To find the largest possible value of p[a∪b]−p[a∩b], we need to first calculate both probabilities separately. The probability of a union b (p[a∪b]) can be found using the formula:
p[a∪b] = p[a] + p[b] - p[a∩b]
Substituting the values given in the problem, we get:
p[a∪b] = 0.7 + 0.9 - p[a∩b]
Now, we need to find the largest possible value of p[a∪b]−p[a∩b]. This can be done by minimizing the value of p[a∩b].
Since p[a∩b] is a probability, it must be between 0 and 1. Therefore, the smallest possible value of p[a∩b] is 0.
Substituting p[a∩b]=0, we get:
p[a∪b] = 0.7 + 0.9 - 0 = 1.6
Therefore, the largest possible value of p[a∪b]−p[a∩b] is:
1.6 - 0 = 1.6
In other words, the largest possible value of p[a∪b]−p[a∩b] is 1.6.
This means that if events a and b are not mutually exclusive (i.e., they can both occur at the same time), the probability of at least one of them occurring (p[a∪b]) is at most 1.6 times greater than the probability of both of them occurring (p[a∩b]).
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I have no idea how to do this ….
The value of ∛64 will be equal to 4.
What is a radical expression?In mathematics, a number r is said to be the nth root of a number x if it is raised to the power n. where n is a positive integer, also referred to as the root's degree. Degree 3 roots are referred to as cube roots, while degree 2 roots are known as square roots.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The radical expression will be solved as,
∛64 = ∛ ( 4 x 4 x 4 )
∛64 = ∛ ( 4³ )
∛64 = 4
Hence, the solution for ∛64 will be 4.
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Is 0 an exponential function?
0 is not an exponential function.
We know that the general form of exponential function f with base b is defined as:
f(x) = b^x
where b > 0 and b is not equal to 1
and x is any real number.
If it is negative b < 0, the function is undefined for -1 < x < 1.
If in an exponential function the base is less than zero, then it would make the function values complex for certain fractional values.
If the base of exponential function is 0 then function would create a graph which violates the properties / definition of exponential functions.
Also, we can not write 0 in exponential function form.
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What is the value of −7 + (−12) + 81?
−100
−76
62
86
Find the slope of that passes through (5,2) and (8, 9)
Answer:
slope = [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, 2 ) and (x₂, y₂ ) = (8, 9 )
m = [tex]\frac{9-2}{8-5}[/tex] = [tex]\frac{7}{3}[/tex]
y+x^2 -4 simplify the expression
6
5 divided by 1
7 =
y + x² - 4 is already in simplest form and the value of 6/5 ÷ 1/7 is 8.4.
What is simplest form?A fraction with a reasonably prime numerator and denominator is the simplest form. It denotes that the fraction's numerator (upper or top portion) and denominator (lower or bottom portion) share no common component other than 1. A fraction is a value that denotes a portion of a larger whole.
A fraction's simplest form is also known as its reduced form. 3/4 is the simplest form of a fraction with a common component of one, for example. However, because 2/4 can be reduced further and expressed as 1/2, it is not the simplest form. In this case, 1/2 and 2/4 are equivalent fractions.
We have given two question
y + x² - 4 simplify and 6/5 ÷ 1/7 = ?
Lets simplify
y + x² - 4 is already in simplest form
For
6/5 ÷ 1/7
= 6/5 × 7/1
= 42/5
= 8.4
Thus, y + x² - 4 is already in simplest form and the value of 6/5 ÷ 1/7 is 8.4.
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PLEASE HELP ME I NEED THIS DONE AS SOON AS POSIBLE
a. Liam wants to know how the function would need to change to reflect the amount of money the business will take in. Use this function to model a function for gross sales. (Gross sales are the total amount of money the flowers sell for.)
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b. Liam knows that his cost (c) in terms of the units of mums sold (x) can be modeled by the function Replace the variable x in this function with the function that gives the number of units sold (x) in terms of price p. What does this turn the function c into?
