If a woman making $29,000 a year receives a cost-of-living increase of 2. 6%, what will her new salary be?

The intersection of plane ACG and plane BCG is, CG.

We have to give that,

Name the intersection of plane ACG and plane BCG.

Since A plane is defined using three points.

And, The intersection between two planes is a line

Now, we are given the planes:

ACG and BCG

By observing the names of the two planes, we can note that the two points C and G are common.

This means that line CG is present in both planes which means that the two planes intersect forming this line.

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The complete question is,

Name the intersection of plane ACG and plane BCG

a. AC

b. BG

c. CG

d. the planes do not intersect

The interval of convergence for the power series representation of f(x) is (-1, 1).

To find the power series representation of the function f(x) = x/36 - x² centered at x = 0, we can express it as a sum of terms involving powers of x.

Step 1: Write the function in a simplified form:

f(x) = (1/36)x - x²

Step 2: Identify the pattern and coefficients:

We observe that the pattern involves alternating powers of x, with the coefficients being (1/36) for the odd powers and -1 for the even powers.

Step 3: Write the power series representation:

f(x) = (1/36)x - x² = (1/36)x - (x²)(1)

Using the power series notation, we can express f(x) as:

f(x) = ∑(n = 0 to ∞) [aₙxⁿ]

= (1/36)x - x²

The power series representation centered at x = 0 is:

f(x) = (1/36)x - x²

Step 4: Determine the interval of convergence:

To find the interval of convergence, we need to examine the convergence of the power series. In this case, the power series has two terms: (1/36)x and -x².

Since both terms involve x raised to a power, the series will converge for values of x that make these terms approach zero.

For the first term, (1/36)x, the series will converge for all x values.

For the second term, -x², the series will converge if |x²| < 1, which means |x| < 1. This gives us the interval of convergence as -1 < x < 1.

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The question is -

Find a power series representation for the function. (Give your power series representation centered at x = 0.)

f(x) = x / 36 - x²

Determine the interval of convergence. (Enter your answer using interval notation.)

Answer:

Explanation:

Given:

Qd = 479 - 3P

where:

Qd = the quantity of residential landscape cleanings per week that people in the local area would be willing to purchase

P = monthly price in dollars

We plug in the given price of 39 dollars per month into Qd = 479 - 3P. So,

Therefore, the quantity demanded at a price of 39 dollars per month is 362.

The equation of the perpendicular line in slope intercept form is

y = (-3/4)x - 9/4.

The slope is defined as the rate of change of the y-axis with respect to

x-axis.

We know equation of a line in slope intercept form is y = mx + b, where slope = m and y-intercept = b.

We also know that perpendicular lines have a slope that is negative reciprocal of each other.

Given line is 8x - 6y = -5.

-6y = - 8x - 5.

-y = (-8/6)x - 5/6.

-y = (-4/3)x - 5/6.

y = (4/3)x + 5/6.

∴ Slope(m) = 4/3.

So, the line which is perpendicular has a slope(m) = -3/4 with points (1,-3).

∴ - 3 = (-3/4)(1) + b.

- 3 = -3/4 + b.

b = 3/4 - 3.

b = -9/4.

∴ The equation of the line is y = (-3/4)x - 9/4.

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Weighing 59 kgs while playing basketball burns 8.9 calories.

The formula for calories brunt is,

= (time) × (MET × 3.5) × (weight/200).

Given, Playing basketball carries a met value of 8 and you weigh 130lbs or roughly 59kg.

∴ In a minute no. of calories brunt will be,

= 1 × 8 × 3.5 × (59/200).

= (28×59/200).

= (1771/200).

= 8.9 calories.

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A quantity that is compounded continuously follows the next equation:

Where:

Now, the interest rate in decimal notation is determined by dividing the percentage by 100:

Now, we are asked to determine the time required for the quantity to double. Therefore, we need to determine "t" when:

Substituting in the formula we get:

Now, we can cancel out the "P":

Now, we solve for "t". First, we take the natural logarithm to both sides:

Now, we use the following property of logarithms:

Applying the property we get:

We have that:

Therefore:

Now, we divide both sides by "r":

Now, we substitute the value of "r":

Solving the operations:

Therefore, the right option is A.

The standard deviation of the age distribution of passenger train cars is 3.33 years.

Let's assume X is the age of the passenger train cars, then we know that the mean (μ) is 19.4 years. Also, we can calculate the z-score for the given percentile as follows:

z = (x - μ) / σ

where x is the value of the age that corresponds to the given percentile, and σ is the standard deviation.

