the australian official lottery has scratch-off instant lottery tickets that can be purchased for $1. the probability of winning a prize is 1 in 4. (a) mr. urban is feeling lucky one day and decides to purchase 100 of the scratch-off instant lottery tickets. find the probability that fewer than 20 tickets are winners.

The vertices of the polygon before and after dilation are shown below

preimage         Image

J (-5, 3)            J' (-5/2, 3/2)

K (2, 3)            K' (1, 3/2)

L (2, -3)           L' (1, -3/2)

M (-5, -3)        M' (-5/2, -3/2)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The rule used in  transformation is as follows

(x, y) for a scale factor of r → (rx, ry)

Applying the rule to the vertices  of the polygon we have

preimage                                  Image

J (-5, 3)      (1/2 * -5, 1/2 * 3)      J' (-5/2, 3/2)

K (2, 3)       (1/2 * 2, 1/2 * 3)       K' (1, 3/2)

L (2, -3)      (1/2 * 2, 1/2 * -3)       L' (1, -3/2)

M (-5, -3)    (1/2 * -5, 1/2 * -3)     M' (-5/2, -3/2)

Learn more about dilation at:

https://brainly.com/question/30239118

#SPJ1

Given the polynomial Q(x)=4x^3-3x+1,

P(x) = 8x^3 - 6x + 2

Generally, To find P(x), we can start by substituting

P(x) = 2*(Q(x) + P(x)) into the equation:

P(x) = 2*(Q(x) + P(x))

This simplifies to:

P(x) = 2*(4x^3 - 3x + 1 + P(x))

Expanding and rearranging the equation gives:

P(x) = 8x^3 - 6x + 2 + 2P(x)

Subtracting 2P(x) from both sides of the equation gives:

P(x) - 2P(x) = 8x^3 - 6x + 2

This simplifies to:

-P(x) = 8x^3 - 6x + 2

Adding P(x) to both sides of the equation gives:

0 = 8x^3 - 6x + 2 + P(x)

Therefore, the polynomial P(x) that satisfies the equation

P(x) = 2*(Q(x) + P(x)) is:

P(x) = 8x^3 - 6x + 2

Read more about polynomial

https://brainly.com/question/11536910

#SPJ1

The value of a is 2

We can use the slope-intercept form of a line, y = MX + b, to find the equation of the line.

The slope (m) of the line can be found using the following formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

So, m = (5 - (-5)) / (4 - (-1)) = 10/5 = 2

Now, we can use the point-slope form of a line, y-y1 = m(x-x1)

where (x1,y1) is any point on the line and m is the slope of the line.

In this case, we will use the point (x1, y1) = (–1, –5)

so, y-y1 = m(x-x1) = -5 - 2(-1-x) = -5-2+2x

Now we know that the point (a,1) is also on the line, we can substitute the value of x and y in the equation

so, 1 - (-5) = 2(a - (-1))

1 +5 = 2a+2

6 = 2a+2

4 = 2a

a = 2

Therefore, the value of a is 2.

Learn more about linear equations in two variables and slopes of lines in the coordinate plane here: https://brainly.com/question/7385537

#SPJ4

The possible length of the third side of the triangle is x>52 inches.

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. If the sum of the two sides is equal to the third side, then the two sides will coincide with the third side so a triangle cannot be formed. Hence, the sum of the two sides must be greater than the third side for the triangle to be formed.

Given: Sides of two sides of a triangle as 15 and 37 inches.

let the third side of the triangle be x.

then x>15+37

       x>52 inches.

Hence, The possible length of the third side of the triangle is x>52 inches.

Learn more about triangles here:

https://brainly.com/question/2456591

#SPJ1

Transformations that have been applied to function f(x) to get g(x) are translation, reflection, and dilation.

The process of transforming the existing graph or graphed equation, to create a variation of the following chart is called graph conversion. Transformations such as translation, reflection, and dilation have been applied to function f(x) to produce g(x).

Therefore, the answer is "translation , reflection , and dilation".

