By Solving the given identity equation we get A = 32/5, B = 36/5, C = 1/10 and D = -7/2.
Given (3x³ + 4x² - 6x)/(x² + 2x + 2)(x² - 1) = (Ax + B)/(x² + 2x + 2) + C/(x - 1) + D/(x + 1)
Taking LCM in RHS
(3x³ + 4x² - 6x)/(x² + 2x + 2)(x² - 1) = ((Ax + B)(x² - 1) + C(x² + 2x + 2)(x + 1)+ D(x² + 2x + 2)(x - 1))/(x² + 2x + 2)(x² - 1)
3x³ + 4x² - 6x = Ax³ - Ax+ Bx² - B + C(x³ + 3x² + 4x + 2)+ D(x³ + x² -2)
3x³ + 4x² - 6x = (A + C + D)x³ + (B + 3C + D)x² +(-A + 4C)x - B + 2C -2D
Comparing coefficients of RHS with LHS
So, A + C + D = 3 --(1)
B + 3C + D = 4 --(2)
- A + 4C = -6 --(3)
- B + 2C -2D = 0 --(4)
We have 4 variables and 4 equations. Solving them, we get
A = 32/5, B = 36/5, C = 1/10 and D = -7/2
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Line G has a slope of 5/4. Line H is perpendicular to line G, what is the slope of line g.
Answer:
Step-by-step explanation:
The slope of a line perpendicular to another line with slope m is the negative reciprocal of m. So if the slope of line G is 5/4, the slope of line H, which is perpendicular to line G, would be -4/5.
find the equation of the sphere if one of its diameters has endpoints
The equation of the sphere with the given endpoints is: (x - x0)² + (y - y0)² + (z - z0)² = r²
where x0 = (x1 + x2) / 2, y0 = (y1 + y2) / 2, z0 = (z1 + z2) / 2, and r = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²) / 2.
The Sphere is what?All points on a sphere are at a set distance from the centre, making it a three-dimensional geometric object. It is thought to be one of the most basic three-dimensional shapes and is a perfect circle.
A sphere with centre (x, y, z) and radius r has the equation:
(x - x0)² + (y - y0)² + (z - z0)² = r²
If one of the diameters of the sphere has endpoints (x1, y1, z1) and (x2, y2, z2), then the center of the sphere can be found by finding the midpoint of the two endpoints:
x0 = (x1 + x2) / 2
y0 = (y1 + y2) / 2
z0 = (z1 + z2) / 2
The radius can be found by finding the distance between the two endpoints:
r = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²) / 2
Therefore, the equation of the sphere with the given endpoints is:
(x - x0)² + (y - y0)² + (z - z0)² = r²
where x0 = (x1 + x2) / 2, y0 = (y1 + y2) / 2, z0 = (z1 + z2) / 2, and r = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²) / 2.
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Explain why −4 = [tex]\sqrt{2-x}-2[/tex] has no real solution
The square root of a negative number is not a real number, the equation has no real solution.
How true is the assertion?The equation −4 = √(2-x)−2 has no real solution because the square root of a negative number is not a real number.
If we expand the equation, we get:
-4 = √(2-x) - 2
-4 + 2 = √(2-x)
-6 = √(2-x)
Squaring both sides of the equation, we get:
36 = 2-x
x = -34
Since the square root of a negative number is not a real number, the equation has no real solution.
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DUE IN A FEW MINUTES HELP ME (1-3)
a) The like terms are B, D, F
b) The equivalent expression is option A
c) The little 5 outside would multiply all the exponents. Option D
What are like terms?
We know that the like terms are the terms that have the same kind of algebraic exponents and can easily be added or subtracted as the case may be. Hence we have to look out for the factors that do have the same exponents.
We would have in the second question;
3x^2 + 2x - 4 + 5x^2 - 4x + 5
Collecting the like terms;
3x^2 + 5x^2 + 2x - 4x - 4 + 5
8x^2 - 2x + 1
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give three examples of irrational numbers including one irrational number greater than 5
Answer:
Step-by-step explanation:
Pi (π) is an irrational number that represents the ratio of the circumference of a circle to its diameter. Pi cannot be expressed as a simple fraction, so it's an irrational number. Pi is approximately equal to 3.14159...
