Find the sale price after a discount of 30% offa snowboard that originally cost $529

Answer:-4

Step-by-step explanation:

11,7,3,-1,-5,......they have a difference of -4

11-4=7

7-4=3

3-4=-1

-1-4=-5

Recursive formula for the given sequence is \(a_{n}=a_{n-1}-4\)

A recursive formula is a formula that defines any term of a sequence in terms of its preceding term(s).

Consider

The first term \(a_{1} =11\)

second term \(a_{2}=7\)

Common difference = 7-11 = -4

Third term \(a_{3}=3\)

Common difference = 3-7 =- 4

Fourth term \(a_{4}=-1\)

Common difference = -1-3= -4

Then the formula for the sequence is \(a_{n}=a_{n-1}-4\)

Hence, the Recursive formula for the give sequence is \(a_{n}=a_{n-1}-4\)

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Answer:

B.  6

Step-by-step explanation:

The triangles are similar by AA Similarity.

The lengths of corresponding sides of the triangles are proportional.

AB/PQ = AC/PR

20/5 = 24/PR

4 = 24/PR

4PR = 24

PR = 6

Answer: PR = 6

Answer:

3

Step-by-step explanation:

from angles on a line = 180°

therefore

(14x + 70 + 20x +8)°= 180°

34x + 78 =180

34x = 180-78

34x= 102

x = 102/34

x= 3

Answer:

3

Step-by-step explanation:

!

The three factors that need to be taken into account when determining the sample size are the margin of error, level of confidence, and standard deviation.

To determine the sample size required to estimate the mean with a given level of confidence, we need to consider three factors. The first factor is the margin of error, which is the maximum distance between the sample mean and the true population mean that can be tolerated and is denoted by E.

The second factor is the level of confidence, which is the probability that the true population mean lies within the margin of error of the sample mean. This is denoted by (1-α), where α is the level of significance. Therefore, the level of confidence is 1 - α.

The third factor is the population standard deviation (σ) or the variance (σ²). If the population standard deviation is not given, we can use the sample standard deviation as an estimate. However, if the population size is greater than 30 and the distribution is normal, the sample mean can be used to estimate the population mean. On the other hand, if the population size is less than or equal to 30, the sample mean can be used to estimate the population mean only if the population distribution is normal.

Therefore, it is crucial to consider the distribution of the population when deciding if the sample mean can be used to estimate the population mean.

In summary, the three factors that need to be taken into account when determining the sample size required to estimate the mean with a given level of confidence are the margin of error, level of confidence, and population standard deviation (σ) or the variance (σ²). It is essential to understand each of these factors to accurately determine the required sample size.

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Let p be the proportion of defectives in the shipment. Since p = 0.10 and we have a sample of n = 10 components drawn from the shipment, then from the binomial distribution we get:

Let p be the proportion of defectives in the shipment.

Thus, the probability that the distributor will return the shipment if the proportion of defectives in the batch is in fact 10% is 0.2639.

Summary:In summary, we are given that the proportion of defectives in the shipment is 10% and we are asked to find the probability that the distributor will return the shipment if 10 components are sampled and more than 1 of the 10 is defective. We can calculate this probability using the binomial distribution, which yields a probability of 0.2639.

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Answer:

6 and 8 are corresponding.

2 and 4 is corresponding.

Step-by-step explanation:

and 2 and 7 is alternate.

3 and 6 are alternate.

An apple cost $1.2 and the orange cost $1.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, she bought 5 apples and 4 oranges for $10. This will be 5a + 4o = 10

The friend bought 5 apples and 5 oranges for $11. This will be 5a + 5o = 11

Equate the equations

5a + 4o = 10

5a + 5o = 11

Subtract

o = 1

The value of orange is $1

The value of apple will be:

5a + 4o = 10

5a + 4(1) = 10

5a + 4 = 10

Collect like terms

5a = 10 - 4

5a = 6

Divide

a = 6/5

a = 1.2

Apple cost $1.2

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Answer:

S'' = (\(-\frac{3}{2} , \frac{9}{2}\) )