To learn more about transformation of graphs, visit the link:

brainly.com/question/12202719

#SPJ4

Answer:

A) Translation

B) Reflection

C) Dilation

Step-by-step explanation:

85.41  cubic inches of the treasure chest is taken up by the coins

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Remember that the volume of a cylinder is given by:

volume = (height)×pi×(radius)²

Where pi = 3.14

Then here the volume of each coin is:

V = (0.0625)(3.14)(1.6)²

= 0.5024 in³

And there are 170 coins, so the total volume is:

170×0.5024

85.408 in³

85.41 in³

Hence, 85.41  cubic inches of the treasure chest is taken up by the coins

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ1

Answer:

c or 85.41

Step-by-step explanation: its simple

Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

What is transformation ?

A transformation is a function that changes the position, size, or shape of an object or a graph. In mathematics, transformations are often used to map a function from one coordinate space to another. There are several types of transformations, including translations, rotations, reflections, and scalings.

Part A: Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

Part B:

Horizontal stretching/shrinking: k is the horizontal scale factor.

Vertical stretching/shrinking: k is the vertical scale factor.

Part C:

Horizontal stretching/shrinking: g(x) = f(kx)

Vertical stretching/shrinking: g(x) = kf(x)

Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

To learn more about transformation visit : brainly.com/question/11709244

#SPJ4

Four lines be chosen from four horizontal lines and four vertical lines in a plane such that a rectangular region is enclosed in 36 ways.

The four horizontal lines can be chosen in 4 choose 2 = 6 ways because we have to pick 2 out of 4, and the four vertical lines can be chosen in 4 choose 2 = 6 ways as well as

4C2 = 4!/ (2!×2!)

4C2 = 6

The total number of ways to pick four lines that enclose a rectangular region is 6×6 = 36, where each combination of two horizontal lines and two vertical lines forms a rectangle.

It's important to notice that the order of choosing the lines doesn't matter, so we use the combination formula (nCr) instead of permutation formula (nPr).

To know more on combination problem

https://brainly.com/question/29110744

#SPJ4

Using the addition operation, the position of the earthworm relative to the surface is 16 inches below the surface.

One of the four basic mathematical operations, including subtraction, division, and multiplication, is the addition operation.

Using the addition operation involves adding two or more addends to determine the sum.  It also involves using the addition operand (+) and the equal symbol (=).

The initial position of the earthworm below the surface = 9 inches

The depth it moved down to find moister soil = 7 inches

The current position = 16 inches (9 + 7) below the surface.

Thus, based on the addition operation, the earthworm is 16 inches below the surface in its endless search for moister soil.

Learn more about mathematical operations at https://brainly.com/question/4721701

#SPJ1

Answer: C

Step-by-step explanation:

Yes, the conditions for constructing a t confidence interval are met. The sample size is 10, which is greater than 30, and the sample is a random sample of 10 deliveries from a large number of deliveries made.

1. Constructing a t confidence interval requires that the sample size is greater than 30, so the first condition that must be met is that the sample size is greater than 30.

2. The second condition that must be met is that the sample is a random sample of the population of interest. In this case, the sample is a random sample of 10 deliveries from a large number of deliveries made.

Since both conditions are met, the conditions for constructing a t confidence interval are met.

Yes, the conditions for constructing a t confidence interval are met. The sample size is 10, which is greater than 30, and the sample is a random sample of 10 deliveries from a large number of deliveries made.

Learn more about sample here

https://brainly.com/question/25894237

#SPJ4

The dimension of the room is width = 6 meters and length = 12 meters.

What is rectangle ?

A rectangle is a four-sided polygon with opposite sides that are parallel and of equal length. It has four right angles. The two parallel sides are called the length and the width. The length is the longer of the two sides, while the width is the shorter of the two sides.

Let's assume the width of the rectangular room is "w" and the length of the rectangular room is "l"

We know that the perimeter of a rectangle is the sum of twice the length and twice the width: P = 2l + 2w

Given that the perimeter is 36 meters, we can substitute that into the equation ,

36 = 2l + 2w

We also know that the length is 2 times the width, so we can substitute that into the equation: I = 2w

Now we have two equations ,

36 = 2(2w) + 2w

36 = 6w

So the width of the room is 6 meters. To find the length, we can use the information that the length is 2 times the width ,

l = 2w = 2*6 = 12 meters

So the dimension of the room is width = 6 meters and length= 12 meters.

