let y1 and y2 denote the proportions of two different types of components in a sample from a mixture of chemicals used as an insecticide. Suppose that y1 and y2 have the joint density function given by
f(y1,y2) = 2, 0<=y1<=1, 0<=y2<1, 0<= y1+y2 <=1 and 0 elsewhere.
Notice that Y1 +y2 <= 1 because the random variables denote proportions withint he same sample.
Find
a.) P(y1<=3/4, y2<=3/4)
b.) P(y1<=1/2, y2<=1/2)
Answers
The values of the samples are:
a.) P(y₁<=3/4, y₂<=3/4) = 7/8
b.) P(y₁<=1/2, y₂<=1/2) = 1/2
For this case we have two random variables Y1 and Y2, the joint density function is given by:
f(y₁,y₂(=2, ≤ y₁ ≤ 1, 0 ≤ y₂ ≤y₂, 0 ≤ y₁+y₂ ≤1
And 0 for other case.
We know that Y₁+Y₂≤1
Let Y1 =X and Y2 =Y we can plot the joint density function. First we need to solve the slope line equation from the condition y₁+y₂≤1
And we got that y₂≤1 - y₁ or equivalently in our notation y ≤ 1-x . And we know that the two random variables are between 0 and 1. So then the joint density plot would be given on the figure attached.
Part a
In order to find the probability that:
P(Y₁<=3/4, Y₂<=3/4) we can use the second figure attached.
We see that we have two triangles with the same Area, on this case
A = bh/2 = 1/4×1/4/2 and then the total area for both triangles is
At = 2 ×1/4×1/4/2
Since our density function have a height of 2 since the joint density is equal to 2 then we can find the volume for the two triangles like this :
Vt = 2 × 2 ×1/4×1/4/2
And then we can find the probability like this:
P(Y₁<=3/4, Y₂<=3/4) = 1 - 2 × 2 ×1/4×1/4/2
= 7/8
Part b
For this case w want this probability:
P(Y₁<=1/2, Y₂<=1/2) we can use the third figure attached.
We see that we have two triangles with the same Area, on this case
A = bh/2 = 1/2×1/2/2 and then the total area for both triangles is
At = 2 ×1/2×1/2/2
Since our density function have a height of 2 since the joint density is equal to 2 then we can find the volume for the two triangles like this :
Vt = 2 × 2 ×1/2×1/2/2
And then we can find the probability like this:
P(Y₁<=1/2, Y₂<=1/2) = 1 - 2 × 2 ×1/2×1/2/2
= 1/2
Hence we get the required answer.
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Related Questions
For an art project, you are using a piece of cloth that is cut out in the shape of a right triangle. Find the area of the cloth. A triangle with side lengths 6 inches, 6 inches, and 8.5 inches.
Answers
Answer:
\(A=17.99\ in^2\)
Step-by-step explanation:
Given that,
A triangle with side lengths 6 inches, 6 inches, and 8.5 inches.
We need to find the area of the cloth.
The side lengths form an isosceles triangle. The formula for the area of the isosceles triangle is given by :
\(A=\dfrac{1}{2}\times b\times h\)
Where
\(h=\sqrt{a^2-\dfrac{b^2}{4}}\)
So,
\(A=\dfrac{1}{2}\times b\times \sqrt{a^2-\dfrac{b^2}{4}}\)
Put a = 6 and b = 8.5
So,
\(A=\dfrac{1}{2}\times 8.5\times \sqrt{6^2-\dfrac{8.5^2}{4}}\\\\A=17.99\ in^2\)
So, the area of the cloth is equal to \(17.99\ in^2\).
Graph the solution to the following system of inequalities.
y<-3x-8
y≥ 2x+3
Answers
The graphical solution for the given inequalities is attached in the answer.
What is inequalities?
Inequalities are the difference between two values indicates whether one is smaller, larger, or simply not equal to the other.
a b asserts that a and b are not equal.
