The number of dollars each day we can spend in the remaining days is, $97
What is division?Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.
We denote division by '÷' this symbol.
Given that,
Amount left in promotion budget = $668.00
Amount we need to spend on the last day = $85.00
The number of dollars in can spend each day = ?
Total amount can spend in remaining days = $668.00 - $85.00
= $583
Each day can spend = 583/6
= 97
Hence, the number of dollars can spend each day, $97
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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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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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1.)Which of the following statements about time-series forecasting is true? A. It makes extensive use of the data collected in the qualitative approach. B. It is based on expert’s subjective opinion. C. It is based on the assumption that future demand will be the same as past demand. D. The analysis of past demand helps predict future demand. 2.)A researcher wants to test if elementary school children spend less than 30 minutes per day on homework. The alternative hypothesis for this example will be that the population mean is: A. less than 30 minutes B. equal to 30 minutes C. not equal to 30 minutes D. less than or equal to 30 minutes 3.) Normal probability distribution is applied to: A. a subjective random variable B. a discrete random variable C. any random variable D. a continuous random variable
1) "The analysis of past demand helps predict future demand" is true about Time series forecasting.
2) A researcher wants to test if elementary school children spend less than 30 minutes per day on homework. The alternative hypothesis for this example will be that the population mean is: less than 30 minutes.
Hence, option (A) is the correct choice.
3) Normal probability distribution is applied to: a continuous random variable
Hence, option (d) is the correct choice.
A time series is a sequence of data points indexed in time order in mathematics. A time series is most frequently defined as a succession of photos taken at evenly spaced moments in time. As a result, it is a series of discrete-time data.
Time series forecasting is the process of making scientific forecasts based on time stamped data from the past. It entails developing models based on previous data and utilizing them to make observations and drive future strategic decisions.
The straight-line approach, moving averages, simple linear regression, and multiple linear regression are the four basic forecast methodologies. The straight-line and moving average techniques both presume that the company's past results will be broadly consistent with future results.
We are provided the following details:
- Average mu in the population: 30
The following is an alternate theory.
[tex]$$H_1: \mu < 30 \text { ( Claim ) }$$[/tex]
For this case, the alternative hypothesis is that the population mean is less than 30 minutes.
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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.
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 -
f(x) has been horizontally compressed by a factor of 3, translated left 2, up 4 and reflected across the x-axis. Which equation represents the transformed
equation?
O g(x)=√√(x + 2) + 4
O g(x) = -√√(x+2)+4
O g(x) = -√3 (2+2)+4
g(x) = -√3 (2+2)+4
O g(x) = -√2-2 +4
O g(x)=√(-2) + 4
Answer:
g(x) = -√3 (x/3 + 2) + 4.
Step-by-step explanation:
Circle A with center at (3, 4) and radius of 2 is similar to circle B with center at (−4, −5) and radius of 3. An incorrect informal argument for proving the two circles are similar is shown.
Step 1 Translate circle B to the right 9 units and up 7 units to form concentric circles.
Step 2 Dilate circle B to be congruent to circle A using scale factor of k equals r sub two over r sub one equals two thirds period
Step 3 When an object is dilated, the dilated object is similar to the pre-image, thus the two circles are similar.
Which step is incorrect, and how can it be fixed?
Group of answer choices
All steps are correct
Step 1, circle B should have been translated 7 units right and 9 units up
Step 3, replace "dilated" with "translated"
Step 2, circle B should have been dilated using scale factor of k equals r sub two over r sub one equals three halves
The required incorrect step is step 1, circle B should have been translated 7 units right and 9 units up. Option A is correct.
What is a circle?The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Here,
Circle A with a center at (3, 4) and a radius of 2 is similar to circle B with a center at (−4, −5) and a radius of 3.
To translate the circle B over circle A is given as 7 units right and 9 units up.
Thus, the required incorrect step is step 1, circle B should have been translated 7 units right and 9 units up. Option A is correct.
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Writing vectors v1,…,v4 that are parallel to the boundaries of the feasible set, computing z.vi for each boundary, and using the information to put arrows on each boundary indicating the direction in which the objective function z increases. Name Find max z(x,y) = "-3x" - 6y +8 Subject to g,(x,y) = "-3x" - 2y = "-6" = b, g2(x,y) = 5x – 2y = 40=b2 gz(x,y) = 2x + 4y - 8 = b; g4(x,y) = x + y = 5 = 54
The final result would be a feasible set with arrows indicating the direction of increase of the objective function z.
The feasible set can be found by solving the system of equations g1, g2, g3 and g4.
g1: -3x - 2y = -6
g2: 5x - 2y = 40
g3: 2x + 4y - 8 = 0
g4: x + y = 5
Solving for x and y,
We will get the coordinates of the feasible set: (2,2), (5,0), (0,5).
Next, we find the vectors that are parallel to each boundary:
g1: (-3, -2),
g2: (5, -2),
g3: (2, 4),
g4: (1,1)
To determine the direction in which the objective function z increases, we compute z.v1 for each boundary:
z.v1 = (-3, -2) * (-3, -6) = 18 + 12 = 30
z.v2 = (5, -2) * (-3, -6) = -15 - 12 = -27
z.v3 = (2, 4) * (-3, -6) = -6 - 24 = -30
z.v4 = (1,1) * (-3, -6) = -3 - 6 = -9
Based on the results, we can see that the objective function z increases in the direction of vector v2 and decreases in the directions of vectors v1, v3, and v4.
To put arrows on each boundary indicating the direction in which the objective function z increases, we would place arrows pointing towards the direction of vector v2 on g2 and away from the direction of vector v2 on g1, g3 and g4.
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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.
Perform the indicated operation and simplify the result.
Answer:
Where is the equation?