The square root of 2 is another example of an irrational number. This number cannot be expressed as a simple fraction either, so it's also irrational. The square root of 2 is approximately equal to 1.41.
The number e is greater than 5 and is also an irrational number. e represents the base of the natural logarithm and is approximately equal to 2.71828...
Which of the following expressions is y' given that y=sin [(x – 1)? (x + 1)]? A. y'=-(x – 3) (x – 1) cos [(x – 1)º (x + 1)] B. y' = -(3x – 1) (0 - 1) cos cos [(x – 1)? (x +1)] C. y' = -(x+3)(x - 1) cos(x – [(x – 1)? (x + 1)] D. y' = (3x + 1) (2 – 1) cos [(x – 1)? (x + 1)] + • E. y' = (3x – 1) (2 – 1) cos Os [(x – 1)º (x + 1)]
For y=sin [(x – 1)^2(x + 1)], the differentiation of y will be
y'=cos[(x-1)^2(x+1)]((x-1)^2+2(x^2-1)).
What is differentiation?
In calculus, differentiation is one of the two important concepts apart from integration. Differentiation is a method of finding the derivative of a function. Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables. The most common example is the rate change of displacement with respect to time, called velocity. The opposite of finding a derivative is anti-differentiation.
If x is a variable and y is another variable, then the rate of change of x with respect to y is given by dy/dx. This is the general expression of derivative of a function and is represented as f'(x) = dy/dx, where y = f(x) is any function.
Let y = f(x) be a function of x. Then, the rate of change of “y” per unit change in “x” is given by:
dy/dx
Now,
Given function
Y=sin[(x-1)^2(x+1)]
therefore its differentiation is
y'=cos[(x-1)^2(x+1)]((x-1)^2*1+(x+1)*2*(x-1))
y'=cos[(x-1)^2(x+1)]((x-1)^2+2(x^2-1))
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Right Question:-
Which of the following expressions is y' given that y=sin [(x – 1)^2(x + 1)]
The correct answer is E: y' = (3x – 1) (2π – 1) cos [(x – 1)π (x + 1)].
What do you mean by derivatives?The derivative of a function is a mathematical concept that describes the rate of change of the function at a particular point. It represents the slope of the function at that point and provides information about how the function is changing with respect to its input.
Formally, the derivative of a function f(x) at a point x is defined as the limit of the change in the function value as the change in the input approaches zero, i.e.:
f'(x) = lim h -> 0 (f(x + h) - f(x)) / h
The derivative can be calculated using various techniques, including differential calculus and numerical methods.
The derivative has many applications in physics, engineering, and economics, among other fields. For example, in physics, the derivative of the position function of an object gives its velocity, while the derivative of the velocity function gives its acceleration. In finance, the derivative of a stock price function gives the rate of change of the stock price, which is an important measure of risk.
The derivative of y = sin [(x – 1)π (x + 1)], using the chain rule, is:
y' = cos [(x – 1)π (x + 1)] * [(x + 1)π – (x – 1)π]
= cos [(x – 1)π (x + 1)] * 2π
= 2π cos [(x – 1)π (x + 1)]
So, the correct answer is E: y' = (3x – 1) (2π – 1) cos [(x – 1)π (x + 1)].
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Barrett is looking at a building on the school grounds
which is shaped like a rectangle as shown. He knows the
building has a height of 25x feet and a width of 28x feet 25X
with a diagonal of 180 feet.
6. What is the value of x? Round your answer to the nearest hundredth. X
180
What is the height of the building? Round your answer to the nearest hundredth.
The height of the building is 120 ft.
What is Pythagoras theorem?According to Pythagoras theorem, we can write the relation between hypotenuse, base and perpendicular as -
(hypotenuse)² = (base)² + (perpendicular)²
(h)² = (b)² + (p)² ... Eq { 1 }
Given is that Barrett is looking at a building on the school grounds which is shaped like a rectangle as shown. He knows the building has a height of {25x} feet and a width of {28x} feet with a diagonal of 180 feet.
We can apply the Pythagoras theorem to the building as -
(diagonal)² = (height)² + (width)²
180 x 180 = 625x² + 784x²
32400 = 1409x²
x² = 32400/1409
x² = 23
x = 4.8 ... Eq { 1 }
Height of the building would be -
{h} = 25x = 25 x 4.8
{h} = 120 ft
Therefore, the height of the building is 120 ft.