If a b, then a must be less than b.
When a > b, it is said a is greater than b.
When a > b, it is said a is greater than b.
{above two are the strict inequalities}
When a ≤ b, it is said a is less than or equal to b
when a ≥ b, it is said a is greater than or equal to b.
Graphing the inequality is the process of identifying the region of the number line that includes values that would "satisfy" the given inequality.
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assume that the amount of time a person experiences cold virus symptoms are normally distributed with a mean of 7.5 days and a standard deviation of 1.5 days. what proportion of cold sufferers experience symptoms for more than 8 days?
Answers
According to the given mean and standard deviation values, we find out that the proportion of cold sufferers that experience symptoms for more than 8 days is equal to 0.129 or 12.9%.
It is given to us that -
Amount of time a person experiences cold virus symptoms are normally distributed with
a mean of 7.5 days
and, a standard deviation of 1.5 days
We have to find out the proportion of cold sufferers that experience symptoms for more than 8 days.
Now, from the given information, we have
Mean = μ = 7.5
Standard deviation = σ = 1.5
and, X = 8
Now, the proportion of cold sufferers that experience symptoms for more than 8 days can be represented as -
P(X > 8)
= P{[(X-μ)/σ] > [(8-7.5)/1.5]}
=P(Z>0.33)
Looking at the z-score values, we find out that
P(Z>0.33) = 0.129 = 12.9%
Thus, from the given mean and standard deviation values, we find out that the proportion of cold sufferers that experience symptoms for more than 8 days is equal to 0.129 or 12.9%.
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The median weight for a 5 foot tall male to enlist in the US Army is 114.5 lbs. This weight can vary by 17.5 lbs. Write and solve an absolute value inequality to represent the weight of a 5 foot male who would not meet the minimum or maximum weight requirement allowed to enlist the Army.
Answers
An absolute value inequality that represents the weight of a 5-foot male who would not meet the minimum or maximum weight requirement allowed to enlist in the Army is 97 lbs < x < 132 lbs.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The median weight for a 5 foot tall male to enlist in the US Army is 114.5 lbs. This weight can vary by 17.5 lbs. Therefore, the inequality can be written as,
(114.5 - 17.5) lbs < x < (114.5 + 17.5) lbs
97 lbs < x < 132 lbs
Hence, an absolute value inequality that represents the weight of a 5-foot male who would not meet the minimum or maximum weight requirement allowed to enlist in the Army is 97 lbs < x < 132 lbs.
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What+percent+of+a+data+set+is+represented+by+the+total+area+under+a+normal+distribution+curve?+100%+75%+25%+50%
Answers
The total area under a normal distribution curve represents 100% of the data set. The normal distribution curve is a continuous probability distribution that is symmetric and bell-shaped.
It is often used to model real-world data. The area under the curve represents the probability of an event occurring within a certain range of values.
To understand this concept better, let's consider an example. Imagine we have a data set that follows a normal distribution, such as the heights of a group of people. The normal distribution curve is bell-shaped, with the mean height in the center and the majority of the data falling within a certain range.
The area under the curve represents the probability of observing a certain range of values. Since the total area under the curve accounts for all possible values in the data set, it corresponds to 100% of the data.
In this case, the correct answer is 100%. This means that the total area under a normal distribution curve represents the entirety of the data set.
To summarize, the total area under a normal distribution curve represents the entire data set, which is equivalent to 100% of the data set.
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On a test with 25 problems, Grace got 88% correct. How many problems did Grace get correct?
Answers
Answer:
3 I think forgive me if im wrong.
Step-by-step explanation:
3) During the last week of April, Ryan Foss produced 900 dolls. Ryan
receives $.96 per doll, less any defective units. What was Ryan's
gross pay for the last week of April?
Answers
Ryan's gross pay for the last week of April was $864, assuming that 96% of the dolls produced were non-defective.
