a. find all solutions of the recurrence relation an = 2an−1 2n2. b. find the solution of the recurrance relation in part (a) with initial condition a1 = 4.

Using this formula, we can find a1 by plugging in a19 (the 19th term) and n=19: a19 = a1 + (19-1)(d) => -101 = a1 + 18(-119/17), Simplifying this equation, we get: a29 = -33, the value of a29 is -33.

Given two terms in an arithmetic sequence, to find the recursive formula, we need to find the common difference of the sequence first. This can be found by using the formula: common difference (d) = (a36 - a19)/(36 - 19) = (-220 - (-101))/(36 - 19) = -119/17.

Next, we can use the recursive formula for arithmetic sequences which is: an = a1 + (n-1)dwhere an represents the nth term in the sequence, a1 represents the first term, and d is the common difference that we just found.Using this formula, we can find a1 by plugging in a19 (the 19th term) and n=19: a19 = a1 + (19-1)(d) => -101 = a1 + 18(-119/17).

Simplifying this equation, we get: a1 = -101 + (18)(119/17) = 7.Next, we can use the formula again to find a29 (the 29th term) by plugging in a1 and n=29: a29 = a1 + (29-1)(d) => a29 = 7 + 28(-119/17)Simplifying this equation, we get: a29 = -33Therefore, the value of a29 is -33. Answer: a29 = -33.

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Answer:

-----------------------

40% of the total number is 6.

Find the total number x:

The function’s equation written in factored form and in vertex form are respectively;

f(x) = 2x(x - 4)

f(x) = 2(x - 2)² - 8

The factored form of a quadratic function is;

f(x) = a(x - p)(x - q)

where:

p and q are the x-intercepts

a is a constant

Now, we are given x-intercepts as; (0, 0) and (4, 0)

Thus;

f(x) = a(x - 0)(x - 4)

f(x) = ax(x - 4)

To find a, substitute the given vertex (2, -8) into the equation and solve for a:

2a(2 - 4) = -8

-4a = -8

a = 2

Thus;

f(x) = 2x(x - 4)

The vertex form of a quadratic equation is;

f(x) = a(x - h)² + k

where:

(h, k) is the vertex

a is constant

Since vertex is (2, -8), then we have;

f(x) = a(x - 2)² - 8

Put the coordinate (0, 0) to find a;

0 = a(0 - 2)² - 8

4a = 8

a = 2

Thus;

f(x) = 2(x - 2)² - 8

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===================================================

Explanation:

Let's solve the first equation for y

4x - 2y = 6

4x-6 = 2y

2y = 4x-6

y = (4x-6)/2

y = (4x/2) - (6/2)

y = 2x - 3

After doing so, we see that 4x-2y = 6 is equivalent to y = 2x-3

Therefore, the original system of equations is effectively listing the same equation twice (one has a different form compared to the other).

Both equations in this system produce the same graph, which leads to infinitely many solutions. All solutions are on the line y = 2x-3.

You can say that all solutions are in the form (x, 2x-3) where x is any real number you want.

-------------------------------

Here's another approach using substitution

4x - 2y = 6 ... start with the first equation

4x - 2( y ) = 6

4x - 2( 2x-3 ) = 6 .... replace y with 2x-3; ie plug in y = 2x-3

4x - 2(2x) - 2(-3) = 6

4x - 4x + 6 = 6

0x + 6 = 6

0 + 6 = 6

6 = 6

We get a true statement. The last equation is always true regardless of what we plug in for x, so this is another way to see how we get to infinitely many solutions.

Side note: the system is considered dependent since one equation depends on the other. The system is also consistent since it has at least one solution.

Answer:

El método de igualación consiste en despejar la misma incógnita en las dos ecuaciones y después igualar los resultados.

Los pasos a seguir son los siguientes:

sistema de ecuaciones

En primer lugar, elegimos la incógnita que deseamos despejar. En este caso, empezaré por la «x» y despejo la misma en ambas ecuaciones.

x+y=7; x=7-y

5x-2y=-7; 5x=2y-7

x=(2y-7)/5

Una vez hemos despejado, igualamos:

7-y = (2y-7)/5

5.( 7-y) = (2y -7)

35 -5y= +2y -7

42=7y

y=42/7=6

y=6

Por último, sustituimos el valor que hemos calculado despejando la otra incógnita en una de las ecuaciones iniciales.

Answer:

We would have saved $12.

Step-by-step explanation:

First off, we know that the original price is $40.

