If the partial derivative is equal to zero for all values of x then it indicates that the function is constant.
What is a partial derivative?
In differential calculus, partial derivative is defined as the rate of change of multivariable functions concerning change in just one of its variables.
Consider the restriction of f to a line y=c,
then
[tex] \frac{∂f}{∂x}(x \: c) = fx(f \: c) = 0[/tex]
Pick 2 points a and b, then by mean value theorem there is x0, such that
[tex]fx(x \: c) = \frac{f(b \: c) - f(a \: c)}{b - a} = 0[/tex]
[tex]⟹f(b \: c) - f( \: a \: c) = 0⟹f(b \: c) = f(a \: c)⟹f(x \: c) = const.[/tex]
We can show the same way that f(c,y)=const.
Combining f(x,c)=const and f(c,y)=const to get f(x, y)=const.
Hence, If the partial derivative is equal to zero for all values of x then it indicates that the function is constant.
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Who were the Greek oligarchs?
Answer:
"Broadly speaking, an oligarchy is a form of government characterized by the rule of a few persons or families. More specifically, the term was used by Greek philosopher Aristotle in contrast to aristocracy, which was another term to describe rule by a privileged few."
Step-by-step explanation: I hope this helps with something
A certain statistic dˆ is being used to estimate a population parameter d. The expected value of dˆ is not equal to d. What property does dˆ exhibit?.
The statistic's bias is a quality that the statistic does not display, according to the Central Limit Theorem for proportions.
Central limit theorem:
According to the central limit theorem in statistics, samples will be normally distributed and their means will be roughly equal to those of the entire population when the big sample size has a finite variance.
Given,
A certain statistic The population parameter d is being estimated using the function d. D's predicted value is not the same as D.
Find the property that does d display in this case.
According to the Central Limit Theorem, the following is true for a proportion p in an n-person sample:
Value anticipated, μ = p
Standard deviation: s = √p(1 - p) /n
Therefore,
The statistic is biased because the expected value in this case differs from the expected.
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He brightness of some stars can fluctuate over time. Suppose that the brightness of a certain star can be modeled by the following: B(t) = 7. 8 + 10. 8sin((2pi/63)t) In this equation, B(t) represents the magnitude of brightness, and t is the time (in days). Suppose we start at t = 0 days. During the first 63 days, when will the star's magnitude of brightness be 13? Do not round any intermediate computations, and round your answer(s) to the nearest day. Please especially explain the portion when calculating arcsin - thanks!
The days needed are 5 days
What is the rate of decay?The reduction in radioactive nuclei per unit of time is the rate of decay, or activity, of a sample of a radioactive substance.
How is the decay rate calculated?The rate of change is determined by the equation dN/dt = N, where is the decay constant, assuming N is the size of a population of radioactive atoms at a given time t and dN is the amount by which the population decreases in time dt.
What is the decay factor?Exponential decay is the opposite of exponential growth; it has a constant multiplier that is less than 1 when a quantity decreases by the same amount over equal intervals of time. This quantity also referred to as the decay factor, can be written as (1-r).
From the above question
B= 7.8+10.8sin((2pi/63)t)
B=13=7.8+10.8 sin((2pi/63)t)
sin((2pi/63)t)=13/27
(2pi/63)t=sin(13/27)=0.502344 radians
t=5 days
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describe the center and spread of the data using either the mean and standard deviation or median and iqr. describe how you determined which one to use.
For symmetric distributions without outliers, the mean should be used to get the measure of center.
What are the Center and Spread of the data?
The spread in the data measures how far the numbers in the data set are away from the mean and the center in the data measures the standard deviation.
To determine the measure of center for symmetric distributions without outliers, one should use the mean. They should use the median to determine the measure of center in all other situations. The range is a suitable metric for determining the spread of a distribution.
However, the interquartile range should be used when using the median as the measure of center, and the standard deviation should be used when using the mean as the measure of center.
Hence, For symmetric distributions without outliers, the mean should be used to get the measure of center.
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Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
A random selection of an Endure All battery has a 10.56% probability of lasting more than 550 hours.
Explain the term z score?A Z-score is a metric that quantifies how closely a value relates to a mean of a set of values. Standard deviations as from mean are used to measure Z-score. A Z-score of zero means the data point is entirely score is the same as the mean score.The Z score is utilized to calculate how far the raw score deviates from the mean.
The Z score is calculated as follows:
z = (x - μ)/σ
Given that x > 550 and μ = 500, σ = 40:
z = 550 - 500 / 40
z = 1.25
Following the normal distribution chart,
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Therefore, there is a 10.56% chance that a randomly chosen Endure All battery would survive longer than 550 hours.
