Write an equation that helps D'angela determine the amount of money she must save each month to 500$ in her saving account

The calculated degrees of freedom for the t-test is 18

The degrees of freedom (df) for an independent t-test with two samples can be calculated using the following formula:

df = (n1 + n2) - 2

Where n1 is the sample size of the first group and n2 is the sample size of the second group.

In this case, the first sample has N = 8 and the second sample has N = 12.

Therefore, the degrees of freedom for the t-test will be:

df = (8 + 12) - 2

df = 18

So the t-test for this experiment will have 18 degrees of freedom.

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The number of days it will take 5 workers to create 20 products, found using the work rate for 1 worker is 80 days

Work rate is the rate at which a specified work is completed.

The number of days it will take 10 workers to create 20 products = 40 days

Therefore;

The number of days it will take 1 worker to create 20 products = 40 × 10 days = 400 days

Where 1 worker can create 20 products in 400 days, then;

The work rate for one worker indicates;

The number of days it will take 5 workers to create 20 products can be found by dividing the number of days it will take 1 worker to create the 20 products by 5

5 workers will take = 400 days ÷ 5 = 80 days

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The image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin is (2, 1).

To rotate a point counterclockwise about the origin, we can use the following formulas:

(x', y') = (y,-x)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the rotated point

In this case, we want to rotate the point (-1, 2) by 270° counterclockwise about the origin.

So, we have

(x', y') = (2,1)

Therefore, the image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin is (2, 1).

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Answer: Box plot:    |       o

19 |          

18 |          

17 |          

16 |          

15 |       o  

14 |     o      

13 |          

12 |   o     o

11 | o  o  o  

10 |          

9 | o  o      

8 |   o      

7 |  o        

  |___________

Line plot: 19|

18|

17|

16|

15|     o

14|   o

13|

12| o   o

11|o o o

10|

9|o o

8|  o

7|o

 |___________

   1 2 3 4 5 6 7 8 9 10  (data index)

Step-by-step explanation:

The area of circle is represented by quadratic expression A = π · x², for a radius x = 5 units, the area of circle equals 25π square units.

In this question we need to derive the area formula for a circle as a function of radius and compute the value of the figure for a given radius. According to geometry, the area of a circle (A), in square units, is described by following quadratic equation:

A = π · x²

Where x is the radius of the circle, in units.

If we know that x = 5, then the area of the circle is now computed:

A = π · 5²

A = 25π

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Answer:

38 stduentstudents

Step-by-step explanation:

2(100)=$200, if 100 students attend.

38(2)=$76

Breaking even means getting back the same amount you spent. The exact answer would be 37.5, but you can't have half a student.

Answer:0.67

Step-by-step explanation:

Symbol notation

A negative real number is any real number that is less than zero.

A positive real number is any real number that is greater than zero.

Zero is neither positive nor negative.

(a)  The negative of z is not greater than 6

If the negative of z is not greater than 6, then it is less than or equal to 6.

-z ≤ 6.

(b)  The negative of m is not less than -6

If the negative of z is not less than -6, then it is greater than or equal to -6.

-m ≥ -6.

Answer:

380

Step-by-step explanation:

The formula for the area of a circle is A = pi r^2

radius is half the diameter so you would do 11 (half of diameter) to the second power, which is 121. Now you would do 121 times pi, which would be 380.132711084. When rounded to the nearest whole, it is 380.

SORRY IF THIS DIDN'T MAKE SENSE!

A

Step-by-step explanation:

There is 1 number that is a multiple of both 3 and 4.

9 numbers are a multiple of 4 and not 3.

9 numbers are a multiple of 3 and not 4.

1 number is not a multiple of 3 or 4.

Hope this helps!

Answer:

A

If u plug it into desmos u get a straight line

Answer: The reflection of (-8,2) after a reflection over the line y=x is (2,-8)

Step-by-step explanation: The reflection on a graph refers to the preimage that has been reversed.

