The algebraic fraction which is an equivalent fraction with the denominator 24a^3b^2 is 15b/24a^3.
To find an equivalent fraction with the denominator 24a^3b^2, we need to find a common denominator for the two fractions 5b and 8a^3. This common denominator is 24a^3b^2.
To find an equivalent fraction for 5b, we can multiply both the numerator and denominator by the same factor to obtain the desired denominator. To do this, we need to find a factor that would give us a denominator of 24a^3b^2 when multiplied with 8a^3.
The factor that would give us a denominator of 24a^3b^2 is 3.
So, the equivalent fraction for 5b with the denominator 24a^3b^2 is (5b * 3)/(8a^3 * 3) = 15b/24a^3.
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what is convergence radius calculator
A convergence radius calculator is a tool used in calculus to calculate the radius of convergence for a power series using the ratio test.
To calculate the convergence radius of a power series, one can use a formula known as the "ratio test". The ratio test involves taking the limit of the absolute value of the ratio of successive terms in the series, as n approaches infinity. If this limit exists and is less than 1, then the series converges absolutely. The convergence radius can then be found as the reciprocal of this limit.
For example, given the power series:
∑(n=0 to infinity) [tex](x-2)^n / n^2[/tex]
we can use the ratio test to find the convergence radius as follows:
[tex]|(x-2)^(n+1) / (n+1)^2| / |(x-2)^n / n^2|[/tex]
= [tex]|(x-2) / (n+1)|^2 * (n^2 / (x-2)^2)[/tex]
= [tex](n^2 / (n+1)^2) * (1 / (x-2)^2)[/tex]
= [tex]n^2 / ((n+1)^2 * (x-2)^2)[/tex]
Taking the limit of this expression as n approaches infinity, we get:
[tex]lim(n- > ∞) (n^2 / ((n+1)^2 * (x-2)^2))[/tex]
= [tex]1 / (x-2)^2[/tex]
Since this limit exists and is less than 1 for all x except x=2, the power series converges absolutely for all values of x within a radius of [tex]1/(x-2)^2[/tex] centered at x=2. Therefore, the convergence radius of the power series is 1.
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Analyze the linear inequalities and determine if the solution set is the shaded region above or below the boundary
line.
Warm-Up
y> -1.4x +7
y> 3x-2
y <19-5x
y>-x-42
y < 3x
y<-3.5x+2.8
Solution Set Shaded Above
Solution Set Shaded Below
Answer:
The graph in the attached figure
we have
----> inequality A
The solution of the inequality A is the shaded area below the dashed line
The slope of the dashed line A is positive m=2
The y-intercept of the dashed line A is (0,-5)
The x-intercept of the dashed line A is (2.5,0)
----> inequality B
The solution of the inequality B is the shaded area above the dashed line
The slope of the dashed line B is negative m=-3
The y-intercept of the dashed line B is (0,1)
The x-intercept of the dashed line B is (1/3,0)
The solution of the system of inequalities is the shaded area between the two dashed lines
using a graphing tool
The graph in the attached figure
GIVE ME BRAINLIEST IF IM CORRECT :)
If f(1) = 0, what are all the roots of the function ? use the remainder theorem.
By using synthetic division, we can find all the roots of the function f(x) = x³ + 3x² - x - 3 and determine that the roots are 1, -1, and -3.
A root of a function is a value for x that makes the function equal to zero.
In this case, we have a function f(x) = x³ + 3x² - x - 3 and we know that f(1) = 0. To find all the roots of this function, we can use the remainder theorem.
The remainder theorem states that if we divide a polynomial by a linear expression (such as x - a), the remainder will be equal to the value of the polynomial at that value of x (a). In other words, if we write f(x) = (x - a)q(x) + r, where r is the remainder, then f(a) = r.
So, if we divide our function f(x) by x - 1, the remainder will be equal to f(1), which we know is zero. Therefore, (x - 1) is a factor of f(x), and the function has a root at x = 1.
