The value of s(x) depends on the value of x since s is a function of x.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Here,
We know that for any function f(x) ; x represents the independent variable i.e. the variable whose value is defined and y=f(x) denotes the dependent variable i.e. the variable whose value is defined corresponding to the independent variable.
i.e. it depends on the variable x.
Similarly here s(x) is the dependent variable since it is defined corresponding to the variable x.
Hence, The value of s(x) depends on the value of x, since s is a function of x.
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The number of cigarettes smoked in 1925 was approximately __ billion
The number of cigarettes smoked in 1925 was approximately 1.3 billion.
What was the percentage of smokers in 1960?42 percent, Focus Area (2002) February 2011 Over the past 50 years, there has been a significant decline in the number of Americans who smoke. Smoking was generally tolerated in the 1960s, with 42 percent of Americans reportedly regularly smoking.Smoking was significantly more common among males than women around the end of the 1920s. Around 65% of men smoked up until around 1960, but that number dropped to 25% by the year 2000. Smoking among women grew from a low of approximately 5% around the year 1930 to about 35% in 1975.The number of cigarettes smoked in 1925 was approximately 1.3 billion.To learn more about cigarettes refer to:
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Perform the indicated operation and simplify the result.
Answer:
Where is the equation?
Step-by-step explanation:
I need it to solve this problem
Given that u=(2, - 1,1),v=(1,1)
A library manager is interested in the number of people using the library. She decides to perform a count every 28th day for one year, starting next Monday. What type of sampling method is this?
answer choices
a. Systematic sampling
b. Convenience sampling
c. Stratified sampling
d. Quota sampling
A library manager is interested in the number of people using the library. She decides to perform a count every 28th day for one year, starting next Monday. The systematic sampling method is this.
Hence, option (a) is the correct choice.
The library manager employs systematic sampling as a sample approach.
Systematic sampling is a form of probability sampling approach in which sample members are drawn from a larger population at random but with a set, periodic interval.
The sampling interval is determined by dividing the population size by the desired sample size.
Systematic sampling is a technique for picking a sample from a larger population at regular intervals. In this scenario, the library manager selects a sample of library users by tallying the number of persons every 28th day.
It is a systematic sampling approach since the intervals (28th day) are fixed and systematic.
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Simplify this problem! thank you
Answer:
-3y
Step-by-step explanation:
-√(9y²) = -√((3y)²)
= -3y
Divide R60 in the ratio 1:2
In order to divide the amount Rs.60 in the ratio 1:2
We take x as the variable that replicates the 1st amount + 2nd amount = Rs.60
Putting the values into a equation we get
1x + 2x = 60
3x = 60
x = [tex]\frac{60}{3}[/tex]
x = 20
Hence the amounts are ,
1x = 20
2x = 2 x 20 = 40
the function f is defined by f={(-6,11),(-13,-2),(-2,-12),(11.-9),(8,1)} what is the domain of f? enter your answer in set notation
What is the range of f? enter your answer in set notation
What is the domain of f^-1? Enter your answer in set notation
The domain of [tex]f^{-1}[/tex] is the set of all the y-values of the ordered pairs, which are {11, -2, -12, -9, 1}.
What is domain?A domain is an area of administrative autonomy, authority, or control within the Internet. Domains are defined by the organization or entity that owns them, and are made up of a series of letters and/or numbers that follow the “dot” or period. For example, a domain name may be “example.com” or “example.org”. Domain names are used to identify and locate computers on the Internet and to route email.
The domain of f is the set of all the x-values of the ordered pairs, which are {-6, -13, -2, 11, 8}.
The range of f is the set of all the y-values of the ordered pairs, which are {11, -2, -12, -9, 1}.
The domain of f-1 is the set of all the y-values of the ordered pairs, which are {11, -2, -12, -9, 1}.
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Which statement is true?
Question 9 options:
A)
|–3| = 3 and –|–4| = –4
B)
|–3| = 3 and |–4| = –4
C)
–|3| = 3 and |4| = 4
D)
|–3| = 3 and –|4| = 4
Answer:
A
Step-by-step explanation:
Because (--3) is equal to 3 becuas ethe negative is not oustide the value and -(-4) is euqal to =4
So therefore, A is correct.
Find the LCM of 1-x^2 and (x-1)^3
The LCM of 1-x^2 and (x-1)^3 is (x-1)^3.
How to find the LCM of the Polynomial?To find the LCM, we take the polynomial with the highest degree (which determines the degree of the LCM) and then make sure that it contains all the terms from the other polynomials.