So, if we take an example of (x,y), over a reflection on the y-axis, then the answer would be (y,x)

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The total cost of the bracelet after tax cost addition would be = $21.2

The initial cost of the bracelet = 20$

The percentage of tax = 6%

The cost of tax = 6/100 ×20/1 = $1.2

The total cost of the bracelet after the addition of tax would be = 20+1.2 = $21.2

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Answer: 7 [tex]\frac{1}{7}[/tex] lbs

Step-by-step explanation:

    We will divide the 50 lbs bag by 7, to represent te 7 dogs.

50 lbs food / 7 dogs = 7 [tex]\frac{1}{7}[/tex] lbs

The width of the rectangle is 5.

The area of a rectangle is given by the formula:

Area = Length x Width

where Length and Width are the measurements of the two adjacent sides of the rectangle.

For example, if a rectangle has a length of 6 units and a width of 4 units, then its area would be:

Area = Length x Width

Let's start by using the formula for the area of a rectangle:

Area = Length x Width

We are given that the area of the rectangle is 30xF²y and that one of its sides (length) is 6xy. Substituting these values into the formula, we get:

30x²y = (6xy) x Width

Simplifying the right-hand side by multiplying 6xy by Width, we get:

30x²y = 6x²y x Width

Dividing both sides by 6x²y, we get:

Width = 30x²y / 6x²y

Simplifying the right-hand side by canceling out the common factors of 6, x², and y, we get:

Width = 5

Therefore, the width of the rectangle is 5.

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Answer:

B is the correct answer

Step-by-step explanation:

The general form of the equation for a circle centered at the origin (0, 0) is x^2 + y^2 = r^2, where r is the radius of the circle. The radius can be calculated as the distance between the center O (0, 0) and point B (4, 5) on its circumference using the distance formula: r = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((4 - 0)^2 + (5 - 0)^2) = sqrt(16 + 25) = sqrt(41). Therefore, the equation for the given circle centered at O (0, 0) is x^2 + y^2 = 41. The correct answer is B. x^2 + y^2 − 41 = 0.

The phrase represents that the expression is the cost of a product that is priced at $25.75 per unit with an additional fixed cost of $10.

The expression 25.75x + 10 represents a phrase that involves a numerical value that is dependent on a variable x.

We can think of this expression as a linear function, where x is the independent variable and 25.75x is the dependent variable that is multiplied by a coefficient of 25.75.

The constant term of 10 represents a fixed value that is added to the result of the multiplication.

One possible phrase that can be represented by this expression is the cost of a product that is priced at $25.75 per unit with an additional fixed cost of $10.

The variable x in this case would represent the number of units of the product being purchased.

Multiplying the price per unit by the number of units purchased (25.75x) gives us the variable component of the cost, and adding the fixed cost of $10 to this gives us the total cost of the purchase.

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The measure of the angle between the vectors is approximately 41.41 degrees.

When we join two line segments at a single point, an angle is formed, or we can say, an Angle is a combination of two line segments at a common endpoint. This common point is called Vertex of the angle and the two line segments are sides or arms of the angle formed.The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

To find the angle between two vectors, we can use the dot product formula:

cos(theta) = (u · v) / (|u| |v|)

where u · v is the dot product of u and v, and |u| and |v| are the magnitudes of u and v, respectively.

First, let's calculate the dot product of u and v:

u · v = 3 × 4 + 4 × 3 = 24

Next, we need to calculate the magnitudes of u and v:

|u| = √(3² + 4²) = 5

|v| = √(4² + 3²) = 5

Now we can plug these values into the formula for cosine:

cos(theta) = (u · v) / (|u| |v|)

cos(theta) = 24 / (5 * 5)

cos(theta) = 24 / 25

To find the measure of the angle, we need to take the inverse cosine (or arccos) of this value:

theta = arccos(24/25)

theta ≈ 0.7227 radians or 41.41 degrees

So the measure of the angle between the vectors is approximately 41.41 degrees.

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Answer: (3, -2.333) or (3, -7/3)

Step-by-step explanation:

We're given an x value (x=3) when looking at the coordinate, so we're trying to find what y is equal to given the equation. We can plug in x=3 into 5x+3y=8 and isolate for y.