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n average newspaper contains at least 16 pages and at most 87 pages. how many newspapers must be collected to be certain that at least two newspapers have the same number of pages?
Total 39 newspapers must be collected to be certain that at least two newspapers have the same number of pages.
A typical newspaper has 9 pages minimum and 46 pages maximum.
We must determine the maximum number of newspapers that can be published with various page counts
9, 10, 11, 12 .......................... 45, 46
All numbers are in arithmetic order, as we can see
The first term of series(a(1)) = 9
The difference between terms = a(2) - a(1)
The difference between terms = 10 - 9
The difference between terms = 1
The formula of nth term of arithmetic series
a(n) = a + (n - 1)d
we know a(n) = 46
Now putting the values
46 = 9 + (n - 1)1
Now solve
46 = 9 + n - 1
46 = 8 + n
Subtract 8 on both side, we get
n = 38
Then, newspapers must be collected to be certain that at least two newspapers have the same number of pages = 38 + 1 = 39
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Select the correct answer.
Which equation is equivalent to the formula below?
An equation y = a(x - h)² + k is equivalent to the formula a = (y - k)/(x - h)², So Option D is correct
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
The equation,
y = a(x - h)² + k
Equivalent equation = ?
by using rules of algebra, we can transform given equation,
the rules of algebra
1. If a number is in division operation then when it goes to another side of equal to, it will be in multiplication operation or vice-versa.
2. If a number is in addition operation then when it goes to another side of equal to, it will be in subtraction operation or vice-versa.
So,
by transferring k to the left hand side,
y - k = a(x - h)²
Now, by transferring (x - h)² to the left hand side,
(y - k)/(x - h)² = a
Hence, the equivalent equation is, a = (y - k)/(x - h)²
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PLSSS HELP I WILL GIVE BRAINLIESTT
The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 50%, interpret the likelihood of randomly selecting a terrier from the shelter.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event
Answer:
Equally likely and Unlikely, I would say.
Step-by-step explanation:
Think about it. You have a 50/50 chance of getting a terrier. 50 and 50 are equal. Likely and Unlikely. I'd say that's the answer and that's my reasoning.
Answer:
likely
the answer is ^
Logic Can you add two mixed numbers and get a sum of 2? Explain
Answer: Yes as long as one of the two mixed numbers is negative
Step-by-step explanation:
Answer: Yes, the sum of two mixed numbers can be equal to 2 but only of one of the mixed numbers is negative
Step-by-step explanation:
Find the volume of the solid obtained by rotating the region enclosed by
y=x2, y=5x,
about the line x=0 using the method of disks or washers.
Volume = ∫∫ =
The required volume of the solid obtained by rotating the region is 56π/15 cubic units.
How we volume of the solid obtained by rotating the region?To find the volume of the solid obtained by rotating the region enclosed by y = x² and y = 5x about the line x = 0 using the method of disks or washers, we need to first determine the bounds of the region.
The intersection of y = x² and y = 5x occurs when x = 1, so the region to be rotated is the portion of the graph of y = x² that lies above y = 5x and to the left of x = 1.
Next, we use the method of disks (or washers) to find the volume of the solid generated by rotating the region about the x-axis. The method of disks involves dividing the region into thin vertical slices, approximating each slice as a disk, and finding the volume of the sum of these disks.
The volume of each disk is given by the formula V = πr²h, where r is the radius (distance from the center of the disk to the circumference) and h is the height (distance from the center of the disk to the x-axis). In this case, the radius is equal to the height of the slice and the height is equal to the difference between the maximum and minimum values of y in that slice.
The bounds of integration for the radius are x = 0 to x = 1. We integrate from x = 0 to x = 1, finding the volume of the sum of the disks:
V = π [tex]\int_0^1[/tex] (x² - 5x)² dx = π [tex]\int_0^1[/tex](x^4 - 10x³ + 25x²) dx
This definite integral can be solved to yield:
V = π × (x⁵/5 - 5x⁴/4 + 25x³/3) evaluated from x=0 to x=1
V = π × (1/5 - 5/4 + 25/3) = 56π/15 cubic units
So the volume of the solid generated by rotating the region enclosed by y = x² and y = 5x about the x-axis is 56π/15 cubic units.
