a girl is paid $840 for a basic fortnight of 25 hours . calculate her basic rate.

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The greatest common factor of 4x³y² and 12x²y is: 4x²y.

The GCF is a term used to refer to the largest common factor between any two or more numbers (Greatest Common Factor). The GCF of two natural integers, x and y, is the largest possible number that equally and completely divides both x and y. GCF is typically calculated using the following three techniques: division, multiplication, and prime factorization.

Now in the given question,

4x³y² can be written as = 2×2×x×x×x×y×y

12x²y can be written as = 2×2×3×x×x×y

The common factors among them are:

2×2×x×x×y = 4x²y.

Therefore, the greatest common factor of 4x³y² and 12x²y is: 4x²y.

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In answering the question above, the solution is Hence, after sanding, expressions the thickness of the carbon brushes is 0.61 inches, or 0.61 decimal inches.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

The carbon brushes were originally 5/8 inches thick, however during the sanding process, 0.015 inches were removed, resulting in the following new thickness:

0.625 - 0.015 Equals 0.61 inches for 5/8.

We divide this by 1 inch to get the decimal equivalent:

1 inch / 0.61 inches equals 0.61

Hence, after sanding, the thickness of the carbon brushes is 0.61 inches, or 0.61 decimal inches.

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Answer:Juan has already run a total of 2.3 + 5.6 = 7.9 miles on Monday and Wednesday.

To reach his goal of running 12 miles by Saturday, he still needs to run an additional 12 - 7.9 = 4.1 miles.

Therefore, Juan needs to run 4.1 more miles to meet his goal of running 12 miles by Saturday.

Step-by-step explanation:

Using Algebraic expression,  It will take approximately 3.47 years for an investment of $930,000 to double at an annual interest rate of 20%, compounded continuously.

Algebraic expression can be defined as combination of variables and constants.

The formula for continuous compound interest is given by:

[tex]A = Pe^{(rt)}[/tex]

where A is the amount after time t, P is the initial principal, r is the annual interest rate (as a decimal), and e is the constant 2.71828... (also known as Euler's number).

To find the time it takes for an investment to double at a 20% annual interest rate, we need to solve for t in the equation:

[tex]2P = Pe^{(rt)}[/tex]

Dividing both sides by P, we get:

[tex]2 = e^{(rt)}[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2) = rt ln(e)[/tex]

Since ln(e) = 1, we can simplify to:

ln(2) = rt

Solving for t, we get:

[tex]t = ln(2) / r[/tex]

Substituting P = $930,000 and r = 0.20, we get:

[tex]t = ln(2) / 0.20t = 3.47 years[/tex]

Therefore, it will take approximately 3.47 years for an investment of $930,000 to double at an annual interest rate of 20%, compounded continuously.

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Answer:

Step-by-step explanation:

We can use the given formula to set up an equation and solve for x:

V = 20,000(0.8)x

where V is the value of the car after x years.

We want to find x when the value of the car is $8,200, so we set V equal to 8,200 and solve for x:

8,200 = 20,000(0.8)x

Dividing both sides by 20,000:

0.41 = 0.8x

Taking the natural logarithm of both sides:

ln(0.41) = x ln(0.8)

Dividing both sides by ln(0.8):

x = ln(0.41) / ln(0.8)

Using a calculator:

x ≈ 6.11

Therefore, it will take about 6.11 years for the car to be worth $8,200.

The weight of the lead in the beaker is 0.21 pounds.

A cone is a three dimensional shape with slant sides and a circular surface. Its volume can be defined as the amount of substance that it can contain.

volume of a cone = 1/3 [tex]\pi[/tex]r^2*h

where r is the radius of its circular surface, and h is its height.

In the given question, we have;

r = d/2 = 1/2

  = 0.5 inches

h = 2 inches

Thus,

volume of the cone-shaped beaker = 1/3 [tex]\pi[/tex]r^2*h

                                 = 1/3 *22/7*(0.5)^2*2

                                 = 0.524

The volume of the lead in the cone-shaped beaker is 0.524 cubic inch.

Weight of the lead in the beaker = 0.524*0.41

                                                     = 0.2148

The weight of the lead in the beaker is 0.21 pounds.

