (4)(0.002) = 0.899.
(b) Let Y be the division of time that the repair specialist is active. At that point, Y can be communicated as
Y = T/(T + R),
where T is the full time that machines are not running
and R is the entire time that went through on repairs.
We know that
T has an Erlang dispersion with parameters
n = 4 and λ = 1/8 (since the running time of each machine has exponential dissemination with cruel 8 hours).
Subsequently, the anticipated esteem of T is E(T) = n/λ = 32 hours.
Additionally, R has an exponential dispersion with cruel 4 hours,
so E(R) = 4 hours. In this way, we have:
E(Y) = E(T/(T + R))
= E(T)/E(T + R)
= 32/(32 + 4)
= 0.889.
In this manner, ready to anticipate the repair professional to be active around 88.9% of the time.
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Find four rational number between-1and-1/2
Answers
Answer:
For finding 4 rational numbers between two numbers we just multiply the numerator and denominator
Rational numbers -1 and -1/2 are -1/4,-1/8,-1/12,-1/16
This means the four rational numbers are -1/4,-1/8,-1/12,-1/16
Calculate the area of the shaded section of this sh 5 cm 7 cm 12 cm 3 cm 8 cm Not drawn accurately
Answers
Step-by-step explanation:
Same method, just different numbers....YOU should be able to do this one after I showed you the other one ! :
Area of trapezoid - area of parallelogram = shaded area
8 * ( 12+7) / 2 - 5x3 = ????? cm^2
The 25 students in Jay's class have a choice of three extracurricular activities. Of the total number of students, 8 choose soccer, 6 choose math club and the rest choose chorus.
What is the probability that Jay chooses chorus? Enter your answer as a simplified fraction. plspls
Answers
The probability that Jay chooses chorus is 11/25.
We have,
The total number of students in Jay's class is 25, and 8 choose soccer and 6 choose math club.
Therefore, the number of students who choose chorus is:
25 - 8 - 6 = 11
The probability that Jay chooses chorus is the ratio of the number of students who choose chorus to the total number of students:
P(chooses chorus) = 11/25
Thus,
The probability that Jay chooses chorus is 11/25, which is already in simplified form.
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Answer:
Answer is 11/25
Step-by-step explanation:
I took the K12 test
List the sample space for rolling a fair eight-sided die.
S = {1}
S = {8}
S = {1, 2, 3, 4, 5, 6}
S = {1, 2, 3, 4, 5, 6, 7, 8}
Answers
The sample space for rolling a fair eight-sided die is {1, 2, 3, 4, 5, 6, 7, 8}.
We have to find the sample space for rolling a fair eight-sided die.
The sample space for rolling a fair eight-sided die consists of all the possible outcomes of a single roll of the die.
As the die has eight sides numbered from 1 to 8, the sample space can be represented as:
S = {1, 2, 3, 4, 5, 6, 7, 8}
Therefore, the sample space for rolling a fair eight-sided die is {1, 2, 3, 4, 5, 6, 7, 8}.
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in a bag, there are 14 red, 11 blue and 5 green sweets. one sweet is picked out of the bag, what is the probability that it is neither red or blue?
Answers
In a bag, there are 14 red, 11 blue and 5 green sweets. one sweet is picked out of the bag. Therefore, the probability of picking a sweet that is neither red nor blue is 1 - 5/6 or 1/6.
In the bag, there are 14 red, 11 blue, and 5 green sweets, totaling 30 sweets. We want to find the probability of picking a sweet that is neither red nor blue, which means we are looking for the probability of picking a green sweet.
To calculate the probability, use the following formula:
Probability = (Number of desired outcomes) / (Total number of possible outcomes)
In this case, the number of desired outcomes is the number of green sweets, which is 5. The total number of possible outcomes is the total number of sweets in the bag, which is 30.
So, the probability of picking a green sweet is:
Probability = 5/30
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5:
Probability = 1/6
Therefore, the probability of picking a sweet that is neither red nor blue (i.e., a green sweet) is 1/6.
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