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6. A recipe calls for 2/3 cup strawberries, 1/4 cup sugar, 1/2 cup walnuts, and 3/4 cup of
flour. Order the amounts from least to greatest. Which ingredient does the recipe require the least amount of? Explain how you know.
Answer:
1. Order from least to greatest: 1/4 cup sugar, 1/2 cup walnuts, 2/3 cup strawberries, 3/4 cup of flour
2. Sugar is the ingredient the recipe requires the least amount
Step-by-step explanation:
1.
2/3 cup of strawberries, 1/4 cup sugar, 1/2 cup walnuts, and 3/4 cup of
flour.
8/12 cup of strawberries, 3/12 cup sugar, 6/12 cup walnuts, and 9/12 cup of flour
Order from least to greatest: 1/4 cup sugar, 1/2 cup walnuts, 2/3 cup strawberries, 3/4 cup of flour
2.
Sugar is the ingredient the recipe require the least amount
5. Which of these is a statistics tool used to find the approximate "middle" in a set of data?
O A. Percentage
OB. Total
C. Range
O D. Mean
The mean is a statistics tool used to find the approximate "middle" in a set of data.
What is statistics?Statistic is a branch of mathematics that deal with the collection analyzes interpretation and presentation of data it is used to summarize analyze and compare data in order to draw conclusion and make decisions statistical method are used in a wide variety of field including economics finance business engineering medicine psychology social science and many others.
It is calculated by adding the values of the data set and dividing the sum by the number of items in the data set. The mean is also known as the average, and it can be used to compare sets of data and to measure the central tendency of a data set.
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jan and judy are two math geniuses. jan calculates the probability that three distinct numbers chosen at random without replacement from the set below would have an even sum. judy calculates the probability that three distinct without replacement numbers chosen at random from the set below would have an even product. what is the positive difference between the two probabilities they calculate (assuming they did so correctly!)? express your answer as a common fraction. {2, 3, 5, 7, 8, 9, 10}
The positive difference between the two probabilities is 11/35.
To calculate the probability that three distinct numbers chosen at random without replacement from the set would have an even sum, Jan would consider the number of ways to choose three even numbers (4 choose 3) and divide that by the total number of combinations of three numbers (7 choose 3).
To calculate the probability that three distinct numbers chosen at random without replacement from the set would have an even product, Judy would consider the number of ways to choose three numbers such that the product is even (3 choose 2) and divide that by the total number of combinations of three numbers (7 choose 3).
The positive difference between the two probabilities would be the difference between these two calculations. In this case, 11/35 is a positive difference, meaning that the probability of having an even product is 11/35 higher than the probability of having an even sum.
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The velocity v in feet per second of a freely falling object that has fallen h feet can be represented by v=8h1/2. Find the velocity of an object if it has fallen a distance of 144 ft
Therefore , the solution of the given problem of velocity comes out to be 33.94 ft/sec is the velocity.
Define velocity.Looking at something from a distance allows us to calculate its speed. An object's speed determines how far it can travel in a certain amount of time. Utilizing the equation velocity = distance/time, velocity is computed. Miles per hour (mph), kilometers an hour (km/h), and meters a second (m/s) are the three most common units of speed (mph).
Here,
Given :
=> v = (8h) ^ 1/2
=> v = √8h
We separate the variables whose values we want to be determined in the aforementioned problems.
(1) We change the variable to become
v = √8h in order to solve for v.
Using the supplied as a replacement,
v = √8 * 144 = 33.94 ft/sec
Therefore , the solution of the given problem of velocity comes out to be 33.94 ft/sec is the velocity.
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debras rectangular vegetable garden measures 9 1/3 yard by 12 yard a bottle of fertilizer costs $14.79 if debra needs to mix 1/8 cups of fertilizer with water for each square yard of her garden how many cups of fertilizer does she need
The amount of fertilizer Debra needs is 14 cups.
What is Area?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Given that,
Debra's rectangular vegetable garden measures 9 1/3 yard by 12 yard.
Area of a rectangle = Length × Width
Area of the rectangular garden = 12 × 9 1/3
= 12 × 28/3
= 112 square yard
Number of cups of fertilizer needed for 1 square yard = 1/8 cups
Number of cups of fertilizer needed for 112 square yard = (1/8) × 112
= 14 cups
Hence 14 cups of fertilizer are needed for the whole garden.