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Answer:

No triangles can be constructed

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

In this problem

4+5>9  ------> is not true / is wrong

therefore

No triangles can be constructed with the given side lengths

Hope this helped !

P(sum of 8 | sum > 7) = 2/36 = 1/18

So the probability of rolling a sum of 8 given that the sum is greater than 7 is 1/18 or approximately 0.056.

We must first ascertain the total number of outcomes where the sum is larger than 7 in order to calculate the likelihood that the sum of two fair dice will be 8.

A sum larger than 7 can only result in the following outcomes: (2,6), (3,5), (4,4), (5,3), and (6,2). As there are six alternative outcomes for each die roll, there are 36 permutations in which these five events can occur.

We must now count the number of these 36 outcomes that have a sum of 8. There are just two outcomes that could satisfy this requirement: (2,6) and (3,5). Hence, provided that the sum is more than 7, the following is the likelihood of rolling an 8:

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The equation that represents the relationship is y = 1/3x

The missing graph in the complete question is added as an attachment

From the question, we have the following points that can be used in our computation:

(x, y) = (0, 0) and (3, 1)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx

Using the points, we have

1 = 3m

Divide

m = 1/3

Substitute 1/3 for m in y = mx

y = 1/3x

Hence, the function of the relation is y = 1/3x

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Answer:

( x − a ) 2 + ( y − b ) 2 = r 2

The estimate for the value of 5^(3/2) using the tangent line approximation of the function y = x^(3/2) at x = 4 is 11.

To estimate the value of 5^(3/2), we can use the tangent line approximation of the function y = x^(3/2) at x = 4.

First, we need to find the slope of the tangent line at x = 4. To do this, we take the derivative of the function y = x^(3/2):

y = x^(3/2)

y' = (3/2)x^(1/2)

y'(4) = (3/2)(4)^(1/2) = 3

So the slope of the tangent line at x = 4 is 3.

Next, we need to find the equation of the tangent line at x = 4. To do this, we use the point-slope form of the equation of a line, using the point (4, 8):

y - 8 = 3(x - 4)

y = 3x - 4

Now we can estimate the value of 5^(3/2) by substituting x = 5 into the equation of the tangent line:

y = 3x - 4

y = 3(5) - 4

y = 11

Therefore, an estimate for the value of 5^(3/2) using the tangent line approximation of the function y = x^(3/2) at x = 4 is 11.

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Answer: Without seeing the actual scatter plot, it is difficult to make a definitive conclusion about the relationship between the number of swings and the number of hits. However, there are a few things that the coach can look for in the scatter plot to gain some insights:

Positive correlation: If the scatter plot shows a generally upward trend, with more hits occurring as the number of swings increases, this suggests a positive correlation between the two variables. In other words, players who take more swings tend to have more hits during the tournament.

Negative correlation: On the other hand, if the scatter plot shows a generally downward trend, with fewer hits occurring as the number of swings increases, this suggests a negative correlation between the two variables. In this case, players who take fewer swings tend to have more hits during the tournament.

No correlation: If the scatter plot shows no clear trend or pattern, with hits occurring randomly across different numbers of swings, this suggests no correlation between the two variables. In this case, there is no apparent relationship between the number of swings taken and the number of hits during the tournament.

Overall, the coach can use the scatter plot to gain some insights into the relationship between the number of swings and the number of hits, but more advanced statistical analysis may be necessary to make definitive conclusions.

Step-by-step explanation:

a. The critical points are (0,0), (0,k), (k,0), and (k,k).

b. x³ and y³ are always non-negative, it can see that this critical point is a local minimum.

c. The function has a local minimum for all k > 0

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

(a) To find the critical points of f(x, y) = x³ + y³ - 3xy, we need to find where the partial derivatives with respect to x and y are equal to zero:

∂f/∂x = 3x² - 3ky = 0

∂f/∂y = 3y² - 3kx = 0

Solving these equations simultaneously, we get:

x = y

3x² - 3kx = 0

Substituting the first equation into the second, we get:

3x² - 3kx = 0

3x(x - k) = 0

So x = 0 or x = k. Since x = y, we also have y = 0 or y = k.

