Final answer:
Advanced calculus covers computational aspects and applications of calculus in multiple dimensions, while real analysis focuses on the theoretical fundamentals, such as rigorous development of the real number system and proof-based examination of limits and continuity.
Explanation:
The difference between advanced calculus and real analysis lies in the focus and depth of the subjects. Advanced calculus, also known as calculus III in some curricula, typically extends the study of calculus to multiple dimensions, covering topics such as partial derivatives, multiple integrals, and vector calculus. It focuses more on the computational aspects and applications of calculus.
Real analysis, on the other hand, delves deeper into the theoretical underpinnings of calculus and analysis. It deals with the rigorous development of the real number system, sequences and series, continuity, differentiation, integration, and convergence. Real analysis puts a strong emphasis on proof and logical reasoning, providing a foundation for the truth and logic behind the mathematics used in calculus.
While both subjects are mathematically advanced, real analysis is considered to be more abstract and is often a stepping stone for further study in pure mathematics. Familiarity with calculus is often a prerequisite before studying real analysis as it lays the groundwork for the more complex theoretical concepts.
what is the value for x (5x+15) (3x-3)
The value of x in the expression (5x+15) (3x-3) is 15x^2 + 30x - 45.
Explanation:The expression (5x+15) (3x-3) represents the multiplication of two binomials. To find the value of x, we can use the distributive property to simplify the expression:
Multiply the terms within the first set of parentheses: 5x * 3x = 15x^2.Multiply the terms within the second set of parentheses: 5x * -3 = -15x.Multiply the terms between the parentheses: 15 * 3x = 45x.Multiply the constant terms within the parentheses: 15 * -3 = -45.Putting it all together, we have 15x^2 - 15x + 45x - 45. Combining like terms, the expression simplifies to 15x^2 + 30x - 45.
So, the value for x in the given expression is 15x^2 + 30x - 45.
Measurement is ___________ when it yields the same values across repeated measurement of the same event.
The answer is reliable. A measure is assumed to have a high reliability if it yields parallel results under steady conditions. It is the characteristic of a set of test scores that relates to the quantity of accidental or random error from the measurement procedure that might be rooted in the scores. Marks that are highly reliable are precise, reproducible, and constant from one testing time to another. To be exact, if the testing method were to be repeated with a different group of test takers, fundamentally the same results would be gotten.
Find x if et = 3x+2 and em = 5x
Answer:
x = 6
Step-by-step explanation:
The centroid (T) always splits the lines so one side is 2/3 and the second is 1/3 of the entire median line. This can also be written as 2x + x. That being said, ET isn't equal to EM, it's only equal to 2/3 of EM so that's what you have to write.
3x + 2 = 2/3 * 5x
3x + 2 = 10/3 x
*3 (3x+2) = *3(10/3x)
9x+6 = 10x
-9x -9x
x = 6
The value of x is 6.
TrianglesThe polygon has three sides. the sum of all the internal angles is 180 degrees.
Given
ET = 3x+2
EM = 5x
To findThe value of x.
How to find the value of x?We know that the centroid of triangles divides it into 2:3.
Then
[tex]\begin{aligned} \dfrac{ET}{EM} &= \dfrac{2}{3} \\\\ \dfrac{3x+2}{5x} &= \dfrac{2}{3} \\\\ 3x+2 &= \dfrac{2}{3} * 5x \\\\ 3x+2 &= \dfrac{10x}{3} \\\\ 3x - \dfrac{10x}{3} &=-2\\\\ \dfrac{-x}{3} &= -2 \\\\ x &= 6\end{aligned}[/tex]
Hence the value of x is 6.
Thus the value of x is 6.
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What is the slope of a line that is perpendicular to the line that goes through (5,4) and (-2,-3)?
First, let us solve for the slope of the line which it intersects with:
m’ = (y2 – y1) / (x2 – x1)
m’ = (-3 – 4) / (-2 – 5)
m’ = 1
The slope of the perpendicular line is the negative reciprocal, therefore:
m = - 1 / m’
m = - 1 / 1
m = -1
So the slope of the line is -1.
Let n be a nonzero integer. find a domain on which f (x) = (1 − xn)1/n coincides with its inverse. hint: the answer depends on whether n is even or odd.
I believe that the correct equation given is:
f(x) = (1-x^n)^(1/n)
From this, we can say that:
When n is an
odd number then f(x) is cubic root function. The domain is (-infinite,
+finite)
When n is an even number then f(x) is sqrt root
function. The domain is (0, +finite)
The mean weight of a litter of kittens is 3.1 pounds, with a standard deviation of 0.9 pound. Lawrence wants to know the weight of the kitten he is buying, but the seller only has the z-score of 1.22. How much does the kitten weigh?
The weight of kitten is 4.198 pounds
What is z-score?A z-score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation units.
Given that, the mean weight of a litter of kittens is 3.1 pounds, with a standard deviation of 0.9 pound, Lawrence wants to know the weight of the kitten he is buying, but the seller only has the z-score of 1.22.
