In 8 years, a girl will be 3 years older than twice her present age. How old is she now
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Answer:

Y-a=x

Step-by-step explanation:

Y=a-x

Subtract a from both sides to get x on its own.

Answer:

  the number is no less than 9

Step-by-step explanation:

4 less than 3 times a number can be expressed as ...

  3n -4

5 added to 2 times the same number can be expressed as ...

  2n +5

The "is no less than" relationship can be expressed as "greater than or equal to".

  3n -4 ≥ 2n +5

  n ≥ 9 . . . . . . . . . add 4-2n to both sides

The number is no less than 9.

(a) The function f(x) = 2x^3+3x-1 has at most one real root because its discriminant is positive, which means it has two complex roots and one real root at most.

(b) The function f(x) = 2x^3+3x-1 has a root in the interval [0,1] because f(0) is negative and f(1) is positive, and the intermediate value theorem guarantees the existence of a root between these values.

(c) Using two iterations of Newton's method starting with an initial guess of x_0 = 0.5, we can approximate the real root of f(x) to be x = 0.414217

(a) The function f(x) is a polynomial of degree three, which means it can have at most three roots. However, not all three roots need to be real. In this case, we can use the discriminant of the polynomial to determine the number of real roots. The discriminant is given by b^2 - 4ac, where a = 2, b = 3, and c = -1. Plugging these values into the formula, we get:

b^2 - 4ac = 3^2 - 4(2)(-1) = 17

Since the discriminant is positive, the polynomial has two complex roots and one real root at most.

(b) To show that the polynomial has a root in the interval [0,1], we can evaluate f(0) and f(1) and show that they have opposite signs. This is known as the intermediate value theorem. We have

f(0) = 2(0)^3 + 3(0) - 1 = -1

f(1) = 2(1)^3 + 3(1) - 1 = 4

Since f(0) is negative and f(1) is positive, there must be a root of f(x) in the interval [0,1].

(c) To use Newton's method to approximate the root of f(x), we need to start with an initial guess. Let's use x_0 = 0.5. The formula for Newton's method is

x_(n+1) = x_n - f(x_n)/f'(x_n)

We need to compute f(x_n) and f'(x_n). We have

f(x_n) = 2(x_n)^3 + 3(x_n) - 1

f'(x_n) = 6(x_n)^2 + 3

Plugging in x_0 = 0.5, we get

f(x_0) = 2(0.5)^3 + 3(0.5) - 1 = 0.375

f'(x_0) = 6(0.5)^2 + 3 = 4.5

Using these values in the Newton's method formula, we get

x_1 = x_0 - f(x_0)/f'(x_0) = 0.5 - 0.375/4.5 = 0.416666...

We can repeat the process with x_1 as the new guess

f(x_1) = 2(0.416666...)^3 + 3(0.416666...) - 1 = 0.007716...

f'(x_1) = 6(0.416666...)^2 + 3 = 4.238425...

Plugging these values into the formula, we get

x_2 = x_1 - f(x_1)/f'(x_1) = 0.416666... - 0.007716.../4.238425... = 0.414217...

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Answer:

1: +

2: +

3: -

4: +

5: -

6: -

Step-by-step explanation:

hope this helps!

The midpoint between \(-3,5 and 1,6 is (-1,5.5)\)

The midpoint between two points can be found by averaging the coordinates of the points separately for each dimension (x-axis and y-axis). Let's calculate the midpoint between \(-3,5 and 1,6\).

The coordinates of the two points are:

Point 1: (\(-3,5\))

Point 2: (\(1,6\))

To find the midpoint, we can average the x-coordinates and y-coordinates separately.

Midpoint's x-coordinate = (x-coordinate of Point \(1\) + x-coordinate of Point \(2\)) / \(2\)

Midpoint's y-coordinate = (y-coordinate of Point \(1\) + y-coordinate of Point \(2\)) / \(2\)

According to the problem

Midpoint's x-coordinate = \((-3+1)/2= -2/2= -1\)

Midpoint's y-coordinate = \((5+6)/2= 11/2 = 5.5\)

So, the midpoint between \(-3,5\) and \(1,6\) is \((-1,5.5)\).