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Solve each system in Exercises 1 - 4 by using elementary row operations on the equations or on the augmented matrix. Follow the systematic elimination procedure described in this section. 2x_1 + 4x_2 = -4 5x_1 + 7x_2 = 11
Using row elimination method the solution of the system equation is [tex]x_1=12,x_2=-7[/tex].
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given system equation is
[tex]2x_1+4x_2=-4[/tex]
[tex]5x_1+7x_2=11[/tex]
The augmented matrix of the given equation is
=> B = [A ,b] = [tex]\left[\begin{array}{ccc}2&4&-4\\5&7&11\\\end{array}\right][/tex]
Multiply the 1st row by 1/2 then
=> [tex]\left[\begin{array}{ccc}1&2&-2\\5&7&11\\\end{array}\right][/tex]
Add -5times the first row to the second row then
=> [tex]\left[\begin{array}{ccc}1&2&-2\\0&-3&21\\\end{array}\right][/tex]
Multiply 2nd row by -1/3 then
=> [tex]\left[\begin{array}{ccc}1&2&-2\\0&1&-7\\\end{array}\right][/tex]
Add 2 times the second row to the first row then
=> [tex]\left[\begin{array}{ccc}1&0&12\\0&1&-7\\\end{array}\right][/tex]
Hence the given system equation reduce to [tex]x_1=12 , x_2=-7[/tex] which is required solution.
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Joe's savings increased by 4. 5%.
His savings are now £125. 40.
What were his savings before the increase?
Answer:
120
Step-by-step explanation: 125.4/104.5x100
List all of the combinations
write your answer like this:(10p, 1p)
You must write all you ansers in one line
a) There are 10 different combinations of pairs of coins.
b) List of the combinations:
(10p, 1p), (10p, 50p), (10p, 2p), (10p, 20p), (1p, 50p), (1p, 2p), (1p, 20p), (50p, 2p), (50p, 20p), (2p, 20p)
What is combination?A combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
Given,
Angela has coins of
10p, 1p, 50p, 2p, 20p
a) Combination of pulling out two coins
= ⁵C₂
= (5!)/(5-2)!×(2!)
= 5 × 4 × 3 × 2 × 1/3 × 2 × 1 × 2 × 1
= 120/12
= 10
b) Taking 10p as one coin
(10p, 1p), (10p, 50p), (10p, 2p), (10p, 20p),
Taking 1p as one coin, as repetition is not allowed
(1p, 50p), (1p, 2p), (1p, 20p),
Taking 50p as one coin, as repetition is not allowed
(50p, 2p), (50p, 20p),
Taking 2p as one coin, as repetition is not allowed
(2p, 20p)
a) Hence, 10 is the total number of combinations of pairs of coins
b) All combinations are:
(10p, 1p), (10p, 50p), (10p, 2p), (10p, 20p), (1p, 50p), (1p, 2p), (1p, 20p), (50p, 2p), (50p, 20p), (2p, 20p)
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The complete question is as follows:
Angela has the following coins in her pocket:
10p 1p 50p 2p 20p
She pulls out two coins at random.
a) How many different combinations of pairs of coins are there
b) List all of the combinations,
write your answers like this: (10p, 1p)
You must write all of your answers on one line.
6
Determine whether the pair of figures is similar. If so, find the scale factor. Explain your reasoning.
Next Question
W
A) Yes; A WZX-A YZX because A WZX A YZX; 1.
B) Yes: A WZX-A YXZ because ZWZXZYZX and WZ YZ:1
a
C) No; not all of the corresponding angles are congruent.
D) No: there is no way to determine if the corresponding sides are promotional
B) Yes: A WZX-A YZX because ZWZXZYZX and WZ YZ:1a
The statement is incorrect. It should be:- B) Yes: A WZX ~ A YZX because corresponding angles ZWZX and ZYZX are congruent and corresponding sides WZ and YZ are proportional, with a scale factor of 1.
What is scale factor?A scale factor is a numerical representation of the size disparity between two comparable figures. When two figures have the same shape but different sizes, they are said to be comparable. To put it another way, one figure is an expansion or contraction of the other.
The ratio of the lengths of the corresponding sides in the two figures is the scale factor. For instance, if the scale factor is 2, one figure will be twice as large as the other, and if it is 1/2, one figure will be half as large as the other. The comparable sides in one figure are typically k times longer than the corresponding sides in another if the scale factor is k.