Therefore, the critical points are:

(0,0), (0,k), (k,0), and (k,k).

To determine the nature of these critical points, we need to compute the second partial derivatives of f(x):

∂²f/∂y² = 6y

∂²f/∂x∂y = -3k

At the point (0,0), we have:

∂²f/∂x² = 0

∂²f/∂y² = 0

∂²f/∂x∂y = 0

So we cannot use the second derivative test to determine the nature of this point.

At the point (0,k), we have:

∂²f/∂x² = 0

∂²f/∂y² = 6k

∂²f/∂x∂y = -3k

The determinant of the Hessian matrix is:

∂²f/∂x² × ∂²f/∂y² - (∂²f/∂x∂y)² = 0 - (-3k)² = 9k² > 0

Since ∂²f/∂y² is positive, we have a local minimum at the point (0,k).

Similarly, we can show that the points (k,0) and (k,k) are also local minima when k > 0.

(b) When k = 0, the partial derivatives are:

∂f/∂x = 3x² = 0

∂f/∂y = 3y² = 0

So x = y = 0 is the only critical point.

The second partial derivatives are:

∂²f/∂x² = 6x = 0

∂²f/∂y² = 6y = 0

∂²f/∂x∂y = 0

So we cannot use the second derivative test to determine the nature of this point. However, since the function is symmetric about the x and y axes, and x³ and y³ are always non-negative, we can see that this critical point is a local minimum.

(c) To find the values of k for which f(x) has a local minimum or maximum, we need to consider the discriminant of the Hessian matrix at each critical point:

For the point (0,k):

∂²f/∂x² × ∂²f/∂y² - (∂²f/∂x∂y)² = 0 - (-3k)² = 9k² > 0

So function has a local minimum for all k > 0

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Answer: To calculate the tip amount, we need to multiply the bill amount by the percentage tip as a decimal:

Tip amount = 0.20 x $76 = $15.20

To find the total amount to pay, we add the bill amount and the tip amount:

Total amount = $76 + $15.20 = $91.20

Rounding this to the nearest dollar gives:

Total amount = $91

Therefore, you need to pay $91 in total if you leave a 20% tip on a $76 bill.

Step-by-step explanation:

The area of the irregular room is  82.5 ft²

It is important to note that the area of a triangle is represented with the formula

A = 1/2bh

Given that;

From the image shown, we have that;

Area of the figure = sum of the areas of the two triangle

This represented as;

Area = 1/2 × 14(6) + 1/2 × 9(9)

expand the brackets

Area = 1/2 (84) + 1/2(81)

divide the values

Area = 42 + 40. 5

Add the values

Area = 82.5 ft²

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The ball with the greater maximum height is the second ball

From the question, we have the following parameters that can be used in our computation:

f(t) - 4t^2 + 16t

g(t) = -16t^2 + 64t + 192

Differentiate and set them to 0

-8t + 16 = 0

-32t + 64 = 0

Solve for t

t = 2 in both cases

So, we have

f(2) = -4(2)^2 + 16(2) = 16

g(2) = -16(2)^2 + 64(2) + 192 = 256

Hence, the ball with the greater maximum height is the second ball

To do this, we set the function to 0 and calculate t

So, we have

f(t) = -4t^2 + 16t = 0

g(t) = -16t^2 + 64t + 192 = 0

Using a graphing tool, we have

t = 4

t = 6

This means that the first ball landed first

To change the term, we set the constant term in g(t) = -16t^2 + 64t + 192 to a negative number > -192

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Answer:

To solve this problem, we need to use vector addition. We can start by breaking down each force into its x and y components.