The degree of (x-1)^3 is 3 and the degree of 1-x^2 is 2.
So, we take (x-1)^3 as the starting point for the LCM and then add any missing terms from 1-x^2.
In this case, (x-1)^3 already contains all the terms from 1-x^2, so the LCM is (x-1)^3.
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consider the differential equation (a) this equation is close to the simpler equation , determine the largest step size such that euler's method is stable, i.e. for the equation .
The stability limit depends on the specific form of the equation, so you may need to adjust this value based on the specific equation you are working with.
The euler's methodThe stability condition for the Euler's method applied to the equation
y' = f(x,y) is given by the following inequality:
|hf(x,y)| <= 1,
where h is the step size. To determine the largest step size for which Euler's method is stable, we need to find the maximum value of |hf(x,y)|. This maximum value is often referred to as the stability limit.
In your case, the equation is close to the simpler equation y' = a, which has the solution y = a*x + b. The stability limit for the Euler's method applied to this equation is 1, so we can take h <= 1 as the largest step size for which the method is stable. However, the stability limit depends on the specific form of the equation, so you may need to adjust this value based on the specific equation you are working with.
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An athlete wants to supplement his daily diet with beef and plant proteins. The content of iron, calcium, and vitamins (in milligrams per spoonful) is given in the table:
Product Iron Calcium Vitamins
Beef Protein 6 3 2
Plant Protein 2 3 4
Which graph shows the number of spoonfuls of beef protein and plant protein he needs to include in his diet to receive at least 18 milligrams of iron, 21 milligrams of calcium, and 16 milligrams of vitamins?
The correct graph for the supplements is attached below.
What is the bar chart?A bar chart is a graph that uses bars to represent and compare data. The length of the bar represents the magnitude of the data being displayed, with longer bars indicating larger values.
Bar charts can be used to display data for one or more categories, and can be either vertical or horizontal. They are commonly used to compare and visualize the distribution of categorical data.
The correct bar graph that shows the distribution of the supplements have been shown in the image that is attached to the answer that we have here.
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The sum of a number, half the number, and 5 times the number
The expression that represents the sum of a number, half the number and 5 times the number is given as follows:
6.5x.
In which x is the number.
How to obtain the expression?The number in this problem is unknown, hence the variable that represents the number is given as follows:
x.
Half the number is given as follows:
x/2 = 0.5x.
Five times the number is given as follows:
5x.
Then the sum of all these amounts is given as follows:
x + 0.5x + 5x = 6.5x.
We just combine the like terms, as they all have the same letter and exponent, hence we just add the coefficients.
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22 in
98 in
27 in 22 in
What is the
perimeter of this
red polygon?
[?] in
The perimeter of the polygon is 169 inches.
The perimeter of a polygon is the total length of its sides. The tangents from a given circle are used to create the polygon in this problem.
We will apply the idea that if two tangents are drawn from the same point outside of a given circle, their lengths will always be identical.
This polygon has eight sides, which indicates that there are four pairs because their lengths are equal.
Therefore, the perimeter is equal to double the total of the four sides that were supplied to us.
Radius = 2(22+27+22+98)
perimeter is two (169)
Diameter: 338 inches
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Complete question -
is 14 a polynomial or a non-polynomial
is x+1 a polynomial or a non-polynomial
is 14 vx a polynomial or a non-polynomial
is x-2 -2x+4 a polynomial or a non-polynomial
Answer:
14 is a polynomial.
x+1 is a polynomial.
14vx is not a polynomial.
x-2 -2x+4 is a polynomial.
14 is a polynomial, x+1 is a polynomial, 14vx is not a polynomial, x-2 -2x+4 is a polynomial.
A polynomial is an equation made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables.
Polynomials are algebraic expressions with indeterminates and constants in them. Polynomials can be thought of as a mathematical dialect. They are used to express numbers in practically every subject of mathematics and are quite significant in others, such as calculus.
Polynomials cannot include the following:
Variables with negative or fractional exponents.Variables in the numerator.Variables that fall under a radical.Special characteristics. (trig functions, absolute values, logarithms, and so on).To know more about Polynomials,
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A runner is jogging at a constant speed of 3.3 miles per hour.
Find the distance d
that the runner jogs as a function of the time spent jogging t
. Call this function d(t)
. Use *, an asterisk, for any multiplication and /, a slash, for any division.
d(t)=
Find the inverse function by expressing the time spent jogging t
in terms of the distance jogged d
. Call this function t(d)
. Use *, an asterisk, for any multiplication and /, a slash, for any division.
t(d)=
The function for distance jogged is d(t) = 3.3t and the inverse of the function is d(t)⁻¹ = 3.3/t.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Let, 'd' be the distance covered in miles, and 't' is the time in hours.
