You roll a six sided die. What is the
probability of rolling a given number three times in a row?

Each side of quadrilateral A changed by a factor of 1/4

When quadrilateral A was reduced the size of each angle remain unchanged

The dimensions of quadrilateral A are 16, 10, 6, 20

The dimensions of quadrilateral B are  4, 2.5, 1.5, 5

comparing the two dimensions

Let the factor be r

4r = 16

r = 16/4

r = 4

2.5r = 10

r = 10/2.5

r = 4

1.5r = 6

r = 6/1.5

r = 4

5r = 20

r = 20/5

r = 4

Therefore we can conclude that quadrilateral B was increased by 4, similarly, quadrilateral A was reduced by a factor of 1/4

16 * 1/4 = 4

10 * 1/4 = 2.5

6 * 1/4 = 1.5

20 * 1/4 = 5

since the reduction are similar quadrilateral A is similar to quadrilateral B

and the size of each angle were not affected

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yes

Step-by-step explanation:

5

The number that has the same value as 14 tens is 140.

In the given question we have to find the number that has the same value as 14 tens.

As we know that we count the numbers as ones, tens, hundreds and so on.

Place value labels like tens and ones notify us of a number appears digit's value. More than one digit can be used to create a number. As a result, to better understand the value of each digit, we employ place value labels such as ones, tens, hundreds, and thousands.

So in the ones place having 0 and in tens have 14.

So if we write the number that has the same value as 14 tens, then the number is 140.

Hence, the number that has the same value as 14 tens is 140.

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The degree of a polynomial in factored form is the number of zeros or roots of that polynomial.

Given:

Degree of a polynomial:

Degree is the highest or the greatest power of a variable in a polynomial equation.

ex : 2x^2 + 2xy^2

Degree = 3

Degree of a polynomial in factored form:

Degree of a polynomial in factored form is the number of zeros or roots of that polynomial.

Example:

= (x-1) (x-2) (x-3)

number of roots = 3

Degree = 3

= (y-5)(y+3/2)(y-4)(y+1)

number of roots = 4

Degree = 4

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The circumcenter and Incenter of a triangle can be found this way :

Finding the incenter

The junction of a triangle's three angle bisectors is where you may locate its incenter. The incenter has an intriguing attribute as a result of its position: it is equally removed from each of the triangle's three sides. This feature is unique to this point. Like centroids, incenters are always contained within their triangles.

Two triangles are depicted in the above image along with their incenters and incircles (circles drawn inside the triangles so the circles barely touch the sides of each triangle). The incircles' centers are known as the incenters. (If you want to fit in with the in-crowd, don't talk about this "in" stuff too much.)

Finding the circumcenter

The point where the perpendicular bisectors of the triangle's sides meet is the triangle's circumcenter. Due to its position, the circumcenter has an intriguing property: it is equally removed from each of the triangle's three vertices.

In the illustration above, two triangles are shown along with their circumcenters and circumcircles (circles drawn around the triangles so that they pass through the vertices of each triangle). The centers of the circumcircles are known as the circumcenters.

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The rate of change of the table is -500

The average rate of change of a function, graph, table or ordered pair is simply the slope of the relation

The function is represented by the table of values

The interval of the function are the x values

So, we make use of  x values

x = 0 and x = 2

Start by calculating f(0) and f(2)

From the table, we have

f(0) = 30000

f(2) = 29000

So, the average rate over these intervals is calculated as:

Average rate = [f(2) - f(0)]/[2 - 0]

Substitute known values

Average rate = [30000 - 29000]/[0 - 2]

Simplify

Average rate = -500

Hence, the rate of change is -500

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The function of piecewise graph shown in the figure is,

f(x) = {y = 6   for x < -5

        { [tex]y = -\frac{19}{9}x-\frac{5}{9}[/tex]    for -5 ≤x < 5

        { y = 8/5x -14   for x ≥ 5

What is piecewise function?

A piecewise-defined function in mathematics is a function with several sub functions, each of which has a certain interval in the domain for which it is applicable. Piecewise definition is a method of expressing the function, not a property of the function.

From graph we can see that the first function is a line y = 6

Hence, f(x) = {y = 6    for x < -5}

Now to find the equation of second function.

From graph we get two points (-5, 10) and (4, -9).