Next, we can divide f(x) by (x - 1) to get a quotient, q(x), and a new remainder, r. We can repeat this process, dividing q(x) by another linear expression until we have no more remainders.
The roots of f(x) will be the values of x that we used as factors in each step of the division process.
This process of dividing a polynomial by a linear expression to find its roots is called synthetic division.
Complete Question
If f(1) = 0, what are all the roots of the function f(x) = x³ + 3x² - x - 3. Use the remainder theorem.
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Vector u = (-3, 8), and vector v = (-14, 6). Match each vector operation with the magnitude of its resultant vector
The magnitude of given operations of vectors are found.
What are Vectors?Quantities with the independent characteristics of magnitude and direction are called vectors.
Given:
u = (-3, 8) and v = (-14, 6)
So, 3u = (-9, 24) and 2v = (-28, 12)
3u - 2v = (-9+28, 24-12)
3u - 2v = (19, 12)
Magnitude of 3u - 2v = √19² + 12² = √505 units
2u = (-6, 16) and 3v = (-42, 18)
2u - 3v = (36, -2)
Magnitude = √36² + (-2)² = √1300 units
u = (-3, 8) and 4v = (-56, 24)
u + 4v = (-59, 32)
Magnitude = √(-59)² + 32² = √4505 units
5u = (-15, 40) and v = (-14, 6)
5u - v = (-1, 34)
Magnitude = √1157 units
7u = (-21, 56) and 2v = (-28, 12)
7u - 2v = (7, 44)
Magnitude = √1985 units.
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What is 20% off 250000 ?
From the given information provided, 20% off 250000 is 50000, and the discounted price is 200000.
The formula for calculating percentage is:
percentage = (part/whole) x 100
Here's an example:
Let's say you got 35 out of 50 questions correct on a test. To calculate the percentage of questions you answered correctly, you would use the formula as follows:
percentage = (35/50) x 100
percentage = 0.7 x 100
percentage = 70%
To calculate 20% off 250000, you can multiply 250000 by 20% (which is 0.20 in decimal form) and then subtract the result from 250000:
250000 - (0.20 x 250000) = 250000 - 50000 = 200000
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the population of a school is 800 students and is increasing at a rate of 2%per year.
Answer: Increases by 16 students per year
Step-by-step explanation:
100% = 800
2% = x
So between 100% and 2%, the scale factor would be 50 since 100 / 2 = 50
Then 800 / 50 would be 16
So..
1 Year = 816 students
2 Years = 832 students
3 Years = 848 students
4 Years = 864
And so on..
Write the linear equation for the graph below.
Answer:
y = 6x
Step-by-step explanation:
The line is sloping up at a rate of 6 y units per 1 x unit. So the slope is 6/1 (6x)
The image of a trapezoid is shown.
An isosceles trapezoid with a short base of 3 meters and a height of 5 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.
What is the area of the trapezoid?
70 m2
38 m2
35 m2
19 m2
Answer: 35m2
Step-by-step explanation:took the test and i got it right
An isosceles trapezoid with a short base of 3 meters and a height of 5 meters then the area of the trapezoid is 35 m²
What is the area of the trapezoid?
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
We can start by finding the length of the long base. Since the trapezoid is isosceles, we know that the length of the portion of the large base from the left vertex to the perpendicular is equal to the length of the portion from the right vertex to the perpendicular. Let's call the length of the long base "x":
x = 4 + 7 = 11 meters
Now we can use the formula for the area of a trapezoid:
Area = (1/2) * (short base + long base) * height
Substituting the values we have:
Area = (1/2) * (3 + 11) * 5
Area = 7 * 5
Area = 35 m²
Therefore, the area of the trapezoid is 35 m².
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What is the simplest form of the radical expression?
√2+√5/√2-√5
can yall help me with this question immediately pls?
The diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.
