BALL
AVENGER
Know When to Hold 'Em
Jack, Brooke and Caroline are chatting after school about a new special edition comic book
that just exploded on the scene. One of the friends owns a signed comic acquired before
the author and artist became famous, while the other two friends are eager to get their
hands on a signed copy. Read the scenarios below and decide if Jack should sell his comic
book to Brooke, make a trade with Caroline or hold on to his signed comic.
Time Required: 10 minutes
LESSON 21: STUDENT ACTIVITY SHEET 1
JACK (SELLER):
Jack collects comic books and last year he went to a local convention to check out some
new artists. He found one he thought was amazing and decided to buy an autographed
comic by him at the show for $5. Fast forward one year and the author is now hugely
popular, with everyone clamoring to buy his comics. Autographed comic books are flying
off local shelves at $25 each and some are even selling for $50 online. Jack's unsure if he
should keep the comic, make a trade or sell it now that it's worth so much money.
Should Jack sell, hold or trade? Why?
BROOKE (BUYER):
Brooke collects rare and original comic books. She loves the new series and needs an
autographed copy of the original comic book to add to her collection. She is willing to pay
whatever it takes to buy it and offers Jack $100 for it.
CAROLINE (TRADER):
Caroline would really like to have a signed copy of the comic book, but there's no way she
can afford to pay $25 or $50 to buy one. She does have three comic books from another
author that she, Jack and Caroline all like a lot. She offers Jack her three comic books for
his autographed comic.

The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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Answer:

595.

Step-by-step explanation:

Take $2000 and subtract $810 from it. You now have the total of the two pieces of equipment without the extra pricing. You should get $1,190. Then divide that number by 2. You will get $595.

1st Piece of Equipment = $595

2nd Piece of Equipment = $1,405

2nd Piece is $810 more expensive and the two pieces combined is $2,000.

Answer:

A= –5x2 + 4x – 7y + 14 = 0

C= 9x2 – 12xy + 4y2 + 4x – y + 5 = 0

D= 12x + 6y – 5y2 + 14 = 0

Step-by-step explanation:

I finished the assignment from Edge2020

The equation which would produce a parabola from the provided options are equation first and forth,

\(-5x^2 + 4x - 7y + 14 = 0\)

\(12x + 6y -5y^2 + 14 = 0\)

To of identify the type of conic section from an equation whether it is parabola, or not, let suppose the equation as,

\(Ax^2+By^2+Cx+Dy+E=0\)

If In this equation,

Either \(A=0\) or \(B=0\), but not both. Then it is the equation of parabola.

The first equation is,

\(-5x^2 + 4x - 7y + 14 = 0\)

There is no square term of y. Thus, this is the equation of parabola.

The second equation is,

\(-x^2 + 6x + y^2 - 8 = 0\)

This is not the equation of parabola, as there is two square terms of variable x and y.

The third equation is,

\(9x^2 - 12xy + 4y^2 + 4x - y + 5 = 0\)

Similar to the second equation, here is also two square terms of different variable. Thus, it is not a equation of parabola.              

The fourth equation is,

\(12x + 6y -5y^2 + 14 = 0\)

This equation is the equation of parabola, as there is only a single square term.

The fifth equation is,

\(20x^2 + 10xy - y^2 + 3x - 6y + 5 = 0\)

This is now the equation of parabola because of two square terms.

Hence, the equation which would produce a parabola from the provided options are equation first and forth,

\(-5x^2 + 4x - 7y + 14 = 0\)

\(12x + 6y -5y^2 + 14 = 0\)

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The possible amounts Susan will spend on candy is $25 and above.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, since Susan will buy more than 6 pounds of candy, the same expression will be illustrated by x.

x > ($4 × 6)

x > $24

In this case, she'll have to spend $25 or more.

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Answer:

3 decimal 75 is the answer

Answer: 151sq

Step-by-step explanation:

You may use the formula for a cylinder's surface area to determine the candle's surface area:

SA = 2πr^2 + 2πrh

Given: 

Radius (r) = 3 inches

Height (h) = 5 inches

Pi (π) = 3.14 (approximately)

Now, enter the values into the formula to get:

SA = 2 * 3.14 * 3^2 + 2 * 3.14 * 3 * 5

SA = 2 * 3.14 * 9 + 2 * 3.14 * 3 * 5

SA = 56.52 + 94.2

SA ≈ 150.72 square inches

The candle has a surface area of around 151 square inches.

We got x = 16.54 by using Pythagorean theorem .

What is the Pythagorean theorem in plain English?

angle of semicircle is always be 90° .

   18² = 7.1² + x²

    324 = 50.41 + x²

     x² = 324 - 50.41

          = 273.59

    x = √ 273.59

    x = 16.54

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Answer:

7)  Domain:  (-∞, ∞)

    Range:  [-1, ∞)

8)  Domain:  (-∞, ∞)

    Range:  (-∞, ∞)

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

Domain & Range

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

From inspection of the graph, the minimum y-value is y = -1.  

The end behavior of the relation is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the range of the relation is restricted:  [-1, ∞)

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

The end behavior of the function is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

2 is the correct answer of this question

The cuboid in question has a surface area of 202 square units.