Step-by-step explanation:

coordinate of x is (-2 , 6)

scale factor to transform the triangle is 3/2

so to find S' use this scale factor

formula :

(x , y) = (kx , ky)    (k means scale factor)

S(-2 , 6) = S'(3/2 *-2 , 3/2 * 6)

S'(-3 , 9)

now to find S'' again use the same formula

(x , y ) = (kx , ky)

this time take S' and to find S'' use 1/2 as scale factor

S'(-3 , 9) = S''(1/2 *-3 , 1/2 * 9)

S''(-3/2 , 9/2)

The transformation is S'' = (-3/2, 9/2). The correct option is A.

Scale factor refers to the ratio of corresponding lengths or measurements between two similar objects or figures. It represents how much one object has been scaled or enlarged/reduced compared to another object.

The scale factor is determined by dividing the length or measurement of a corresponding side or dimension of one object by the length or measurement of the corresponding side or dimension of the other object. It provides a quantitative relationship between the two objects.

The coordinate of x is (-2, 6). The scale factor to transform the triangle is 3/2 so to find S' use this scale factor.

formula :

(x , y) = (kx, ky)    (k means scale factor)

S(-2 , 6) = S'(3/2 x -2 , 3/2 x 6)

S'(-3 , 9)

Now to find S'' again use the same formula:

(x , y ) = (kx, ky)

this time take S' and to find S'' use 1/2 as the scale factor.

S'(-3 , 9) = S''(1/2 x -3 , 1/2 x 9)

S''(-3/2 , 9/2)

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The amount each of them pays when their electricity bill is $110, $165, and $352 respectively, in the ratio 2:4:5, are:

1) $20, $40, $50

2) $30, $60, $75

3) $64, $128, $160

To find out how much each of them pays, we'll use the given ratio of 2:4:5 and divide the total bill among them accordingly.

Total bill: $110

The total ratio is 2+4+5=11.

Greg's share: (2/11) * $110 = $20

Harry's share: (4/11) * $110 = $40

Ian's share: (5/11) * $110 = $50

Therefore, Greg pays $20, Harry pays $40, and Ian pays $50.

Total bill: $165

The total ratio is still 2+4+5=11.

Greg's share: (2/11) * $165 = $30

Harry's share: (4/11) * $165 = $60

Ian's share: (5/11) * $165 = $75

Therefore, Greg pays $30, Harry pays $60, and Ian pays $75.

Total bill: $352

The total ratio remains the same: 2+4+5=11.

Greg's share: (2/11) * $352 = $64

Harry's share: (4/11) * $352 = $128

Ian's share: (5/11) * $352 = $160

Therefore, Greg pays $64, Harry pays $128, and Ian pays $160.

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The solution set can be described as the line {(2-4t, -1-t, 3t-2, -5-6t)} in R4.  This line can be defined by a vector (4, 1, 1, -6) and any point on the line (2, -1, 0, -5).

The solution set can be described by the line {(2-4t, -1-t, 3t-2, -5-6t)} in R4. To describe this line, we need a point on the line and a vector. The point on the line can be found by setting t = 0, so the point is (2, -1, 0, -5). The vector can be found by subtracting the point from each of the coordinates of the solution set, so the vector is (4, 1, 1, -6). This vector can be used to describe the line in R4, as any point on the line can be expressed as a multiple of the vector plus the initial point on the line. Therefore, the solution set of the system of equations can be described as the line {(2-4t, -1-t, 3t-2, -5-6t)} in R4, defined by the point (2, -1, 0, -5) and the vector (4, 1, 1, -6).

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Answer:

54.68 miles I believe

Step-by-step explanation:

To solve the given linear programming problem using the graphical method, we can plot the constraints and then find the feasible region.