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the right-hand side of the gompertz equation is f (y ) = r y ln( k y ). find the first four terms of the taylor series for this f (y ) about y = k by using the formula we found in example 2, (3).
The first four terms of the Taylor series for the right-hand side of the Gompertz equation, f(y) = ry ln(ky), about y = k is: f(y) = rk ln(kk) + (y - k)(2r) + (y - k)² / 2! (r / k) + (y - k)³ / 3! (-r / k²).
To determine this :
The right-hand side of the Gompertz equation is f(y) = ry ln(ky). To find the first four terms of the Taylor series for this f(y) about y = k, we can use the formula:
f(y) = f(k) + (y - k)f'(k) + (y - k)² / 2! f''(k) + (y - k)³ / 3! f'''(k) + ...
Where f'(k), f''(k), and f'''(k) are the first, second, and third derivatives of f(y) evaluated at y = k, respectively.
First, we need to find the derivatives of f(y):
f'(y) = r ln(ky) + r
f''(y) = r / y
f'''(y) = -r / y²
Next, we evaluate these derivatives at y = k:
f'(k) = r ln(kk) + r = 2r
f''(k) = r / k
f'''(k) = -r / k²
Finally, we substitute these values into the Taylor series formula:
f(y) = f(k) + (y - k)f'(k) + (y - k)² / 2! f''(k) + (y - k)³ / 3! f'''(k)
f(y) = rk ln(kk) + (y - k)(2r) + (y - k)² / 2! (r / k) + (y - k)³ / 3! (-r / k²)
This is the first four terms of the Taylor series for f(y) about y = k.
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a hypothesis test of a regression coefficient finds that the null hypothesis is rejected at the 5% level. this means:
In a hypothesis test of a regression coefficient, if the null hypothesis is rejected at the 5% level, it means that the evidence in the data provides strong evidence against the null hypothesis.
The 5% level refers to the level of significance, which is a threshold used to determine whether the results of the hypothesis test are statistically significant or not. If the null hypothesis is rejected at the 5% level, it means that the p-value, which is a measure of the strength of the evidence against the null hypothesis, is less than 0.05. In other words, the likelihood of obtaining the observed results if the null hypothesis were true is less than 5%. This is considered to be strong evidence against the null hypothesis, and we reject the null hypothesis in favor of the alternative hypothesis.
In conclusion, if a hypothesis test of a regression coefficient finds that the null hypothesis is rejected at the 5% level, it means that the evidence in the data provides strong evidence against the null hypothesis, and the results are considered to be statistically significant.
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5.) On February 3rd, Cardi B borrowed $17,500.00 at 6.5% exact interest to buy a new car. She had to pay back
a maturity value of $17,873.97 to pay off the loan. On what day did Cardi pay back the loan?
Cardi B paid back the loan on February 3rd + 122.72 days = May 16th.
What do you mean by interest?Interest is a fee charged by a lender to a borrower for the use of money. It represents the cost of borrowing money and is typically expressed as a percentage of the loan amount. Interest is paid over a period of time and is calculated based on the principal amount of the loan, the interest rate, and the length of the loan term.
Simple interest is calculated only on the principal amount of the loan, while compound interest is calculated on both the principal and the accumulated interest over time. Compound interest results in a faster growth of the loan balance compared to simple interest.
Let's call the number of days Cardi B had the loan "d". The exact interest can be calculated as follows:
Interest = Principal * Rate * (Number of days / 365)
From the information provided, we know that the maturity value was $17,873.97 and the principal was $17,500.00, so the interest can be calculated as follows:
Interest = $17,873.97 - $17,500.00 = $373.97
We can now use the formula for exact interest to find the number of days:
$373.97 = $17,500.00 * 0.065 * (d / 365)
Solving for d:
d = 365 * ($373.97 / ($17,500.00 * 0.065))
d = 365 * ($373.97 / $1137.50)
d = 365 * (0.3288)
d = 122.72
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Suri and Halima are discussing exponential functions. Halima says the function f(x) = x10 increases
to infinity faster than f(x) = 2*. Suri says the opposite, that f(x) = 2* increases to infinity faster
than f(x) = x10. Who is correct and why?
