If you have to divide by a variable, be sure to explain why it is not zero or why it cannot be zero
1. Let A(x,y,z) = 12 +3+ y2 - 2y MULTIPLIERS
(a) Find the global maximum and minimum of A(3,7.2) subject to the constraint ar* + y + z = 2
(b) Find the global maximum and minimum of Als, y.) on the closed bounded dornain ** + y + x2 <16.
Answers
(a) There is no extreme value of A subject to the given constraint,
(b) For x = 0, y + z² ≤ 16.
y is between -4 and 4. In this case, f(y,z) = y² and the maximum value is 16.
For x = ±y, z = 4 - y².
y is between -2 and 2. In this case, f(y,z) = 2y² - y⁴ and the maximum value is 2.
When dividing by a variable, one should always keep in mind that the variable cannot be equal to zero. In other words, if the value of the variable is zero, the function or expression will not be defined or will give an undefined result. The reason is that division by zero is not defined in the set of real numbers.
Therefore, one should exclude the value of zero from the domain of the function or expression.
In part (a) of the given question, we are asked to find the global maximum and minimum of A(x,y,z) = 12 + 3x + y² - 2y subject to the constraint x + y + z = 2.
Let's find the partial derivatives of A with respect to x, y, and z.
∂A/∂x = 3
∂A/∂y = 2y - 2 = 2(y - 1)
∂A/∂z = 0
Now, we have to solve the system of equations consisting of the partial derivatives and the constraint equation.
\(3 = \lambda_1 + \lambda_2,\\2y - 2 = \lambda_1 + \lambda_2,\\\lambda_1x + \lambda_2x = 0,\\\lambda_1y + \lambda_2y - 1 = 0,\\\lambda_1z + \lambda_2z = 1.\)
Substituting the values of the partial derivatives, we get:
\(\lambda_1 + \lambda_2 = 3,\\\lambda_1 + \lambda_2 = -2,\\\lambda_1(3) + \lambda_2(0) = 0,\\\lambda_1(y - 1) + \lambda_2(y - 1) = 0,\\\lambda_1(0) + \lambda_2(1) = 1.\)
The second and third equations are contradictory. So, under the given constraint, A has no extreme value.
In part (b), we are asked to find the global maximum and minimum of A(x,y,z) = x² + y² on the closed bounded domain x² + y + z² ≤ 16.
Let's use the method of Lagrange multipliers to solve the problem. We have to find the critical points of the function f(x,y,z) = x² + y² subject to the constraint x² + y + z² = 16.
We have to solve the system of equations consisting of the partial derivatives of f, the partial derivatives of the constraint function, and the equation of the constraint function.
2x = λ(2x),
2y = λ(1),
2z = λ(2z).
Substituting the value of λ from the second equation into the first equation, we get: x = 0 or x = ±y.
Substituting the values of x and λ from the first and second equations into the third equation, we get:
z = 4 - y² or z = 0.
Since the constraint is x² + y + z² ≤ 16, we have to consider the following cases:
Case 1: x = 0, y + z² ≤ 16.
So, y is between -4 and 4. The maximum value of f(y,z)=y² is 16 in this case.
Case 2: x = ±y, z = 4 - y².
So, y is between -2 and 2. The maximum value of f(y,z) = 2y² - y⁴ is 2 in this case.
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Related Questions
I need help and I can’t find any sadly. Help!!
Answers
Answer:
See answer below.
Step-by-step explanation:
3x - 2 = 4 Given
+2 = +2
3x = 6 Addition Property of Equality
3x/3 = 6/3
x = 2 Division Property of Equality
What type of number is 33/3?
Answers
Answer:
A Fraction
Step-by-step explanation:
33/3 is a fraction because it consists of a numerator and a denominator.
what do the symbols p with hat on top, x with bar on top, and s represent? variables of interest sample statistics defined variables population parameters
Answers
The symbols p,x, and s represent sample statistics.
- p (pronounced "p-hat") is the sample proportion. It is used to estimate the population proportion. It is computed as the number of successes in the sample divided by the sample size.