[tex]5(3)+3y=8\\15 + 3y=8\\3y=-7\\y=-\frac{7}{3}[/tex]

Answer:

y= -2 1/3

Step-by-step explanation:

Since you have x, you put x into the equation and work through the problem.

5(3)+3y=8

15+3y=8, then subtract 15 from both sides

3y=(-7), then divide both sides by 3

y=(-7)/3 or (-2 1/3)

The break-even point for the division is as follows:

The break-even point is the unit or dollar value where the total revenue equals the total costs.

The total costs consist of the fixed and variable costs.

Selling price per unit of the income tax app = $8

The variable cost per unit = $3

Contribution margin per unit = $5 ($8 - $3)

Contribution margin ratio = 62.5% ($5 ÷ $8 x 100)

Fixed cost per month = $20,000

Break-even point in units = Fixed Costs/Contribution margin per unit

= 4,000 units ($20,000 ÷ $5)

Break-even point in dollars = Fixed Costs/Contribution margin ratio

= $32,000 ($20,000 ÷ 62.5%)

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Find the break-even point for the division.

Answer:

(7x² / 6x - 10)

Step-by-step explanation:

To divide rational expressions, we flip the second fraction (the divisor) and multiply it with the first fraction (the dividend). Then we simplify the resulting expression, if possible.

So,

(7x² /2x +6) ÷ (3x -5/ x+3)

= (7x² /2x +6) * (x+3/3x -5)

= 7x²(x+3) / 2(x+3)(3x -5)

= 7x² / 6x - 10

Therefore, the quotient of the given rational expressions is (7x² / 6x - 10), which cannot be further reduced.

Answer:

2

7x

3

​

+18x+3−

x

5

​

Short Solution Steps

7x

2

/2x+63x−5/x+3

Express  

2

7x

2

​

x as a single fraction.

2

7x

2

x

​

+6×3x−

x

5

​

+3

Multiply 6 and 3 to get 18.

2

7x

2

x

​

+18x−

x

5

​

+3

To add or subtract expressions, expand them to make their denominators the same. Multiply 18x+3 times  

2

2

​

.

2

7x

2

x

​

+

2

2(18x+3)

​

−

x

5

​

Since  

2

7x

2

x

​

 and  

2

2(18x+3)

​

 have the same denominator, add them by adding their numerators.

2

7x

2

x+2(18x+3)

​

−

x

5

​

Do the multiplications in 7x

2

x+2(18x+3).

2

7x

3

+36x+6

​

−

x

5

​

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and x is 2x. Multiply  

2

7x

3

+36x+6

​

 times  

x

x

​

. Multiply  

x

5

​

 times  

2

2

​

.

2x

(7x

3

+36x+6)x

​

−

2x

5×2

​

Since  

2x

(7x

3

+36x+6)x

​

 and  

2x

5×2

​

 have the same denominator, subtract them by subtracting their numerators.

2x

(7x

3

+36x+6)x−5×2

​

Do the multiplications in (7x

3

+36x+6)x−5×2.

2x

7x

4

+36x

2

+6x−10

​

Step-by-step explanation:

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The scale factor of the dilation is 48.

The scale factor is a mathematical concept that describes the ratio of the lengths, areas, or volumes of two similar geometric figures. Similar figures have the same shape but may have different sizes.

When one figure is a dilation (a type of transformation that changes the size of a figure without changing its shape) of another figure, the scale factor is the ratio of the corresponding side lengths or dimensions of the two figures.

The scale factor of the dilation is the ratio of the length of the image to the length of the original object. In this case, the length of the image is 12 millimeters and the length of the original object is 0.25 millimeters. Therefore, the scale factor is:

scale factor = length of image/length of the original object

scale factor = 12 mm / 0.25 mm

scale factor = 48

So the scale factor of the dilation is 48.

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Answer:

The equation of function g after horizontal compression by a factor of 3 is:

g(x) = 7(3x) + 1 = 21x + 1

To substitute a numerical value for k into the function equation, we need to know the value of k. It is not given in the question, so we cannot provide a numerical answer.

