What property is 7(x-y)=7x-7y

The Taylor series formula in summation notation f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n } where f^n(a) denotes the nth derivative of f(t) evaluated at t = a.

Since the functions f(t) and g(t) have not been given in the question, I cannot provide a specific answer to this question. However, I can provide a general approach to finding the power series expansion of a function about a point.

To find the power series expansion of a function f(t) about a point t = a, we can use the Taylor series formula:

f(t) = f(a) + f'(a)(t-a) + (1/2!)f''(a)(t-a)^2 + (1/3!)f'''(a)(t-a)^3 + ...

where f'(a), f''(a), f'''(a), ... are the first, second, third, and higher-order derivatives of f(t) evaluated at t = a.

To find the first four nonzero terms of the power series expansion, we can calculate the values of f(a), f'(a), f''(a), and f'''(a) at t = a, substitute them into the Taylor series formula, and simplify the resulting expression. The first four nonzero terms will be the constant term, the linear term, the quadratic term, and the cubic term.

To find the general term of the power series expansion, we can write the Taylor series formula in summation notation:

f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n }

where f^n(a) denotes the nth derivative of f(t) evaluated at t = a. The general term of the power series expansion is given by the expression in the curly braces. We can use this expression to find any term in the series by plugging in the appropriate values of n and f^n(a).

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Given:

Required:

Solution:

First, set y = 4 ( 3x - 5), then solve for x in terms of y

Lastly, write the answer using x as a variable

Answer:

The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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Answer:

56667x

Step-by-step explanation:

i have

the an

swer please check if it is correct or bo

Answer:

Step-by-step explanation:

√(2x-1)^2   with  x ≥ 1/2

With x = 1/2

we have √(2(1/2)-1)^2

= √(1-1)^2

= 0.

So √(2x-1)^2 ≥ 0.

To reach your fundraising goal of $75, you will need to sell 150 pencils for $0.50 each and 0 bracelets for $1.00 each.

To reach your fundraising goal of $75, you can sell pencils for $0.50 and bracelets for $1.00.

1. Calculate the total amount of money needed to reach the goal:
  Goal amount = $75

2. Determine the number of pencils and bracelets you need to sell to reach the goal:
  Let's assume you sell x number of pencils and y number of bracelets.

  The amount raised from selling pencils = x * $0.50
  The amount raised from selling bracelets = y * $1.00

  The total amount raised from both items should be equal to the goal amount:
  x * $0.50 + y * $1.00 = $75

3. Simplify the equation:
  0.50x + 1.00y = 75

4. Solve for one variable in terms of the other:
  Let's solve for x in terms of y:
  0.50x = 75 - 1.00y
  x = (75 - 1.00y) / 0.50

5. Substitute the value of x into the equation:
  (75 - 1.00y) / 0.50 * 0.50 + y * $1.00 = $75
  75 - 2y + y = 75
  -y = 0
  y = 0

6. Find the value of x:
  x = (75 - 1.00 * 0) / 0.50
  x = 75 / 0.50
  x = 150

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According to the question For ( a ) the amount and concentration of salt at any time \(\(t\)\) can be \(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\) . For ( b ) the limiting concentration of salt in the tank is 0.25 kg/L.

To determine the amount and concentration of salt at any time in the tank, we need to consider the inflow of saltwater, outflow of water, and evaporation. Let's denote the time as \(\(t\)\) in hours.

a. Amount and Concentration of Salt at any time:

Let's denote the amount of salt in the tank at time \(\(t\) as \(S(t)\)\) in kg and the concentration of salt in the tank at time \(\(t\) as \(C(t)\) in kg/L.\)

Initially, the tank contains 100 L of water with a salt concentration of 0.1 kg/L. Therefore, at \(\(t = 0\)\), we have:

\(\[S(0) = 100 \times 0.1 = 10 \text{ kg}\]\)