What is diameter?Diameter is the line jwhich passes through the center of a circle and joins two points on the circumference of the circle.
To find the diameter of the Ferris wheel which is a circle, we see that the grpah gives the height of a passenger on the Ferris wheel as a function of the number of complete cycles since the ride started.
Now, the diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.
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Write an equation in slope-intercept form for the line that passes through the points (0, 5) and (1, 3)?
Answer:
Step-by-step explanation:
y= -2x + 5
A global denim brand announced in 2010 that it is launching a new collection of jeans which are made with reduced consumption of water during the manufacturing process. While usual manufacturing of a pair of jeans requires approximately 42 litres of water, this collection would reduce the water usage by a minimum of 28%. Do you think this initiative by the company is beneficial for water conservation? How much water can be conserved in litres, on a pair of jeans?
The number of liters of water that can be conserved will be 11.76 liters. The initiative by the company is beneficial for water conservation.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The number of liters of water that can be conserved is given as,
⇒ 28% of 42
⇒ 0.28 x 42
⇒ 11.76 liters
The number of liters of water that can be conserved will be 11.76 liters. The initiative by the company is beneficial for water conservation.
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What is 200 Micrograms (mcg) in Milligrams (mg)?
To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms, 200 micrograms (mcg) is equal to 0.2 milligrams (mg).
When we want to convert a unit of measurement to another unit of measurement, we use conversion factors to make the conversion. In the case of converting micrograms (mcg) to milligrams (mg), we need to know that 1 milligram is equal to 1000 micrograms. This means that to convert any value from micrograms to milligrams, we need to divide by 1000.
To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms.
So, to convert 200 mcg to mg, we divide 200 by 1000:
200 mcg ÷ 1000 = 0.2 mg
Therefore, 200 micrograms (mcg) is equal to 0.2 milligrams (mg)
It is important to understand the concept of unit conversions because it is a crucial aspect of many scientific and engineering calculations. Knowing how to convert units of measurement allows us to work with data that is expressed in different units and compare results from different experiments. In addition, being able to convert units is a valuable skill for everyday life, such as when reading nutrition labels or measuring medication dosages.
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HELP ME PLEASE!!!!! FAST ASAP HELP
PICTURE ATTACHED
A company logo is made up of a desire and two identical triangles as shown in this image
What is the area of the logo
The area of the logo is given as 139 cm
How to solve for the areaIn order to get the area of the shape, i would have to get the area of the triangles first
area of a triangle = 1/2 b * h
base = 9 / 2 = 4.5
h = 6
area = 1/2 * 9 * 6
= 27
Area of 2 triangle = 2 x 27
= 58
The are aof the square = a * a
= 9 * 9
= 81
The total area of the logo is given as 81 + 58
= 139 cm
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sketch a graph for days 0-9
According to the information in the table, the graph would look like the one in the attached image.
How to graph the information in the table?To graph the information in the table we must carefully observe the information. In this case, the relationship is decreasing because the number of infected is decreasing as time increases. In accordance with the above, the curve that shows this relationship is a decreasing curve.
In this case, we must locate the time on the x axis and the infected on the y axis and mark a point in the areas where the data coincide. Later we must graph a line that joins the points and our graph would be finished.
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HELP ASAP!!
Simplify the expression.
the expression negative one fifth j plus three fourths minus the expression five halves j plus seven eighths
The simplified expression is given as follows:
-27j/10 - 1/8.
How to simplify the expression?The expression for this problem is defined as follows:
-j/5 + 3/4 - (5j/2 + 7/8).
The negative sign means that every term in the parenthesis has the signal exchanged, hence:
-j/5 + 3/4 - 5j/2 - 7/8.
Then the expression is simplified combining the like terms, as follows:
With j: -j/5 - 5j/2 = -2j/10 - 25j/10 = -27j/10.Constant: 3/4 - 7/8 = 6/8 - 7/8 = -1/8.Meaning that the expression is of:
-27j/10 - 1/8.