-x (pronounced "x-bar") is the sample mean. It is used to estimate the population mean. It is computed as the sum of all the values in the sample divided by the sample size.
- s is the sample standard deviation. It is used to estimate the population standard deviation. It measures how spread out the data is in the sample. It is computed as the square root of the sum of the squared deviations from the sample mean divided by the sample size minus one.
These sample statistics are used to make inferences about the corresponding population parameters, which are denoted by Greek letters such as μ (mu) for the population mean and σ (sigma) for the population standard deviation.
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A company has to decide whether to invest money in the development of a microbiological product. The company's research director has that there is a 60% chance that a successful development could be achieved in 2 years. However, if the product had not been successfully developed at the end of this period, the company would abandon the project, which would lead to a loss in present-value terms of $ 3 million. (Present value is designed to take the company's time preference for money into account. The concept is explained in Chapter 8) In the event of a successful development, a decision would have to be made on the scale of production. The returns generated would depend on the level of sales which could be achieved over the period of the product's life. For simplicity, these have been catorized as either high or low. If the company opted for large-volume production and high sales were achieved, then net returns with a present-value of $6 million would be obtained. However, large-scale production followed by low sales would lead to net returns with a present value of only $1 million.In contrast, if the company decided to invest only small-scale production facilities then high sales would generate net returns with a present value if facilities then high sales would generate net returns with a present value of $4 million and low sales would generate net returns with a present value of $2 million. The company's marketing manager estimates that there is a 75% chance that high sales could be achieved.(a) Construct a decision tree to represent the company's decision problem. (b) Assuming that the companys objective is to maximize its expected returns, determine the policy that it should adopt. (c) There is some debate in the company about the probability that was estimated by the research diretor. Assuming that allo other elements if the problem remain the same, determine how low this probility would have ti be before the option of not developing the product should be chosen. (d) before the final decision us nade the company us taken iver by a bew owner, who has the utilities shown below for the sums of money involved in the decision. (The owner has no ointerest in other attributes which may be associated with the decision, such as developing a prestige product or maintaining employment.) What implications does this have for the policy that you iidentified in (b) and why?Present value of net returns New owner's utility-$3m, $0m, $1m, $2m, $4m, $6m 0, 0.6, 0.75, 0.85, 0.95, 1.0
Answers
The optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.
The initial node represents the decision whether to invest in the development of the microbiological product.
The two possible outcomes are a successful development or failure after 2 years.
(b) To determine the policy that the company should adopt to maximize its expected returns, we need to calculate the expected value at each decision node.
Starting from the end nodes and working backwards, we have:
For large-scale production with high sales:
Expected value = 0.75 x $6m + 0.25 x $1m = $4.25m
For large-scale production with low sales:
Expected value = 0.75 x $1m + 0.25 x $6m = $1.75m
For small-scale production with high sales:
Expected value = 0.75 x $4m + 0.25 x $2m = $3.5m
For small-scale production with low sales:
Expected value = 0.75 x $2m + 0.25 x $4m = $1.75m
At the 2-year node, the expected value for a successful development is:
For large-scale production:
Expected value = 0.75 x $4.25m + 0.25 x $1.75m = $3.5m
For small-scale production:
Expected value = 0.75 x $3.5m + 0.25 x $1.75m = $2.81m
Finally, at the initial node, the expected value for investing in the development is:
Expected value = 0.6 x $3.5m + 0.4 x (-$3m) = $0.1m
Therefore, the policy that the company should adopt to maximize its expected returns is to invest in the development of the microbiological product, choose large-scale production if the development is successful, and choose small-scale production otherwise.
(c) If the probability of a successful development is lower than a certain threshold, the option of not developing the product should be chosen. Let p be this threshold probability. Then the expected value at the initial node is:
Expected value = p x $0m + (1-p) x (-$3m) = -$3m + $3mp
Setting this equal to zero and solving for p, we get:
p = 1
Therefore, if the probability of a successful development is lower than 100%, the company should not invest in the development of the microbiological product.
(d) The new owner's utilities represent their preferences for the sums of money involved in the decision.
The utilities are increasing and concave, indicating diminishing marginal utility of money.