Step-by-step explanation:
I need it to solve this problem
Elimination method
7) 2x + 2y = 8
x + y = -2
Answer:No solution because 0≠12, so it like a trick question.
Step-by-step explanation: There is no solution because if you multiply the bottom equation by -2 everything will cancel making 0≠12.
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.
The following adjusted trial balance was drawn from the records of the Dakota Company. Account Title Dr Cr Cash 500 Equipment 2,000 Accounts Payable 1,000 Common Stock 700 Retained Earnings 600 Service Revenue 900 Operating Expenses 600 Dividends 100 Totals 3,200 3,200 Based on the information in the trial balance, the total amount of the debit column is
The total amount of the debit column in the adjusted trial balance is $5,400.
To find the total amount of the debit column in the adjusted trial balance, we need to sum up all the debit amounts listed in the accounts of teh given question.
Debits represent money being paid out of a particular account;
Looking at the trial balance provided, we can identify the following accounts with debit balances:
1. Cash: $500
2. Equipment: $2,000
3. Accounts Payable: $1,000
4. Common Stock: $700
5. Retained Earnings: $600
6. Service Revenue: $900
7. Operating Expenses: $600
8. Dividends: $100
In order to find the total amount of the debit column, we add up all these amounts,
Which gives us:
$500 + $2,000 + $1,000 + $700 + $600 + $900 + $600 + $100 = $5,400
Therefore, the total amount of the debit column in the adjusted trial balance is $5,400
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Please help me with this question.
The false statement regarding Legendre polynomials is given as follows:
E) [tex]P_{2k}(0) = (-1)^k\frac{(2k)!}{2^{2k}k!}, k \in N[/tex]
What are Legendre functions?The Legendre function of order v is the function that is a solution to the differential equation presented as follows:
(1 - x²)y'' - 2xy' + v(v + 1)y = 0.
Examples of Legendre polynomials are given as follows:
[tex]P_0(x) = 0[/tex][tex]P_1(x) = x[/tex][tex]P_2(x) = 0.5(3x^2 - 1)[/tex][tex]P_3(x) = 0.5(5x^3 - 3x)[/tex][tex]P_4(x) = 0.125(35x^4 - 30x^2 + 3)[/tex]From the polynomial of order 2, with k = 2, we have that:
[tex]P_4(0) = 0.375[/tex]
While:
[tex](-1)^2 \times \frac{4!}{16 \times 2!} = \frac{24}{32} = 0.75[/tex]
Different result, hence statement D is false.
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a glass jar containing five red 7 green 9 blue an 11 yellow marbles if a single marble is picked at random from the jar what is the probabilty of it beign a blue marble?
If a single marble is picked at random from the jar then the probability of it begin a blue marble is 9/32.
A glass jar containing five red 7 green 9 blue an 11 yellow marbles.
If a single marble is picked at random from the jar then we have to determine the probability of it begin a blue marble.
Red Marble = 5
Green Marble = 7
Blue Marble = 9
Yellow Marble = 11
Total Marble = Red Marble + Green Marble + Blue Marble + Yellow Marble
Total Marble = 5 + 7 + 9 + 11
Total Marble = 32
The probability of it begin a blue marble = Blue Marble/Total Marble
The probability of it begin a blue marble = 9/32
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A Vending machine at Canada's Wonderland dispenses candies for children in a park. The machine only accepts a quarter (Q: 25 cents), a dime (D: 10 cents) and/or a nickel (N: 5 cents). You cannot put two coins of the same value though. You can choose a different type of candies from the machine: Gummies-5 cents, Licorice-10 cents, Lollipops-15 cents, Caramels-35 cents, Chocolate-40 cents. The machine dispenses a candy only if the exact amount is entered. I You are asked to design the simplest circuit that will control the situation and dispense a candy. 1. Create the truth table for the above requirements
The truth table for the above requirements is shown as the relationship between the coins inserted (N/D/Q) and the candies dispensed (Gummies/Licorice/Lollipops/Caramels/Chocolate).
What is Truth table?
A truth table is a mathematical table used in logic that spells forth the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables.
The truth table for the vending machine scenario is represented in following figure.
The table shows the relationship between the coins inserted (N/D/Q) and the candies dispensed (Gummies/Licorice/Lollipops/Caramels/Chocolate). A 1 in the table indicates that the candy is dispensed, while a 0 indicates that it is not.
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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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A box contains orange balls and green balls. The number of green balls is seven more than 2 times the number of orange balls. If there are 73 balls altogether, then how many green balls and orange balls are there in the box?
Answer:
52-green
15-orange
Step-by-step explanation:
g + o = 67
g = green, o = orange, x = total = 3o + 7
use substitution: (3o + 7) + o = 67
solve for o:4o + 7 = 67
4o = 60o
= 60/4 = 15
solve for g:
g + 15 = 67
g = 52
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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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
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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From a point within a triangle, Segments are drawn to the vertices. A necessary.and sufficient condition that the three triangles formed have equal areas, is that the point be:
(A) such that the three angles formed each have a
measure of 120°
(B) the centre of the inscribed circle
(C) the centre of the circumscribed circle
(D) the intersection of the medians
Option D is the correct Answer. A necessary and sufficient condition that the three triangles formed have equal areas, is that the point be the intersection of the medians.
To divide a triangle into three triangles of equal area is to find the centroid the point where the medians intersect. After determining the centroid point G below, construct the segments connecting the vertices to the centroid. The three triangles created are of equal area.
So from a point within a triangle, line segments are drawn to the vertices. A necessary and sufficient condition that the three triangles thus formed have equal areas is that the point be the intersection of the medians of the triangle.
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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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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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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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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.
Given the equation t(n)=3n-5 What is the 10th term?
Put n = 10
t(10) = 3(10) - 5 = 30 - 5 = 25
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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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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