What was Ryan's gross pay for the last week of April?If Ryan produced 900 dolls during the last week of April and receives $.96 per doll, his gross pay before any defective units are taken into account is:
900 dolls x $0.96/doll = $864
If we need to check if a certain percentage of the dolls produced were defective, we can multiply the gross pay by the percentage of non-defective units to find Ryan's actual gross pay.
For example, if 95% of the dolls produced were non-defective, Ryan's gross pay would be:
$864 x 0.95 = $820.80
Therefore, Ryan's gross pay for the last week of April was $820.80, assuming that 95% of the dolls produced were non-defective.
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Find extreme point(s) at the interval (-[infinity],[infinity]) and decide if the extreme points are min or max.
a) f(x)=x2 +x–6
b) f(x)=x3 +x2
Use Graphical method to solve the following problems
Draw a graph
Identity the feasible area
Find all corner point feasible solutions (CPFS) and identify the optimal solution if they have any
a) Max s.t.
x1 + x2
2x1 + 5x2 <= 5
x1+ x2<=5
3x1+ x2<=15
x1, x2 >= 0
b) Min s.t.
x1 + x2
-x1+ x2<=5
x2 <= 3
3x1+ x2>=7
x1, x2 >= 0
Answers
a) To find the extreme points and determine if they are minimum or maximum, we need to take the derivative of the function and set it equal to zero.
a) f(x) = x^2 + x - 6
Taking the derivative:
f'(x) = 2x + 1
Setting it equal to zero and solving for x:
2x + 1 = 0
2x = -1
x = -1/2
To determine if it is a minimum or maximum, we can examine the concavity of the function. Since the coefficient of x^2 is positive (1), the function opens upward and the critical point at x = -1/2 is a minimum.
b) f(x) = x^3 + x^2
Taking the derivative:
f'(x) = 3x^2 + 2x
Setting it equal to zero and solving for x:
3x^2 + 2x = 0
x(3x + 2) = 0
This gives two critical points:
x = 0 and x = -2/3
To determine if they are minimum or maximum, we need to examine the concavity of the function. Since the coefficient of x^3 is positive (1), the function opens upward. The critical point at x = 0 is a minimum, while the critical point at x = -2/3 is a maximum.
b) Graphical method:
To solve the problem graphically, we will draw a graph representing the constraints and find the feasible area. Then we will identify the corner point feasible solutions (CPFS) and determine if there is an optimal solution.
a) Maximize subject to:
x1 + x2
2x1 + 5x2 <= 5
x1 + x2 <= 5
3x1 + x2 <= 15
x1, x2 >= 0
b) Minimize subject to:
x1 + x2
-x1 + x2 <= 5
x2 <= 3
3x1 + x2 >= 7
x1, x2 >= 0
Unfortunately, the given optimization problems are incomplete as there are no objective functions specified. Without an objective function, it is not possible to determine an optimal solution or solve the problem graphically.
Please provide the objective function for the optimization problems so that we can proceed with the graphical solution and find the optimal solution, if any.
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a) The extreme point for the function f(x) = x² + x - 6 is a minimum point.
b) The extreme point for the function f(x) = x³ + x² is neither a minimum nor a maximum point.
Step 1: For the function f(x) = x² + x - 6, to find the extreme points, we can take the derivative of the function and set it equal to zero. By solving for x, we can identify the x-coordinate of the extreme point. Taking the second derivative can help determine if it is a minimum or maximum point. In this case, the extreme point is a minimum because the second derivative is positive.
Step 2: For the function f(x) = x³ + x², finding the extreme points follows the same process. However, after taking the derivative and solving for x, we find that there are no critical points. Without any critical points, there are no extreme points, meaning there are no minimum or maximum points for this function.
In summary, for the function f(x) = x² + x - 6, the extreme point is a minimum, while for the function f(x) = x³ + x², there are no extreme points.