This means that the new owner is risk-averse.
The policy identified in (b) may not be optimal for the new owner because their utilities are different from the present-value net returns.
To determine the optimal policy for the new owner, we need to use the new owner's utility values to calculate the expected utility of each decision branch in the decision tree.
If the company invests in large-scale production and high sales are achieved, the expected utility is 0.75 * 0.95 * 1.0 * $6m = $4.285m.
If the company invests in large-scale production and low sales are achieved, the expected utility is 0.75 * 0.95 * (1 - 0.0) * $1m = $712,500.
If the company invests in small-scale production and high sales are achieved, the expected utility is 0.75 * 0.05 * 1.0 * $4m = $150,000.
If the company invests in small-scale production and low sales are achieved, the expected utility is 0.75 * 0.05 * (1 - 0.0) * $2m = $75,000.
If the company decides not to invest in the product, the expected utility is 0.25 * (1 - 0.6) * $0m + 0.25 * 0.6 * (1 - 0.0) * -$3m = -$450,000.
Therefore, the optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.
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What is the value for x when solving the equation –x (–1) = 3x (–5) using algebra tiles? x = –1 x = 1 x = 2 x = 3
Answers
The value of x in the equation –x (–1) = 3x (–5) is x = 1
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
–x (–1) = 3x (–5)
Remove the bracket in the above equation
-x - 1 = 3x - 5
Collect the like terms in the above equation
3x + x = 5 - 1
Evaluate the like terms in the above equation
4x = 4
Divide both sides by 4 in the above equation
x = 1
Hence, the value of x in the equation –x (–1) = 3x (–5) is x = 1
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Answer:
-3, or D
Step-by-step explanation:
The sum of two numbers is 48 one number is 3 times as large as the other what are the numbers
Answers
Suppose the numbers are, x and y.
So, x+y=48……(1)
And one number is 3 times as large as the other.
So , x=3y……….(2)
Now if put value of x from result (2) to result (1) then,
3y+y=48
So, y= 12
And So, x=3y=3(12)= 36
Someone help me pls
Answers
Answer:
W) 1/18=10/180
N) 2/15=4/30
F) 7/12= 84/144
S) 9/25= 36/100
D) 7/20=35/100
T) 9/10=36/40
M) 19/20=95/100
Step-by-step explanation:
W) is 10/180 as you need to multiply the numerator as the denominator.
N) is 4/30 as you need to multiply the numerator as the denominator.
F) is 84/144 as you need to multiply the numerator as the denominator.
S) is 36/100 as you need to multiply the numerator as the denominator.
D) is 35/100 as you need to multiply the numerator as the denominator.
T) is 36/40 as you need to multiply the denominator as the numerator.
M) is 95/100 as you need to multiply the numerator as the denominator.
What is the formula for AFC?
Answers
The formula for Average Fixed Cost (AFC) is: AFC = FC / Q. Where FC represents the total fixed costs incurred by a firm and Q represents the quantity of output produced by the firm.
AFC is a per-unit measure of the fixed cost of production, and represents the amount of fixed cost that is attributed to each unit of output. As the quantity of output increases, the AFC decreases, since the fixed costs are spread out over a larger number of units. AFC is an important concept in economics and business, as it is used to calculate other cost measures such as average total cost and average variable cost.
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LINEAR EQUATIONS
2(x-1)=3(x+1)
Answers
Compare the expression 3 8 and 3 5 x 3 3 using the properties of multiplication what do you notice
Answers
Using the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power, it can be seens that that the two expressions are equal to each other.
The properties of multiplication state that when multiplying two expressions with the same base, we can add their exponents together. This means that 3 to the fifth power x 3 to the third power is equal to 3 to the eighth power.
In mathematical notation, this looks like:
3^8 = 3^5 x 3^3
Using the properties of multiplication, we can add the exponents together:
3^8 = 3^(5+3)
Simplifying the exponent:
3^8 = 3^8
This shows that the two expressions are equal to each other. Therefore, we can conclude that 3 to the eighth power and 3 to the fifth power x 3 to the third power are the same value.
Note: The question is incomplete. The complete question probably is: Use the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power.