Since the ball is 30% off, we'll multiply $40 by 70% to find the price it's sold by after the discount. 70% in decimal form is 0.70, so we would multiply 40(0.70)

40(0.70) = 28

This means that after a 30% discount, the price of the soccer ball is $28.

To find how much we saved, we would subtract $28 from $40.

40-28 = $12

$12 is the amount of money you saved.

Answer:

\(\huge\boxed{\sf 11.74\ in.\²}\)

Step-by-step explanation:

Area of Rectangle:

Length = 11.8 in.

Width = 3.6 in.

Area = Length * Width

Area = 11.8 * 3.6

Area = 42.48 in.²

Area of 3 circles:

Diameter = 3.6 in.

Radius = D/2 = 3.6/2 = 1.8 in.

\(\sf Area = \pi r^2\\\\Area = (3.14)(1.8)^2\\\\Area = (3.14)(3.24)\\\\Area = 10.18\ in.^2\)

Area of 3 circles = 3(10.18) = 30.5 in.²

Area of the figure when the 3 circles are cut:

= Area of the rectangle - Area of 3 circles

= 42.28 - 30.5

= 11.74 in.²

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

3 Blue Umbrellas

Step-by-step explanation:

Given

\(B \to Blue\)

\(Y \to Yellow\)

\(R \to Red\)

From the question, we have:

\(Y + R = 6\) ---- i.e. 6 are not blue

\(B + R = 6\) ---- i.e. 6 are not yellow

\(B + Y = 6\) ---- i.e. 6 are not red

Required

The number of blue umbrellas

Make B the subject in: \(B + Y = 6\)

\(B = 6 - Y\)

Substitute: \(B = 6 - Y\) in \(B + R = 6\)

\(6 - Y + R = 6\)

Collect like terms

\(R - Y = 6 - 6\)

\(R - Y = 0\)

Rewrite:

\(R = Y\)

Substitute \(R = Y\) in \(Y + R = 6\)

\(Y + Y = 6\)

\(2Y = 6\)

Divide both sides by 2

\(Y=3\)

Recall that: \(B = 6 - Y\)

\(B = 6 - 3\)

\(B = 3\)

The Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

To investigate whether the span of a person's dominant hand is greater than that of their non-dominant hand, the most appropriate statistical technique would be the Paired samples t-test.

The Paired samples t-test is used when comparing the means of two related groups or conditions. In this case, the dominant and non-dominant hands are related because they belong to the same individuals in the study. By comparing the means of the dominant and non-dominant hand spans, we can determine if there is a significant difference between the two.

The other options listed, ANOVA (Analysis of Variance), Independent samples t-test, Wilcoxon's matched-pairs signed rank test, and Mann-Whitney U test, are not suitable for this scenario because they are designed for different types of comparisons:

- ANOVA is used when comparing the means of three or more independent groups, which is not the case here.

- Independent samples t-test is used when comparing the means of two independent groups, which is not the case here as the measurements are paired.

- Wilcoxon's matched-pairs signed rank test and Mann-Whitney U test are non-parametric tests that are used when the data do not meet the assumptions of parametric tests. However, in this case, we have paired measurements, and the paired samples t-test is the appropriate parametric test.

Therefore, the Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

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Answer:

Ye :)

Step-by-step explanation:

Let's denote the cost of one basket of chicken strips as 'c' and the cost of one small soda as 's'.

From the given information, we can create a system of equations:

Equation 1: 3c + 4s = 22.29

(The total cost of three baskets of chicken strips and four small sodas is $22.29.)

Equation 2: 9c + 2s = 43.47

(The total cost of nine baskets of chicken strips and two small sodas is $43.47.)

We now have a system of two equations. To determine the exact cost of each item, we can solve this system of equations.

Using either substitution or elimination method, let's solve the system:

Equation 1 multiplied by 9: 27c + 36s = 200.61

Equation 2 multiplied by 3: 27c + 6s = 130.41

Now, subtract Equation 2 from Equation 1:

27c + 36s - (27c + 6s) = 200.61 - 130.41

30s = 70.2

Divide both sides by 30:

s = 70.2 / 30

s = 2.34

Substitute the value of 's' back into Equation 1:

3c + 4(2.34) = 22.29

3c + 9.36 = 22.29

3c = 22.29 - 9.36

3c = 12.93

Divide both sides by 3:

c = 12.93 / 3

c = 4.31

Therefore, the cost of one basket of chicken strips is $4.31, and the cost of one small soda is $2.34.