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Select the correct answer.
Which graph shows a quadratic equation with complex roots?
Answer:
Step-by-step explanation:
GraphA shows the quadratic equation with complex roots.
Answer:
Step-by-step explanation:
Use the ruler to measure the length of RS to the nearest centimeter.
The length of RS is __ Centimeters.
The answer should be 18cm
Here is why I think that:
On the ruler, you should count from 9 to 26
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.
The total tick marks from 9 to 26 is = to 18
(I know that R is resting above the number eight, do not count that one, many people make that mistake)
Please let me know in the comments if
somehow my calculation is wrong.
Please help me with this. It will be really appreciated <3!
Find the value of y
7 x 7 x 7 x 7 x 7 x 7 =7y
Thank you a lot if you do! This is no rush <3
Answer: y = 16807
Step-by-step explanation:
7 * 7 * 7 * 7 * 7 * 7 = 117649
7^16807 = 117649
hypotheses: h0: pass/fail rates are school. h1: pass/fail rates are school. which of the following best fits the blank spaces above?
The correct option is independent of, dependent on for the given sets of hypothesis H0: Pass/fail rates are _____ school. H1: Pass/fail rates are _____school.
What is hypothesis?A hypothesis is a statement that makes sense in light of the available information but hasn't been proved true or wrong. A hypothesis in statistics is a claim that will serve as the foundation for hypothesis testing (also known as a statistical hypothesis). A straightforward hypothesis is a claim that expresses the relationship between precisely two variables. a dependant and a single independent. Take the statement "Smoking is a significant cause of lung cancer" as an example. Smoking is an independent variable that influences the dependent variable, lung cancer.
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find the temperature (in k) at which the root-mean-square speed of ch4 molecules is the same as the root-mean-square speed of o2 molecules at 448.8 k.
Temperature of ch4 will be 150K
given :-
[tex]\sqrt{2} speed of 02 = 448.8[/tex]
u.avg. = [tex]\sqrt{8rt/\pi m} \\[/tex]
u.avg ch4 = [tex]\sqrt{8rt1/\pi 16}[/tex]
hence , mass of ch4 = 12 +4 = 16
Methane (US: MEH-thayn, UK: MEE-thayn) is a chemical compound with the chemical formula CH4 (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas.
The molar mass of oxygen atom O
O
is 15.99
This is only the mass of 1 oxygen atom so the molar mass of oxygen molecule O is 15.99
is double the number, i.e. approximately 32
u.avgO2 = [tex]\sqrt{8r(300)/\pi (32)}[/tex]
u.avgch4 = u.avgo2
[tex]\sqrt{8rt1/\pi 16}[/tex] = [tex]\sqrt{8r(300)/\pi (32)}[/tex]
==> t1/16 = 300/32
==> t1 = 150 K
They have same average velocity when the temperature of CH4 is 150 K
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is the square root of open paren x negative 3 close paren squared equals 3 negative x ? (1) x is not equal to 3 (2) negative x times the absolute value of x is greater than 0
The square root of open paren x negative 3 close paren squared =
3 negative x negative x times the absolute value of x is greater than 0.
Let the equation be: |x−3|=3−x|x−3|=3−x
When x>3x>3, then RHS is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true.
When x≤3x≤3, then LHS=|x−3|=−x+3=3−x=RHSLHS=|x−3|=−x+3=3−x=RHS
x≠3x≠3
Thus,
−x|x|>0−x|x|>0, this inequality implies that x<0x<0, hence x<3x<3.
Hence option b becomes the correct option i.e, negative x times the absolute value of x is greater than 0.
Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.
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11. There is a $10 monthly membership fee to download music. There is
a $0.50 fee for each song downloaded.
a. Write a linear equation that models the cost of downloading x songs
per month.
b. Graph the equation.
c. What is the cost of downloading 15 songs?
Answer:
A) y=0.5x+10 C) 17.5 dollars (don't forget your units)
Step-by-step explanation:
a) 0.5 is the price paid per song, or x, and 10 is the price that does not change for a month, so we can say that y=0.5x+10
c) to download 15 songs, we substitute x by 15
y=0.5(15)+10
y=7.5 + 10
y=17.5
and for b, im sorry but I cannot graph here.
let $w 1, w 2, \dots, w n$ be complex numbers. a line $l$ in the complex plane is called a mean line for the points $w 1, w 2, \dots, w n$ if $l$ contains points (complex numbers) $z 1, z 2, \dots, z n$ such that \[\sum {k
The slope of the line is going to be m = 163.