Then we can find the optimal solution by plotting the objective function and finding the minimum value within the feasible region. So, the given LP problem is:\(Min Z = 25A + 25Bsubject to:4A + 3B ≥ 245A + 27B ≥ 24A, B ≥ 0\)Let's plot the constraints one by one:\(4A + 3B ≥ 24On plotting 4A + 3B = 24,\) we get a straight line passing through the points (0, 8) and (6, 0) as shown below:\(5A + 27B ≥ 24On plotting 5A + 27B = 24\), we get a straight line passing through the points (4.8, 0) and (0, 0.89) as shown below:

The optimal solution is the point where the objective function intersects the feasible region. This occurs at the point (4, 4) with \(Z = 25(4) + 25(4) = 200\).Hence, the optimal solution of the given LP problem is \(A = 4, B = 4 and Z = 200.\)

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The partial derivative of z with respect to x is -1/3, and the partial derivative of z with respect to y is -2/3.

If the equation F (x, y, z) = 0 determines z as a differentiable function of x and y, then we can apply the implicit function theorem to obtain the following equations:

partial z/ partial x = -Fx / Fz
partial z/ partial y = -Fy / Fz

where Fx, Fy, and Fz denote the partial derivatives of F with respect to x, y, and z, respectively. These equations hold at the points where Fz is not equal to 0.

To find the values of partial z/ partial x and partial z/partial y at a given point, we need to evaluate the partial derivatives of F at that point and substitute them into the above equations. For example, let's say we are given the point (1, 2, 3) and the equation F(x, y, z) = x^2 + y^2 + z^2 - 25 = 0.

At the point (1, 2, 3), we have:

Fx = 2x = 2
Fy = 2y = 4
Fz = 2z = 6

Since Fz is not equal to 0 at this point, we can use the above equations to find:

partial z/ partial x = -Fx / Fz = -2/6 = -1/3
partial z/ partial y = -Fy / Fz = -4/6 = -2/3

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Answer:

17

Step-by-step explanation:

Answer:

17 links

Step-by-step explanation:

1. 13 Links and 17 links are rusted. Since we need to find out the number of links that are not rusted, we need to add 13+17.

a.  13  + 17 = 30

2. Now since we added the number of lines rusted, we now should subtract the ones rusted and the one not rusted to get the answer.

a. 47-30 = 17

FINAL ANSWER: 17

Answer:

Step-by-step explanation

Frist, the area = ab = 30 m^2 and the perimeter = 2(a + b) = 34 m or a + b = 17 m (2). Solving (1) and (2), a = 15 m and b = 2 m. Since it is a rectangle, the dimensions are (all in m) so the answer is: 15, 2, 15, 2.

Answer:

THe kitchen is 8 by 10

Step-by-step explanation:

x = width

y = length

Area = xy = 80 m²

Perimeter = 2x + 2y = 36 m

2x = 36 - 2y

x = 18 - y   substitute into equation 1

(18 - y)(y) = 80

-y² + 18y - 80 = 0    find roots of y by factoring

y² - 18y + 80 = 0

(y - 8)(y - 10) = 0

y = 8, 10

Since xy = 80, then:

x = 80/10 = 8, or, x = 80/8 = 10

Now you have your dimensions: 8 and 10

To check the answers:

8 x 10 = 80 m²

2(8) + 2 (10) = 36 m

Answers are correct!

Answer:

Option 1 is you answer

Step-by-step explanation:

iReady approved!!!!

Circle B is the result of dilating circle A with A as the center of dilation by a scale factor of 4/5.

Two shapes are said to be similar if they have the same shape, and the ratio of their corresponding sides are in the same proportion.

Circle B is the result of dilating circle A with A as the center of dilation by a scale factor of 4/5.

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Las cantidades requeridas de ingredientes para la preparación de alfajores son 3,5 barras de mantequilla, 3,5 bolsas de manjar, 2 tazas de maicena y 9 / 4 tazas de harina.

Sabrina entrega un vuelto de 10,4 soles por el pago de 100 soles por la compra de 7 docenas de 12,80 soles.