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F(x)=4x+2 FIND THE INVERS SHOW WORK
Given To find Solution: First, we replace with and with : Now, we finally replace with Therefore, the inverse of is
Answer:y=(x-2)/4
Step-by-step explanation:
y=4x+2
4x=y-2
x=(y-2)/4
y=(x-2)/4
Write the following ratio in simplest form: 32 min : 36 min (1 point) a. 8 : 9 b. 8 : 36 c. 32 : 9 d. 128 : 144
The simplest form of the given ratio 32 min : 36 min is equal to
option a. 8 : 9.
Ratio is equal to
32 min : 36 min
Factors of 32 are = 1, 2, 4, 8, 16, 32
Factors of 36 are = 1, 2, 3, 4, 6, 9, 12, 18, 36
Greatest common factor of 32 and 36 is equal to 4
Simplest form of the given ratio is equal to
32 min : 36 min
= ( 8 × 4 ) min : ( 9 × 4 ) min
'4' get cancelled with other we get,
= 8 min : 9 min
Therefore, the simplest form of the given ratio by taking out common factors is equal to option a. 8 : 9 .
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What is the LCM of 3 and 5 and 3?
Answer:15
Step-by-step explanation:
Bonnie bakes a pan of brownies and cut them into 12 equal pieces after lunch 8/12 of the brownies are left her friends eat half of those brownies with dinner what fraction of the whole pan of brownies do they eat with dinner
Answer:
4/12
Step-by-step explanation:
8/12 ÷ 2 = 4/12
Answer: 1/3
Step-by-step explanation:
8/12 divided by 2 is 1/3
What is the value of x, given that the two prisms are similar?
Answer:
A. 10
Step-by-step explanation:
2/4 = x/20
1/2 = x/20
2x = 20
x = 10
Answer: 10
A 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association, so some suggested that having male pattern baldness might somehow cause a person to have a severe reaction to COVID-19 (since they had been bald before catching COVID-19, so that the disease could not have caused their baldness). Which option below was most likely a lurking variable?
Age
Diet
Height
Weight
If a 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association: A. Age is the most likely lurking variable in this scenario.
What is a lurking variable?In this case, the relationship between male pattern baldness and severe COVID-19 reactions may be influenced by age, as older individuals are more likely to experience both male pattern baldness and severe COVID-19 symptoms.
Age could also affect other factors such as overall health and immune system function, which may contribute to the severity of COVID-19 symptoms.
Diet, height, and weight may also be related to overall health and immune system function, but they are less likely to be related specifically to male pattern baldness
Therefore, age is the most likely lurking variable in this scenario.
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Solve for x
Show proofs
Help
The length of the rise x is 25.5
How to determine the value of the side length xFrom the question, we have the following parameters that can be used in our computation:
Length = 17
Angle = 27 degrees
The rise, x is then calculated using the following laws of tangent
tan(27) = 13/x
Make x the subject
So, we have the following representation
x = 13/tan(27)
Evaluate the expression
This gives
x = 25.5
Hence, the value of x is 25.5
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An ice cream store charges 75 cents for each scoop of ice cream and 25 cents for each cone. The formula c=0.75x+0.25
can be used to determine c, the total cost for an ice cream cone with x scoops of ice cream. According to the formula, how much should it cost to buy an ice cream cone with 4 scoops of ice cream?
Responses
A loan of $25,000 has an annual simple interest rate of 5.5%. The total cost of the loan is $38,750. How much total interest will you pay?
The solution is, total interest will you pay is $13750.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
given that,
A loan of $25,000 has an annual simple interest rate of 5.5%.
The total cost of the loan is $38,750.
so, total interest will you pay = $(38750 - 25000)
= $13750
Hence, The solution is, total interest will you pay is $13750.
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2.