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On April 5, 2019, Janeen Camoct took out an 65% loan for $16,000. The loan is due March 9, 2020. Janeen’s terms are ordinary interest. Sabrina Bowers took out the same loan as Janeen. Sabrina’s term, however, are exact interest. (Ignore leap year) (Use days in a year table.)
a. What is Sabrina's difference in interest? (Do not round intermediate calculations. Round your answer to the nearest cent.)
b. What will she pay on March 9, 2020? (Do not round intermediate calculations. Round your answer to the nearest cent.)
Answers
Sabrina's difference in interest is approximately $7,050.68, and she will pay approximately $23,050.68 on March 9, 2020.
To calculate Sabrina's difference in interest and the amount she will pay on March 9, 2020, we need to consider the interest calculations for both Janeen and Sabrina.
a. Sabrina's Difference in Interest:
Since Sabrina's terms are exact interest, the interest is calculated based on the exact number of days.
First, let's determine the number of days between April 5, 2019, and March 9, 2020:
Number of days = 365 (days in a year) - 31 (days in March) - 4 (days in April) = 330 days
Now we can calculate Sabrina's interest:
Interest = Principal x Rate x Time
Interest = $16,000 x 65% x (330/365)
Interest = $16,000 x 0.65 x 0.90410958904
Interest ≈ $7,050.68
b. Sabrina's Payment on March 9, 2020:
To find the total amount Sabrina will pay, we need to add the interest to the principal.
Total Payment = Principal + Interest
Total Payment = $16,000 + $7,050.68
Total Payment ≈ $23,050.68
Therefore, Sabrina's difference in interest is approximately $7,050.68, and she will pay approximately $23,050.68 on March 9, 2020.
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Each month, the charge for a cell phone plan consists of a flat fee of $42, plus $12 per gigabyte of data.
Which equation represents the total monthly charge for the plan, C(d) dollars, as a function of the number
of gigabytes of data, d ?
A. C(d) = 12(42)d
B. C(d) = 12d +42
C. C(d) = 42d + 12
D. C(d) = (12 + 42)d
Answers
Answer:
B.) C(d)= 12d+42
Step-by-step explanation:
A flat fee means it is only paid once and doesn't increase or decrease.
The gigabytes of data fluctuate how much you pay the 12 dollar amount.
Meaning 12d represents the price of data and +42 shows the flat rate.
Overall giving us the equation C(d)= 12d+42.
1. biotech research center is working to develop a new vaccine for the west nile virus. the project is so important that the firm has created three teams of experts to work on the project from different perspectives. team 1 has an 86 percent chance of success, team 2 an 87 percent chance of success, and team 3 a 65 percent chance. what is the probability that biotech will develop the
Answers
Probability that the vaccine will be developed = \(\frac{99363}{100000}\)
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probality of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Here,
Team 1 has an 86 % chance of success of developing a new vaccine
Team 1 has 100 - 86 = 14% chance of failure of developing a new vaccine
Team 2 has an 87 % chance of success of developing a new vaccine
Team 2 has 100 - 87 = 13% chance of failure of developing a new vaccine
Team 3 has an 65 % chance of success of developing a new vaccine
Team 3 has 100 - 65 = 35% chance of failure of developing a new vaccine
Probability that the vaccine will not be developed =
\(\frac{14}{100} \times \frac{13}{100}\times \frac{35}{100}\\\frac{637}{100000}\\\)
Probability that the vaccine will be developed =
\(1 - \frac{637}{100000}\\\\\frac{100000-637}{100000}\\\\\frac{99363}{100000}\)
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Q3: Write the equation in slope-intercept form of the line that is parallel to the
graph of each equation and passes through the given point.
1. y = 3x + 6; (4, 7)
3. y = 1/2 x + 5; (4,-5)
Answers
The equations of the lines are y = 3x - 5 and y = (1/2)x - 7
What is an equation?An equation is an expression that shows how numbers and variables are related to each other.