Let x be the weight of the kitten
We know that,
z = (x- mean)/σ
Therefore,
1.22 = (x-3.1)/0.9
(1.22)(0.9) = x -3.1
x = 4.198
Hence, the weight of kitten is 4.198 pounds
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Antonio purchased adult and child tickets for the fair. Tickets cost $29.35 for each adult and $17.45 for each child. Let x represent the number of adult tickets purchased and y represent the number of child tickets purchased. Write an expression to represent the total cost of the tickets Antonio purchased.
$29.35y + $17.45x
$29.35x + $17.45y
($29.35 + $17.45)(x + y)
($29.35 - $17.45)(x + y)
What is the smallest number greater than 100 that is :
a)divisible by two ?
b)divisible by ten?
c)divisible by four ?
The smallest number greater than 100 divisible by 2 is 102, divisible by ten is 110, divisible by four is 104.
What is Divisibility Test?It is an easy method of determining the divisibility of a number by a particular divisor, by just observing the number and not actually dividing it.
The number is 100
A smallest number greater than 100 has to be found which is divisible by 2.
All even numbers are divisible by 2, a number which has 0, 2, 4, 6, 8 at its ones position are divisible by 2.
The smallest number from 100 which is divisible by 2 is 102.
A smallest number greater than 100 has to be found which is divisible by 10.
A number is divisible by 10, if it has 0 at its ones position.
The number after 100 which has 0 at its ones position is 110.
A smallest number greater than 100 has to be found which is divisible by 4.
If last two digit of a number forms 00 or are divisible by 4, then the number is divisible by 4.
The smallest number from 100 which is divisible by 4 is 104.
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A sealed rectangular box measuring 8 x 6 x 18 contains 864 sugar cubes, each measuring 1 x 1 x 1. How many sugar cubes are touching the box?
Final answer:
A total of 456 sugar cubes touching the box.
Explanation:
To calculate the number of sugar cubes touching the box, we must consider the cubes that lie along each face of the box without double-counting the cubes that touch corners and edges.
The box dimensions are 8 x 6 x 18 inches, and each sugar cube is 1 x 1 x 1 inch.
For the top and bottom faces (6 x 18), we have
6*18 = 108 sugar cubes touching the box on each face, totaling 216 for both the top and bottom.
For the front and back faces (8 x 18), since we must exclude the top and bottom rows, we have
(8-2) x (18-2) = 6 x 16 = 96 sugar cubes for one face and 192 for both.
For the sides (8 x 6), excluding the top and bottom rows again, we have
(8-2) x (6-2) = 6 x 4 = 24 sugar cubes on one side and 48 in total for the two sides.
Adding all these together, we get 216 (top and bottom) + 192 (front and back) + 48 (sides) = 456 sugar cubes touching the box.
Remember, this method assumes a single layer of sugar cubes is in direct contact with the inside surface of the box.
What is the numerator of the fraction equivalent to 25/135 that has a denominator of27
Solve x + 9 = 18 - 2x
The solution to the equation x + 9 = 18 - 2x is x = 3.
What is the solution to the equation?Given the equation in the question:
x + 9 = 18 - 2x
To solve the equation x + 9 = 18 - 2x, first, collect and combine the x terms on one side of the equation and the constant terms on the other side:
x + 9 = 18 - 2x
Add 2x to both sides of the equation:
x + 2x + 9 = 18 - 2x + 2x
x + 2x + 9 = 18
3x + 9 = 18
Subtract 9 from both sides of the equation:
3x + 9 - 9 = 18 - 9
3x = 18 - 9
3x = 9
Isolate x by dividing both sides by 3:
x = 9/3
x = 3
Therefore, the value of x is 3.
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Solve for x.
7(x - 3) = 4(x + 5)
7(x-3) = 4(x+5)
distribute:
7x-21 = 4x+20
add 21 to both sides
7x = 4x +41
subtract 4x from both sides
3x = 41
divide both sides by 3
x = 41 /3 = 13.67 ( repeating 6's) so it can be 13 2/3 as a fraction
the answer is 13 2/3
The equations y = -0.38x + 56.6 and y = 0.38x + 43.4 represent the percent of men and women, respectively, receiving bachelor's degrees, where x is the number of years since 1968. in approximately what year did the same percent of men and women receive bachelor's degrees?
Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25o angle with the ground and when the string makes a 45o angle with the ground? Round to the nearest tenth.
A) 14.2 feet
B) 17.1 feet
C) 47.6 feet
D) 55.2 feet
Answer:
its 14.2
Step-by-step explanation:
A rabbit lure on a greyhound racetrack is set to travel once around the track at 50 feet per second, and then its speed is increased to 65 feet per second for the second loop around the track. If the total time it takes for the lure to go around the track twice is 184 seconds, what is the distance once around the track?