We must sum together the areas of all six faces to determine a cuboid's surface area.

The dimensions of the given cuboid are:

length (l) = 9 units

width (w) = 5 units

height (h) = 4 units

The area of each face is given by:

Top and bottom faces:\(lw = 9 * 5 = 45\) square units each

Front and back faces: \(lh = 9 *4 = 36\) square units each

Left and right faces: \(wh = 5 * 4 = 20\) square units each

Therefore, the total surface area of the cuboid is:

\(2(lw + lh + wh) = 2(45 + 36 + 20)\\ = 2(101) \\= 202 \ square \ units\)

Hence, the surface area of the given cuboid is 202 square units.

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The percent of the bags of chips weigh less than 176 grams is b 16%

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

Mean = 180

Standard deviation = 4

Bags of chips weigh less than 176 grams

This means that

x = 176

So, the z-score is

z = (176 - 180)/4

Evaluate

z = -1

The percent of the bags of chips weigh less than 176 grams is represented as

P = P(z < -1)

Using a graphing calculator, we have

Percentage = 0.15866

So, we have

Percentage = 16%

Hence , the percentage is 16%

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Answer:

Step-by-step explanation:

The length of the line segment between two points in a plane can be calculated using the distance formula. Given two points (x1, y1) and (x2, y2), the distance between them is given by the following formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the two points are (3, 5) and (7, 3). Plugging these values into the formula, we get:

d = √((7 - 3)^2 + (3 - 5)^2)

d = √((4^2) + (2^2))

d = √(16 + 4)

d = √20

So, the length of the line segment between the two points (3, 5) and (7, 3) is √20.

\(\bf Step-by-step~explanation:\)

Kareem's statement: 4:1 is equal to 12:9. Let's see if this is correct.

\(\bf Step ~1:\)

We have to simplify the ratios. Since 4:1 is already simplified, we do not have to do anything with it. 12:9 could be simplified. To do so, we need to find the greatest common factor (GCF) of both numbers. The GCF of 12 and 9 is 3. Since 3 is the GCF for both numbers, we divide them by 3.

\(\bf 12 /3=4\\9/3=3\)

First number: 4

Second number: 3

Ratio: 4:3

\(\bf Step~2:\)

We compare the ratio 4:3 to 4:1. Since they have different values, they are not equivalent to each other.

\(\large\boxed{\bf Our~final~answer: ~Kareem~is~wrong.}\)

\(\bf {Explanation~in~Step~1}\)

4 : 1 and 12 : 9 are not equivalent

Kareem is wrong

Correct question:

Kareem says that the ratio 4:1 is equivalent to the ratio 12:9 because

4 + 8 = 12 and 1 + 8 = 9. Is Kareem correct? Explain how you know

4 : 1 is in its simplest form already

12 : 9

= 12/9

= 4/3

= 4 : 3

Therefore,

4 : 1 and 12 : 9 are not equivalent

Kareem is wrong based on his assumption that 4 + 8 = 12 and 1 + 8 = 9

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Answer:

\(f(x)^{-1} = \sqrt[4]{\frac{x}{3} }\)

Step-by-step explanation:

given f(x) = 3x^4

so let f(x) be y and to find inverse notation, we have to make x the subject

y = 3x^4

\(\frac{y}{3}\) = x^4

x = \(\sqrt[4]{\frac{y}{3} }\)

so, inverse notation is:

\(f(x)^{-1} = \sqrt[4]{\frac{x}{3} }\)

The perimeter of the sector of the circle is determined to be 28.428 cm.

The area of the sector is given as 40 cm² and the radius of the given circle is mentioned as 7 cm.

In order to calculate the perimeter we need to find the value of the angle of the sector and the arc length as well.

∴ Area of the sector = angle of the sector/ 360° × πr²

⇒ 40 = x/360° × 22/7 × (7)²

⇒x = 40 × 360/ 22 × 7

⇒x = 93.506°

Arc length = angle of the sector/360° × π × 2 × r

Arc length = 93.506°/360° × 22/7 × 2 × 7 = 11.428 cm

∴ Perimeter = arc length + radius +radius

Perimeter = 11.428 + 7 + 7 = 28.428 cm

The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.

In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:

Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)

Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)

Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8

Total sugar consumed = 22/8 + 1/4

Total sugar consumed = (22 + 2)/8

Total sugar consumed = 24/8

Total sugar consumed = 3 units of sugar.

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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y=1/3x+4 is perpendicular to y=-3x-4,

y=2/5x-7 is perpendicular to y=-5/2x+7,

y=-5/2x+8 is perpendicular to y=2/5x+6,

y=-2x+6 is perpendicular to y=1/2x+3 and  

y=7/5x-9 is perpendicular to y=-5/7x-11.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We know that the product of slopes of perpendicular lines is -1.

mM=-1

m is slope of one line and M is the slope of perpendicular line.

