The equation of the rational function with the given features is given as follows:
F(x) = [4(x² + 5x + 4)]/(x² - x - 6).
How to define the rational function?A rational function is a fraction, in which both the numerator and the denominator contain instances of the variable x.
Considering the x-intercepts, the numerator of the function is defined as follows:
y = a(x + 4)(x + 1)
y = a(x² + 5x + 4).
Considering the y-intercept at (0,4), the leading coefficient a is given as follows:
a = 4.
The vertical asymptotes determine the zeros of the denominator, which is given as follows:
(x + 2)(x - 3) = x² - x - 6.
Hence the function is defined as follows:
F(x) = [4(x² + 5x + 4)]/(x² - x - 6).
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PLEASE HELP!!! VERY URGENT
A person walks due south from point A for 500 yards and then due west for 300 yards, arriving at point B. Answer the following questions using complete sentences. 2 points for each correct answer and 2 points for each correct explanation.
i. What is the person's displacement from the starting point? How did you calculate this? Be sure to round to the nearest hundredth.
ii. From point B, in what direction would the person have to look in order to be looking back at point A (the starting point)? Give your answer as a true bearing calculated to the nearest hundredth of a degree. Explain how you got this answer.
iii. A friend is standing at point A looking at point B. In what direction would that friend be looking? Give your answer as a true bearing calculated to the nearest hundredth of a degree. Explain how you got this answer.
The answers are mentioned below.
What do you mean by Displacement?In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.
i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500^2 + 300^2) = 583.1 yards (rounded to the nearest hundredth).
ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the direction in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using trigonometry, where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500. Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 360 - 31.39 = 328.61 degrees (rounded to the nearest hundredth).
iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 90 + 59.04 = 149.04 degrees (rounded to the nearest hundredth).
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i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500² + 300²) = 583.1 yards
What do you mean by Displacement?In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.
i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle.
Therefore, the displacement can be calculated as the
√(500² + 300²)
= 583.1 yards (rounded to the nearest hundredth).
ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the ²in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using ², where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500.
Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be
360 - 31.39
= 328.61 degrees (rounded to the nearest hundredth).
iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees.
However, the true bearing is measured from the north and therefore, the true bearing would be
90 + 59.04
= 149.04 degrees (rounded to the nearest hundredth).
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Solve for x with the given measures
y=-2x-5 solve algebraically
The graph of ordered pairs (0, -5), (1, -3), (2, -1), (3, 1) is given below.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is y=2x-5.
Substitute x=0, 1, 2, 3, 4, ..... in the equation y=2x-5, we get
When x=0,
y=-5
When x=1,
y=-3
When x=2,
y=-1
When x=3
y=1
So, the ordered pair is (0, -5), (1, -3), (2, -1), (3, 1) and so on.
Therefore, the graph of ordered pairs (0, -5), (1, -3), (2, -1), (3, 1) is given below.
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Find a polynomial function of degree 4 with the zeros -3 (multiplicity 2) and 3 (multiplicity 2), whose graph passes through the point (-4,245).
The polynomial function of degree 4 is,
⇒ f (x) = 5 (x + 3)² (x - 3)²
What is mean by Function?Relation between set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.
Given that;
Zeroes of function is,
⇒ -3 (multiplicity 2) and 3 (multiplicity 2),
And, It passes through the point (-4,245).
Now, The polynomial function of degree 4 is,
⇒ f (x) = A (x - (- 3))² (x - 3)²
⇒ f (x) = A (x + 3)² (x - 3)²
Since, It passes through the point (-4,245).
Hence, Put x = - 4, y = 245
⇒ 245 = A (- 4 + 3)² (- 4 - 3)²
⇒ 245 = A (- 1)² (- 7)²
⇒ 245 = A × 49
⇒ A = 245/49
⇒ A = 5
Thus, The polynomial is,
⇒ f (x) = A (x + 3)² (x - 3)²
⇒ f (x) = 5 (x + 3)² (x - 3)²
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The area of a rectangular living room is 192 square feet. The length of the room is 8 feet less than twice the width. What is the width of the living room in feet?
Answer:
The width of the living room is 10 feet.
Step-by-step explanation:
Let the width of the living room is w.
And the length of the room is 2w - 8 ft.