\(\[C(0) = 0.1 \text{ kg/L}\]\)

Considering the inflow, outflow, and evaporation rates, the amount of salt in the tank at any time \(\(t\)\) can be calculated as:

\(\[S(t) = S(0) + \text{Inflow} - \text{Outflow} - \text{Evaporation}\]\)

The inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L. Thus, the amount of salt entering the tank per hour is:

\(\[\text{Inflow} = \text{Inflow rate} \times \text{Concentration} = 55 \times 0.2 = 11 \text{ kg/h}\]\)

The outflow rate is 44 L/h, so the amount of salt leaving the tank per hour is:

\(\[\text{Outflow} = \text{Outflow rate} \times C(t) = 44 \times C(t) \text{ kg/h}\]\)

The evaporation rate is 11 L/h, and as only water evaporates, it does not affect the salt concentration in the tank.

Therefore, the amount and concentration of salt at any time \(\(t\)\) can be expressed as follows:

\(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)

\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\)

b. Limiting Concentration:

The limiting concentration refers to the concentration reached when the inflow and outflow rates balance each other, resulting in a stable concentration. In this case, the inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L, and the outflow rate is 44 L/h. To find the limiting concentration, we equate the inflow and outflow rates:

\(\[\text{Inflow rate} \times \text{Concentration} = \text{Outflow rate} \times C_{\text{limiting}}\]\)

\(\[55 \times 0.2 = 44 \times C_{\text{limiting}}\]\)

\(\[C_{\text{limiting}} = \frac{55 \times 0.2}{44} = 0.25 \text{ kg/L}\]\)

Therefore, the limiting concentration of salt in the tank is 0.25 kg/L.

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The point-slope form of equation of the line perpendicular to the line y = 5x + 6 nd passing through (-3,3) is x + 5y = 12.

If two lines are perpendicular to each other, then the product of slopes of these two lines is equal to -1.

The provided line is y = 5x + 6,

The slope M₁ of the line is equal to the coefficient of x,

M₁ = 5

Let the slope of the perpendicular line is M₂,

So, we can write,

M₁M₂ = -1

M₂ = -1/5.

Now, we can use the point slope form of the equation of line, according to which is if line passes through (a,b) and have slope m then the equation of the line will be,

(y-a) = m(x-a)

This form of line is called Point-slope form of line.

Then, the equation of the line with slope -1/5 and passing through (-3,3) will be,

(y-3) = -1/5(x+3)

-5y+15 = x+3

x + 5y = 12

The above equation is the required equation of line in point slope form.

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Answer:

9 dollars

Step-by-step explanation:

Solve with a system of equations

Let adult tickets be a and student tickets be s

1. 8a + 13s = 176

2. 4a + 4s = 68

3. s = 17 - a

Equation 2 is friendlier, so let's divide all the numbers by 4.

a + s = 17

Equation is s = 17 - a

Substitute s in equation 1

8a + 13(17-a) = 176

8a + 221  - 13a = 176

221 - 5a = 176

5a = 45

a = 9

The price of an adult ticket is 9 dollars

Hope this helps :)

Answer:

a = - 2, b = 5

Step-by-step explanation:

expand the right side using FOIL and compare the coefficients of like terms on both sides.

(x + a)² + b

= x² + 2ax + a² + b

compare terms with x² - 4x + 9

coefficients of x- term

- 2a = 4 ( divide both sides by - 2 )

a = - 2

compare constant terms

a² + b = 9

(- 2)² + b = 9

4 + b = 9 ( subtract 4 from both sides )

b = 5

Answer:

P = -10

Step-by-step explanation:

P = 4 - 2r

P = 4 - 2 (-7)

P = 18

Answer:

P = 18

Step-by-step explanation:

p = 4 - 2r

p = 4 - 2(-7)

p = 4 + 14

p = 18

Therefore, your answer would be P = 18

The 30th term of the arithmetic sequence is 265

What is an arithmetic sequence in math?