Here, we have been told that the sum of the numbers is going to be -
= ∑[tex]w _{k}[/tex]= 3 + 504i (i)
The other set of complex numbers is (z₁, z₂, ....[tex]z_{k}[/tex]) and their sum is going to be = ∑[tex]z_{k}[/tex]= 3 + 504i (ii)
If we write the number 3+504i in the standard form for complex numbers i.e., a+bi with respect to the summations, we get -
= ∑[tex]a_{k}[/tex]= 3 (III)
= ∑[tex]b_{k}[/tex]= 504 (Iv)
The standard equation is of the form, y = mx+3. Substituting the polar coordinates, we get -
= [tex]b_{k}[/tex] = m[tex]a_{k}[/tex] + 3
Now, if we use all of the given values in equations (iii) and (iv) for k, we get -
= 504 = 3m + 15
Now, on simply solving for m, we get -
= 3m = 504 - 15 = 489
= m = 489/3
= m = 163
Henceforth, we find out that the slope of the line, m is 163.
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Use the number line to represent the solution to 2.4x−6>−13.2.
Answer:
The answer should be (8,0)
Which of the following would best describe the situation that a second-degree polynomial regression equation would be used to model?
A) An exponential growth trend
B) A cosine function
C) A parabola
D) It depends on the number of independent variables.
(C) A parabola is the best representation of the situation that a second-degree polynomial regression equation would be used to mimic.
What is a Parabola?A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.
It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
A parabola can be described using a point and a line.
The situation that a second-degree polynomial regression equation would be used to simulate is best described by a parabola.
The phrase "parabolic move" originated as trader jargon.
It describes when a stock experiences an increase in price that resembles the right side of a parabolic curve: A parabolic move happens when the stock's price rises at an exponentially faster rate.
Therefore,(C) a parabola is the best representation of the situation that a second-degree polynomial regression equation would be used to mimic.
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Write the equation of the line that passes through the points (2, 7) and (5,-2).
Answer:
y = -3x + 13
Step-by-step explanation:
Assuming the line is linear, you can use the point-slope equation of a line.
(y - y) = m (x - x)
The y and x variables come from the points on the line. Points are written in the form (x, y). In the point (2,7), 2 is x and 7 is y.
1. Plug your points in.
(7 - - 2) = m (2 - 5)
2. Solve for m (the slope)
(7 + 2) = m (2 - 5)
(9) = m (-3)
9 = -3m
m = -3
3. Write an equation of the line with the slope you found.
You can write this equation in different forms, but I'll use the slope-intercept form.
y = mx + b
You'll have to find b, the y-intercept. You can plug one of your points in for x and y as well as your slope, m, and solve for b.
7 = -3(2) + b
7 = -6 + b
b = 13
Therefore, the equation is y = -3x + 13
-3x-4y=12 solve for Y
If a = 3 and b = 5, find a/(a+b)=.
Answer: 5/3 or 1.67
Step-by-step explanation:
What is the area of triangle ABC if a = 7, c = 11, and B = 55°?
Round the answer to the nearest hundredth.
The area of the triangle is 31.54 square units
How to determine the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
We have the following values
a = 7 units
c = 11 units
B = 55 degrees
The area of the triangle is calculated using the following area formula
Area = 1/2absin(C)
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 7 * 11 * sin(55 degrees)
Evaluate
Area = 31.54
Hence, the area is 31.54 square units
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Shane can hike 10 miles in 5 hours. If he hikes for 8 hours, then how many miles will he travel
Answer: 13.33
Step-by-step explanation: I could be wrong
what is
c=2.80g c=8.30g
A computer chess game and a human chess champion are evenly matched. They play fourteen games. Find probabilities for the following events.
(Round all answers to four decimal places.)
(a) They each win seven games. P =
(b) The human chess champion wins eleven games. P =
(c) The computer wins at least eleven games. P =
The probability that they each win six games is 0.225.
Given : A computer chess game and a human chess champion are evenly matched. They play twelve games.
To find : The probability that they each win six games?
Applying binomial distribution,
Here n=12 and p=0.5
(a) They each win seven games. P =
[tex]P(X=k)=\frac{n !}{k !(n-k) !} \times p^k \times(1-p)^{n-k}[/tex]
The probability that they each win six games is k=6.