First to find the slope

[tex]m = \frac{-9-10}{4+5} = \frac{-19}{9}[/tex]

Now to find the equation of line, using slope point form

[tex]y - 10 = \frac{-19}{9} (x-(-5))\\y-10=-\frac{19}{9}x-\frac{95}{9} \\ y=-\frac{19}{9}x-\frac{95}{9} + 10\\y = -\frac{19}{9}x -\frac{5}{9}[/tex]

So, f(x) = { [tex]y= -\frac{19}{9}x-\frac{9}{5}[/tex],    for -5 ≤ x < 5}

Now to find the equation of third line.

From graph we get two points (5, -6) and (10, 2).

First to find the slope of the line

[tex]m = \frac{2-(-6)}{10-5} = \frac{8}{5}[/tex]

Now to find the  equation of line, using slope point form

[tex]y-(-6)=\frac{8}{5}(x-5)\\ y+6=\frac{8}{5}x-8\\ y = \frac{8}{5}x - 14[/tex]

So, f(x) = {[tex]y = \frac{8}{5}x-14[/tex],   for x ≥ 5}.

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Side-Angle-Side (SAS) Rule prove the congruency of the triangle

What is a triangle ?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Triangles can be divided into three sorts based on the lengths of their sides, and they are: Scalene. Isosceles. Equilateral.

The Side-Angle-Side rule is used to demonstrate whether a set of triangles is congruent. According to the SAS rule, two sides and the included angle of one triangle must equal two sides and the included angle of another triangle in order for the two triangles to be considered congruent.

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1) The estimated probability of patrick flipping a head with his coin is; 0.45

2) The margin of error for Patrick's estimated probability is; 0.218

3) The confidence interval for the chance of flipping a head with his coin is; CI = (0.232, 0.668)

No, the 95% confidence interval does not contain 50% as a probability, so it will be illogical to think that Patrick's lucky coin has a probability different from 0.5

We are given;

Number of trials; n = 20

Number of successful outcomes; x = 9

Thus; Proportion; p^ = x/n = 0.45

Now, the formula for the confidence interval of proportions is;

CI = p^ ± z√(p^(1 - p^)/n)

where;

z√(p^(1 - p^)/n) is margin of error

1) Probability of Patrick flipping a head with his lucky coin is;

p^ = x/n = 9/20 = 0.45

2) The margin of error is from the formula;

z√(p^(1 - p^)/n)

z for 95% confidence level is 1.96. Thus'

E = 1.96√(0.45(1 - 0.45)/20)

E = 0.218

3) Confidence interval is;

CI = 0.45 ± 0.218

CI = (0.232, 0.668)

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Answer: See attached.

Step-by-step explanation:

        This slope-intercept form equation shows us that there is a y-intercept of -7. This means that (0, -7) will be a point on the line. Next, we have a slope of positive 3. This means we will count up three units, right one unit, plot a point. Then we repeat.

Answer:

start at the y-intercept, plot some points using the slope, then connect them using a straight line.

Step-by-step explanation:

Generally you'll have an equation in slope-intercept form, which is denoted as: [tex]y=mx+b[/tex]

This is a really useful form for a couple of reasons, and it has two key features. Firstly, the "m" represents the slope of the linear equation.

This makes sense the definition of slope is: [tex]\frac{\text{change in y}}{\text{change in x}}[/tex]

and we can generally define the points:

[tex]\text{at x = 1, y = }m(1)+b\implies m+b\\\text{at x = 2, y = } m(2)+b\implies m + m + b\\\text{at x = 3, y = }m(3) + b\implies m + m + m +b\\\text{and so on...}[/tex]

as the x value increases by 1, the change in y is the "m" value, we have one more "m" than the previous x-value, so the slope is the "m" value, which is the coefficient of the x variable.

The second key feature of slope-intercept form is the y-intercept, which is represented as "b" in this form. This also makes sense because the y-intercept is simply when the x-value is zero, and if you plug in x=0 into the equation, you're only left with the "b" value

Knowing these two things we can analyze the equation given:

[tex]y = 3x-7[/tex]

since it's given in slope-intercept form, we know that slope = 3, and y-intercept = -7. We immediately know one point, which is the y-intercept, since the x-value is going to be zero at the y-intercept, so one point on the graph is: (0, -7)

now from this point we can draw the graph by going to the right one, and up three, by definition of a slope (as x increases by 1, the y-value increases by 3).

We can do something similar on the left side, except instead of right one and up three, we go left one, and down three. You may be asking why down three? Well as you go right one, you go up three, this means if you compare the previous point to the new point, the previous point is down three compared to the new point (which is to the right one), so if you were to go back, you would be going left one and down three.