En este problema debemos determinar la cantidad requerida de ingredientes para la preparación de alfajores, se tiene como referencia una tabla de preparación, de modo que se puede determinar las cantidades requeridas mediante regla de tres simple:

y' = (p' / p) × y

Where:

A continuación, determinamos los ingredientes requeridos y los faltantes en cada caso:

Barra de mantequilla:

y' = (60 / 24) × 1

y' = 2,5 barras

y'' = 6 barras - 2,5 barras

y'' = 3,5 barras

Bolsas de manjar

y' = (60 / 24) × 1

y' = 2,5 bolsas

y'' = 6 bolsas - 2,5 bolsas

y'' = 3,5 bolsas

Maicena

y' = (60 / 24) × (1 / 2)

y = 5 / 4 tazas

y'' = 5 / 4 tazas - 1 / 4 tazas

y'' = 2 tazas

Tazas de harina

y' = (60 / 24) × (3 / 2)

y' = 15 / 4 tazas

y'' = 15 / 4 tazas - 3 / 2 tazas

y'' = 9 / 4 tazas

Tazas de azúcar en polvo

y' = (60 / 24) × (1 / 2)

y' = 5 / 4 tazas

y'' = 5 / 4 tazas - 10 tazas

y'' = - 35 / 4 tazas (Tiene exceso de azúcar en polvo).

En consecuencia, los faltantes para la preparación de 60 alfajores son los siguientes: 3,5 barras de mantequilla, 3,5 bolsas de manjar, 2 tazas de maicena y 9 / 4 tazas de harina.

Por último, determinamos el vuelto tras el pago de 100 soles peruanos:

C = 100 soles - 7 · 12,80 soles

C = 10,4 soles

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Answer:

\(\displaystyle m\angle RTU=73^\circ\)

Step-by-step explanation:

Interior Angle of a Circle

An interior angle of a circle is formed at the intersection of two lines that intersect inside a circle.

Lines AC and BD of the figure attached below intersect forming arcs p and q. The measure of the interior angle x  is:

\(\displaystyle x=\frac{p+q}{2}\)

The question includes the drawing of a circle with lines US and RV intersecting at point T. The measure of the interior angle RTU is:

\(\displaystyle m\angle RTU=\frac{68^\circ+78^\circ}{2}\)

\(\displaystyle m\angle RTU=\frac{146^\circ}{2}\)

\(\boxed{\displaystyle m\angle RTU=73^\circ}\)

The bounds for a 95% confidence interval could be option (B) 72 and 79

We know that the 98% confidence interval has bounds of 73 and 80. This means that if we were to repeat the same experiment many times, we would expect that 98% of the time, the true population mean would fall within this range.

To find the bounds for a 95% confidence interval, we can use the fact that a higher confidence level corresponds to a wider interval, and a lower confidence level corresponds to a narrower interval.

Since we want a narrower interval for a 95% confidence level, we can expect the bounds to be closer to the sample mean. We can calculate the sample mean as the midpoint of the 98% confidence interval

(sample mean) = (lower bound + upper bound) / 2 = (73 + 80) / 2 = 76.5

Next, we can use the formula for a confidence interval:

(sample mean) ± (z-score) × (standard error)

where the z-score depends on the desired confidence level, and the standard error depends on the sample size and sample standard deviation. Since we don't have this information, we can assume that the sample size is large enough (i.e., greater than 30) for the central limit theorem to apply, and we can use the formula

standard error = (width of 98% CI) / (2 × z-score)

For a 98% confidence interval, the z-score is 2.33 (found using a standard normal distribution table or calculator). Plugging in the values, we get

standard error = (80 - 73) / (2 × 2.33) = 1.70

Now, we can use this standard error to calculate the bounds for a 95% confidence interval

(sample mean) ± (z-score) × (standard error) = 76.5 ± 1.96 × 1.70

Simplifying, we get

(lower bound) = 76.5 - 3.33 = 73.17

(upper bound) = 76.5 + 3.33 = 79.83

Therefore, the correct option is (B) 72 and 79

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Answer:

check online for more information

It takes the second marathoner 4 hours and 40 minutes to complete the marathon.

Let's assume the distance of the marathon is "d" miles.