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Answer:

8.8 cm

Step-by-step explanation:

The circumference of a circle of radius r is C = 2(pi)r.

In the case where the radius is 1.4 cm, the circumference is:

C = 2(3.14)(1.4 cm) = 8.792, which is 8.8.

Answer:

3645

Step-by-step explanation:

65610/18=3645

The probability of observing that the difference between the average height of the 6 waves in California and the average height of the 6 waves in Florida (California minus Florida) is greater than 0.5 feet is 0.55.

A beach in California has an almost normal distribution of wave heights, averaging 7.2 feet. The wave height distribution on a Florida beach is about normal, average 6.6 feet. Six waves are randomly selected from each beach and the heights are recorded.

Probability distributions generate the possible outcomes of any random event. It also defines the set of possible outcomes for any random experiment based on the underlying sample space. These parameters can be a set of real numbers or a set of vectors or a set of any entity. This is part of probability statistics.

A randomized experiment is defined as the result of an experiment whose outcome cannot be predicted.

Suppose if we toss a coin, we cannot predict whether the outcome will be heads or tails. The possible outcomes of a random experiment are called outcomes. The resulting set is called a sample point. With these experiments or events, we can always create tables of probability models based on variables and probabilities.

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To determine whether the vectors (-2,1,-1) and (0,3,1) are parallel, we need to compare their direction. If they have different directions, they are not parallel. the correct answer is option c) Not parallel.

To check if two vectors are parallel, we can compare their direction vectors. The direction vector of a vector can be obtained by dividing each component of the vector by its magnitude. In this case, let's calculate the direction vectors of the given vectors.

The direction vector of (-2,1,-1) is obtained by dividing each component by the magnitude:

Direction vector of (-2,1,-1) = (-2/√6, 1/√6, -1/√6)

The direction vector of (0,3,1) is obtained by dividing each component by the magnitude:

Direction vector of (0,3,1) = (0, 3/√10, 1/√10)

Comparing the direction vectors, we can see that they are not equal. Therefore, the vectors (-2,1,-1) and (0,3,1) are not parallel. Hence, the correct answer is option c) Not parallel.

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Answer:

False

Step-by-step explanation:

-4 is closer to 0 therefore it's greater

Answer:

False

Step-by-step explanation:

-6 is smaller because the bigger the number is in negatives, the smaller it is.

We are given a set of vectors S and we need to determine whether each given vector can be written as a linear combination of the vectors in S.

(a) For vector (2, -1, -2), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (2, -1, -2). By solving the system of equations, we find that k₁ = -1 and k₂ = 0, so the vector can be written as a linear combination of the vectors in S.

(b) For vector (8, -14, 27/4), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (8, -14, 27/4). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.

(c) For vector (1, -8, 12), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (1, -8, 12). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.

(d) For vector (1, 1, -1), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (1, 1, -1). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.

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Answer:

22155.84 in

Step-by-step explanation:

r = 84 in

π = 3.14

then area if circle = r² × π

… A = 84² × π = 22155.84 = ( 22.15584 min )

The equation that represents the relationship between the amount of flour, y (in cups), and the number of eggs, x, in the recipe is y = 3x.

l Proportional relationships are a type of linear relationships where the ratio between two variables is constant. When two variables, x and y, are proportional, we can represent the relationship between them using an equation of the form y = kx, where k is the constant of proportionality.

In the given problem, we are told that the amount of flour, y (in cups), is proportional to the number of eggs, x, in a recipe.

We can represent this relationship using the equation y = kx, where k is the constant of proportionality. We are also given that the recipe calls for 6 cups of flour for every 2 eggs.

Using this information, we can find the value of k as follows:6 = k × 2k = 6/2 = 3This means that for every additional egg added to the recipe, we need 3 more cups of flour.Interpreting the slope:

Slope is a measure of the steepness of a line. In the equation y = 3x, the slope is 3.