Answer:

May be minus

Step-by-step explanation:

minus 2 and minus 6 means minus 8b than we have to find out the value of b so 8into 4 is equal to 32

Answer:

the answer is D. (10, ∞)

Step-by-step explanation:

Every neighborhood of A contains a point of B and every neighborhood of B contains a point of A, which implies that A=B.

To show that there exists a sequence of rational numbers converging to any real number x, we can use the fact that the rational numbers are dense in the real numbers. This means that between any two real numbers, there exists a rational number.

So, let x be any real number. We can construct a sequence of rational numbers {q_n} such that q_n is the rational number between x-1/n and x+1/n. In other words,

q_n = a/b, where a and b are integers such that x-1/n < a/b < x+1/n and b > n

Then, it can be shown that as n approaches infinity, q_n converges to x. Therefore, there exists a sequence of rational numbers converging to any real number x.

To prove that A=B, we need to show that every neighborhood of A contains a point of B and every neighborhood of B contains a point of A.

First, let's consider any neighborhood of A. Since {a_n} converges to A, we know that there exists some positive integer N such that for all n > N, |a_n - A| < ε/2, where ε is the radius of the neighborhood.

Now, since B is an accumulation point of {a_n : n ∈ J}, we know that there exists some integer j ∈ J such that |a_j - B| < ε/2.

Thus, we have:

|A - B| ≤ |A - a_j| + |a_j - B| < ε/2 + ε/2 = ε

This shows that B is also in the neighborhood of A.

Next, let's consider any neighborhood of B. Since B is an accumulation point of {a_n : n ∈ J}, we know that there exists some positive integer M such that there are infinitely many n ∈ J satisfying |a_n - B| < ε/2.

Now, let n_1, n_2, n_3, ... be a subsequence of {a_n} such that |a_ni - B| < ε/2 for all i ≥ 1.

Since {a_n} converges to A, we know that there exists some positive integer N such that for all n > N, |a_n - A| < ε/2.

Let N' be the maximum of N and n_1, so that for all n > N', we have:

|a_n - A| < ε/2 and |a_n - B| < ε/2

Then, we have:

|A - B| ≤ |A - a_n| + |a_n - B| < ε/2 + ε/2 = ε

This shows that A is also in the neighborhood of B.

Therefore, we have shown that every neighborhood of A contains a point of B and every neighborhood of B contains a point of A, which implies that A=B.

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Percentage change expresses the ratio of the change in the amount of an initial quantity to the initial quantity as a percentage.

Mathematically, the formula for percentage change, C, can be presented as follows;

\(C = \dfrac{x_{2} - x_{1} }{ x_{1} } \times 100\)

Where:C = The percentage change

\(x_{1} \) = The original value

\(x_{2} \) =The new value

Graphically, percentage change can be presented as follows;

When the number of fruits that drops from a three each month, changes from 10 to 8, the percentage change is therefore;

\( C = \dfrac{10-8}{10} = 20\% \)The percentage change is 20%

Initial number of fruits that drops monthly from the tree;

##########

The new number of fruits that drops from the tree on the specified month;

########

The difference in the number of fruits that drops from the tree is 2, which corresponds to the 20 % calculated for the percentage change.

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The partial derivatives ∂N/∂u, ∂N/∂v, and ∂N/∂w when u=9, v=4, and w=3 are:

\(∂N/∂u = 96\)

\(∂N/∂v = 19\)

\(∂N/∂w = 35\)

To find the indicated partial derivatives, we can use the chain rule of differentiation. Starting with ∂N/∂u, we have:

\(∂N/∂u = (∂N/∂p) \times (∂p/∂u) + (∂N/∂q) \times (∂q/∂u) + (∂N/∂r) \times (∂r/∂u)\)

Substituting the given values for p, q, and r, we get:

\(∂N/∂u = (1 + q) \times 1 + (p + r) \times w + u \times w\)

Using the values of p, q, and r in terms of u, v, and w, we get:

\(∂N/∂u = (1 + v + uw) + (u + vw + w + uv) \times 3 + 9 \times 3\)

Simplifying the expression, we get:

\(∂N/∂u = 60 + 4u + 3v + 12w\)

We can find ∂N/∂v and ∂N/∂w by applying the chain rule of differentiation and using the given values for u, v, and w. Substituting the values, we get:

\(∂N/∂v = 3u + 4 + 3w\)

\(∂N/∂w = 3u + 3v + 2\)

The chain rule allows us to find the partial derivatives of a function with respect to its variables, by breaking down the function into its component parts and differentiating each part separately.

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The leader of the campfire girls troop can appoint 3 out of 14 members to clean up the camp in 364 ways.