A linear function is in the form:
y = mx + b
Where m is the rate of change and b is the initial value
Two lines are parallel if they have the same slope
1) y = 3x + 6; (4, 7)
The parallel line would have a slope of 3 and pass through (4, 7), hence:
y - 7 = 3(x - 4)
y = 3x - 5
2) y = (1/2)x + 5; (4, -5)
The parallel line would have a slope of 1/2 and pass through (4, -5), hence:
y - (-5) = (1/2)(x - 4)
y = (1/2)x - 7
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A shop sells dress fabric for $2.97 per metre.
A customer buys 9 metres of this fabric.
Calculate the change he receives from $50.
Answers
Answer:
He recives 23.17$
Step-by-step explanation:
2.97 × 9= 26.73
50$-26.73 = 23.27
What is the absolute value of -5
Answers
Answer:
5
Step-by-step explanation:
72,12,2 simplest form
Answers
Answer:
456748
Step-by-step explanation:
you 463uy2iuswhk then 13456
GEOMETRY PROOFS!
Given:
Prove: △MAN ≅ PET
refer to attachments
WILL GIVE BRAINLIEST! PLS HELP!
Answers
Given that:
In ∆AMN and ∆TPE
MA = PE (Side )
∠AMN = ∠TPE (angle)
MN = PT (Side)
By SAS Property
∆ MAN =~ ∆ PET
∆ MAN =~ ∆ PET are congruent triangles .
Answer:- ∆ MAN =~ ∆ PET
Additional comment:
SAS Property:-
In two triangles , The two sides and the included angle are equal to the corresponding two sides and the included angle of the second triangle then they are congruent and this property is called Side-Angle-Side (SAS) Property.
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Integrate by hand the following functions: adr b) (42³-2r+7) dz Upload Choose a File
Answers
The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.
To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:
∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C
where C is the constant of integration.
Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.
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3. Solve the equation.
3(3 - 3x) = 2(x + 3) - 30
a. X= 7
b. x= 3
C. X=-7
d. x=-3
Help
Answers
Answer:
free points thx
Step-by-step explanation:
Answer:
x = 3
Step-by-step explanation:
Hope this helps and have a nice day :)
mp of a book is rs. 250 if the shopkeeper allows 14% discount to his customers and gains 25% . find the cp.
Answers
The cost price that was used to get the book is: R.S 172
How to find the cost price?The parameters given are:
Marked Price: M.P = RS. 250
Discount allowed = 10%
The formula to find the selling price here will be:
S.P = M.P * (100 - Discount)/100
Thus:
S.P = 250 * (100 - 14)/100
S.P = 250 * 0.86
S.P = R.S 215
Since the profit is 25%, then we have:
Cost Price = (S.P * 100)/(100 + Gain%)
Cost price = (215 * 100)/(100 + 25)
Cost Price = 21500/125
Cost price = R.S 172
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2. For each diagram, solve for the variable. Be sure to include the names of any
relationships you used to get your solution.
Answers
2. a. The measure of angle x is equal to 100°.
b. The measure of the unknown variable angle x is 40°.
c. The measure of angle x is 14°.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
a. We know, The measure of an exterior angle of a triangle is the sum of two opposite interior angles.
Therefore, m∠x = 10° + 90°.
m∠x = 100°.
b. We know, Pairs of corresponding angles are equal.
Therefore, In the smaller triangle,
180° - 140° = 40°.
The corresponding angle is 110°.
Therefore, x = 180° - 110° - 40° = 30°.
c. We know pairs of corresponding angles are equal.
Therefore, 3x + 7° = x + 35°.
3x - x = 35° - 7°.
2x = 28°.
x = 14°.
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four less than a number is 25
Answers
Answer: 29
Step-by-step explanation:
For the random variables below, indicate whether you would expect the distribution to be best described as geometric, binomial, Poisson, exponential, uniform, or normal. For each item, give a brief explanation of your answer. Please be specific in the explanation
1. The number of days that we have to wait before the first Daily 4 number drawn in the California State Lottery is a 6. (Each day, this number is equally likely to be any of the 10 digits.)