Now from these points you can do the same thing to extend the line a bit, and since it's a linear equation you can connect them using a straight line.

I also attached a graph from desmos to illustrate what I was saying a bit and also show the graph.

In the triangle given, using cosine law, the unknown side is equal 13.14 unit

The sine rule can be used to find an angle from 3 sides and an angle, or a side from 3 angles and a side. The cosine rule can find a side from 2 sides and the included angle, or an angle from 3 sides.

In this case, we can use only cosine rule to determine the unknown side in the triangle

This is because we have two known sides and one angle

This is given as

a² = b² + c² - 2bcCosA

Substituting the values into the equation

a² = 15² + 17² - 2(15)(17)cos48

a² = 172.74

a = √172.74

a = 13.14 unit

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Answer:the answer should be

Step-by-step explanation: option D or

answer

Answer:

23 Tens

15 hundredth

7 thousandth

Answer: A

Step-by-step explanation:

The quotient is the result of the division between two numbers.

Answer:

n/3

Step-by-step explanation:

When you divide you get a quotient.

n divided by 3 will equal a quotient.

Answer: [tex]11\sqrt{3}-7\sqrt{6}[/tex]

Step-by-step explanation:

[tex]7\sqrt{3}-4\sqrt{6}+\sqrt{48}-\sqrt{54}\\\\=7\sqrt{3}-4\sqrt{6}+\sqrt{16 \cdot 3}-\sqrt{9 \cdot 6}\\\\=7\sqrt{3}-4\sqrt{6}+\sqrt{16}\sqrt{3}-\sqrt{9}\sqrt{6}\\\\=7\sqrt{3}-4\sqrt{6}+4\sqrt{3}-3\sqrt{6}\\\\=11\sqrt{3}-7\sqrt{6}[/tex]

Equivalent rational expressions with Denominator = (5q + 6)(q-3)(9-8)

The portion of a fraction that lies below the fractional bar is known as the denominator. The denominator displays the total number of constituent elements. A horizontal bar between two integers and occasionally the sign "/" are indicators of a fraction.

The "fractional bar" is a name for this bar or symbol. The "numerator" is the number at the top, while the "denominator" is the number that comes after the fractional bar.

The numerator and denominator of any fraction a/b are 'a' and 'b,' respectively. Part of a whole is represented by a fraction. It can be demonstrated mathematically by dividing two numbers.1)

[tex]2/5q^2 -9q -185q^2-9q -18 = 0\\\\5q^2 + 6q -15q -18 =0\\\\5q^2 -15q + 6q-18 = 0\\\\5q(q-3) + 6(q-3) = 0\\\\(q-3)(5q+6) = 0\\\\ q-3=0 \\\\5q+6=0\\\\ q=3 \\\\ q= -6/5\\\\[/tex]

therefore,

[tex]2/(q-3)(5q+6)\\\\2/(q-3)(5q+6) * q-8/q-8\\\\= 2(q-8)/(q-3)(5q+6)(q-8)[/tex]

equivalent rational expressions with denominator

[tex](5q+6)(q-3)(q-8): 110q/5q^2 -34q -48\\\\5q^2-34q +48= 0\\\\5q^2-40q + 6q-48=0\\\\5q(q-8) + 6(q-8)= 0\\\\(q-8)(5q+6) =0\\\\[/tex]

Therefore,

[tex]10q/(q-8)(5q+6)\\\\Therefore, 10q/(q-8)(5q+6) * q-3/q-3\\\\= 10q(q-3)/(q-8)(5q+6)(q-3)\\\\[/tex]

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The graph of exponential function y = 5.2^x

exponential function in the form y = ab^x + c

Exponential function:

An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is also a variable, and a is a constant called the base of the function.

where

a is the initial y - intercept.

b is the constant ratio.

c is the horizontal asymptote.

So, in this problem, we have:

constant ratio = 2

y-intercept at y = 5

horizontal asymptote at y = 0

The graph is in the image uploaded.

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Answer:

Step-by-step explanation:

1) Subtract 5 from both sides.

[tex]m-5=-0.5d[/tex]

2) Divide both sides by -0.5.

[tex]-\frac{m-5}{0.5} =d[/tex]

3) Switch sides.