The number of members in the campfire girls troop

= 14

The number of members the leader of the campfire girls troop can appoint at a time = 3

The number of ways to appoint r members out of n members

= nCr = n!/(r)!×(n-r)!

Therefore, the number of ways in which the leader of the campfire girls troop can appoint 3 out of 14 members to clean up the camp

= 14C3 = 14!/(3)!×(14-3)! = 364 ways

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Answer:

75%

Step-by-step explanation:

3/4 ie 75/100. .........edge

Answer:

p = 12

Step-by-step explanation:

total sales: 20p

total cost: 185 + 55

20p = 185 + 55

20p = 240

p = 12

12 photographs sold.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15.

let the number of photograph sold is p.

So, total sales = 20p

and, total cost

= 185 + 55

So,

20p = 185 + 55

20p = 240

p = 12

Hence, 12 photographs sold.

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In order to estimate the coefficients of linear regression equations that explain the connection between one or more independent quantitative variables and a dependent variable, researchers frequently use the ordinary least squares regression (OLS) method (simple or multiple linear regression), this is ordinary about it.

Because it is the smallest sum of squares of errors, also known as the "variance," the term "least squares" is employed. In a regression analysis, independent variables are shown on the horizontal x-axis and dependent variables are shown on the vertical y-axis.

A linear regression approach that is used to estimate a model's unknown parameters is known as the ordinary least squares (OLS) method.

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The stationary points on the curve \(\( y=\frac{x^{2}}{1+x^{4}} \)\) are located at the coordinates \(\( (0, 0) \), \( (1, \frac{1}{2}) \), and \( (-1, \frac{1}{2}) \)\).

To find the coordinates of stationary points on the curve given by the equation \(\( y=\frac{x^{2}}{1+x^{4}} \)\) , we need to find the points where the derivative of the function with respect to x is equal to zero.

Find the derivative of the function y with respect to x.

Taking the derivative of y with respect to x using the quotient rule, we have:

\(\[ \frac{dy}{dx} = \frac{(1+x^4)(2x) - (x^2)(4x^3)}{(1+x^4)^2} \]\)

Simplifying the numerator, we get:

\(\[ \frac{dy}{dx} = \frac{2x + 2x^5 - 4x^5}{(1+x^4)^2} \]\)

\(\[ \frac{dy}{dx} = \frac{2x - 2x^5}{(1+x^4)^2} \]\)

Set the derivative equal to zero and solve for x.

Setting \(\( \frac{dy}{dx} = 0 \),\) we have:

\(\[ \frac{2x - 2x^5}{(1+x^4)^2} = 0 \]\)

Since the numerator is equal to zero, we have:

\(\[ 2x - 2x^5 = 0 \]\)

\(\[ 2x(1 - x^4) = 0 \]\)

From this equation, we can see that either 2x = 0 or 1 - x⁴ = 0.

For 2x = 0, we get x = 0.

For 1 - x⁴ = 0, we have:

\(\[ x^4 = 1 \]\)

\(\[ x = \pm 1 \]\)

So we have three potential values for x: x = 0, x = 1, and x = -1.

Find the corresponding y values for the stationary points.

To find the y values, substitute the x values into the original equation \(\( y=\frac{x^{2}}{1+x^{4}} \)\):

For x = 0, we have \(\( y = \frac{0^2}{1+0^4} = 0 \)\) .

For x = 1, we have \(\( y = \frac{1^2}{1+1^4} = \frac{1}{2} \)\) .

For x = -1, we have \(\( y = \frac{(-1)^2}{1+(-1)^4} = \frac{1}{2} \)\) .

Therefore, the coordinates of the stationary points on the curve are:

\(\( (0, 0) \), \( (1, \frac{1}{2}) \), and \( (-1, \frac{1}{2}) \).\)

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Answer:2,2

Step-by-step explanation:

Answer:

Hi, the answer is a.

Step-by-step explanation:

1. 1800-200=1600

2. As 1800 is total x will be smaller amount. so....

3. when we write a subtraction statement bigger number - smaller number..

4. So answer will be 1600-x

The expression that represents the money left in his wallet in rupees will be 1600 - x. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Naren had Rs. 1800 in his wallet. He spent Rs. x on a watch and 200 to watch a cricket match.

Then the expression is given as,

⇒ 1800 - x - 200

Simplify the expression, then we have

⇒ 1800 - x - 200

⇒ 1600 - x

The expression that represents the money left in his wallet in rupees will be 1600 - x. Then the correct option is A.