2. The amount of time before the next plane crash in the United States.
3. The number of typographical errors on a page in the rough draft of a report.
4. The number of times that a rifle shooter hits a target if he shoots 10 times.
5. The number of phone calls that a salesperson gets in the next hour.
6. The number of minutes that the salesperson is waiting before her next phone call.
7. The time of day that a meteor enters the Earth's atmosphere.
Answers
1. The number of days that we have to wait before the first Daily 4 number drawn in the California State Lottery is a 6.
This can be best described as a geometric distribution. The geometric distribution models the number of trials needed to achieve the first success in a sequence of independent trials with a constant probability of success.
In this case, each day can be considered a trial, and the probability of success (drawing the number 6) is the same for each trial (1/10).
2. The amount of time before the next plane crash in the United States.
This cannot be easily classified into one specific distribution. The occurrence of plane crashes typically does not follow a specific distribution pattern, and the time between crashes can vary widely.
It may be more appropriate to consider an exponential distribution, assuming that the events occur randomly and independently over time.
3. The number of typographical errors on a page in the rough draft of a report.
This can be best described as a Poisson distribution. The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space, given a known average rate of occurrence.
In this case, the typographical errors occur randomly and independently on the page, and the average rate of occurrence can be estimated.
4. The number of times that a rifle shooter hits a target if he shoots 10 times.
This can be best described as a binomial distribution. The binomial distribution models the number of successes (hitting the target) in a fixed number of independent trials (shooting 10 times), where each trial has the same probability of success (hitting the target).
The probability of hitting the target can be estimated based on the shooter's skill level.
5. The number of phone calls that a salesperson gets in the next hour.
This can be best described as a Poisson distribution. The Poisson distribution is commonly used to model the number of events that occur in a fixed interval of time, given a known average rate of occurrence.
In this case, the phone calls occur randomly and independently, and the average rate of occurrence can be estimated.
6. The number of minutes that the salesperson is waiting before her next phone call.
This can be best described as an exponential distribution. The exponential distribution is commonly used to model the time between events in a Poisson process, where events occur randomly and independently over time.
In this case, the salesperson's waiting time follows an exponential distribution if the phone calls arrive randomly and independently according to a Poisson process.
7. The time of day that a meteor enters the Earth's atmosphere.
This cannot be easily classified into one specific distribution. The time of day that a meteor enters the Earth's atmosphere is subject to various factors and is not expected to follow a specific distribution pattern.
It may be more appropriate to consider a uniform distribution if the meteor entry times are equally likely throughout the day or a more complex distribution if there are known patterns or influences on meteor entry times.
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Find the sum of the first 10 terms of the following sequence. Round to the nearest hundredth if necessary.
Answers
The sum of the first ten terms that we can find in the series would give us 12714.
What is a geometric sequence?A geometric sequence, also known as a geometric progression, is a sequence of numbers in which each term after the first is found by multiplying the preceding term by a constant value called the common ratio (r).
We know that;
a = 2
r = 5/2
The sum of the first ten terms is now;
\(S10 = 2(1 - (2.5)^{10} )/1 - 2.5\)
S10 = -19071/-1.5
S10 = 12714
Thus the sum of the sequence is 12714.
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A randomized controlled trial in which each subject is assigned to a combination of at least two independent variables is an example of a/an:
Answers
A randomized controlled trial in which each subject is assigned to a combination of at least two independent variables is an example of a Factorial Design.
In statistics, a full factorial experiment is one in which all potential combinations of the levels across all of the factors are taken into account by the experimental units. A full factorial experiment has two or more factors with discrete possible values or "levels" in its design. A fully crossed design is another name for a full factorial design. Using such an experiment, the researcher can examine how each element affects the response variable as well as how different factors interact with one another.