This is an arithmetic sequence since there is a common difference between each term. In this case, adding 9 to the previous term in the sequence gives the next term. In other words,   \(a_{n}\)= \(a_{1}\)+ d ( n - 1 )

Arithmetic Sequence: d = 9

This is the formula of an arithmetic sequence.

\(a_{n}\) =  \(a_{1}\) + d ( n - 1 )

Substitute in the values of   \(a_{1}\) = 4 and  d = 9

 \(a_{n}\)= 4 + 9 ( n - 1 )

\(a_{n}\)= 4 + 9n - 9

\(a_{n}\) = 9n - 5

.30th term =   \(a_{n}\) =   \(a_{1}\)+ d ( n - 1 )

=  \(a_{30}\)= 4 + 9 ( 30 -1 )

   \(a_{30}\)=   4 + 9 x 29

  \(a_{30}\)= 265

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Answer: 24

Step-by-step explanation:

m - 8 = 16

m = 24

Answer:

24

Step-by-step explanation:

To find the value of "m", you need to plug n = 8 into the equation.

m - n = 16                             <---- Original equation

m - 8 = 16                             <----- Plug 8 in for "n"
   + 8  + 8                             <---- Isolate "m" by adding 8 to both sides

m = 24                                  <----- Final answer

Answer:

455

Step-by-step explanation:

The probability that Ella chooses the picture with the dog is 1/5 or 0.2, which can also be expressed as a percentage, 20%.

Probability is a measure of the probability of an event. It measures the certainty of an event. The probability formula  is given; P(E) = number of positive results / total number of results.

The probability of choosing a picture with a dog is the ratio of the number of dog pictures  to the total number of pictures.  We learn that Ella drew 40 different images for the art exhibit, eight of which feature a dog. Therefore, the probability of choosing a picture with a dog is:

8/40

Simplifying this fraction, we get:

1/5

So the probability that Ella chooses the picture with the dog is 1/5 or 0.2, which can also be expressed as a percentage, 20%.

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Answer:

a.) 12 + x = < -8

b.) x + -8 > 12

c.) -8 - x < 12

Answer:

2v + 3

Step-by-step explanation:

Rewright the equation and distribute the negative symbol ( 5v + 5 - 3v - 2 )

Next, combine like terms and you will get 2v + 3.

Answer:

2v + 3

Step-by-step explanation:

Remove the parentheses and combine like terms

5v-3v = 2v

5 - 2 = 3

The matrix expression is \(a^-1 = [a11^{-1}, -a11^{-1} a21 a22^{-1}; 0, a22^{-1}]\)

Matrices are arrays of numbers arranged in rows and columns, and they are used to represent and manipulate data in many areas of mathematics, including linear algebra and engineering. Matrix inverse is an important concept in matrix mathematics and is represented by the symbol "\(a^{-1}\)".

When two matrices, a11 and a22, are given, the expression for the inverse of the overall matrix a can be obtained in terms of a11, a22, and a21, which is the matrix that connects a11 and a22. The expression for a^-1 can be found using the formula:

\(a^-1 = [a11^{-1}, -a11^{-1} a21 a22^{-1}; 0, a22^{-1}],\)

where a11^-1 and a22^-1 are the inverses of matrices a11 and a22, respectively.

It is important to note that for the inverse to exist, both a11 and a22 must be nonsingular, meaning that their determinants must not be zero. The matrix inverse is a useful tool for solving systems of linear equations, and it also has applications in other areas such as cryptography and computer graphics.

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Answer: 89 miles driven in the afternoon

Step-by-step explanation:

    Let x be the total number of miles driven in the morning, and y in the afternoon.