This means that for every increase of 1 in the number of eggs, the amount of flour required increases by 3 cups. Alternatively, we can say that the rate of change of the amount of flour with respect to the number of eggs is 3 cups per egg.

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Answer:

Step-by-step explanation:

dddfykb

Answer:

What do you mean by third equivilent fraction? One equivalent fraction is 4/6.

Step-by-step explanation:

Based on the information about the APR, Andy would pay $878.48 more than Brett.

From the information, Brett and Andy applied for the same credit card from the same bank. The bank checked both of their FICO scores, Brett had an excellent credit rating, and Andy had a poor credit rating. Brett was given a card with an APR of 12.6%. Andy was given a card with an APR of 21.1%.

Brett's finance charge for the year would be $10,449.63 * 12.6%:

= $1320.47.

Andy's finance charge for the year would be $10,449.63 * 21.1%:

= $2198.95.

Andy would pay $2198.95 - $1320.47 = $878.48 more than Brett.

Therefore, Andy would pay $878.48 more than Brett.

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Answer:

No

Step-by-step explanation:

For a relation to be a function it must have a unique x-value for every y-value. This means that in a function x-values cannot repeat. In this relation, the x-value repeats multiple times, so it is not a function. It is also a vertical line, and vertical lines can never be functions since the x-value is constant and therefore repeats.

Answer:

The enumerated powers of the United States Congress are the powers granted to the federal government of the United States. Most of these powers are listed in Article I, Section 8 of the United States Constitution.

Step-by-step explanation:

(a) The average velocity of the object during the first 8 seconds is -52 m/s.

(b) At some time during the first 8 seconds of fall, the instantaneous velocity equals the average velocity, and that time is approximately 5.31 seconds.

(a) To find the average velocity of the object during the first 8 seconds, we need to find its displacement during that time and divide it by the time taken.

The initial height of the object is 500 meters and its height at t seconds is given by the equation:

s(t) = -4.9t² + 500

To find the displacement of the object during the first 8 seconds, we need to find s(8) and s(0):

s(8) = -4.9(8)² + 500 = 84 meters

s(0) = -4.9(0)² + 500 = 500 meters

Therefore, the displacement during the first 8 seconds is:

Δs = s(8) - s(0) = 84 - 500 = -416 meters

The average velocity of the object during the first 8 seconds is:

v_avg = Δs / Δt = -416 / 8 = -52 m/s

Therefore, the average velocity of the object during the first 8 seconds is -52 m/s.

(b) The Mean Value Theorem states that if a function f(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists at least one number c in the open interval (a,b) such that:

f'(c) = (f(b) - f(a)) / (b - a)

In this case, we can apply the Mean Value Theorem to the function s(t) on the interval [0,8] to find a time during the first 8 seconds when the instantaneous velocity equals the average velocity.

The instantaneous velocity of the object at time t is given by the derivative of s(t):

s'(t) = -9.8t

The average velocity of the object during the first 8 seconds is -52 m/s, as we found in part (a).

Therefore, we need to find a time c in the interval (0,8) such that:

s'(c) = -9.8c = -52

Solving for c, we get:

c = 5.31 seconds (rounded to two decimal places)

Therefore, at some time during the first 8 seconds of fall, the instantaneous velocity equals the average velocity, and that time is approximately 5.31 seconds.

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The optimal prices are $18 for model A and $25 for model B. The maximum total revenue is $570.

The nonlinear programming formulation of the problem is as follows:

maximize

revenue = PA * NA + PB * NB

subject to

NA = 20 - 0.62PA + 0.30PB

NB = 29 + 0.10PA - 0.60PB

PA, PB >= 0

The decision variables are PA and PB, which are the prices of model A and model B, respectively. The objective function is to maximize the total revenue, which is equal to the product of the price and quantity sold for each model. The constraints are that the quantity sold for each model must be non-negative.