Given,
The area of the room is 192 feet^2, by using the formula of area of a rectangle we get,
A = l × w
192 = (2w - 8) × w
Now,
192 = 2w^2 - 8w ( By expanding)
200 = 2w^2 (By adding 8w to both sides)
100 = w^2 (Dividing both sides by 2)
If we take square root on both sides,
w = 10
So,
The width of the living room is 10 feet.
A differentiable function f(x,y) has the property that f(5,4)=7 and fx(5,4)=-3 and fy(5,4)=7. Find the equation of the tangent plane at the point on the surface z=f(x,y) where x=5, y=4
The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) is z = -3x + 7y + 8.
In 3-space, the plane tangent to a surface at a point can be imagined similarly to how we can see the line perpendicular to a curve at a point in 2-space.
The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) can be found using the following formula:
z - [tex]z_{0}[/tex] = fx([tex]x_{0}[/tex],[tex]y_{0}[/tex])(x - [tex]x_{0}[/tex]) + fy([tex]x_{0}[/tex],[tex]y_{0}[/tex])(y - [tex]y_{0}[/tex])
where ([tex]x_{0},y_{0},z_{0}[/tex]) is the point on the surface at which we want to find the tangent plane, and fx([tex]x_{0}[/tex],[tex]y_{0}[/tex]) and fy([tex]x_{0}[/tex],[tex]y_{0}[/tex]) are the partial derivatives of f with respect to x and y, respectively, evaluated at ([tex]x_{0}[/tex],[tex]y_{0}[/tex]).
In this case, we have [tex]x_{0}[/tex] = 5, [tex]y_{0}[/tex] = 4, [tex]z_{0}[/tex] = f(5,4) = 7, fx(5,4) = -3, and fy(5,4) = 7. Substituting these values into the formula, we get:
z - 7 = (-3)(x - 5) + (7)(y - 4)
Simplifying this equation, we get:
z = -3x + 7y + 8
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Please help:) calculus asking about delta functions
The value of delta such that the statement is true is:
δ = 0.0002
How to find delta?
We want to find δ such that:
if |x -3| < δ, then |5x - 15| < ε
So we have two absolute value inequalities to work with.
With ε = 0.001
If we take the second inequality and replace epsilong, we will get:
|5x - 15| < 0.001
We can take 5 as a common factor on the left side to get:
5*|x - 3| < 0.001
Dividing both sides by 5 gives:
|x - 3| < 0.001/5
|x - 3| < 0.0002
Then the value of delta is 0.0002.
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I need answer please thanks
The total amount of the single payment will be $6,924.95.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
The rate of interest is given as,
r = 0.0775 / 2
r = 0.03875
The amount for 2 years is given as,
A = $1,300 × (1 + 0.03875)⁴
A = $1513.52
The amount for 5 years is given as,
A = $3,700 × (1 + 0.03875)¹⁰
A = $5,411.43
The total amount of repayment is given as,
Total amount = $1513.52 + $5411.43
Total amount = $6,924.95
The total amount of the single payment will be $6,924.95.
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A 10-ft pendulum swings through an angle of 40°6'. What is the length of the arc that the tip of the pendulum travels? Round
intermediate calculations to 3 decimal places. Round your final answer to the nearest hundredth of a foot.
The length of the arc that the tip of the pendulum travels is approximately 7 feet.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
We can use the formula for the length of an arc of a circle to find the length of the arc that the tip of the pendulum travels:
Arc length = (angle/360) x 2πr
where: angle = the central angle (in degrees or radians) that the arc subtends and r = the radius of the circle
First, we need to convert the angle from degrees and minutes to decimal degrees.
There are 60 minutes in a degree, so:
40°6' = 40 + 6/60 = 40.1 degrees
Now we can plug in the values:
Arc length = (40.1/360) x 2π(10 feet)
Arc length = 6.99 feet
Hence, the length of the arc that the tip of the pendulum travels is approximately 7 feet.
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Hexagonal prism B is the image of
hexagonal prism A after dilation by a scale
factor of 2. If the surface area of hexagonal
prism B is 172 cm2, find the surface area of
hexagonal prism A, the preimage.
The surface area of hexagonal prism A is 9√3x² cm². We are given that hexagonal prism B is the image of hexagonal prism A after dilation by a scale factor of 2.
Therefore, all corresponding sides of prism A and prism B are in the ratio of 1:2. Let the side length of the base of hexagonal prism A be 'x'. Then, the side length of the base of hexagonal prism B is '2x'.