    Firstly, we know the total miles driven.

x + y = 248

    Next, we know he drove 70 fewer miles in the morning.

x - 70 = y

    Our system of equations:

x + y = 248

x - 70 = y

\(-----------------------------------------\)

    To solve, we will substitute one of the equations into the other.

x + y = 248

x + (x - 70) = 248

2x = 318

x = 159 miles in the morning

    To solve for miles driven in the afternoon, we will substitute this value back into one of the equations and solve for y.

x - 70 = y

(159) - 70 = y

y = 89 miles driven in the afternoon

The graph of the first five terms can be seen in the image at the end.

We know that we have an arithmetic sequence:

3, -10, -23, -36

The common difference is what we get when we subtract two consecutive terms, we will get:

d = -36 - (-23) = -3

Then the recursive relation is:

a(n) = a(n - 1) - 13

At the moment we know:

a(1) = 3

a(2) = -10

a(3) = -23

a(4) = -36

Then fifth term will be:

a(5) = a(4) - 13 = -36 - 13 = -49

Now to graph it, we use the "n-th" value as the input, then we need to graph the five points (1, 3), (2, -10), (3, -23), (4, -36), (5, -49).

The graph can be seen in the image below:

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As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

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Answer:6,299,406

Step-by-step explanation:

Three out of six questions that you can ask about the statistical validity of a bivariate correlation are: All the statistical validity questions do not apply in the same way when bivariate correlations are represented as bar graphs because statistical validity questions address issues of internal validity (causality) rather than issues of external validity (generalizability).

Statistical validity questions are concerned with establishing whether the relationship between the two variables is likely to be a true relationship or just a chance occurrence. Statistical validity can be assessed by determining whether the correlation coefficient is statistically significant (i.e., whether the relationship observed is likely to be a true relationship or just a chance occurrence) and the strength of the correlation.

Statistical significance testing requires a large sample size, and as a result, the correlation coefficient may be statistically significant even if the effect size is small. Therefore, it is important to consider both statistical significance and effect size when evaluating the statistical validity of a bivariate correlation.

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We want to see how much the population of goats grows each year. We will see that the correct option is c: 17%.

We know that:

The population can be modeled with an exponential equation as:

P(t) = A*(1 + r)^t

Where:

So we have:

P(t) = 1500*(1 + r)^t

And we know that after 11 years the population is 8,400, so we have:

P(11) = 1500*(1 + r)^11 = 8400

Now we can solve this for r:

(1 + r)^11 = 8400/1500 = 5.6

(1 + r) = (5.6)^(1/11) = 1.17

r = 1.17 - 1 = 0.17

r = 0.17

To get it in percentage form, you just need to multiply it by 100%

0.17*100% = 17%

This means that the population increases a 17% each year, so the correct option is c.

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The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.

First, we can check the limit as x approaches 3 from the left:

lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞

Next, we can check the limit as x approaches 3 from the right:

lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞

Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.

Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

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The original slope's reciprocal will be the opposite of the perpendicular slope. To determine the intercept, b, enter the supplied point and the new slope into the slope-intercept form (y = mx + b). Rewrite the following equation in standard form: ax + by = c.

The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.

The slope is m and the y-intercept is b in the equation y=mx+b in slope-intercept form. Some equations can also be rewritten so that they resemble slope-intercept form. For instance, y=x can be written as y=1x+0, resulting in a slope and y-intercept of 1 and 0, respectively.

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The limit as x approaches one is infinity.

\(lim_{x\to1}\frac{x + x {}^{2} + {x}^{3} + ... + {x}^{100} - 1000}{1 - x} =\infty\)

The limit of a function, f(x) as x approaches a given value b, is define as the value that the function f(x) attains as the variable x approaches the given value b.

From the given question, as x approaches 1,

substituting x into 1 - x,

the denominator of the function approaches zero, because 1 - 1 = 0 and thus the function becomes more and more arbitrarily large.

Thus, the limit of the function as x approaches 1 is infinity.