To learn more about rectangle visit : brainly.com/question/29123947

#SPJ4

Answer: The answer is C hope this helps :)

Step-by-step explanation:

The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The height of a ball after its second bounce was 80 cm. The ball had a rebound factor of 0.7. Then the height of the ball from where it is dropped is given as,

0.7h = 80

h = 80 / 0.7

h = 14.3 cm

h ≈ 115 cm

The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

The solutions to the equation y/ (y- 4) - 4/ (y + 4) = 32/ y are approximately 30.948, 4.627 and -3.575.

The given equation is y/ (y- 4) - 4/ (y + 4) = 32/ y

Let us simplify the left hand side (LHS) :

Make the denominator same to (y - 4)(y + 4)

y/ (y- 4) - 4/ (y + 4) = (y/ (y- 4))×((y + 4)/(y + 4)) - (4/ (y + 4))×((y - 4)/(y - 4))

y/ (y- 4) - 4/ (y + 4) = ( y(y + 4) - 4(y - 4))/ (y - 4)(y + 4)

y/ (y- 4) - 4/ (y + 4) = (y² + 4y - 4y + 16)/ (y² - 16)

y/ (y- 4) - 4/ (y + 4) = (y² + 16)/ (y² - 16)

Now plugging this simplified version in LHS

(y² + 16)/ (y² - 16) = 32/ y

y(y² + 16) = 32(y² - 16)

y³ - 32y² + 16y + 32×16 = 0

The solutions are approximately 30.948, 4.627 and -3.575.

To know more on cubic polynomial

https://brainly.com/question/1417425

#SPJ4

Answer: C. 3

Step-by-step explanation:

Using the trapezoid midsegment theorem,

[tex]\frac{4x+8x+3}{2}=4x+7.5\\\\\frac{12x+3}{2}=4x+7.5\\\\12x+3=8x+15\\\\4x+3=15\\\\4x=12\\\\x=3[/tex]

Answer:

[tex]k { { { {y6444396}^{46446?} }^342{?} }^66 {6 { { {6636163 \\ }^{2} }^{2} }^{2} }^{2} {?} }^{?} \times \4166441frac{?}{?} [/tex]

Step-by-step explanation:

djdkkwkwnsjididjfjrje

Answer:

[tex]-\frac{1}{64}[/tex]

Step-by-step explanation:

We have:

[tex][( \frac{1}{15} - \frac{2}{5}) * (-\frac{3}{4})^{3}] / (-9)[/tex]

Now, we will multiply the second fraction in the first parentheses by [tex]\frac{3}{3}[/tex] so we can subtract it from the [tex]\frac{1}{15}[/tex]. Then, we will multiply all of the [tex]\frac{3}{4}[/tex]'s. This gives us:

[tex][( \frac{1}{15} - \frac{2}{5} * \frac{3}{3} ) * (-\frac{3}{4} * -\frac{3}{4} * -\frac{3}{4})] / (-9)[/tex]

Which simplifies to:

[tex][( \frac{1}{15} - \frac{6}{15} ) * (-\frac{27}{64})] / (-9)[/tex]

Simplifying:

[tex][(-\frac{5}{15} ) * (-\frac{27}{64})] / (-9)[/tex]

Multiplying in our brackets gives us:

[tex]\frac{9}{64} / (-9)[/tex]

Now, using the rule of KCF (Keep, Change, Flip), we will keep our first fraction, change our division sign to a multiplication sign, and make the last number its reciprocal. This gives us:

[tex]\frac{9}{64} * -\frac{1}{9} = -\frac{1}{64}[/tex]

So, the equation simplified is [tex]-\frac{1}{64}[/tex].

Hope this helped!

Answer:

a = 0

(0,3)

Step-by-step explanation:

To reduce your department by 15%, you would need to let go of 33 workers.

