The following is a list of student TGA scores from Unit 3:
73, 83, 72, 71, 65, 70, 76, 73, 83, 73

(a) What is the mean score? Show your work.




(b) What is the median score? Show your work.

Answer:

9 : 7

Step-by-step explanation:

4.5 : 3.5 are decimals so we can multiply them both by 2 to get whole numbers. 4.5 doubled is 9 and 3.5 doubles is 7. Therefore the ratio becomes 9:7

Using simple mathematical operations we can conclude that Adriel will earn $2,10,000 after 29 years working at the job.

The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.

The steps that we can memorize using PEMDAS include parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right), and so on.

So, we know that:

Adriel will earn $65,000 this year.

She will get a raise of $5,000 each year.

Then, her salary after 29 years would be:

= (5000 * 29) + 65,000

= 1,45,000 + 65,000

= $2,10,000

Therefore, using simple mathematical operations we can conclude that Adriel will earn $2,10,000 after 29 years working at the job.

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a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36 is

[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]

Let us begin by writing the polynomial factors using the supplied zeros:

Because -2 is a zero, the polynomial has a component of (x + 2).

Because [tex]\sqrt{ 3i }[/tex] is a zero, its conjugate -[tex]\sqrt{ 3i }[/tex] is likewise a zero, implying that the polynomial has a component of (x - [tex]\sqrt{3i}[/tex])(x + [tex]\sqrt{3i}[/tex]) = (x2 + 3).

Similarly, because [tex]\sqrt{2i}[/tex] is a zero, its conjugate -[tex]\sqrt{ 2i }[/tex] is also a zero, implying that the polynomial has a component of (x - [tex]\sqrt{ 2i }[/tex])(x + [tex]\sqrt{ 2i }[/tex]) = (x2 + 2).

Finally, we know that the y-intercept is 36, which means that the polynomial's constant term is 36 when x=0.

When we add these components together, we get:

[tex]f(x) = (x + 2)(x^2 + 3)(x^2 + 2) + 36[/tex]

Extending on this, we get:

[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]

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Answer:

A

Step-by-step explanation:

Answer:

Answer:

12 ounces

Step-by-step explanation:

Let x = Small Mug

& y = Large Mug

Then we write the given statement in an equation form as below:

2x + 1y = 20 ounces of coffee ---------------> EQUATION 1

3y - 1x = 32 ounces of coffee ----------------> EQUATION 2

Let us solve the above equation for y;

Multiply Equation 2 by '2', we get;

-2x + 6y = 64 ----------------------> Equation 3

Add Equation 1 and Equation 3, we get;

(2x + y) + (-2x + 6y) = 64 + 20

7y = 84

Divide the above equation by 7, we get;

y = 84 / 7

or, y = 12

Hence, One Large mug can hold 12 ounces of coffee.

Step-by-step explanation:

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: (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)

Answer:

2) [tex](3x+2)^{2}[/tex]

3) [tex](2x+5)(2x-5)[/tex]

4) [tex](x^{2} +8)(x^{2} -8)[/tex]

Step-by-step explanation:

A method I was taught was the snowflake method whenever there were numbers in front of [tex]x^{2}[/tex] (ex [tex]4x^{2} and 9x^{2}[/tex]) picture shown below (you can search up some videos if you would like)

The snowflake method is really efficient and helps factor polynomials faster

For 3 and 4, you basically have to find the square root of the number without the [tex]x^{2}[/tex] and make sure (for example 25) one parenthesis had -5 and the other had +5. Number 4 had [tex]x^{4}[/tex], [tex]x^{2}*x^{2}[/tex] is  [tex]x^{4}[/tex] so you would include that in the equation. To double check, use foil.

Using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.

A% is a mathematical figure or ratio that denotes a percentage of 100.

Ratios, fractions, and decimals are some of the numerous ways to represent a dimensionless connection between two numbers.

The symbol "%" is generally written after the integer to denote percentages.

A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics.

So, in the given situation we will use percentages to get what % of recyclable plastic is used as follows:

= 460/100 * 20

= 4.60 * 20

= 92 grams

Therefore, using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.

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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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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!

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]

Answer:

A. m∠X = 50°, AC = 3 cm

Step-by-step explanation:

If ABC is congruent to XYZ then the corresponding angle and sides are congruent so:

∠A = ∠X

∠B = ∠Y

∠C = ∠Z

and

AB = XY

BC = YZ

AC = XZ

Because we know m∠A is 50° and ∠A and ∠X are congruent then m∠X is also 50°

And because we know XZ is equal to 3 cm and XZ and AC are congruent  then AC is also 3 cm

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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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 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:

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 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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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: 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 transformation in words for picture 6 is a rotation of 90° counterclockwise or 90° counterclockwise rotation.

The algebraic rule for the above transformation is (x, y) → (-y, x).

The transformation in words for picture 7 is a reflection across the line x = -3.

The algebraic rule for the above transformation is [tex]Ref_{x=-3} \triangle ABC[/tex].

The transformation in words for picture 8 is a reflection across the x-axis.

The algebraic rule for the above transformation is (x, y) → (x, -y).

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of quadrilateral RSTUVW, the coordinates of W of the image is as follows:

(x, y)                               →            (-y, x)

Ordered pair W  = (-1, 3) → Ordered pair R' = (-(3), -1) = (-3, -1).

In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). Therefore, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

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Answer:0.67

Step-by-step explanation:

Answer:300

Step-by-step explanation:

We can find the answer the simple way.

There are 10 triangles in a regular pentagon

We used pythagorean theorm to find side b, 12

12*5*0.5 is 30

30*10 is 300

Answer:

A

If u plug it into desmos u get a straight line

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 correct answer as a trinomial in descending degree order is -2x^2 + 6x + 4

Here's the step-by-step solution with the figures:

(5x^2 + 10x - 5) - (7x^2 + 4x - 9)

= 5x^2 + 10x - 5 - 7x^2 - 4x + 9 (distribute the negative sign)

= (5x^2 - 7x^2) + (10x - 4x) + ( -5 + 9) (collect like terms)

= -2x^2 + 6x + 4 (simplify and arrange in descending degree order)

Therefore, the simplified expression in descending degree order is -2x^2 + 6x + 4.

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