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When we are computing a simple linear regression line, there are certain conditions that must be met for this model to be valid. One of these conditions is the equal spread condition. Which of these answers best explains how we check to make sure that this condition is met? a. Make sure there is similar spread around the sample mean of x. b. Make sure there is similar spread around the line at each value of x.
c. Make sure that there is similar spread around the sample mean of y. d. Make sure all outliers are only below the line.
Answers
The answers that best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.
How we check to make sure that this condition is met?The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.
To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.
Therefore the correct option is C.
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0.93+0.80 rounded to the nearest whole number
Answers
Answer:
1.73 rounded to the nearest whole number is 2
Answer: 2
Step-by-step explanation: 1.73 since 7 is high round up.
Find the missing value for the parallelogram
Answers
Answer:
y = 85°
z = 35°
x = 60°
Step-by-step explanation:
y) 180 - 120 = 60, therefore:
180 - (35 + 60)
=> y = 85
z)
=> z = 35
x)
180 - (35 + 85)
=> x = 60
Hope this helps!
Answer:
to find y
you find the bottom right angle
which is 180-120 = 60
then you do 60+35 = 95
then 180 -95 because the sum of all angles in a triangle is 180
so the answer is 85 = y
There is a rule where the alternate angles between the parallel lines are identical
if y = 85 that means that the angle next to 35 is 85
same for angle z, if the top right 35, that means that angle z = 35
Now you add 35 + 85 = 120
180 - 120 = 60 = angle x
In summary
x=60
y=85
z=35
Hope that answers your question
Don't hesitate to leave a comment if you are confused about something
Step-by-step explanation:
1. decide whether or not each equation represents a proportional relationship.
a. volume measured in cups (c) vs. the same volume measured in ounces (z): c =
) =
b. area of a square (a) vs. the side length of the square (s): a = 32
c. perimeter of an equilateral triangle (p) vs. the side length of the triangle (s):
3s =p
d. length (l) vs. width (w) for a rectangle whose area is 60 square units: l =
: 0
Answers
Equations b and c represent a proportional relationship.
a. This equation does not represent a proportional relationship because there is no proportionality constant. A proportional relationship can be written in the form y = kx, where x and y are variables and k is a constant.
b. This equation represents a proportional relationship because the area of a square is proportional to the side length of the square. The proportionality constant is 32.
c. This equation represents a proportional relationship because the perimeter of an equilateral triangle is proportional to the side length of the triangle. The proportionality constant is 3.
d. This equation does not represent a proportional relationship because there is no equation given. To determine whether length and width are proportional for a rectangle whose area is 60 square units, we would need to know the values of the length and width. A proportional relationship can be written in the form y = kx, where x and y are variables and k is a constant.
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The study of the new CPMP Mathematics methodology described in Exercise 7 also tested staudent's abilities to solve word problems. This table shows how the CPMP and traditional groups performed. What can you conclude?
Math program n Mean Standard deviation
CPMP 320 57. 4 32. 1
Traditional 273 53. 9 28. 5
Answers
The CPMP mathematics methodology seems to be more effective on average at helping students solve word problems compared to the traditional method.
There is a greater variation in performance among students in the CPMP group. We can compare the CPMP and traditional math program groups' performance on solving word problems by looking at the mean and standard deviation.
1) Observe the mean scores:
- CPMP: 57.4
- Traditional: 53.9
The CPMP group has a higher mean score than the traditional group, indicating that students in the CPMP group performed better on average.
2) Observe the standard deviations:
- CPMP: 32.1
- Traditional: 28.5
The CPMP group has a higher standard deviation than the traditional group, meaning that the scores in the CPMP group are more spread out. This suggests there's a greater range of performance levels among students in the CPMP group.
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Mark thought of three consecutive odd integers. He added the first to twice the third and
multiplied this sum by -3. The result was 3 less than the product of 8 and the opposite of
the second. What were the numbers?
Answers
To solve this problem, we'll need to use algebraic expressions. Let's start by breaking down the information given to us.
The problem states that we need to multiply a sum by -3. Let's call this sum "x." So, -3x is our first algebraic expression.