M=-1/m

y=1/3x+4

The perpendicular line is y=-3x-4

y=2/5x-7

The perpendicular line is y=-5/2x+7

y=-5/2x+8

The perpendicular line is y=2/5x+6

y=-2x+6

The perpendicular line is y=1/2x+3

y=7/5x-9

The perpendicular line is y=-5/7x-11.

Hence, the lines with corresponding perpendicular lines are

y=1/3x+4---> y=-3x-4

y=2/5x-7-----> y=-5/2x+7

y=-5/2x+8----->y=2/5x+6

y=-2x+6---->y=1/2x+3

y=7/5x-9-----> y=-5/7x-11.

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Answer:

12 pieces

Step-by-step explanation:

4 4/5 = 24/5 / 2/5 = 12

Answer:

f^-1(x) = (x² + 21)/7

Step-by-step explanation:

Since f(x) = y = √(7x – 21), to find the inverse of f(x) we have to write x in terms of y in order to make x the dependent variable and y the independent variable. The steps involved are:

Step 1: square both sides of the equation, y = √(7x – 21). Doing that, we have:

y² = 7x – 21

Step 2: Add 21 to both sides of the resulting equation. Doing that, we have:

y² + 21 = 7x

Step 3: Divide both sides of the equation by 7. Doing that we have:

x = (y² + 21)/7

Step 4: Replace x with f^-1(x) and y with x. Doing that, we have:

f^-1(x) = (x² + 21)/7

Answer:look at explanation

Step-by-step explanation:

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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Answer:

Step-by-step explanation:

5 1/4

Answer:là

5

với số dư

1

.

5

1

4

Step-by-step explanation:

The Distance between Amanda and the rope is approximately 2317.9 ft.

Let's denote the distance between Amanda and the rope by x. Then, the distance between Jeremiah and the rope is 4000 - x (since they are separated by a horizontal distance of 4000 ft). We can use trigonometry to find the value of x.

First, let's consider Amanda's angle of elevation. We can see that the triangle formed by Amanda, the rope, and the helicopter is a right triangle with angle 60°. Therefore, we have:

tan(60°) = x/h

where h is the height of the helicopter above the ground. Solving for h, we get:

h = x/tan(60°)

Next, let's consider Jeremiah's angle of elevation. We can see that the triangle formed by Jeremiah, the rope, and the helicopter is also a right triangle, but with angle 30°. Therefore, we have:

tan(30°) = (4000 - x)/h

Substituting the expression for h that we obtained earlier, we get:

tan(30°) = (4000 - x)/(x/tan(60°))

Simplifying this expression, we get:

tan(30°) = (4000tan(60°) - x)/x

Solving for x, we get:

x = 4000tan(60°)/(tan(60°) + √3)

Using a calculator, we can evaluate this expression to get:

x ≈ 2317.9 ft

Therefore, the distance between Amanda and the rope is approximately 2317.9 ft.

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Answer:

See Below.

Step-by-step explanation:

We want to show that the normal line to the parabola:

\(y^2=8x\)

At the point (2, 4) meets the parabola again at (18, -12).

First, find the tangent line to the parabola at the point (2, 4). We can take the derivative of both sides with respect to x:

\(\displaystyle \frac{d}{dx}\left[ y^2\right]=\frac{d}{dx}\left[8x\right]\)

Implicit differentiation:

\(\displaystyle 2y\frac{dy}{dx}=8\)

Therefore:

\(\displaystyle \frac{dy}{dx}=\frac{8}{2y}=\frac{4}{y}\)

Then the slope of the tangent line to the point (2, 4) is:

\(\displaystyle \frac{dy}{dx}\Big|_{y=4}=\frac{4}{(4)}=1\)

Thus, the slope of the normal line is -1.

And since it passes through the point (2, 4), by the point-slope form:

\(y-(4)=-1(x-2)\)

Simplify:

\(y=-(x-2)+4\)

By letting x = 18:

\(y=-(18-2)+4=-16+4=-12\)

So, the normal line indeed passes through (18, -12).

Answer:

answer is in the picture.

On solving the provided question, we can say that F= The lifting force is 27135 0.003357*250*180*180 = F=27135, surface area

The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.

The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.

F= k*a*v^2

a= 250

v=190

30300=k*250*{190^2}

k= 0.03357

F= 0.003357*250*180*180

F=27135

The lifting force is 27135

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The volume of the clay brick is 2.25 cubic inches and the weight of the clay brick is 0.1575 pounds

The volume of the clay brick, we need to use the dimensions provided. The length of the brick is 1 inch and the width is 2 \(\frac{1}{4}\) inches. We can assume the height of the brick is also 1 inch since it is not specified.

The formula for the volume of a rectangular object is

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

Using the given dimensions, we can calculate the volume of the brick:

V = (1 inch) x (2 \(\frac{1}{4}\) inches) x (1 inch)

V = (1 inch) x (2.25 inches) x (1 inch)

V = 2.25 cubic inches

V = 2.25 inches³

Since the density of the clay is given as 0.07 pounds per cubic inch, we can find the weight of the brick using the formula:

Weight = Volume x Density

Weight = 2.25 inches³ x 0.07 pounds/inches³

Weight = 0.1575 pounds

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