Therefore, From the given information d(t) = 3.3t.
Let, d(t) = y.
So, y = 3.3t.
t = 3.3/y.
d(t)⁻¹ = 3.3/t.
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A Bernoulli differential equation is one of the formsdy/dx + P(x)y = Q(x)y^n (*) Observe that, if n 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y^(1-n) transforms the Bernoulli equation into the linear equation du/dx + (1 - n)P(x)u = (1 - n)Q(x). Consider the initial value problem xy’ + y = 2xy^2, y(1) = 4. (a) This differential equation can be written in the form (*) with P(x) = ___,Q(x) =___, and n = ___.(b) The substitution u = ___ will transform it into the linear equation Du/dx + ___ u = ___(c) Using the substitution in part (b), we rewrite the initial condition in part (c) u(1) = ____(d) Now solve the linear equation in part (b). and find the solution that satisfies the initial condition in part (c) U(x) = ____(e) Finally, solve for yy(x) = ____
the answer for this question is i don't know
So , bye
(a) This differential equation can be written in the form (*) with P(x) = 1, Q(x) = 2x, and n = 2.
(b) The substitution u = 1/y will transform it into the linear equation Du/dx + 0u = -2x
(c)Using the substitution in part (b), we rewrite the initial condition in part u(1) = 1/y(1) = 1/4.
(d) the linear equation in part (b) is y = 1/(C - x) and the solution that satisfies the initial condition in part (c) U(x) = -y⁻¹ = -x + C,
(e) Finally, solve for y(x) = 1/(1/4 + 1 - x) = 4/(5 - x).
What is Bernoulli differential equation?
A Bernoulli differential equation is a type of non-linear ordinary differential equation of the form:
dy/dx + P(x)y = Q(x)yⁿ
where P(x) and Q(x) are functions of x and n is a constant. The equation is named after the Swiss mathematician Jakob Bernoulli.
These types of differential equations are important in various fields of science, such as physics, engineering, and economics. They are non-linear, meaning that the dependent variable y appears in both linear and non-linear terms, making them difficult to solve in general.
a) This differential equation can be written in the form (*) with P(x) = x, Q(x) = 2x, and n = 2.
b) The substitution u = y⁻¹ will transform it into the linear equation du/dx - xu = -2x.
c) Using the substitution in part (b), we rewrite the initial condition as u(1) = 1/4.
d) Now we solve the linear equation in part (b). The characteristic equation is given by d/dx(e[tex]\mathrm{(\int -xdx))}[/tex] = -xe[tex]\mathrm{(\int -xdx))}[/tex] which has the general solution u(x) = Ce[tex](-x^2/2)[/tex].
Using the initial condition, we find C = 1/4, so u(x) = 1/4e[tex](-x^2/2)[/tex].
e) Finally, we solve for y. From u = y⁻¹, we have y = 1/u = 4e[tex](-x^2/2)[/tex].
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2._____________is based on what actually occurred during such an event
PROBABLITY
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
Estimate the mean of the distribution. You are given full credit if the estimate is within 2 units of the actual mean. It is okay to use decimals in your answer.
The estimated mean of the distribution for the given question will be 10.
Mean = 13 + 52 + 48 + 28 + 28 + 23 + 14 + 13 + 10 + 4 + 2 + 4 + 2 + 1 + 1 + 0 + 2 + 0 + 0 + 0 + 1 + 1 + 1 + 1 + 1
Total number =25
Now, divided the sum by 25
We get, the mean is equal to 10.
In mathematics, particularly in statistics, there are various types of means. Every mean serves to condense a specific set of data, frequently to help understand the overall significance of a particular data set. Only numerical variables, whether continuous or discrete, can be used to calculate the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.
Note that the illustration for graph is: (check the attached image)
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Simplify each radical expression as much as possible_ Assume that the variables represent any reaLnumbers, Use the absolute Value button only when necessary (a) (2x + 8 06 (b) Vy
The simplified form of the expression (2x+8)^6 is[tex]64x^6 + 1536x^5 + 15360x^4 + 819204x^3 + 245760x^2 + 393216x + 262144.[/tex]
To simplify the expression (2x + 8)^6, we need to raise the binomial (2x + 8) to the power of 6. This can be done using the binomial theorem.