Using the standard normal distribution table, we find that the z-score for the 16th percentile is -0.99. Therefore, we can write:

-0.99 = (24.0 - 19.4) / σ

Solving for σ, we get:

σ = (24.0 - 19.4) / -0.99 = 4.64

Therefore, the standard deviation of the age distribution of passenger train cars is 3.33 years (rounded to two decimal places)

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Answer:

\(x = 152\)

because these angles are infront of each other

Answer:

x = 152

Step-by-step explanation:

x and 152° are vertical angles and are congruent , then

x = 152

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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The rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.

We know that,

The Base is growing at the rate of 1 cm per sec.

Height is growing at the rate of 2 cm per sec.

Area of triangle: 1/2 × b × h

The rate of change will be:

1/2 × b × h

1/2 × 4/1 × 7/2

28/4

7 cm per sec

Therefore, the rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.

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According to the given information, location 2 will cost the least to the company to mine, with a total cost of $202,500.

An expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, division, and exponentiation) that represent some combination of numbers or other mathematical objects. Expressions can be simple, such as a single number or variable, or complex, such as a series of terms connected by operators. Expressions can be evaluated, simplified, and manipulated using algebraic techniques to solve problems and analyze mathematical relationships.

To determine the total cost of mining at each location, we need to consider the cost of land, equipment, and mining and reclamation. We can calculate the total cost for each location as follows:

Location 1: $100,000 (cost of land) + $5,000 (cost of equipment per day) x 30 (days taken to mine) = $250,000

Location 2: $10,000 (cost of land) + $4,500 (cost of equipment per day) x 45 (days taken to mine) = $202,500

Location 3: $35,000 (cost of land) + $3,500 (cost of equipment per day) x 120 (days taken to mine) = $455,000

Location 4: $6,000 (cost of land) + $7,000 (cost of equipment per day) x 65 (days taken to mine) = $451,000

Therefore, According to the given information, location 2 will cost the least to the company to mine, with a total cost of $202,500.

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Answer:

x = 34

Step-by-step explanation:

A straight line is 180 degrees

We can sum angles to form a straight line

x+12 + 100 +x = 180

Combine like terms

2x+112 = 180

2x+112-112 = 180-112

2x = 68

Divide each side by 2

2x/2 = 68/2

x = 34

answer:

=x+12+100+x =180

=x+x+12+100=180

=2x+112=180

=2x=180-112

=2x=68

=2/2x=68/2

=x=34

Answer:

x = \(\sqrt{3}\)/6

Step-by-step explanation:

30-60-90 triangles have legs in the ratio of 1 : \(\sqrt{3}\) : 2

create a proportion:  (6 ÷\(\sqrt{3}\)) = (1÷x)

cross-multiply:  6x = \(\sqrt{3}\)

divide by 6

Answer:

1/4

Step-by-step explanation:

Since there is replacing, each time you need to pick one of the 8 red checker out of 16 checkers.

First draw: p(red) = 8/16 = 1/2

Second draw: p(red) = 8/16 = 1/2

p(red and red) = 1/2 * 1/2 = 1/4

Answer:

No

Step-by-step explanation:

It is never a right triangle unless it says so, it normally has a little square box thing on the angle that is right

The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.

When two rays are linked at their ends, they create an angle in geometry.

The sides or arms of the angle are what are known as these rays. Read on to learn about the various components of an angle.

Hence, The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

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Answer:

it has to be 12*16=10*10+10*2+10*6+2*6=100+20+60+12=192

Step-by-step explanation:

Ahlam needs to give the shopkeeper $15 more to get a balance of $25.

Word problems in Mathematics are mathematical approaches we make use of in our ongoing day to day activities. Algebra leading to word problems usually consist of numbers, variables, and its arithmetic operations.

Ahlam bought goods worth = $90, If she gave the shopkeeper $100, then she will collect $100 - $90 = $10 back.

But if the shopkeeper did not have an exact balance and Ahlam decided to give the shopkeeper $x to get a balance of $25.

Then we can write the expression as:

10 + x = 25

x = 25 - 10

x = 15

Therefore, we can conclude that Ahlam needs to give the shopkeeper $15 more to get a balance of $25.

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Answer: 3750

Step-by-step explanation:

The constant of proportionality in this proportional relationship is 9/7.

From the given table, you can see that as the value of x is increasing, the value of "y" is also increasing.