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What is the solution to the following system of equations
Answers
Answer: x=-2
Step-by-step explanation:
y=x+1
y=-x-3
-x-3=x+1
-4=2x
x=-2
Help please I'll give brainlisttttt ahhhh math grade is slippingggg
Answers
Answer: The most number of skeins Sharon can afford to buy is 3.
Step-by-step explanation:
Step-by-step explanation:
Consider the provided information.
Sharon has at most $25 to spend on her sister's birthday gift.
That means Sharon can spend not more than $25.
She already bought a knitting machine for her, which cost $14.99.
She would also like to get her sister some skeins of yarn to go with it. Each skein costs $2.75.
Let y represent the number of skeins of yarn.
Thus, the required inequality is:
Now solve the above inequality.
Skeins must be an integer.
Hence, the most number of skeins Sharon can afford to buy is 3.
ona wants to bake at most 30 loves of banana bread and nut bread for a bake sale. Each loaf of banana bread sells for $2.50 , And each loaf of nut bread sells for $2.75. Cora wants to make at least $44. Write a system of inequalities to model the situation
If represents the larger of two sample variances, can the f test statistic ever be less than 1?
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No, the F-test statistic cannot be less than 1 when it represents the larger of two sample variances.
The F-distribution is always a positive distribution with a range of values greater than zero. The F-test value is always greater than or equal to 0, but it is not always less than or equal to 1.
The numerator, representing the bigger sample variance, is always greater than or equal to the denominator, representing the smaller sample variance. Consequently, the F-ratio, which is the ratio of the larger to the smaller variance, is always greater than or equal to 1. Thus, an F-test statistic that is less than 1 is mathematically incorrect.
Therefore, an F-test statistic is always a positive number that is greater than or equal to zero and greater than or equal to 1. This is because the numerator of an F-distribution is always greater than or equal to the denominator.
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Express as a polynomial is standard form (4x^5 x y^2)^2
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Given expression: (\(4x^5y^2)^2\) We can simplify this expression as follows:
\((4x^5y^2)^2 = 4^2(x^5)^2(y^2)^2= 16x^(5×2)y^(2×2)= 16x^10y^4\)
Thus, the given expression in standard form is 16x^10y^4. Let's understand each term of this expression and how we got this.Standard form of a polynomial
A polynomial is an expression that consists of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
A polynomial is generally expressed in standard form by arranging the terms in decreasing order of exponents.For instance, a polynomial of degree 3 can be written in the standard form as
\(ax^2 + bx^2+ cx + d.\)
The leading coefficient is a, which is the coefficient of the term containing the highest degree of x. If the leading coefficient is not 1, the polynomial is said to be in non-monic form.The given expression is \((4x^5y^2)^2\)
which is equal to 1
\(6x^10y^4.\)
As we have only one term, that's why it is already in standard form as we do not need to rearrange any terms. So, the answer is
\(16x^10y^4.\)
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someone please help please im begging someone help me ASAP!!! i’m struggling
Answers
Answer:
JK--- TU
KL--- UV
JL---TV
Answer:
JK- TU , KL-UV , JL-TV
Step-by-step explanation:
hope this helps
Aubree's car used 4 gallons to travel 120 miles. How many miles can the car go on one gallon of gas?
Answers
Aubree's car used 1 gallon to travel 30 miles.
The car used 4 gallons to travel 120 miles. We need to calculate the distance car can travel with 1 gallon of gas.
By unitary method;
The distance car can travel = (120/4)*1 =30
Aubree's car used 1 gallon to travel 30 miles.
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On 1 gallon of gas, Aubree`s car can go 30 miles.
This is a question of the unitary method. The unitary method is a technique for solving a problem by first finding the value of a single unit, [by dividing] and then finding the necessary value by multiplying the single unit value.
Aubree`s car used 4 gallons of gas to travel 120 miles. So, to find the miles it travelled on 1 gallon of gas. We can simply just divide the total miles the car travelled by the total litres of gas it used.
Therefore, 120/4=30 miles.
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