For muscle A:

Force = 100 lbs

Angle = 15 degrees

X-component = 100 * cos(15) = 96.93 lbs

Y-component = 100 * sin(15) = 25.04 lbs

For muscle B:

Force = 150 lbs

Angle = 30 degrees

X-component = 150 * cos(30) = 129.90 lbs

Y-component = 150 * sin(30) = 75.00 lbs

For muscle C:

Force = 75 lbs

Angle = 10 degrees

X-component = 75 * cos(10) = 73.83 lbs

Y-component = 75 * sin(10) = 13.03 lbs

Next, we can add up the x and y components separately:

X-component = 96.93 + 129.90 + 73.83 = 300.66 lbs

Y-component = 25.04 + 75.00 + 13.03 = 113.07 lbs

We can use these components to find the magnitude and direction of the resultant force:

Magnitude = sqrt(X^2 + Y^2) = sqrt((300.66)^2 + (113.07)^2) = 321.23 lbs

Direction = tan^-1(Y/X) = tan^-1(113.07/300.66) = 21.65 degrees (measured counterclockwise from the positive x-axis)

Therefore, the resultant force of the muscles is 321.23 lbs at an angle of 21.65 degrees. Here is a diagram to illustrate the vectors:

Step-by-step explanation:

      25.04 lbs    73.83 lbs    129.90 lbs

         /\           /\           /\

        /   \        /   \        /   \

       /      \     /      \     /      \

 100 lbs     15°  75 lbs    10°  150 lbs  30°

      \         /  \         /  \         /

       \      /     \      /     \      /

        \   /        \   /        \   /

      96.93 lbs   13.03 lbs   75.00 lbs

This means that when function f(x) = 4x²- 1 and g(x) = 4x + 8, f(2) - g(2) = 15, and by using the equation as a substitute.

what is function ?

A function in mathematics is a relationship between a set of inputs (also referred to as the domain) and a set of outputs (also referred to as the range), where each input has a unique outcome. Typically, the variable x stands for the input values, the variable y for the output values, and the variable f for the function itself (x). Tables, graphs, equations, and verbal descriptions can all be used to represent functions. In a wide variety of disciplines, including science, engineering, economics, and social studies, they are employed to model relationships between quantities. Functions are frequently used to explain the relationship between two quantities.

given

We must first determine the values of f(2) and g(2) independently using the provided functions in order to evaluate f(2) - g(2):

f(2) = 4(2)² - 1 = 15

g(2) = -4(2) + 8 = 0

These values can now be added to the expression f(2) - g(2) as a substitute:

f(2) - g(2) = 15 - 0 = 15

This means that when f(x) = 4x²- 1 and g(x) = 4x + 8, f(2) - g(2) = 15, and by using the equation as a substitute.

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The scale factor of the dilation for the rectangle ABCD is found as 3.

The ratio of the scale of an original thing to a new object that is a representation of it but of a varying design is known as a scale factor (bigger or smaller).

The rectangle A'B'C'D' is created by dilation of rectangle ABCD.

We shall calculate the ratio of the rectangle's lengths in order to get the scale factor.

A:(1,5) and B:(4,5).

Length of side AB = 4 - 1 = 3

And,

A':(3,15) and B': (12,15).

Length of the side A'B' = 12-3 = 9

Ratio of the sides

AB : A'B' = 3 : 9

AB : A'B' = 1 : 3.

Thus, the scale factor of the dilation for the rectangle ABCD is found as 3.

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If point M is the largest integer less than √ 28, the value of point M is found as 5.

A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Integers include things like -5, 10, 1, 45, 8, 97, and 3,43.

Point M is the largest integer less than √ 28.

√ 28 = 5.29

largest integer which is less than 5.92 is 5.

Thus, if point M is the largest integer less than √ 28, the value of point M is found as 5.

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Answer:

2/5

Step-by-step explanation:

So if you were to half that the bottom stays the same but the top you divide by two which 4 divided by 2 is 2 so you would need 2/5 cup of flour for your new recipe.

Answer is 2

(Nice dog btw)

The sum of 1+1 is equal to 2. When we add 1 to another 1, we are combining or grouping the two quantities, resulting in a total of two. This is a fundamental concept in mathematics, and the process of addition is used to solve a wide range of problems.

The answer to this question is that the parasailer is 600 feet high. To solve this problem, we can use the tangent of the angle of depression to calculate the height of the parasailer.

Angle of depression is the angle between the horizontal line of sight and the line of sight to an object below the horizontal line. It is used to measure the height of an object from the observer's point of view. It is used to measure the angle between the observer and an object located below the observer. It is sometimes referred to as the inverse of the angle of elevation.