The first marathoner runs at a constant speed for 4 hours, so we can find their speed as:

speed = distance / time = d / 4

The second marathoner starts by running at 4 times the speed of the first marathoner, so their speed is:

speed = 4(d / 4) = d

For the second half of the race, the second marathoner's speed drops to 3/4 of the first marathoner's speed. Let's assume it takes "t" hours for the second marathoner to complete the second half of the race. Then, we can write:

d / 2 = (3/4)(d / 4)(t)

Simplifying this equation, we get:

t = (2/3) hours

So the total time it takes the second marathoner to finish the race is:

4 + (2/3) = 4 2/3 hours = 4 hours and 40 minutes.

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The product of the two matrices Q₁Q₂ is orthogonal

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. ... {\displaystyle Q^{\mathrm {T} }Q=QQ^{\mathrm {T} }=I,} where QT is the transpose of Q and I is the identity matrix.

It is said to be an orthogonal matrix if its transpose is equal to its inverse matrix, or when the product of a square matrix and its transpose gives an identity matrix of the same order.

If A is an n*n orthogonal matric, then A*A¹ = A¹*A

Therefore A*A¹ = A¹*A  = 1

This implies that the product Q₁O₂ is orthogonal.

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The gradient of the tangent at x = 2 is equal to 7. This means that the slope of the tangent line to the curve at that point is 7.

To determine the gradient of the tangent when x = 2, it is necessary to use calculus methods.

This means that we need to find the derivative of the function first, and then substitute x = 2 into it to get the gradient of the tangent at that point. In other words, we are finding the slope of the tangent line to the curve at x = 2.

Suppose that the function is given by y = f(x), where f(x) is some algebraic expression that depends on x. To find the derivative of this function, we use the rules of differentiation, which tell us how to find the rate of change of y with respect to x.

For example, suppose that the function is y = x^2 + 3x. Then, the derivative of this function is given by:

y' = 2x + 3

This means that the slope of the tangent line to the curve at any point is equal to the value of the derivative at that point. For instance, if x = 2, then the slope of the tangent is:

y'(2) = 2(2) + 3 = 7

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Answer:180

Step-by-step explanation:      Because it a 80 degree angle

Answer:

Look below

Step-by-step explanation:

There are several methods for solving a system of nonlinear equations, which are a set of equations that cannot be solved using linear methods. Some of these methods include:

Graphical methods: These involve plotting the equations on a graph and finding the points where they intersect, which represent the solutions to the system.

Substitution method: This involves solving one of the equations for one variable in terms of the other, and substituting this expression into the other equation. The resulting equation is then solved for the remaining variable.

Elimination method: This involves adding or subtracting the equations in such a way as to eliminate one of the variables. The resulting equation is then solved for the remaining variable.

Newton's method: This is an iterative method that involves starting with an initial guess for the solution and then using an iterative process to improve the guess until it converges to the true solution.

Broyden's method: This is a variant of Newton's method that involves using a Jacobian matrix to calculate the updates to the solution at each iteration.

To find the composition of two functions f(g(x)) and g(f(x)), you need to apply the outer function to the result of the inner function. For example, if f(x) = x^2 and g(x) = x + 1, then the composition f(g(x)) would be equal to f(x+1) = (x+1)^2, and the composition g(f(x)) would be equal to g(x^2) = x^2 + 1.

To determine if a function is invertible, you need to check if it is one-to-one. A function is one-to-one if every element in the range corresponds to exactly one element in the domain. If a function is one-to-one, it has an inverse function, which is denoted by f^(-1)(x). To find the inverse function, you can solve the original function for the variable in the range and express the variable in the domain in terms of the range. For example, if f(x) = x^2 + 1, then f^(-1)(x) would be the inverse function, which can be found by solving f(x) for x to get x = sqrt(x-1).

The difference quotient is a mathematical concept that is used to approximate the slope of a curve at a particular point. It is defined as the difference between the y-values of two points on the curve, divided by the difference between the x-values of those points. The difference quotient can be written as:

(f(x + h) - f(x))/h

where f is the function, x is the x-value of the point at which the slope is being approximated, and h is a small value that is used to calculate the approximation. To calculate the difference quotient, you can plug the values of f, x, and h into the formula and perform the calculations.

Answer:

-1

Step-by-step explanation:

-1 may be its correct answer