(b) The human chess champion wins eleven games. P =
[tex]\begin{aligned}& P(X=6)=\frac{12 !}{6 !(12-6) !} \times 0.5^6 \times(1-0.5)^{12-6} \\& P(X=6)=\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 !}{6 \times 5 \times 4 \times 3 \times 2 \times 6 !} \times 0.015625 \times 0.015625 \\& P(X=6)=11 \times 2 \times 3 \times 2 \times 7 \times 0.015625 \times 0.015625 \\& P(X=6)=0.225\end{aligned}[/tex]
(c) The computer wins at least eleven games. P =
Therefore, The probability that they each win six games is 0.225.
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Which of the following is equal to √√√√5? (4 points)
O
O
O
O
53
1
56
2
53
3
N/W
52
Answer:
b
Step-by-step explanation:
A school is arranging a field trip to the zoo. The school spends 778.72 dollars on passes for 29 students and 2 teachers. The school also spends 259.26 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Answer:
Step-by-step explanation:
first, you have to divide the total cost of the passes by the number of teachers and students combined. Then you must multiply the individual cost of the pass by the number of students. Finally, you have to take the total cost for student passes and add it to the cost of the lunches, then you answer.
is the pareto distribution a member of a location family? a member of a scale family? a member of a location-scale family? none of the above? explain.
Pareto distribution is a member of a scale family referring fixed values of the shape parameter, it is trivially closed under scale transformations.
The Pareto distribution is a power-law probability distribution used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena. It was initially applied to demonstrate the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population. The pareto principle or 80-20 rule states that 80% of outcomes are due to 20% of causes. Pareto distribution is a member of the scale family distribution which is parameterized by a scale parameter. The larger the scale parameter, the more spread out the distribution.
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my regular recipe for cream of potato soup makes 50 8-ounce servings. i need to make potato soup for 200, but i want to increase the portion size to 12 ounces. what conversion factor should i use to adjust my recipe for the new amount?
The conversion factor you should use to adjust your recipe for the new amount is 6.
What is conversion factor?
A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value.
Equating the conversion factor :
Given: original serving = 50 8-ounce serving
required new serving = 200 12-ounce serving
To find: conversion factor?Original serving = 50×8 ounce = 400 ounce
Required serving = 200×12 ounce
= 2400 ounce
As we know, conversion factor = {Required Yield} ÷ {Original Yield}
∴ Conversion factor =2400 ÷ 400
∴ Conversion factor = 6
Conversion factor is greater than 1 when required yield is supposed to be greater than original yield and conversion factor is less than 1 when required yield is less than original yield.
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the volume of a gas in a container varies inversely with the pressure on the gas. if a gas has a volume of 500 cubic inches under a pressure of 14 pounds per square inch, what will be its volume if the pressure is increased to 19 pounds per square inch? (round off your answer to the nearest cubic inch.)
If the pressure is increased to 19 pounds per square inch, then the volume is 368.42 cubic inches
The volume of the gas = 500 cubic inches
The pressure = 14 pounds per square inch
The volume of a gas in a container varies inversely proportional with the pressure on the gas.
V ∝ 1/P
Where V is the volume and P is the pressure
Then,
V = k/P
Where k is the constant
500 = k/14
k = 500 × 14
k = 7000
The pressure of the gas = 19 pounds per square inch
Volume = 7000 /19
= 368.42 cubic inches
Therefore, the volume is 368.42 cubic inches
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HELP MEEEEEE bc y’all are slay
The correct relation is that both the angles are corresponding angles.
What are corresponding angles?Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.
Given is an arrangement of streets in the form of two parallel lines and a street acting as a transversal.
The angle of library and angle of school are corresponding angles, and corresponding angles between parallel lines are congruent.
Since, angle of library = 42°
angle of school = angle of library
Therefore, angle of school = 42°
Hence, The correct relation is that both the angles are corresponding angles.
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Christina's Pizza sells pizza by the slice for lunch. Today, they sold 76 slices, including 20 slices of pepperoni pizza. What is the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza?
Write your answer as a fraction or whole number.
P(pepperoni)=
Answer:
Step-by-step explanation:
2/6
Find the missing angle measures.
The value of x is 122°.
The value of y is 130°.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
The figure has two parts.
One part is a triangle.
Another part is a heptagon.
We see that,
The three angles sum 180 degrees.
Two angles are equal inside the triangle.
2m + 80 = 180
2m = 180 - 80
2m = 100
m = 50
Now,
y + 50 = 180
y = 180 - 50
y = 130
Now,
The sum of the heptagon angles is 900.
Three angles are the same.
i.e 3x
Two angles are the same.
i.e 130 + 130 = 260
260 + 3x + 135 + 140 = 900
3x + 535 = 900
3x = 900 - 535
3x = 365
x = 365/3
x = 122
Thus,
The value of x is 122°.
The value of y is 130°.
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