We know that the surface area of hexagonal prism B is 172 cm². Using the formula for the surface area of a hexagonal prism, we can write:
172 = 2(3√3)(2x)^2 + 6(2x)h
where h is the height of hexagonal prism B.
Simplifying this equation, we get:
172 = 24√3x² + 12xh
Dividing both sides by 12, we get:
14.33 = 2√3x² + h
Now, since hexagonal prism B is a dilation of hexagonal prism A by a scale factor of 2, the height of hexagonal prism A is half the height of hexagonal prism B. So, the height of hexagonal prism A is h/2.
Using the formula for the surface area of a hexagonal prism, we can write:
SA(A) = 2(3√3)x² + 6x(h/2)
Substituting h/2 for the height of hexagonal prism A, we get:
SA(A) = 2(3√3)x² + 3xh
Substituting 2√3x² + h/2 for h, we get:
SA(A) = 2(3√3)x² + 3x(2√3x² + h/2)
SA(A) = 6√3x² + 3√3x² + (3/2)xh
Substituting 2√3x² for h in the above equation, we get:
SA(A) = 6√3x² + 3√3x² + (3/2)x(2√3x²)
SA(A) = 9√3x²
Therefore, the surface area of hexagonal prism A is 9√3x² cm².
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What is the actual length which is represented by 3.2cm on a scale drawing with scale 1cm to 4cm
Answer: 12.8 cm
Step-by-step explanation:
Multiply 3.2 by the scale of 4 to get 12.8.
Convert 40 fluid ounces to pints.
Answer:The answer is 2.5 pints.
Assuming that the relationship is exponential, which equation best represents the curve of best fit for this set of data?
The equation that best represents the curve of best fit for this set of data is y = ae^{bx}, where a and b are constants to be determined by the data points.
What is Equation?An equation is a mathematical expression that uses symbols, such as numbers and variables, to represent a relationship between two or more values or quantities. Equations are used to describe physical laws, solve problems and to make predictions. Equations are fundamental to all areas of mathematics and science, and their use is essential for understanding and exploring the natural world.
This equation is an example of an exponential function, which is used to model data that increase or decrease at an increasing rate. The constants a and b can be determined using a least-squares regression to find the line of best fit. The equation can then be used to extrapolate future values from the data points.
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in a recent survey of 500 people,it was found that 2800 read Concord and 2300 read guardian while 400 read both papers. How many read neither
300 people read neither of the papers.
How to find how many read neither?Set theory is a branch of mathematical logic that studies sets, which are collections of objects. It is a fundamental theory in mathematics and can be used as a foundation for all other areas of mathematics.
Total population n(ξ) = 5000
Number of people reading Concord, n(C) = 2800
Number of people reading Guardian, n(G) = 2300
Number of people reading both = n(C ∩ G)] = 400
Number of people reading any of the newspaper = n(C ∪ G)] = n(C) + n(G) - n(C ∩ G) = 2800 + 2300 - 400 = 4700.
Number of people reading none of them is equal to = Total population - Number of people reading any of the newspaper = 5000 - 4700 = 300
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Suppose a biologist tagged 53 penguins in antarctica during mating season. The next year, they caught 82 and found that 11 of them had tags. Estimate the total number penguins in the area.
It can be estimated that there are 395 penguins in the area.
What is Proportion ?Proportion is a mathematical comparison between two numbers. According to proportion, two sets of specified numbers are said to be directly proportional to each other if they increase or decrease in the same ratio. Symbols of proportions include "::" and "=".
We approach this problem by doing a simple proportion.We can presume that the same proportion of penguins were tagged during mating season if the biologists discovered 11 tagged individuals out of 82 penguins.
The proportion should therefore be [tex]x:53=82:11[/tex] where x represents the total number of penguins. By solving this proportion, we may determine what x is worth:
[tex]11x=53*82\\\\11x=4346\\\\x=395.0909[/tex]
Since there is no such thing as half a penguin, we can round off the answer to the nearest unit.
395 penguins are in the area according to our estimation.