(5x-2)(2x
+ 7)
= (5x)(2x) - 2(7)
= 10x² - 14
A.10x14
B.10x² +31x 14
C.7x + 5
D.10x + 5
The resultant of the given expression (5x-2)(2x+7) is 10x² + 31x - 14
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent mathematical relationships and can be used to solve equations and perform calculations.
For example, the expression "3x + 2" is an algebraic expression that contains the variable "x", the numbers "3" and "2", and the mathematical operations of addition and multiplication.
Given expression ,
(5x-2)(2x+7)
= (5x-2)(2x+7) = 5x(2x) + 5x(7) - 2(2x) - 2(7)
= 10x² + 35x - 4x - 14
= 10x² + 31x - 14
Therefore, The resultant of the given expression (5x-2)(2x+7) is 10x² + 31x - 14
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Write the equation of the line that passes through the points (4, -3) and (8,5). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.
An equation of the line that passes through the points (4, -3) and (8,5) is y + 3 = 2(x - 4).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data points (4, -3), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-3) = (5 - (-3))/(8 - 4)(x - 4)
y + 3 = 8/4(x - 4)
y + 3 = 2(x - 4)
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Which function is the inverse of g (z) = (²-1)³ — 3?
Of(1) = √2+6+1
Of(1) = 2√2+3+1
O f(1) = 2√1+1+3
O f(1) = √21+2+3
The inverse of function is f(x) = (x - 4)³/8 + 3
What is inverse function?A function that reverses the results of another function is known as an inverse function. If y = f(x), then x = g(y), then a function g is the opposite of a function f. To put it another way, applying f and then g is equivalent to doing nothing. This can be expressed as g(f(x)) = x in terms of how f and g are made up.
Given g(x) = 2(∛x-3)+4
let g(x) = y
y = 2(∛x-3)+4
change the variables since options are in form of x
x = 2(∛y-3)+4
simplify for y
subtract 4 from both side
x - 4 = 2(∛y-3)+4 - 4
x - 4 = 2(∛y-3)
divide both side by 2
(x - 4)/2 = (2(∛y-3))/2
(x - 4)/2 = (∛y-3)
cube both side
((x - 4)/2)³ = ((∛y-3))³
(x - 4)³/8 = y - 3
(x - 4)³/8 + 3 = y
Hence the value f(x) = (x - 4)³/8 + 3 .
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How do you find the two largest numbers in an array in Matlab?
To find the two largest numbers in an array in Matlab, you can use the sort function and indexing to access the two largest elements.
Here's an example:
array = [3, 8, 2, 10, 5];
sorted_array = sort(array, 'descend');
largest_number = sorted_array(1);
second_largest_number = sorted_array(2);
In this example, we have an array of numbers called array. We use the sort function to sort the array in descending order, which means that the largest numbers will be at the beginning of the array. The resulting sorted array is assigned to a new variable called sorted_array.
We then use indexing to access the first and second elements of the sorted array, which will be the two largest numbers. These numbers are assigned to the variables largest_number and second_largest_number, respectively.
It's important to note that if the array contains duplicate values, this method will return the two largest unique values. If you want to find the two largest values including duplicates, you can use the max function twice with the 'omitnan' parameter to handle any NaN values in the array:
array = [3, 8, 2, 10, 5, 10];
largest_number = max(array, [], 'omitnan');
array_without_largest_number = array(array < largest_number);
second_largest_number = max(array_without_largest_number, [], 'omitnan');
In this example, we first find the largest number in the array using the max function with the 'omitnan' parameter to ignore any NaN values. We then create a new array that excludes the largest number, and use the max function again to find the second largest number in the new array.
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Use the drop-down menus to order the decimals from greatest to least.
8.31, 8.296, 8.06, 8.3
Answer:
8.31, 8.3, 8.296, 8.06
Step-by-step explanation:
8.31, 8.296, 8.06, 8.3
The order of decimals from greatest to least is
8.31, 8.3, 8.296, 8.06