The formula for the tangent of an angle is opposite/adjacent. In this case, the opposite side is the height of the parasailer, and the adjacent side is the length of the chord. Therefore, the equation becomes height/400 = tangent (36°).

Solving for the height, we get height = 400 * tangent (36°). Plugging in the value of the tangent (1.732050808) gives us a height of 692.82 feet.

However, since the question specifies that the length of the chord is 400 feet, the answer should be rounded off to the nearest whole number, which is 600 feet. Therefore, the parasailer is 600 feet high.

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Therefore , the solution of the given problem of equation comes out to be  the system of equations has an answer of x = -20 and y = 10.

The same letter is frequently used in mathematical formulas to attempt to enforce variable uniformity among two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Using the outcome y + 6 = 12 as an example, the normalise divides the numbers 12 and b + 6 into 2 parts. The relationship between each symbol component and the amount of lines can be found. A symbol's meaning typically runs counter to itself.

Here,

The set of linear equations can be used to find the values of x and y:

144x + 288y = 1440 \s28x + 84y = 280

By dividing both parts of the second equation by 28, we can begin by making it simpler:

x + 3y = 10

Then, by separating x, we can use this equation to solve for x in terms of y:

x = 10 - 3y

In order to simplify the first problem, we can use this expression in place of x:

=>  144(10 - 3y) + 288y = 1440

=>  1440 - 432y + 288y = 1440

=>  -144y = -1440

=>  y = 10

Given that y = 10, we can solve for x by substituting this number into the equation x + 3y = 10:

=>  x + 3(10) = 10

=>  x + 30 = 10

=> x = -20

As a result, the system of equations has an answer of x = -20 and y = 10.

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Maricopa Success invested $140022.5 in stocks, $64000 in bonds, and $36000 in CDs. The total annual income from the investments was $11877.5.

Income is the money that an individual receives in exchange for work, investments, or other activities. It can be earned from employment, from investments such as stocks and bonds, from business activities, and from government programs. Income can also be earned from other sources such as rents, scholarships, tips, and inheritances. Income is an important source of financial security and can be used to pay for basic needs, to save for future expenses, and to invest in other potential income sources.

To calculate the amount of money Maricopa Success invested in each asset type, we can use the following equation:

Stocks + Bonds + CDs = $190000

To solve for Stocks, we can subtract the amounts invested in Bonds and CDs from the $190000:

Stocks = $190000 - $50000 - $ (11877.5/3.7)
Stocks = $140022.5

To solve for Bonds, we can subtract the amounts invested in Stocks and CDs from the $190000:

Bonds = $190000 - $140022.5 - $ (11877.5/2.75)
Bonds = $64000

To solve for CDs, we can subtract the amounts invested in Stocks and Bonds from the $190000:

CDs = $190000 - $140022.5 - $64000
CDs = $36000

Therefore, Maricopa Success invested $140022.5 in stocks, $64000 in bonds, and $36000 in CDs. The total annual income from the investments was $11877.5.

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Answer

November 5 - Purchase = 1100Unit cost = $40Payable = (1,100*40) 44000 November 7Returns - 25 defective units = 25*40 =1000Terms of sale = 5/10 , n/60If invoices are paid within 10 days , a discount of 5% is given.Therefore payment on November 15 attracts a discount of 5% of the net purchase Journal entries

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

160×5%

[tex]\frac{160 * 5}{100}[/tex] = 8

The equivalent expression of "1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six" is found as. 1.2²/1.4³

Given expression:

" 1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six."

This, becomes.

(1.4³/1.2⁴)⁻⁶

Using rule of exponents for multiplication:

x² × x³ = x² ⁺ ³ = x⁵

Apply in equation.

(1.4³/1.2⁴)⁻⁶ = (1.4³ ⁻ ⁶)/(1.2⁴ ⁻ ⁶)

1.4⁻³/1.2⁻²

Further solving:

x⁻¹ = 1/x

x⁻² = 1/x²

Now,

1.4⁻³/1.2⁻² = (1/1.4³)/(1/1.2²)

1.2²/1.4³

The equivalent expression of "1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six" is found as. 1.2²/1.4³

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Answer:

 8/3 improper fraction

2 2/3  mixed

Step-by-step explanation