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c. Liam wants to calculate the profit his shop would earn from the sale of mums. He knows that it can be done by deducting the costs from the money that the store makes selling mums. Now that he has the functions for the cost and gross sales, can he subtract the function for cost from the function representing the gross sales to arrive at a function for profit? Why?
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d. Find the store’s profit function for selling mums by subtracting the function for cost from the function for gross sales. Consider pr(p) as the profit function.
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e. Is the profit function linear or quadratic?
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f. Liam wants to use the profit function to determine the range of prices at which he can sell mums and make a profit. How can he determine the price range?
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g. Use the quadratic formula to find the factors of the profit function you wrote.
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h. Using the factors you found in part g, find the zeros of the quadratic profit function.
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i. Liam needs to find the range of prices at which he can sell mums and make a profit. Based on the equation, what are the points between which he will earn a profit on his mums?
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j. Liam wants to determine the most profitable price point for the mums. Use the completing the square technique to find this price.
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k. Liam is interested in determining the maximum profit possible for the mums. Find the maximum profit corresponding to the most profitable price point.
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Task 2: A Boat Ride
Jake went on a riverboat tour. After returning from the tour, he was curious to know the speed at which the boat was going. During the tour, he was told that he would travel 10 miles upstream and then 10 miles downstream. He also knows that the river was flowing at a rate of 3 miles/hour and that the tour took about three hours.
The boat moved at a constant speed for the whole journey, although its actual speed varied with the current.
a. Jake wants to know the boat’s actual speed going upstream and actual speed coming downstream. If the boat was moving at a constant speed of x miles per hour, determine the boat’s relative speed in each direction.
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b. Was the time it took the boat to go upstream the same as the time it took to come downstream?
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c. Jake first reasoned that because the boat ride took 3 hours, it must have taken 1.5 hours to go upstream and 1.5 hours to go downstream. Thinking about it further, however, he realized that the ride upstream had to take longer than the trip downstream. What is the reason it took longer to travel one direction than the other?
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d. The time it took the boat to go upstream is U, and the time it took to come downstream is D. What is U + D?
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e. Jake knows that the relationship between distance (d), velocity (v), and time taken (t) is given by d = vt. Rewrite this equation for t.
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f. Using the equation you rewrote in part e, write an equation for the time taken for the upstream trip.
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g. Now construct an equation for the time taken for the downstream trip.
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h. Jake already has the equation U + D = 3, which represents the total time taken for the whole journey. Now that he has individual equations for U and D, he needs to combine these three equations to get a single equation. Construct a combined equation for U + D in terms of x, the constant speed at which the boat was going.
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i. Jake now has an equation with x as the only unknown variable. He needs to solve for x. Transform the equation you found in part h into a quadratic equation, and find the value of x, the constant speed at which the boat traveled.
Type your response here:
Answer::b.
Step-by-step explanation:
Classifying Triangles Card Sort
The link between s, t, and u is therefore u2= t2+s2 and provides the answer to the triangle problem.
Describe the triangle.A triangle is a polygon since it has three parts and three vertices. It is a basic geometric shape. A triangle with the corners A, B, & C is referred to as a triangle ABC. A singular plane & triangle in Geometric shapes are found so when three components are not collinear. Due to its right side and three corners, triangles are considered polygons. The corners of a triangle are defined as the locations at which its three sides meet. 180 degrees is obtained by multiplying three triangle angles.
Here,
Given: Triangle STU is a right triangle in this instance.
Thus,
We learn:
parts s, t, and u
Their connection is as follows:
Given that it's a right triangle
So,
The Pythagoras Theorem states that
=>u²= t²+s²
The link between s, t, and u is therefore u2= t2+s2 and provides the answer to the triangle problem.
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
Question 15(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a heart.