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Answer: the answer is -32

Step-by-step explanation: multiply -2 by itself 5 separate times.

Answer:

-32

Step-by-step explanation:

-2×-2×-2×-2×-2=4×4×-2

=-32

ANSWER:

this the answer it's d

60x + 42y

60x +42y

60x +42y

The distributive property of 6(10x + 7y) is 60x + 42y

Distributive property tells us the order of operations to be followed by us while doing mathematical operations. the order of operations laid by distributive property is given below in chronological order:

1. Solve the brackets.

2.Orders(Exponents and square roots)

3. Division

4. Multiplication.

5.Addition

6. Subtraction

Now using Distributive property on 6(10x+7y)

1. Solve the brackets:

We can't do anything with the part inside the bracket as it contains all unknown values.

Hence, it will be as it is.

6 × 10x + 6 × 7y

2. Orders:

Whenever the index of any term is not shown, it is 1.

If any number is not multiplied by itself, it can be raised to 1.

3. Division:

The given polynomial doesn't have division with a non one number.

4. Multiplication:

6 × 10x + 7 × 7y

60x+42y

5. Addition:

Indefinite values can't be added

60x+42y

6. Subtraction:

No sign of subtraction is seen

Hence ,the distributive property of 6(10x + 7y) is 60x + 42y

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The total distance traveled is 14 miles, and the net displacement from the starting point is 4 miles south.

To determine the total distance traveled, we add the distances traveled in each direction. In this case, we walk 9 miles due north and then 5 miles due south. Therefore, the total distance traveled is 9 miles + 5 miles = 14 miles.

Net displacement refers to the change in position or the straight-line distance from the starting point to the final position. Since we walked 9 miles north and then 5 miles south, the net displacement is determined by subtracting the distance traveled in the opposite direction. Thus, the net displacement is 9 miles - 5 miles = 4 miles south.

It's important to note that while the total distance traveled is 14 miles, the net displacement is only 4 miles south. This indicates that even though we covered a total distance of 14 miles, our final position is 4 miles south of the starting point.

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The Wald test is a statistical test that can be used to test the significance of a group of coefficients in a multiple regression model.

The test statistic is calculated as the ratio of the estimated coefficient to its standard error. If the test statistic is significant, then the null hypothesis that the coefficient is equal to zero can be rejected.

Suppose we have a multiple regression model with three independent variables: age, gender, and education. We want to test the hypothesis that the coefficients for age and education are both equal to zero. The Wald test statistic would be calculated as follows:

Test statistic = (Estimated coefficient for age) / (Standard error of estimated coefficient for age) + (Estimated coefficient for education) / (Standard error of estimated coefficient for education)

If the test statistic is significant, then we can reject the null hypothesis that the coefficients for age and education are both equal to zero. This would mean that there is evidence that age and education are both associated with the dependent variable.

The Wald test is a powerful tool that can be used to test the significance of a group of coefficients in a multiple regression model. However, it is important to note that the test statistic is only valid if the assumptions of the multiple regression model are met. If the assumptions are not met, then the p-value of the Wald test may be inaccurate.

Here are some of the assumptions of the multiple regression model:

* The independent variables are independent of each other.

* The dependent variable is normally distributed.

* The errors are normally distributed.

* The errors have constant variance.

If any of these assumptions are not met, then the Wald test may not be accurate.

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The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point

f(x) = 5x⁶ - 3x⁵

differentiation w.r.t x

=> f'(x) = 30x⁵ - 15x⁴

Putting f'(x) = 0

30x⁵ - 15x⁴ = 0

=> x⁴(30x - 15) =0

=> 30x - 15 = 0

=> x = 15/30

=> x = 0.5 , 0

Critical number is 0.5 , 0

(B) To find where f(x) is increasing

for x > 0.5 ,

(30x-15) > 0 => x⁴(30x - 15) > 0

Therefore , f(x) is increasing at ( 0.5 , ∞ )

(C)To find where f(x) is decreasing

for x < 0.5 ,

(30x-15) < 0 => x⁴(30x - 15) < 0

Therefore , f(x) is decreasing at ( -∞ , 0.5)

(D) Differentiation f'(x) again w.r.t to x

f'(x) = 30x⁵ - 15x⁴

f"(X) = 150x⁴ - 60x³

Substituting critical values of x

=> 150(0.5)⁴ - 60(0.5)³

=>9.375 - 7.5

=> -1.875 < 0 , Hence , x = 0.5 is point of maxima

(E) no point of minima

Similarly , we can solve other parts

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