[tex]d=-\frac{m-5}{0.5}[/tex]

Thank you,

Eddie

The amount of radioactive lead remaining after 4 years, 8 years, and 20 years will be 527.91, 464.48, and 435.69, respectively. And the half-life is 21.66 years.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

An example of 600 g of radioactive lead-210 rots to polonium-210 as per the capability [tex]\rm A(t) = 600 \times e ^{-0.032t}[/tex], where t is time in years.

The amount of radioactive lead remaining after 4 years is given as,

[tex]\rm A(4) = 600 \times e ^{-0.032\times 4}[/tex]

A(4) = 527.91

The amount of radioactive lead remaining after 8 years is given as,

[tex]\rm A(8) = 600 \times e ^{-0.032\times 8}[/tex]

A(8) = 464.48

The amount of radioactive lead remaining after 10 years is given as,

[tex]\rm A(10) = 600 \times e ^{-0.032\times 10}[/tex]

A(10) = 435.69

The half-life is calculated as,

[tex]\rm 300 = 600 \times e ^{-0.032\times t}[/tex]

-0.032t = ln (1/2)

0.032t = -0.693

t = 21.66 years

The amount of radioactive lead remaining after 4 years, 8 years, and 20 years will be 527.91, 464.48, and 435.69, respectively. And the half-life is 21.66 years.

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The two whole numbers that lie between -1 and 3 is 0 and 1.

Given:

Whole numbers:

The whole numbers are defined as positive integers including zero. The whole number does not contain any decimal or fractional part. It means that it represents the entire thing without pieces or Whole numbers is a collection of all the basic counting numbers and 0.

The whole numbers are all the natural number along with zero or 0.

whole number between -1 and 3:

0 , 1, 2

we can take any two.

so whole numbers lie = 0,1,2

Therefore the two whole numbers that lie between -1 and 3 is 0 and 1.

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Full question:

What are the 2 whole numbers that lie between -1 and 3?

The 3 medians of triangle are the line segments that connects a vertex to the midpoint of the opposite side.

A triangle is a three-sided polygon with three vertices and three sides that enclose three angles.It can be an acute-angled, obtuse-angled, or right-angled triangle depending on the angles measured. The sum of a triangle's interior angles is 180 degrees.

Median of a Triangle:-

Thus, the median of triangle line segment that connects a vertex to the midpoint of the opposite side.

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Answer: A and F

Step-by-step explanation:

      This function does not have an amplitude, so there is no vertical stretch/shrink, horizontal stretch/shrink, or reflections. There is, however, a vertical translation of 4 units upwards and a horizontal translation of one unit to the right.

      To see the parent function and this function graphed, see attached.

The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.

What is the hypotenuse leg theorem?

The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Hypotenuse-Leg (HL) for Right Triangles. There is one case where SSA is valid, and that is when the angles are right angles. In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.

Hence, if the hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.

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a. The motion of the bus in each part is given as follows:

b. The graph is classified as follows:

c. The graph is non-linear.

The relation graphed is defined as follows:

Distance x time -> distance as a function of time.

The origin on the graph is the point that the Bus starts and then returns, at the end of the part 5.

Then the graph is also non-linear, as the position changes without linearity, meaning that the acceleration is not uniform.

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Answer:

According to the SAS ( Side Angle Side ) rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the equivalent two sides and angle between the sides of the other triangle.  

Step-by-step explanation:

Two figures are said to be "congruent" if they can be placed exactly over one another.

According to the SAS ( Side Angle Side ) rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the equivalent two sides and angle between the sides of the other triangle.  

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Answer: Equivalent fractions are two or more fractions that are all equal even though they have different numerators and denominators. For example, the fraction 1/2 is equivalent to (or the same as) 25/50 or 500/1000.

*(This is not my work)*

Step-by-step explanation:

The probabilities are given as follows:

a) Hardware product given that it is from company B: (50 - y)/50.

b) Hardware product given that it is from company A: 3/7.

c) The probability in part a is greater than in part B for y < 8.57.

A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes in the context of the experiment.

For item a, the outcomes are given as follows:

Hence the probability is of:

p = (50 - y)/50.

For item b, the outcomes are given as follows:

Hence the probability is of:

30/70 = 3/7.

The inequality for item c is given as follows:

(50 - y)/50 > 3/7

Applying cross multiplication, the solution is obtained as follows:

7(50 - y) > 3(50)

210 - 7y > 150

-7y > -60

7y < 60

y < 60/7

y < 8.57.

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Answer:

Step-by-step explanation: How much is 1 t shirt