0.13
0.25
0.35
0.70
Answer:
For the first question, To determine the probability that a student studied for exactly 1 hour, we can use the formula:
P(X=1) = (number of students who studied for 1 hour) / (total number of students)
In this case,
P(X=1) = 8/30 = 0.27 (rounded to two decimal places)
So the probability that a student studied for exactly 1 hour is 0.27
For the second question, to determine the experimental probability of drawing a heart, we can use the formula:
P(Heart) = (number of times a heart is drawn) / (total number of draws)
In this case,
P(Heart) = 7/20 = 0.35
So the experimental probability of drawing a heart is 0.35
Therefore, the option 3 is the answer.
Step-by-step explanation:
c + –4c + 10 + –10
an
Answer:
-3c
Step-by-step explanation:
During photosynthesis, what is the path or flow of energy among biotic and abiotic parts of an ecosystem?
Answer:
-3c
Step-by-step explanation:
c+-4c+10+-10= c+-4c= -3c
What is the exponential form of 3?
Answer:The 3 in 103 is called the exponent. The expression 103 is called the exponential expression. base → 103 ←exponent
Step-by-step explanation:
5. f(x) = 2x - 7 Ln x; 6. f(x) = 3x^2 + 4x - Inx^5; 7. y = -5t^2 +4-3
The derivatives of the given functions are 2 - 7/x, 6x + 4 - 5/x^4 Inx, -10t + 3 - 1/t Log t, and 6/x In 5 - 4x, respectively.
5. f'(x) = 2 - 7/x;
6. f'(x) = 6x + 4 - 5/x^4 Inx;
7. y' = -10t + 3 - 1/t Log t;
8. y' = 6/x In 5 - 4x
5. To find the derivative of the given expression, apply the chain rule. The derivative of 2x is 2, and the derivative of -7Ln x is -7/x. Thus, the derivative of the function is 2 - 7/x.
6. To find the derivative of the given expression, apply the chain rule. The derivative of 3x^2 is 6x, the derivative of 4x is 4, and the derivative of -Inx^5 is -5/x^4 Inx. Thus, the derivative of the function is 6x + 4 - 5/x^4 Inx.
7. To find the derivative of the given expression, apply the chain rule. The derivative of -5t^2 is -10t, the derivative of 4 is 0, and the derivative of -3t is -3. The derivative of Logt is 1/t Log t. Thus, the derivative of the function is -10t + 3 - 1/t Log t.
8. To find the derivative of the given expression, apply the chain rule. The derivative of 6In5x is 6/x In 5, and the derivative of -2x^2 is -4x. Thus, the derivative of the function is 6/x In 5 - 4x.
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How many formulas are there in quadratic equation class 10?
There are three formulas that can be used to solve quadratic equations in class 10.
The first formula is the Quadratic Formula, which is used to solve any quadratic equation of the form ax² + bx + c = 0. This formula is used to find the two values of x that are the solutions to the equation. The second formula is the Completing the Square formula, which is used to solve any quadratic equation of the form ax² + bx + c = 0. This formula is used to rewrite the equation in the form (x + h)² = p , and then solve for the value of x. The third formula is the Factorization Method, which is used to solve any quadratic equation of the form ax² + bx + c = 0. This method is used to factor the equation into two linear factors, and then use either the Quadratic Formula or the Completing the Square formula to find the two values of x that are the solutions to the equation. All three of these formulas can be used to solve any quadratic equation of the form ax² + bx + c = 0.
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NAFTA recognize the reality of today' economy - globalization and technology. Our future i not in competing at the low-level wage job; it i in creating high-wage, new technology job baed on our kill and our productivity. ~ John F. Kerry
The quote mentioned in the question was given by John F. Kerry who was a famous American personality, he was born on 11 December 1943.
Professionally he was an attorney and later became a politician and, diplomat and he currently serves as the first United States special presidential envoy for climate. He is a member of the Forbes family and the Democratic Party, and that he previously served as the 68th United States secretary of state .
Some of his other popular quotes are , "I saw courage both in the Vietnam War and in the struggle to stop it. I learned that patriotism includes protest, not just military service."