Suri is right. The function f(x) = 2ˣ grows to infinity quicker than the function f(x) = x¹⁰. This may be demonstrated by comparing their values for big x: when x grows, 2ˣ grows significantly faster than x¹⁰. This suggests that 2ˣ approaches infinity more quickly than x¹⁰.
What is function?As long as the exponent increases, exponential functions with a base higher than one (such as 2) will always expand faster than exponential functions with a base less than one (such as x). Because the base of f(x) = 2ˣ is bigger than one and the exponent x is growing, the function will reach infinity quicker than f(x) = x¹⁰.
Here,
Suri is correct. The function f(x) = 2ˣ increases to infinity faster than f(x) = x¹⁰. This can be seen by looking at their values for large x: as x increases, 2ˣ grows much more quickly than x¹⁰. This means that 2ˣ approaches infinity faster than x¹⁰.
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the last digit of the heights of statistics students were obtained as part of an experiment conducted for a class. use the following frequency distribution to construct a histogram. what can be concluded from the distribution of the digits? specifically, do the heights appear to be reported or actually measured?
The frequency distribution of the digits indicates that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements.
Frequency Distribution:
Digit Frequency
0 3
1 5
2 9
3 5
4 3
5 4
6 4
7 4
8 2
9 1
From the distribution of the digits, it appears that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements.
The frequency distribution of the digits indicates that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements. For example, the frequency of the digit '2' is more than twice as high as the frequency of the digits '1' and '3', which is not likely to occur in a set of actual measurements.
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find the value of each trigonometric ratio
The value of tan C is 5/12.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
From the figure,
BA = 15
BC = 36
AC = 39
So,
Tan C = BA / BC = 15/36 = 5/12
Thus,
Tan C is 5/12.
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Suppose you drive from home to your child's school, pick her up, and drive back home, covering a total distance of 25 miles in 1 hour. Which of the following statements are true?a.Your velocity is different on the return home than it is on the way to school.
b.Your average speed for the trip is 25 miles per hour.
c.You must accelerate when you reach the school.
Velocity is the measure of the rate of change of position, or the speed of an object in a specific direction.
Since you drove from home to school and then back home, the velocity on the return home would be different than the velocity on the way to school, since the direction of travel is different.
The average speed for the trip can be calculated by dividing the total distance (25 miles) by the total time (1 hour). Therefore, the average speed of the trip is 25 miles per hour.
Acceleration is the rate of change of velocity, or the rate at which an object speeds up or slows down. In this case, you would have to accelerate when you reach the school in order to pick up your child and then accelerate again when you leave the school in order to return home.
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Please help with problem
21x>5y+49x>2y>2-28x>2y
A point in the solution of the system of inequalities is (2, 0.5)
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
21x>5y+49x>2y>2-28x>2y
Express properly
So, we have the following representation
21x > 5y+49
x > 2y
2 - 28x > 2y
Next, we plot the graphs of the inequality expressions on a plane
(See attachment for the graph)
The shaded region represent the solution
And a point in this region is (2, 0.5)
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Students at Windsor High School wants to order shirts with their school logo, (CUSTOM INK charge
$9.65 per shirt plus a setup fee of $43 RUSH ORDER TEES charges $8.40 per shirt plus a $58 tee For
what number of shirts would the cost be the same? Which company offers a better deal for an order
of 35 shirts?
The number of shirts at which the cost would be same is 12. As, $352 < $380.75, First Company offers a better deal for an order of 35 shirts.
Charge of first company is $9.65 per shirt plus setup fee of $43 &
Charge of another company is $8.40 per shirt plus setup fee of $58
The number of shirts such that the cost of both the companies are same.
Let the required number of shirts be n which can be evaluated as following:
Cost of first company = Cost of another company
⇒ 9.65n + 43 = 8.40n + 58
⇒ 9.65n−8.40n = 58−43
⇒ 1.25n = 15
⇒ n = 151.25
⇒ n = 12
Thus, the number of shirts at which the cost would be same is 12.
First company charges $9.65 per shirt + setup fee of $43
35 shirts = 35 × 9.65 + 43
= $380.75
Second company charges $8.40 per shirt + setup fee of $58
35 shirts = 35 × 8.40 + 58
= $352
As, $352 < $380.75, First Company offers a better deal for an order of 35 shirts.
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