The Binomial Theorem states that for any positive integer n and real numbers a and b, the expansion of the expression (a + b)^n is a sum of terms of the form (a^(n-k) * b^k * C(n,k)), where C(n,k) represents the binomial coefficient, which is equal to n!/(k!(n-k)!).
[tex](a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1) b^1 + ... + C(n, n-1)a^1 b^(n-1) + C(n, n)a^0 b^n[/tex]
Where C(n, k) is the binomial coefficient, given by C(n, k) = n! / (k! (n - k)!).
In this case, a = 2x and b = 8. So, substituting these values into the binomial theorem:
[tex](2x + 8)^6 = C(6, 0)(2x)^6 8^0 + C(6, 1)(2x)^5 8^1 + ... + C(6, 5)(2x)^1 8^5 + C(6, 6)(2x)^0 8^6[/tex]
Expanding each term, and combining like terms, we get:
[tex](2x + 8)^6 = 64x^6 + 1536x^5 + 15360x^4 + 819204x^3 + 245760x^2 + 393216x + 262144[/tex]
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I have a triangle with a measure of 15 cm, what will be its perimeter?
Answer: Its perimeter is 45 cm.
Step by step explanation:
Data :
We have a triangle with a measure of 15 cm
We must simplify taking into account that it is an equilateral triangle, all its sides are equal, therefore the perimeter is the sum of its sides:
P = Sum of its sides[tex]\bf P= 15 + 15 + 15[/tex]
[tex]\boxed{\bf \: P = 45 \: cm}[/tex]
Rpt: Its perimeter is 45 cm.
HELPP!!!
How can you tell whether a graph is a function?
Answer:
Vertical Line Test
Step-by-step explanation:
If a vertical line is drawn on a graph of a relation and only intersects the graph at one point, then that graph represents a function. If there is no vertical line intersecting the graph at two or more points, then the graph does not represent a function.
Solve for r.
V = 4/3πr³
What is r equal to? (Hint: Notice that r is cubed, not squared.)
The value of r is equal to the cube root of (V * (3π/4)).
What is r equal to?To solve for r, we need to rearrange the equation to isolate r.Starting with:V = 4/3πr³Divide both sides by 4/3π:V * (3π/4) = r³Take the cube root of both sides:r = (V * (3π/4))^(1/3)So, the value of r is equal to the cube root of (V * (3π/4)).Note: The equation for the volume of a sphere is V = 4/3πr³, where r is the radius of the sphere.To learn more about volume of sphere refer:
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Given the equation t(n)=3n-5 What is the 10th term?
Put n = 10
t(10) = 3(10) - 5 = 30 - 5 = 25
A sector of a circle has an area of 20 square feet. Find the central angle which forms the sector if the radius is 5 feet. The central angle of the sector isradians. (Type an integer or a simplified fraction.)
The area of a sector of a circle is equal to the central angle multiplied by the radius squared, divided by 2. In this case, the sector of the circle has an area of 20 square feet, the radius is 5 feet, and we need to find the central angle.
The central angle will be 6.28 radians.
To find the central angle, we can rearrange the equation to solve for the angle:
Central Angle = (2 * Area) / (Radius^2)
Substituting the given values, we get:
Central Angle = (2 * 20) / (5^2)
Simplifying, we find that the Central Angle equals 6.28 radians.
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Whoever answers right will get brainliest
Answer this but with top being the following instead of picture
investment a : $3000 invested for six years compounded, semi annually at 7%
Investment b: $5000 invested for five years compounded quarterly at 3.2%.
Answer: $8000 is invested for 6 years
Step-by-step explanation:P=$3,000 r= 7%= 0.07 t= 4 n= 2
What are all the number of miles? Where do I plot the points on the coordinate plane? What is a function that represents the graph?
Therefore , the solution of the given problem of coordinate plane comes out to be Y coordinates comes out to be -3 , -2, -1 , 0, 1,2,3
What is the function of coordinate plane?By portraying the inputs and outputs as a horizontal number line (the x axis) and a vertical number line (the y axis), respectively, the Cartesian coordinate plane enables us to perceive ordered pairs. The quantity in the x component is moved horizontally. Move to the right if x is positive. Move to the left if x is negative.
Here,
Given :
=> -30 , -20 ,-10 ,0 ,10, 20 , 30
=> So ,
Y coordinates comes out to be :
=> -3 , -2, -1 , 0, 1,2,3
An ordered pair of numbers, or x-coordinate and y-coordinate on the x-axis respectively, can be used to represent each point.