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40-32 dived by 8+5-2
39
40-32÷8+5-2
40-4+3
40-1
39
What are the stakeholders in a stakeholder analysis?
The stakeholders in a stakeholder analysis can include both internal stakeholders and external stakeholders.
Stakeholders are a group that expresses interest in the firm and whose activities, whether professional or personal, have an impact on its operations. The process of identifying and evaluating the significance of the important individuals or groups that are impacted by or have the potential to influence a project's or decision's result is known as stakeholder analysis.
A stakeholder analysis may include both internal and external stakeholders, such as community members, customers, suppliers, regulators, and government organisations. Internal stakeholders in a stakeholder study take into account employees and management. Depending on the project's nature, different parties may be involved, and the list of stakeholders may need to be updated as the project moves along.
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Please please please help! 20+ points! Thank you :)
Answer:
CD = 27
Step-by-step explanation:
2(4x - 1) + 2(3x + 3) = 116
8x - 2 + 6x + 6 = 116
14x + 4 = 116
14x = 112
x = 8
3(8) + 3
= 24 + 3
= 27
What is substitution Short answer?
Substitution is the name of the process in algebra which is used for swapping an algebraic letter for its value.
The substitution method is the algebraic method to solve different linear equations. In this method, the value of one variable from one of the equations is substituted in the other equation.
In substitution the following steps are used to solve an equation by substitution method:
Step 1. Simplify the given equation by removing the parenthesis.
Step 2. Solve one of the equations for any unknown value.
Step 3. Substitute step 2 result in the other equation.
Step 4. Now solve the equation which gets from step 3 obtained using elementary arithmetic operations.
Step 5. Finally, solve the final equation for the second variable.
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is -(5/12) = to 5/-12
Answer:
Step-by-step explanation:
-5/12 = 5/-12
yes
Solve:
[tex]sin^2(2x+3)+cos^2(2x+3)=2x+3[/tex]
The solution of the trigonometric equation sin^2(2x+3)+cos^2(2x+3)=2x+3 is x = -1.
How to solve a trigonometric equation?Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles
sin²(2x+3) + cos²(2x+3) = 2x + 3
Remember, the trigonometric identity, sin²θ + cos²θ = 1.
Thus, we can say sin²(2x+3) + cos²(2x+3) = 1. We now have:
sin²(2x+3) + cos²(2x+3) = 2x + 3
1 = 2x + 3
2x = 1-3
2x = -2
x = -2/2
x = -1
Therefore, the solution of the equation is x = -1
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Can a triangle have the sides 5'7 12?
It is not possible to construct a triangle whose sides are 5 cm 7 cm and 12 cm because the sum of two sides(5 cm and 7 cm) are equal to the third sides(12 cm). Two equal sides cannot form a triangle.
In the given question, we have to check that it is possible to construct a triangle whose sides are 5 cm 7 cm and 12 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 5 and 7.
7 + 5 = 12
12 = 12
Now we add 5 and 12
5 + 12 > 7
17 > 7
Now we add 7 and 12
7 + 12 > 5
19 > 5
It is not possible to construct a triangle whose sides are 5 cm 7 cm and 12 cm because the sum of two sides(5 cm and 7 cm) are equal to the third sides(12 cm). Two equal sides cannot form a triangle.
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The complete question is:
Can a triangle have the sides 5 cm 7 cm and 12 cm?
What are the explicit equation and domain for an arithmetic sequence with a first term of 3 and a second term of 5?
Group of answer choices
an = 3 + 2(n − 1); all integers where n ≥ 0
an = 3 + 6(n − 1); all integers where n ≥ 1
an = 3 + 6(n − 1); all integers where n ≥ 0
an = 3 + 2(n − 1); all integers where n ≥ 1
Note that the explicit equation and domain for an arithmetic sequence with a first term of 3 and a second term of 5 is n = 3 + 2(n − 1); all integers where n ≥ 1 (Option D)
What is an arithmetic sequence?Arithmetic progression or arithmetic sequence is a numerical series in which the difference between subsequent terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15..
The first term of the arithmetic sequence is 3, followed by 5. Thus, the common difference is, 5-3 = 2. You use these values to the derived formulas for arithmetic progression. One of these formulas is
An = A1 + (n-1)d
where
An is the nth term in the sequence
A1 is the first term of the sequence
n is the total number of terms within the sequence
d is a common difference.
In this problem, A1 = 5 and d=2. Substituting to the equation,
An = 3 + (2)(n-1)
An = 3 + 2(n-1), where n should be more than 1. In order for it to become a sequence, it should contain more than one term.
Therefore, it is correct to appropriate an explicit equation and domain for an arithmetic sequence with a first term of 3 and a second term of 5 to be: n = 3 + 2(n − 1); all integers where n ≥ 1
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5. You overhear a friend discuss how Americans are frivolous in their spending and waste lots of
money. Use this data on family budgets to argue against his position.
The statement if False.
What is the family budget?A family budget is a game plan for your family's money. Your plan identifies where and how your money comes and goes by focusing on income and expenses. Importantly, it also reflects your family's goals and values by how you spend and save.
Given statement,
You overhear a friend discuss how Americans are frivolous in their spending and waste lots of money.
The most expensive items in American spending are needs like housing, taxes, and transportation, while wants like wants are the least expensive.
In America, besides taxes three largest cost categories are households, transportation and food.
A family's transportation costs are $1,847 more than its food expenses.
Typically, needs make up 80% of expenses rather than wants.
Housing, fees, and medical expenses, continuing to be the same each month. The cost of clothing, entertainment, food, and transportation changes every month.
Hence, we can conclude that, Americans don't necessarily waste money on wants because they have to spend on needs before wants, which results in a lot of spending on things like housing and taxes.
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Pleader help, I’m so confused
Answer:
5•8-(4+2)=34
Step-by-step explanation:
because you need to change the order of operation
which of these is obtained by adding three digit number to 7845. which of the following number lies between 5595 and 5610 a=5509 b=5590 c=5605 d=5611 25x200x4=100x=? a= 25x4 b
a}8945
b}7954
c}7905
d}7854
On adding three digit number 109 to 7845 we get 7954 so the number is 109.
What is a three-digit number added?The one -ended or all of the addends in a 3-digit addition are numbers of three digits. Three-digit numbers can be added by placing them in columns so according their place values. Following that, we start adding the numbers from of the ones and tens columns before finishing with the hundreds column.
What in math is addition?The numbers being added are termed addends, and the outcome of the operation, or the answer we ultimately get, is referred to as the sum. It is a fundamental mathematical operation that we employ on a daily basis. We add numbers in a variety of circumstances.
According to the given information:7845 + 1100
= 8945 so it is wrong
7845+109=7954
109 is 3 digit
and because of that, we won't need to consider any other options. If you checked them again, you would not receive a three-digit number.
so 109 is your answer
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Write an expression, in its simplest form, for the perimeter of this shape.
The diagram is not drawn to scale.
The expression that represents the perimeter of the triangle is 3x
How to determine the perimeter of the triangleFrom the question, we have the following parameters that can be used in our computation:
Side length = x
Triangle type = equilateral triangle
The perimeter of an equilateral triangle can be calculated as
P = 3 * side length
substitute the known values in the above equation, so, we have the following representation
P = 3 * x
So, we have
P =3x
Hence, the perimeter expression is 3x
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The points (–1, –3) and (–5, 9) fall on a particular line. What is its equation in slope-intercept form?
Answer: y = -3x - 6
Step-by-step explanation: y - 9 = ((9 + 3)/(-5 + 1))(x + 5)
y = 9 - 3(x + 5)
y = 9 - 3x - 15
y = -3x - 6
What value(s) of b will cause 2x2 + bx + 128 = 0 to have one real solution? Select all that apply. A. b = 32 B. b = −50 C. b = −20 D. b = –32
The value of b can be -32 or +32 to ensure that the equation has only one true solution.