Next, the problem states that this result (which is -3x) is 3 less than the product of 8 and the opposite of the second. We can represent the opposite of the second as -y (since we don't know the value of the second number, we'll use "y" to represent it). So, the product of 8 and -y is -8y. The problem tells us that -3x is 3 less than -8y, so we can represent this with the expression -8y - 3.
Now we can set these two expressions equal to each other, since they both represent the same value:
-3x = -8y - 3
To solve for x and y, we'll need to use some algebraic manipulation. Let's start by isolating one of the variables. We can do this by adding 8y to both sides:
-3x + 8y = -3
Now let's isolate the other variable by dividing both sides by -3:
x - (8/3)y = 1
So we have two equations:
-3x + 8y = -3
x - (8/3)y = 1
We can use these equations to solve for x and y using a method like substitution or elimination. However, since the problem doesn't ask for specific values of x and y, we don't need to solve for them here.
In summary, the problem involved multiplying a sum by -3 and then finding the result of a specific equation involving that sum. We used algebraic expressions to represent the information given to us and then solved for the two variables involved (x and y) using algebraic manipulation.
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Amanda bought a 6 cup bag of shredded cheese for $6.89. She used 2.25 cups to make lasagna and 1.25 cups to make pizza. How much cheese is left?
Answers
Answer:
3.50 cups
Step-by-step explanation:
6-2.25=4.75
4.75-1.25=3.50
what is the expectation value of energy, 〈h〉, as a function of time? does its time dependence make sense to you?
Answers
The expectation value of energy 〈h〉, as a function of time, depends on the specific physical system under consideration. In quantum mechanics, the expectation value of energy is given by:
〈h〉 = 〈Ψ|H|Ψ〉/〈Ψ|Ψ〉
where H is the Hamiltonian operator of the system, and |Ψ〉 is the wavefunction of the system.
The time dependence of the expectation value of energy can be determined by the time-dependence of the wavefunction |Ψ〉. In general, the time-dependence of |Ψ〉 is governed by the time-dependent Schrödinger equation, which relates the time derivative of the wavefunction to the Hamiltonian of the system.
Whether the time dependence of 〈h〉 makes sense depends on the specific physical system and the physical processes involved. In some cases, the expectation value of energy may oscillate or exhibit periodic behavior, while in other cases it may approach a steady state. The time dependence of 〈h〉 can provide insights into the underlying physics of the system and can be used to make predictions about its behavior.
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please help me im in a rush
Answers
Answer: 69m^2
Step-by-step explanation:
we can find the area of shaded region by subtracting the area of removed region.
so,
area of rectangle= length*width
for area of removed region
=4m*2m=8m^2
for area of larger region
=11m*7m=77m^2
Now final destinaltion
area of shaded region=area of lareger region-area of smaller region
=77m^2-8m^2
=69m^2
Fill in the blank random variable has either a finite or a countable number of values A discrete random variable has either a finite or a countable number of values. probability continuous discrete required
Answers
A discrete random variable has either a finite or a countable number of values.
Discrete random variables are defined as variables that can only take on a finite number of values. If any random variable takes a countable number of all the possible values, it is referred to be a discrete random variable. For instance, while flipping a coin, the random variable X will take the values 0, 1, and 2 depending on the number of heads.
If the value of any variable, such as X, is uncertain, that variable is said to be a random variable. It may also be defined as a function that is crucial in giving values to the results of any random experiment. Depending on the sort of numeric values they include, random variables can be either discrete or continuous.
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simplify the square root of 243
Answers
Answer:
9√3
Step-by-step explanation:
Answer:
\(9\sqrt{3}\)
Step-by-step explanation:
we know that 3*81 = 243, so we can say
\(\sqrt[]{3} * \sqrt{81}\)
And we know that square root of 81 = 9
so we can simplify this to:
\(9\sqrt{3}\)
Hope this helps!
Someone help please!!!!! :(
(Edit: The answer was 126. )
Answers
Answer:
a
Step-by-step explanation:
Last weekend, 15% of the tickets sold at Seaworld were discount tickets. If Seaworld sold 40 tickets in all, how many discount tickets did it sell? Use the percent proportion.