Step-by-step explanation:

When a function is horizontally compressed by a factor of k, we divide the input (x) by k to obtain the new input for the transformed function.

The equation for the horizontally compressed function is:

g(x) = f(x/k)

Substituting f(x) = 7x + 1, we get:

g(x) = 7(x/k) + 1

Simplifying, we get:

g(x) = (7/k)x + 1

Thus, the equation for the transformed function g is obtained by replacing k with the given compression factor.

For example, if the compression factor is 3, then:

g(x) = (7/3)x + 1

And to substitute a numerical value for k, we need to know the value of k. If k = 2, for example, then:

g(x) = (7/2)x + 1

The length of ST is 24.

In geometry, a tangent is a line that touches a curve at a single point, without crossing over the curve at that point. This point of contact is called the point of tangency.

For example, in a circle, a tangent is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at the point of tangency.

Tangents are important in geometry because they allow us to find the slope of a curve at a specific point. The slope of the tangent line at a point on a curve is equal to the derivative of the function representing the curve at that point.

To find the length of ST, we need to find the length of SR and add it to the length of RT.

Using the tangent-tangent theorem, we know that RP is perpendicular to RT at point R. Therefore, angle RPT is a right angle.

We can use the Pythagorean theorem to find the length of RT. Let's call the length of RP "a" and the length of PT "b". Then, we have:

a² = (x+6)² + b² (from right triangle PQR)

a² = (2x-9)² + (b+3)² (from right triangle PSR)

Setting these two equations equal to each other, we have:

(x+6)² + b² = (2x-9)² + (b+3)²

Expanding and simplifying, we get:

x² - 24x + 90 = 0

Solving for x using the quadratic formula, we get:

x = (24 ± √(24² - 4190)) / (2*1) = 15 or 6

Since x cannot be negative, we take x = 15.

Now we can use the Pythagorean theorem to find the length of SR:

a² = (2x-9)² + (b+3)²

a² = (2*15-9)² + (b+3)²

a² = 276 + (b+3)²

We also know that SR = 3, so:

3² = (b+3)²

9 = b² + 6b + 9

b² + 6b - 0 = 0

Solving for b using the quadratic formula, we get:

b = (-6 ± √(6² - 410)) / (2*1) = -3 or 0

Since b cannot be negative, we take b = 0.

Therefore, we have:

a² = (x+6)² + b²

a² = (15+6)² + 0²

a² = 441

So, RT = a = √(441) = 21.

Finally, we have:

ST = SR + RT = 3 + 21 = 24.

Therefore, the length of ST is 24.

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The values of x and y that satisfy the system of equations are x = 8 and y = 4.

To solve for the values of x and y in the system of equations:

x + y = 12

2x + 5y = 36

We can use the method of substitution. Solving the first equation for x, we get:

x = 12 - y

We can substitute this expression for x into the second equation and solve for y:

2(12 - y) + 5y = 36

24 - 2y + 5y = 36

3y = 12

y = 4

Now that we know y is 4, we can substitute this value back into the first equation and solve for x:

x + 4 = 12

x = 8

Therefore, the values of x and y that satisfy the system of equations are x = 8 and y = 4.

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Answer:[tex]18\frac{3}{8}[/tex] yards

Step-by-step explanation:

Formula:

Base x Height ---> [tex]3\frac{1}{2}[/tex] x [tex]5\frac{1}{4}[/tex] = [tex]18\frac{3}{8}[/tex]

The surface area of the square pyramid is 416.23 ft²

The surface area of a square pyramid is given by the formula:

A = a² + 2a√(a²/4 + h²)

Where a is the base length of the square pyramid and h is the height of the square pyramid.

From the figure, we have: a = 10 ft and h = 15 ft

A = a² + 2a√(a²/4 + h²)

A = 10² + 2*10√(10²/4 + 15²)

A = 100 + 20√(100/4 + 225)

A= 100 + 20√250

A = 416.23 ft²

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