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Graph the function y=x/4
Answer:
Step-by-step explanation:
Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not. x −4 −3 −2 P(X=x) 0.55 0.39 0.06 Answer Keyboard Shortcuts First, decide whether the distribution is a discrete probability distribution, then select the reason for making this decision. Decide Reason
Answer:
x −4 −3 −2
P(X=x) 0.55 0.39 0.06
Step-by-step explanation:
Complete this sentence: The longest side of a triangle is always opposite the
• A. angle with the greatest measure
• B. second-longest side
• C. shortest side
• D. angle with the smallest measure
The longest side of a triangle is always opposite the,
A. angle with the greatest measure.
What is the way of classifying a triangle?If a² + b² < c² then it is an acute angle triangle.
If a² + b² = c² then it is a right-angle triangle.
If a² + b² ≥ c² then it is an obtuse angle triangle.
We know, The length of the largest side in a triangle is opposite to the largest angle.
The statement, The longest side of a triangle is always opposite the
angle with the greatest measure.
Because A longer angle will be more spread out and hence the opposite side will be longer too.
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PLEASE HELP ME ASAP
5. The first row of a stem-and-leaf chart appears as follows: 62 | 1 3 3 7 9. Assume whole
number values.
a. What is the "possible range" of the values in this row?
b. How many data values are in this row?
c. List the actual values in this row of data.
Annie made 4 glasses of juice,her 5 friends drank 1/2 glass each.what fraction of juice was left? how to solve it
[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank [tex]\frac{1}{2}[/tex] glass each.
Meaning of fraction = An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.
Annie made 4 glasses of juice
To find = fraction of juice that was left
Total glasses of juice = 4
Her 5 friends drank 1/2 glass each
= 5 × [tex]\frac{1}{2}[/tex]
= [tex]\frac{5}{2}[/tex]
Fraction of juice that left,
5 - [tex]\frac{5}{2}[/tex]
Subtracting by taking LCM,
= [tex]\frac{10 - 5}{2}[/tex]
= [tex]\frac{5}{2}[/tex]
[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank 1/2 glass each.
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In a class of 50 students, 20 play hockey and 35 play football . 10 students play both hockey and football.
The number of students who either play hockey or football is given by the equation n ( A ∪ B ) = 45 students
What is Set Theory Formula?The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
Given data ,
Let the total number of students in the class be n ( U ) = 50 students
Let the number of students who play hockey be n ( A ) = 20 students
Let the number of students who play football be n ( B ) = 35 students
Let the number of students who play hockey and football n ( A ∩ B ) = 10
So , from the set theory n(A∪B) = n(A) + n(B) - n(A⋂B)
Substituting the values in the equation , we get
The number of students who play hockey or football = 20 + 35 - 10
On simplifying the equation , we get
The number of students who play hockey or football = n( A ∪ B ) = 45 students
And , the number of students who do not play hockey or football is given by the equation = n ( U ) - n ( A ∪ B )
On simplifying the equation , we get
The number of students who do not play hockey or football = 50 - 45 = 5 students
Hence , the number of students who play hockey or football is 45 students
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Simplify:
9 – 3 x 2 + 4
Answer:
2
:
5STEP
2
:
Trying to factor as a Difference of Squares:
2.1 Factoring: 5-3x2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 5 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Equation at the end of step
2
:
5 - 3x2 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : -3x2+5 = 0
Subtract 5 from both sides of the equation :
-3x2 = -5
Multiply both sides of the equation by (-1) : 3x2 = 5
Divide both sides of the equation by 3:
x2 = 5/3 = 1.667
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 5/3
The equation has two real solutions
These solutions are x = ±√ 1.667 = ± 1.29099
Two solutions were found :
x = ±√ 1.667 = ± 1.29099
Find dy/dx by implicit different iation xy^2= 4.
The value of after differentiation dy/dx will be ( 4 - y² ) / ( 2xy ).
What is differentiation by parts?By using the concept of differentiation by parts the differential will be done in two parts. In the first part, it is done with respect to y and in the second part the differentiation is done for x.
Given function is xy²= 4. The given expression will be different as below,
dy / dx ( xy² ) - 4 = 0
2xy( dy / dx) + y² = 0
dy / dx = -y / 2x
Therefore, the value of dy/dx upon differentiation will be (4 - y2) / ( 2xy ).
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Describe the relationship between precalculus and calculus. List three precalculus concepts and their corresponding calculus counterparts.
The relationship between precalculus and calculus has been explained and both precalculus and calculus deals with the tangent of the line, slope of the line, y intercept, velocity etc.