This shows that x is directly proportional to y.

If x = 2, y = 1 5/9

2 = (14/9)k

18 = 14k

k = 18/14

k = 9/7

Hence the constant of proportionality in this proportional relationship is 9/7.

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Answer:

1. In mathematics and statistics, the arithmetic mean, or simply the mean or the average, is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey.

2. In statistics and probability theory, a median is a value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

3. The mode is the value that appears most often in a set of data values. If X is a discrete random variable, the model is the value x at which the probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.

4. the set of values that a given function can take as its argument varies.

the solution for the initial value problem is: u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t) where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

The given partial differential equation is:

au(x, t) = 4 * (d²u(x, t) / dt²) / (dx²)

a) BCs (Boundary Conditions):

We have u(0, t) = 0 and u(π, t) = 0.

IC (Initial Condition):

We have u(x, 0) = x.

To solve this initial value problem, we need to find a function f(x) that satisfies the given boundary conditions and initial condition.

The solution for f(x) can be found using the method of separation of variables. Assuming u(x, t) = X(x) * T(t), we can rewrite the equation as:

X(x) * T'(t) = 4 * X''(x) * T(t) / a

Dividing both sides by X(x) * T(t) gives:

T'(t) / T(t) = 4 * X''(x) / (a * X(x))

Since the left side only depends on t and the right side only depends on x, both sides must be equal to a constant value, which we'll call -λ².

T'(t) / T(t) = -λ²

X''(x) / X(x) = -λ² * (a / 4)

Solving the first equation gives T(t) = C1 * exp(-λ² * t), where C1 is a constant.

Solving the second equation gives X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) + C3 * cos(sqrt(-λ² * (a / 4)) * x), where C2 and C3 are constants.

Now, applying the boundary conditions:

1) u(0, t) = 0:

Plugging in x = 0 into the solution X(x) gives C3 * cos(0) = 0, which implies C3 = 0.

2) u(π, t) = 0:

Plugging in x = π into the solution X(x) gives C2 * sin(sqrt(-λ² * (a / 4)) * π) = 0. To satisfy this condition, we need the sine term to be zero, which means sqrt(-λ² * (a / 4)) * π = n * π, where n is an integer. Solving for λ, we get λ = ± sqrt(-4n² / a), where n is a non-zero integer.

Now, let's find the expression for u(x, t) using the initial condition:

u(x, 0) = X(x) * T(0) = x

Plugging in t = 0 and X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) into the equation above, we get:

C2 * sin(sqrt(-λ² * (a / 4)) * x) * C1 = x

This implies C2 * C1 = 1, so we can choose C1 = 1 and C2 = 1.

Therefore, the solution for the initial value problem is:

u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t)

where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

Note: Please double-check the provided equation and ensure the values of a and the given boundary conditions are correctly represented in the equation.

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The equation c₁ · a · c · x / b₁ · d · iₙ can have a solution for x if and only if the matrices a, b, and c are compatible and satisfy certain conditions.

Further information about the matrices and their properties is required to determine the specific solution.

To determine if the equation c₁ · a · c · x / b₁ · d · iₙ has a solution, we need to consider the compatibility and properties of the matrices involved.

Let's break down the equation:

c₁: The first column of matrix c.

a: Matrix a.

c: Matrix c.

x: The solution vector.

b₁: The first row of matrix b.

d: Matrix d.

iₙ: The identity matrix of size n.

For the equation to have a solution, the matrices a, b, and c need to be compatible, meaning their dimensions align appropriately for matrix multiplication. Specifically, the number of columns in matrix a should match the number of rows in matrix c.

Additionally, certain conditions or properties of the matrices may be required to ensure a solution exists. Without additional information about the specific matrices a, b, c, and d, it is not possible to determine the solution for x.

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On solving the provided question we can say that the equation h(x) = 3x / x^2 +5x +7 => \(h(x^2) =\) \(3x^2 / x^4 + 5x^2 + 7\)

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

given h(x) = 3x / x^2 +5x +7

\(h(x^2) =\) \(3x^2 / x^4 + 5x^2 + 7\)

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Answer:

7×6×5×4×3×2×1+5 can be written as  5*[7*6*5*4*3*2*+1] or 5*(1009). So, other than the number and 1, it has 5 and 1009 as its factors too. So it is  a composite number.

Step-by-step explanation:

A composite number is a positive integer that has a factor other than 1 and itself.