What is discriminant of the equation?The discriminant is the quadratic formula section behind the square root symbol: b2-4ac. The discriminant indicates whether there are two solutions, one solution, or none at all. The "discriminant" is the argument (that is, the contents) of the square root, which is the equation b2 4ac, because by utilizing its value, you may "discriminate" between (that is, determine the difference between) the various solution types.
Here,
The discriminant of the equation is ...
d = b² -4ac
d = b² -4(2)(128)
d = b² -1024
In order for there to be one real solution, we must have d=0. So ...
0 = b² -1024
1024 = b²
±√1024 = ±32 = b
The value of b can be -32 or +32 to cause the equation to have one real solution.
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What does a correlation of r =- 0.89 indicate?
The magnitude of the correlation coefficient indicates the strength of the association. For example, a correlation of r = 0.9 suggests a strong, positive association between two variables, whereas a correlation of r = -0.2 suggest a weak, negative association.
How to interpret a correlation coefficient?
The statistical measure of how well changes in the value of one variable predict changes in the value of another is called a correlation coefficient. The value rises or falls together when the variables are positively linked.
Is r or r 2 the correlation coefficient?
The summary table in the Regression output contains the "R" value, which is the coefficient of correlation. The term "coefficient of determination" also applies to R square. To obtain the value of R squared, multiply R by R. In other words, the square of the coefficient of correlation is the coefficient of determination.
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What is the principle of factorization Mcq?
Answer:
The principle of factorization is that every square matrix can be expressed as a product of a lower triangular matrix and upper triangular matrix. On the basis of this fact, these lower and upper triangular matrices help us in finding the unknowns.
Step-by-step explanation:
Hope it helps!
solana purchased 50 boxes of ceramic pottery and 40 boxes of plates on Monday.On Thursday she purchased 58 boxes of ceramic pottery and 46 boxes of plates. the weekly total was 108 boxes of ceramic pottery and 96 boxes of plates. Let c represent the number of ceramic pottery pieces in each box, and let p represent the number of handpainted plates in each box.
Write two equivalent expressions to show the total number of ceramic pottery pieces and handpainted plates that Solana bought.
Both expressions are equivalent
What is the expression in mathematics?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to a specific value or result. Expressions can be simple or complex, and they can be used to represent mathematical relationships or to perform calculations.
Let c represent the number of ceramic pottery pieces in each box, and let p represent the number of handpainted plates in each box.
To find the total number of ceramic pottery pieces that Solana bought, we can use the following expression:
c* (50 + 58) = c*108
This expression shows that the total number of ceramic pottery pieces is equal to the number of ceramic pottery pieces in each box multiplied by the total number of boxes of ceramic pottery that Solana bought.
Alternatively, we can use the following expression:
c50 + c58 = 108*c
This expression shows that the total number of ceramic pottery pieces is equal to the product of the number of ceramic pottery pieces in each box and the number of boxes Solana bought on Monday plus the product of the number of ceramic pottery pieces in each box and the number of boxes Solana bought on Thursday.
Similarly, to find the total number of handpainted plates that Solana bought, we can use the following expression:
p* (40 + 46) = p*86
This expression shows that the total number of handpainted plates is equal to the number of handpainted plates in each box multiplied by the total number of boxes of handpainted plates that Solana bought.
Alternatively, we can use the following expression:
p40 + p46 = 86*p
This expression shows that the total number of handpainted plates is equal to the product of the number of handpainted plates in each box and the number of boxes Solana bought on Monday plus the product of the number of handpainted plates in each box and the number of boxes Solana bought on Thursday.
Both expressions are equivalent, as they provide the same value for the total number of ceramic pottery pieces and handpainted plates that Solana bought.
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