Reducing a department by 15% means that 15% of the current workforce in that department will be let go. To calculate this, you first need to determine the percentage of the total workforce that your department represents. In this case, your department has 220 workers out of 512 workers in the whole company, which represents 43% of the total workforce.

Then, you can calculate the number of workers that need to be let go by multiplying the total number of workers in your department by the percentage that needs to be cut. In this case, that would be

220 x 0.15 = 33 workers

This means that 33 out of the 220 workers in your department would need to be let go in order to achieve a 15% reduction.

To know more on percentage

https://brainly.com/question/29763752

#SPJ4

Answer:

b.

y = 3x + 11, y = 3x + 15

Step-by-step explanation:

Both lines have the same slope, so they are parallel.

Answer:

Step-by-step explanation:

substitute p for 8, because p=8

question 1 :    8+4=12    ----Yes

question 2: 8x8 =64-------Yes

question 3  5x8=35, not 8----No

question 4 2+8=10, not 12----No

Answer:

|1|

Step-by-step explanation:

Because absolute value measures the positive distance from the numeral to 1, the answer could be negative or positive one, which is what the graph shows. So, |1| is the answer.

On solving the provided question, we can say that by linear equation we have 2.5x * cereals = y

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.

2.5 cups of this particular cereal,

the following linear equation, you could calculate how many calories and grams of fiber you were eating.

let x = cereals we eat y = calories

so, equation - 2.5x * cereals = y

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ4

Answer:

Perpendicular Bisector

Answer:

16

Step-by-step explanation:

The side lengths of the original square was 2.  2 x 2 = 4

.25 x 2 = .5

The squares are now 1/2 x 1/2.  One of the 4 original squares will now need 4 new smaller size squares to cover the one square.

4 x 4 = 16

On solving the provided question, we can say that by equation 15+4 = total minutes, they can talk 19 minute

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

x= total minutes -4    the 1st 4 minutes are included in the .30

total cost = .3 + .18 x  

[tex]3 = .3 +.18 x\\2.7 = .18x\\2.7/.18 = x\\15 = x[/tex]

x = total minutes -4

15+4 = total minutes

they can talk 19 minute

To know more about equation visit:

https://brainly.com/question/649785

#SPJ4

On solving the provided question we can say that any triangle's perimeter is the sum of its three sides' lengths = [tex]\x = 360/6 = > x = 60[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Triangle's sides are x, 2x, and 3x Plus 2 ft. Respectively.

Radius is 362 feet.

Any triangle's perimeter is the sum of its three sides' lengths.

[tex]362 = x + 2 x + 3x +2\\6 x +2=362\\6 x= 362-2\\6 x=360\\x = 360/6\\x = 60[/tex]

Triangle's shortest side measures 60 feet.

Middle side = 2 x 2 x 60 ft = second side

Third side equals 3 x + 2 and is measured as 360+2=180+2=182 ft.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ4

Answer: a = 9

Step-by-step explanation:

The given figure formed is a rectangle.

Area of given region (Yellow region) = 24 [tex]unit^{2}[/tex]

Length (l) = 6-2 = 4 units

Breadth (b) = a-3 units

Area = l×b

24 = 4 x (a-3)

6 = a-3

a = 9 units

Assuming an isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object, the three-dimensional object is a: D. cone with a diameter of 12.

In Geometry, there are five (5) major types of triangle based on the length of their sides (side lengths) and angles, and these include the following;

In Mathematics, a right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees (90°).

Generally speaking, the resulting three-dimensional (3-D) geometric object that is formed when a right-angled triangle is continuously rotated about a leg would be a cone. Additionally, the radius of this cone would be equal to 6 because the base of the right-angled triangle is 6.

Therefore, the diameter of this cone can be calculated as follows;

Diameter of cone = 2 × radius of cone

Diameter of cone = 2 × 6

Diameter of cone = 12 units.

Read more on right angle here: brainly.com/question/28453423

#SPJ1

Complete Question:

An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a

answer choices

cylinder with a diameter of 6

cylinder with a diameter of 12

cone with a diameter of 6

cone with a diameter of 12

Answer:

Step-by-step explanation:c