What is the solution to the system of equations below? 2x - 5y = 11 and -2x + 3y = -9
Carly is 3 times her brother's age. The sun of their age is no more than 24 years.
brothers age = x
carly's age = 3x
3x +x <=24
4x<=24
x<=24/4 = 6
brothers age is x<=6
Can someone please help me with math
what is the answer for 5kx+6=7kx solve for x
Does believing in god increases the probability that god does exist
KInda if you love him then he loves personally i dont believe in him but thats everyone decision
There are 10 red marbles and 8 green marbles in a jar. if you take three marbles from the jar (without replacement), the probability that they are all red is:
There are 10 red marbles and 8 green marbles in a jar. So, the probability that all three marbles taken from the jar are red is 0.147.
Given :
Number of red marbles = 10
Number of green marbles = 8
Probability is the department of mathematics concerning numerical depictions of how likely the event is to happen or how likely it is that suggestion is genuine. The probability of an event could be number between 0 and 1 , where o shows difficulty of the event and 1 shows certainty.
Total number of marbles in a jar = 10 + 8 = 18
Total number of red marbles in a jar = 10
So, the probability that all three marbles taken from the jar are red is:
[tex]= \dfrac{10}{18}\times\dfrac{9}{17}\times\dfrac{8}{16}[/tex]
[tex]= 0.147[/tex]
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Triangle A′B′C′ is the image of triangle ABC after a dilation. What is the scale factor of the dilation?
If you know that two triangles are congruent, you know that any unmarked corresponding parts are also congruent by
What is the expanded equivalent of cos(a – b)?
The expanded equivalent of cos(a – b) is cos(a)cos(b)+sin(a)sin(b).
Given that,
The equation is cos(a - b).We need to find the expanded equivalent of the above equation.Based on the above information, the calculation is as follows:
= cos (a - b)
= cos(a)cos(b)+sin(a)sin(b)
Therefore we can conclude that the expanded equivalent of cos(a – b) is cos(a)cos(b)+sin(a)sin(b).
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¿A Sandra qué le gusta hacer los viernes?
A A Sandra le gusta comer papas fritas los viernes.
B A Sandra le gusta comer agua los viernes.
C A Sandra le gusta beber pizza los viernes.
D A Sandra le gusta beber galletas los viernes.
in a survey respondents were asked which type of movie they watched most often. the bar graph shows how many males and how many females said they watched each type of movie most often.
how many more males said they watched action movies than drama movies
2
4
5
8
Answer:
Option D) 8
Step-by-step explanation:
We are given the following information in the question:
A bar graph is given that shows how many males and how many females said they watched each type of movie most often.
To find:
We have to find that how many males said that they watched action movies than drama movies .
In the bar graph:
Number of action movies watched by males = 13
Number of drama movies watched by males = 5
Number of males males said that they watched action movies than drama movies = 13 - 5 = 8
Males watched 8 action movies more than the drama movies.
Hence, the correct option is D.
What is the domain and range of f(x) = |x + 6|?
domain: (negative infinite,infinite); range: f(x) (greater than or equal to) 0
domain: x (less then or equal to)-6; range: (negative infinite,infinite)
domain: x(greater than or equal to)-6 ; range: (negative infinite,infinite)
domain:(negative infinite,infinite) ; range: f(x) (less than or equal to) 0
Answer:
domain: (negative infinite,infinite); range: f(x) (greater than or equal to [tex]0[/tex]
Step-by-step explanation:
we have
[tex]f\left(x\right)=\left|x+6\right|[/tex]
The vertex of the function is the point [tex](-6,0)[/tex]
The domain is the interval--------> (-∞,∞)
The domain is all real numbers
The range is the interval ------> [0,∞)
[tex]f(x)\geq 0[/tex]
The range is all real numbers greater than or equal to zero
To better understand the problem see the attached figure
identify the like terms 3x,4y,4z,5x
The starting salaries of individuals with an mba degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. refer to exhibit 6-4. what is the probability that a randomly selected individual with an mba degree will get a starting salary of at least $30,000
The probability that a randomly selected individual with an MBA degree will receive a starting salary of at least $30,000, considering the mean salary is $40,000, and standard deviation is $5,000, is approximately 97.72%.
Explanation:The question pertains to the use of the normal distribution in probability, particularly in determining the probability of a randomly selected individual with an MBA degree getting a starting salary of at least $30,000. Given that the mean starting salary is $40,000 and the standard deviation is $5,000, we first need to standardize the salary amount to a z-score using the formula z = (X - μ) / σ. In this context, X refers to the salary amount in question, μ is the mean salary, and σ is the standard deviation.
So, z = (30,000 - 40,000) / 5000 = -2. This means the $30,000 salary is 2 standard deviations below the mean. When we look at the standard z-table, we find that the area to the left of z = -2 is approximately 0.0228. However, because we are looking for the probability of a salary being at least $30,000, we need to consider the area to the right, which is 1 - 0.0228 = 0.9772. So, the probability that a randomly selected MBA graduate will have a starting salary of at least $30,000 is approximately 97.72%.
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Which equation best represents the line graphed above?