Precalculus is the study of mathematics or the course that includes algebra, trigonometry etc. to make a student for study the calculus . The precalculus covers the topics likes complex numbers, composite numbers, trigonometric functions, vectors, matrices, probability etc.
Calculus is the study of mathematics that deals with the rate of changes. Applications of the calculus are finding the slope of the curve, finding the area of region, calculation of x intercept and y intercept etc.
Both precalculus and calculus deals with the tangent of the line, slope of the line, y intercept, velocity, acceleration, area, volume etc.
Therefore, the relationship between precalculus and calculus has been explained
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Six years from today you need $10,000. You plan to deposit $1,500 annually, with the first payment to be made a year from today, in an account that pays a 5% effective annual rate. Your last deposit, which
will occur at the end of Year 6, will be for less than $1,500 if less is needed to reach $10,000. How large will your last payment be? Do not round intermediate calculations. Round your answer to the nearest
cent.
Answer:
Step-by-step explanation:
We can use the formula for the future value of an annuity to find the amount you'll have in the account at the end of Year 6. An annuity is a series of equal payments made at equal intervals of time, and the future value of an annuity is the amount you'll have in the future if you invest those payments and earn a given rate of interest.
The formula for the future value of an annuity is:
FV = PMT * (((1 + r)^n - 1) / r)
where:
FV = future value of the annuity
PMT = annual payment amount
r = annual interest rate as a decimal
n = number of payments
In this case:
PMT = $1,500
r = 0.05
n = 6
Plugging in the values:
FV = $1,500 * (((1 + 0.05)^6 - 1) / 0.05)
FV = $1,500 * (1.328867 - 1) / 0.05
FV = $1,500 * 0.328867 / 0.05
FV = $1,500 * 6.577340
FV = $9,865.61
So, the amount in the account at the end of Year 6 will be $9,865.61. To find the last payment, we subtract this amount from the desired future value of $10,000:
$10,000 - $9,865.61 = $134.39
Therefore, your last payment will be $134.39.
Let
U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.
List all the members of the given set. (Enter your answers as a comma-separated list.)
A ∪ (B ∩ C)
On solving the provided question we can say that The sets are as U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.
what is set?A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,
The sets are as U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.
z(180) = (180-185)/4 = -1.25
P(x < 180) = P(z < -1.25)
3)28 C 5
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Isosceles trapezoid KRWT is shown
Given KRWT is an isosceles trapezoid with KR and TW
Prove: WK = TR
An incomplete two-column proof is shown
Answer Choices:
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What is the missing statement in step 3
More info is in the picture
Thank you for any help!
The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In isosceles trapezoid KRWT, the trianngles are ΔKTW and ΔRWT are formed.
In trianngles ΔKTW and ΔRWT, then we have
KW = TR {Given}
∠W = ∠T {Isosceles angles}
WT = WT {Common side}
Then the trianngles ΔKTW and ΔRWT are congruent to each other.
The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.
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Please, answer the question shown below.
D. $402 Million.
Using fitted curve, a similar new blockbuster would expect
C. 290 millionWhat is fitted curve?A fitted curve is a curve that is created to model a set of data points, such that the curve passes as closely as possible to the points. The process of finding a fitted curve is called curve fitting or regression analysis.
Tracing the fitted curve, we have that
week 1 = 150 million
Week 2 = 75 million
Week 3 = 40 million
Week 4 = 25 million
Adding up the amounts
= 150 + 75 + 40 + 25
= 290 million
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Consider a lease for 120,000 square feet of space and specifies base rent of $5 psf. In addition, the lease provides for percentage rent of 3% of sales in excess of the natural breakpoint. a) Calculate the natural breakpoint for this lease.
Answer:
$20M
Step-by-step explanation:
You want the "natural breakpoint" for a lease that specifies rent is the maximum of $5 per square foot for 120,000 square feet, or 3% of sales.
Minimum rentThe minimum rent is ($5/ft²)×(120000 ft²) = $600,000.
BreakpointThe amount of sales that makes $600,000 equal to 3% of sales is ...
$600000 = 0.03s
s = $600000/0.03 = $20,000,000
The "natural breakpoint" is $20M in sales.
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Additional comment
When sales exceeds $20M, 3% of sales is more than $5/ft², so the rent will be based on sales.
Fill in the table for y = 3x - 1
Answer:
1. -7
2. -1
3. 5
Step-by-step explanation:
Substitute the value given into the equation