Therefore,

The limit (as x approaches 1)

\(lim_{x\to1}\frac{x + x {}^{2} + {x}^{3} + ... + {x}^{100} - 1000}{1 - x} = \infty \)

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Answer:

b)280° and c) 270°

A reflex angle is an angle which is more than 180° but less than 360°

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

Step-by-step explanation:

180 is reflex angle.

hope it's helpful

Ans. (a)

SQ and RQ

Ans. (b)

∠RQT

∠TQR

Ans. (c)

Q

(1) To solve this linear programming problem, we need to graph the constraints and find the feasible region. Starting with the first constraint, x + y ≤ 7, we can plot the line x + y = 7 and shade the region below it (since we want x and y to be greater than or equal to 0).

Next, the constraint 2x + y ≤ 12 corresponds to the line 2x + y = 12, and we shade the region below this line as well.
Finally, the constraint y ≤ 4 corresponds to the horizontal line y = 4, which we shade everything below.
The feasible region is the overlapping shaded region of these three constraints.
To maximize f = 2x + 4y within this feasible region, we need to find the corner point with the highest value of f.
Checking the corner points of the feasible region, we have (0,4), (3,4), and (5,2).

Plugging each of these into the objective function f = 2x + 4y, we get:
- (0,4): f = 2(0) + 4(4) = 16
- (3,4): f = 2(3) + 4(4) = 22
- (5,2): f = 2(5) + 4(2) = 18
Therefore, the maximum value of f = 22 occurs at the point (3,4).
(x,y) = (3,4)
f = 22 .

2) Again, we need to graph the constraints to find the feasible region.Starting with the first constraint, x + y ≤ 7, we plot the line x + y = 7 and shade the region below it.The second constraint, 2x + y ≤ 12, corresponds to the line 2x + y = 12, which we shade the region below as well. Finally, the third constraint, x + 3y ≤ 15, corresponds to the line x + 3y = 15, which we shade the region below.

The feasible region is the overlapping shaded region of these three constraints. To maximize f = 2x + 8y within this feasible region, we need to find the corner point with the highest value of f. Checking the corner points of the feasible region, we have (0,0), (0,5), (3,4), and (7,0).

Plugging each of these into the objective function f = 2x + 8y, we get:- (0,0): f = 2(0) + 8(0) = 0
- (0,5): f = 2(0) + 8(5) = 40
- (3,4): f = 2(3) + 8(4) = 34
- (7,0): f = 2(7) + 8(0) = 14, Therefore, the maximum value of f = 40 occurs at the point (0,5). , (x,y) = (0,5)
f = 40.

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The equation of the tangent line to the astroid at the point (-3√3, 1) is: y = -(3√3)^(1/3)x - 3(3√3)^(1/3) + 1

To find the equation of the tangent line to the astroid at the point (-3√3, 1), we need to first find the slope of the tangent line.

We can do this by taking the derivative of the equation of the astroid with respect to x, and then evaluating it at the point (-3√3, 1).

Taking the derivative of x²/³ + y²/³ = 4 with respect to x, we get:

(2/3)x^(-1/3) + (2/3)y^(-1/3) * dy/dx = 0

Solving for dy/dx, we get:

dy/dx = (-x^(1/3))/y^(1/3)

Substituting x = -3√3 and y = 1, we get:

dy/dx = (-(-3√3)^(1/3))/(1^(1/3)) = -(3√3)^(1/3)/1

So the slope of the tangent line at the point (-3√3, 1) is -(3√3)^(1/3).

Now we can use the point-slope form of the equation of a line to find the equation of the tangent line. The point-slope form is:

y - y1 = m(x - x1)

Substituting x1 = -3√3, y1 = 1, and m = -(3√3)^(1/3), we get:

y - 1 = -(3√3)^(1/3)(x + 3√3)

Simplifying, the equation of the tangent line to the astroid at the point (-3√3, 1) is:

y = -(3√3)^(1/3)x - 3(3√3)^(1/3) + 1

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