Written in parenthesis are ordered pairings (x-coordinate, y-coordinate). The source is situated at (0,0).
Check your coordinates, which are two numbers enclosed in parenthesis and separated by a comma, to see how to graph a point on the coordinate plane.
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Construct the cumulative frequency distribution that corresponds to the given frequency distribution. Number Speed of cars 0-29 4 30-59 16 60-89 60 90-119 20 Cumulative Speed Frequensy Less than 30100 Less than 60 80 Less than 90 82 Less than1 201 Cumulative SpeedFrequency Less than 30 Less than 60 20 Less than 90 80 Less than1 20 100 Cumulative Speed Frequency Less than 30 0.04 Less than 60 0.20 Less than 90 0.80 Less than1 201.00
The cumulative frequency distribution table is present below. Cumulative frequency for speed less than 30 is 4 , less than 60 is 20 , less than 90 is 80 less than 120 is 100. So, correct answer is option (b).
The cumulative frequency of a variable's value is the number of values in the collection of data that are less than or equal to the variable's value. Example: Let the raw data be 2, 2, 1, 5, 5, 6, 5, 3, 7, 7, 5, 6. Cumulative frequency of 3 = 4. Cumulative frequency is a frequency distribution table for the predecessor total. The final value is always equal to the sum of all observations, since all frequencies have already been added to the previous sum. We have a data corresponds to the frequencydistribution.
Speed Number of cars
0-29 4
30-59 16
60-89 60
90-119 20
We have to construct the cumulative frequency distribution for the above frequency distribution.Using the above rules we can construct distribution as,
Speed Number of cars Cumulative Freq
0-29 4 4
30-59 16 16 + 4 = 20
60-89 60 60 + 20= 80
90-119 20 20 + 80 = 100
-----------
Total 100
Thus , cumulative frequency for speed less than 30 is 4 , less than 60 is 20 , less than 90 is 80
less than 120 is 100.
Hence, we got the required cumulative frequencies for frequency distribution.
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Complete question:
Construct the cumulative frequency distribution that corresponds to the given frequency distribution. Number Speed of cars 0-29 4 30-59 16 60-89 60 90-119 20 a)Speed Cumulative Frequensy
Less than 30 100
Less than 60 80
Less than 90 82
Less than 120 1
b)Speed Cumulative Frequency
Less than 30 4
Less than 60 20
Less than 90 80
Less than1 20 100
c) speed Cumulative Frequency
Less than 30 0.04
Less than 60 0.20
Less than 90 0.80
Less than120 1.00
A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares fromthe four corners and turning up the sides. Find the side of the square cutout that gives the box the largest possible volume.
a) 0 in.
b) 6 in.
c) 5/3 in.
d) 2450/27 in.
The side of the square cutout that gives the box the largest possible volume
Therefore the answer is d) 2450/27 in.
To find the side length of the square cutouts that give the box the largest volume, we need to find an expression for the volume of the box in terms of the side length of the square cutouts. We can start by subtracting four times the area of one square cutout from the total area of the tin sheet to find the area of the box sides. The volume of the box will then be equal to the area of the box sides multiplied by the height.
The side length of the square cutouts can be represented by x. The area of one square cutout is x^2, so the total area of the four cutouts is
4x^2
The area of the tin sheet is 8 * 15 = 120. The area of the box sides is then
120 - 4x^2
The volume of the box is then (120 - 4x^2) * 8, which we want to maximize. To do this, we can differentiate the expression for the volume with respect to x and set it equal to zero, then solve for x. The solution to this optimization problem is
x = 2450/27, which is the side length of the square cutouts that gives the box the largest volume.
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the first 4 terms in a sequence are 8,5,2,-1... What is the recursive equation?
Answer:
aₙ = aₙ₋₁ - 3, a₀ = 8
Step-by-step explanation:
Minus three every time thus the recursive equation would be aₙ = aₙ₋₁ - 3, a₀ = 8
A two-piece set of luggage costs 122 If sold individually, the large bag costs 30 more than the small bag. What are the individual costs for each bag?
Let x be the cost of the small bag.
The large bag costs x + 30 more than the small bag.
So the cost of the large bag is x + (x + 30) = 2x + 30
The two-piece set of luggage cost is the sum of the cost of the small and large bag, so
122 = x + (2x + 30)
Solving this equation for x, we get:
x = 42
Therefore, the small bag costs 42 dollars and the large bag costs 2*42 +30 = 114 dollars.