Answers
Answer:
6 tickets
Step-by-step explanation:
if f(x)=3x-2 find f-1 (13)
Answers
Answer:
Firstly
f(x)=3x-2=y then
Interchanging x and y we get
x=3y-2
x+2=3y
y=(x+2)/3
f-1(x)=(x+2)/3
f-1(13)=(13+2)/3
f-1(13)=5
A function is defined as a relation between a set of inputs having one output each.
The inverse of function f(x) = 3x - 2 is:
y = (x+2)/3
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
f(x) = 3x - 2
The inverse of f(x):
step 1:
Put f(x) = y
y = 3x - 2
step 2:
switch x and y
x = 3y - 2
step 3:
solve for y
x = 3y - 2
x + 2 = 3y
y = (x+2)/3
Thus,
The inverse of f(x) = 3x - 2 is y = (x+2)/3
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A family of many generations but with only a few emember of each generation is called a?
Answers
A family of many generations but with only a few members of each generation is called a beanpole family pattern
A Beanpole family is a multi-generational family that is long and thin with few aunts, uncles and grandparents. This is a result of extended life expectancy and fewer children being born.
A generation refers to all of the people born and living at about the same time, regarded collectively.
Hence, A family of many generations but with only a few members of each generation is called a beanpole family pattern
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A useful graphical method of constructing the sample space for an experiment is:
a. a tree diagram
b. a pie chart
c. a histogram
d. an ogive
Answers
A useful graphical method of constructing the sample space for an experiment is a tree diagram that is option A.
A tree diagram is a useful graphical method of constructing the sample space for an experiment. It is a type of diagram used to represent the possible outcomes of an event. The diagram is structured in a way that each branch of the tree represents an event that can occur, and each level of the tree represents a stage in the experiment. By using a tree diagram, it is easier to visualize and understand all the possible outcomes of an experiment and the probabilities associated with each outcome. Therefore, option A is the correct answer.
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Which statement best describes the domain of the function represented in the graph?
Answers
Given:
The graph of a function.
To find:
The correct statement for the domain of the given function graph.
Solution:
Domain is the set of x-values for which the function is defined or it is the set of input values.
From the given graph it is clear that it is a linear function with end points (1,2) and (9,14).
So, the given function is defined for \(1\leq x\leq 9\). Here 1 and 9 are including in the set of x-values.
Therefore, the correct option is C, i.e., \(1\leq x\leq 9\) or x between 1 and 9, inclusive.
Suppose the following expression is given: P(X5=3|X4=3,X3=3,X2=1,X1=4, X0=1). a) Write down the "realization" of the stochastic process implied by the above expression, and explain what it means.
Answers
The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.
The realization of the stochastic process implies that the values of the stochastic process are observed at particular points in time. It is denoted by x(t) and takes the form of a function of time t.
If the process is discrete, then the function is a sequence of values at discrete points in time.
A stochastic process is one that evolves over time and the outcomes are uncertain.
The given expression P(X5=3|X4=3,X3=3,X2=1,X1=4, X0=1) gives the probability of X5 being equal to 3 given that X4 is equal to 3, X3 is equal to 3, X2 is equal to 1, X1 is equal to 4, and X0 is equal to 1.
To understand the above expression, suppose we have a stochastic process with values X0, X1, X2, X3, X4, and X5.
The given expression provides the conditional probability of the value of X5 being equal to 3 given that X0, X1, X2, X3, and X4 take specific values.
The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.
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here's all my points plz help
Answers
Answer:
1. A) \(-\frac{4}{5}\) and B) \(-\frac{1}{5}\)
2. A) 4 and B) \(\frac{2}{3}\)
3. A) \(\frac{2}{3}\) and B) 1
4. A) -9 and B) 12
Step-by-step explanation:
Solve for y
anything in front of x is the slope and contants are the y-intercepts
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 2
Blue 10
Green 3
Yellow 19
Purple 20
Based on these results, express the probability that the next spin will land on blue as a decimal to the nearest hundredth.
Answers
Answer:
10/54 = 0.185