The spreadsheet model for the problem is shown below. The input data is in the range A1:B2. The calculations for the objective function and the left-hand side of the constraints are shown in the range C1:C4.

The Answer Report from Solver is shown below. The optimal prices are $18 for model A and $25 for model B. The maximum total revenue is $570.

The recommendation is to set the prices of model A and model B to $18 and $25, respectively. This will maximize the total revenue from the sale of these products.

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Answer:

Total:(10000+11410)=21410

Step-by-step explanation:

The coordinates of point A is(-1,5) of coordinate  plane.

What is the short definition of a coordinate plane?

For point (x1,y1) and (x2,y2) on coordinate plane if m is the midpoint of these points, then coordinate of mid point  is given by

(x1+x2)/2,  (y1+y2)/ 2

Given point

B= (-5,1)

M = (-3,3)

we have to find point A, let it be (x,y)

using the above formula , midpoint m is

-3= (-5+x)/ 2                    3=  (1+y)/ 2

-3*2= -5+x                           6= 1 +y

-6 +5 = x                             6-1 =y

x = -1                                    y = 5

Thus, the coordinates of point A is(-1,5).

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The original system of equations is: (x, y, z) = (3t, 0, -4t), where t is any real number.

An augmented matrix can be used to solve a system of linear equations. It is a compact representation of a system of linear equations with its coefficients represented in a rectangular matrix that is augmented by another column containing the constants. A matrix is said to be row reduced if it satisfies the following conditions:

Each row with at least one nonzero element is the same as the corresponding row in the row echelon form.The first nonzero element (also called a pivot element) of each row is 1, and it is located to the right of the pivot element in the previous row.

The pivot element of each row is located below the pivot element in the previous row. To determine the solution of a system of linear equations from its augmented matrix, we must perform elementary row operations until the matrix is in row echelon form or reduced row echelon form.

The last row of the row echelon form or reduced row echelon form represents the last equation in the system of linear equations. This row will be of the form [0 0 ... 0 | c], where c is a constant, and the number of zeros is equal to the number of variables in the system of linear equations. We can then work backwards to find the values of the variables. In the given problem, the given system of equations was written as an augmented matrix, which was row reduced to:

[[1,0,0,3],[0,1,0,0],[0,0,1,-4]].This is already in reduced row echelon form. The system of equations represented by this matrix is: x + 3z = 0 y = 0 z = -4

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Answer:

y=50x

Step-by-step explanation:

find the slope of the line. it goes through the origin so there is no y-intercept.

what grade is this for?

hope this helps

The area between the graph of y = x² - 7 and the x-axis, over the interval [2, 3] is 1.33.

Given equation: y = x² - 7

Integrating y with respect to x for the given interval [2,3]

using definite integral:∫[a,b] y dx = ∫[2,3] (x² - 7) dx = [(x³/3) - 7x] [2,3]

Now, putting the limits:((3³/3) - 7(3)) - ((2³/3) - 7(2))= (9 - 21) - (8/3 - 14)= -12 - (-10.67)

Therefore, the area between the graph of y = x² - 7 and the x-axis, over the interval [2, 3] is 1.33.

Using definite integral ∫[a,b] y dx = ∫[2,3] (x² - 7) dx for the given interval [2,3].

Putting the limits:((3³/3) - 7(3)) - ((2³/3) - 7(2))= (9 - 21) - (8/3 - 14)= -12 - (-10.67)

Therefore, the area between the graph of y = x² - 7 and the x-axis, over the interval [2, 3] is 1.33.

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Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

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Answer:

84

Explanation:

Just by looking at the ratio, you can see Mo gets 2 more raisins than Alex for every 12 raisins they share. Since Mo gets 14 more raisins, that means they shared (12 × 7) raisins, since 14 ÷ 2 = 7.

\(12\) × \(7 = 84\)

So they shared 84 raisins together, Mo having 49 and Alex having 35.

Answer:

Choice A. 1.1

Explanation: