3. Suppose I have a magnetic six-sided die which makes it not a fair die. I roll the die 500
times and find that I get a “6” 100 times.
a) For this die, what is my best estimate of the probability of rolling a “6”?
b) If I roll this die 30 times, how many “6”s do I expect to get?
c) If I roll a fair die 30 times instead of this “unfair” die, how many “6”s do I expect to get?

Step-by-step explanation:

we know that the two angles with x are equal since they are made with the same lines

so

8x+36=5x+51

solve for x

a. subtract 36 from both sides

8x=5x+15

b. subtract 5x on both sides

3x=15

c. divide by 3

x=3

now to find z

we know a line equals 180

so

(8x+36)+z=180

plug in 3

8(3)+36+z=180

24+36+z=180

60+z=180

z=120

The required value of y(7) is given as y (7)= 4412711.8.

Given that,
Given dy/dt=2y and y(2)=200.

The action of bringing concurrently shorter components into a single system that acts as one is known as integration.

Here,
dy/dt = 2y
dy/y = 2dt
integrate,
logy = 2t + c
[tex]y = e^{2t + c}[/tex]
put t = 2 and y = 200
C = 1.3
Now,
[tex]y= e^[2t + 1.3][/tex]
Substitute t = 7
[tex]y= e^[14 + 1.3]\\y = e^{15.3}[/tex]
y = 4412711.8

Thus, the required value of y(7) is given as y (7)= 4412711.8.

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The number of cups of hot chocolate drink Nathan made is 12 cups.

Convert pint to cup:

1 pi-nt = 2 cups

Total cups of hot chocolate Nathan made = Number of cups of milk Nathan heated + Number of cups of melted chocolate + Number of cream

= 6 + 4 + 2

= 12 cups

Therefore, Nathan made 12 cups of hot chocolate drink.

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The number of prizes that Chris won out of 60 will be 13.

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

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

At the Mayfair Stella, Mary, Cris, and Elli won 60 awards altogether. Mary won 1/3 of them, Stella won 1/5 of them, and Elli got 1/4 of the aggregate.

Then the number of prizes that Chris won is given as,

⇒ 60 - 60 / 3 - 60 / 5 - 60 / 4

⇒ 60 - 20 - 12 - 15

⇒ 60 - 47

⇒ 13

The number of prizes that Chris won out of 60 will be 13.

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Step-by-step explanation:

Note that the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Plug in the slope for m and the given coordinate for x and y:

9 = (7)(2) + b

9 = 14 + b

b = -5

y = 7x - 5

Triangles ΔAEC, ΔECD are congruent.

Three angles and three sides, or the six measuring components, specify the requirements for the congruence of triangles. But if three of these are correctly satisfied, the other three are also satisfied automatically. Axioms for congruency are four such instances.

Triangles are said to be congruent if:

Congruent triangles under the SSS (Side Side Side postulate) condition.

Congruent triangles criterion according to the SAS (Side Angle Side postulate).

Congruent triangles are a requirement of the ASA (Angle Side Angle postulate).

The congruent triangles criterion of the AAS (Angle Angle Side postulate).

Given C is mid point of AD.

and, FE bisects the angle ∠AED.

By SAS Postulate we can say ΔAEC, ΔECD are congruent.

In triangles ΔAEC, ΔECD;

AC=CD (C is mid point)(S);

∠CEA=∠CED (Bisector)(A)

CE=CE (Common side)(S);

So by SAS theorem both are Congruent.

Triangles ΔAEC, ΔECD are congruent.

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Answer:

137 cheap tickets sold, and 65 best seats sold

Step-by-step explanation:

x+y=202

50x+556y=42900

x=202-y

50(202-y)+556y=42900

10100-50y+556y=42900

10100+506y=42900

506y=32890

y=65

x=202-65

x=137

x= Cheap tickets, y= expensive tickets

The function in f(t) form that describes the amount of fuel in the plane at time t will be:

f(t) = 112.25t + 31.425.75

What is the Equation of line?

The equation of the line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

we have given that;

After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.

Now,

Since, After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.

Hence, The equation of line passes through the points (13, 32882) and (31, 34902.5)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (32882 - 34902.5) / ((31 - 13)

m = 2020.5 / 18

m = 112.25

Thus, The equation of the line with slope 112.25 is,

⇒ y - 32885 = 112.25 (x - 13)

⇒ y - 32885 = 112.25x - 1459.25

⇒ y = 112.25x - 1459.25 + 32885

⇒ y = 112.25x + 31.425.75

Therefore, The function in f(t) form that describes the amount of fuel in the plane at time t will be:

f(t) = 112.25t + 31.425.75

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Step-by-step explanation:

Hello. Can you repost the question and just for clarification is this Taylor, Maclaurin Series?

Applying the inscribed angle theorem, the measures of the angles and arcs in the image given are:

Arc QR = 48°

Arc RS = 96°

Arc QPS = 216°

Arc PSR = 186°

Arc SRQ = 144°

The inscribed angle theorem state that the measure of an intercepted arc is equal to twice the measure of the inscribed angle.

Find arc PSR:

Arc PSR = 2(93) [based on the inscribed angle theorem]

Arc PSR = 186°

Find arc QR:

Arc QR = 360 - arc PQ - arc PSR

Substitute

Arc QR = 360 - 126 - 186

Arc QR = 48°

Arc RS = arc PSR - arc PS

Arc RS = 186 - 90

Arc RS = 96°

Arc QPS = 126 + 90

Arc QPS = 216°

Arc PSR = arc PS + arc RS

Arc PSR = 90 + 96

Arc PSR = 186°

Arc SRQ = arc RS + arc QR

Arc SRQ = 96 + 48

Arc SRQ = 144°

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Answer: 48 96

Step-by-step explanation:

Arc QR = 360 - 126 - 186

Arc QR = 48°

Arc RS = arc PSR - arc PS

Arc RS = 186 - 90

Arc RS = 96°

Answer:

The “edge” effect of a tetrahedral container with edge length of 1,000 mm would be 2*r*√3 (r = radius of ball, see diagram below). For a ping pong ball with a diameter of 40 mm, the edge effect would be 2*20*√3 = 69.28 mm. Subtract that from 1,000 mm and you get 930.72 mm of “available space” along the bottom row. Divide 930.72 mm by 40 mm per ball and you get 23.27. So you wouldn’t be able to fit 24 balls along the base, you’d only be able to fit 23 balls. With 23 balls, the total number that a tetrahedron could contain (T) would be T = n(n+1)(n+2)/6 = 2,300 balls, not 2,600.

The quantity of food that would be needed to feed all the cubs for one year is 1825 kg

From the question, we are to determine how much food would be needed to feed all the cubs for one year

From the given information,

"Each cub eats 1.25 kg of food a day"

Assume there are 365 days in a year.

Since there are 4 cubs,

The quantity of food that would feed the cubs for one year = 365 × 4 × 1.25

The quantity of food that would feed the cubs for one year = 1825 kg

Hence, the quantity of food needed is 1825 kg

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Answer:

  20%

Step-by-step explanation:

You want to know the tax rate if the added tax brings the cost of $45 purchase to a total of $54.

The multiplier applied to a purchase cost to add the tax is ...

   (1 +r)

where r is the tax rate.

Here, that means ...

  45(1 +r) = 54

  1 +r = 54/45 = 1.20

  r = 1.20 -1 = 0.20 = 20%

The tax rate Delia paid on the articles she bought was 20%.

Answer:

100<x<500

Step-by-step explanation:

We can create a system of inequalities by using the Triangle Inequality Theorem. This theorem states that the sum of two sides on a triangle is greater than the other sides.
1.) Figure out the first inequality. This would be 300+200>x, or x<500.

2.) Figure out the second inequality. This would be x + 200 > 300, or x>100.
3.) Figure out the third inequality. This would be x + 300 > 200, or x > -100.

4.) Combine these inequalities. By combining these inequalities, we would get 100<x<500.

The correct statements regarding the functions are given as follows:

a)

b)

For item a, the functions are given as follows:

The multiplication by -1/3 means that the vertically compressed by a factor of 3 and reflected over the x-axis, due to the multiplication by the negative number.

For item b, the functions are given as follows:

The transformation is:

x -> x - 2, meaning that the function was shifted right two units.

The intersection with the y-axis is at the value of y when x = 0.

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The critical points for the equation [tex]f(x)=(x^{2} +64)^{\frac{1}{11} }[/tex] is

[tex](x,f(x))[/tex] = [tex](0,2^{\frac{6}{11} })[/tex] = [tex](0,1.46)[/tex]. at x=0

The absolute maximum is at [tex](x,f(x))\\[/tex] = [tex](9,\sqrt[11]{145} )[/tex] =  [tex](9,1.6)[/tex], at x=9.

What is the absolute maximum of an equation?

The highest conceivable values for f are represented by the absolute maximum (sometimes called the global maximum) of a function f(x) (x). Let's imagine the function's critical value, x=c, is present within its domain. If the inequality f(c) [tex]\geq[/tex] f(x), x is a domain, then the function f(x) is said to satisfy an absolute maximum when x=c.

To find the critical points, we find the value of f'(x) and equate to 0.

[tex]\frac{d}{dx} (\sqrt[11]{x^{2}+64} )=0[/tex]

we get x=0.

We see that f'(x) exists for all x between [-8,9].

We also find the endpoints, that is -8 and 9.

Then we calculate f(x) at critical points and endpoints.

We calculate f(x) at 0, -8, and 9.

We get,

for x=0, f(x)= [tex]2^{\frac{6}{11} }[/tex]

for x=-8, f(x)= [tex]2^{\frac{7}{11} }[/tex]

for x=9, f(x)= [tex]\sqrt[11]{145}[/tex]

We see that the value is maximum at x=9, and f(x) becomes [tex]\sqrt[11]{145}[/tex].

Hence we get the absolute maximum is [tex](x,f(x))\\[/tex] = [tex](9,\sqrt[11]{145} )[/tex] = [tex](9,1.6)[/tex]

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Answer:

8

Step-by-step explanation:

The mean of numbers is the sum of the numbers divided by the number of numbers. By this definition, we first have to add up all of these numbers. If we do, we get 48. Now, we figure out the number of numbers, which is 6. Finally, we divide 48 by 6 to get 8.

A total of 396 miles and 2.2 hours will pass between the two trains on the Long.

For additional information on how to handle rate-time-distance or motion problems, scroll down the page.

Moving away from one another are the two trains.

85x + 95x = 396

To solve you combine like terms. The like terms are 85x and 95x

85x + 95x = 180x

Right now, you

180x = 396

Now multiply by 180.

180 divided by 396 equals 2.2.

X= 2.2

That's how you do things, in my opinion.

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Answer:

$23.02

Step-by-step explanation:

You add what she earned to what she had before

$14.27 + $8.75 = $23.02

By finding an evaluating a linear equation we will see that it takes 24 minutes to serve a group of 8 people.

Let's assume that the relation between the number of people and the time it takes to serve them is linear.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

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

Here we have two points:

1 person, 10 minutes, written as (1, 10)

5 people, 18 minutes, written as (5, 18)

Then the slope is:

a = (18 - 10)/(5 - 1)

a = 8/4 = 2

Then the linear equation is:

y = 2x + b

To find the value of b, we can replace the values of one of the points, I will use (1, 10) so we will get:

10 = 2*1 +b

10 = 2 + b

10 - 2 = b

8 = b

The linear equation is:

y = 2x + 8

For 8 customers, the time will be:

y = 2*8 + 8

y = 24

It will take 24 minutes to serve 8 people.

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6x − y < −3 , inequality matches the graph.

Step 1:

Find the equation of the line

we have A(0,3) , B(1,9)

The formula to calculate the slope between two points is equal to

m = (y₂-y₁) / (x₂-x₁)

Substitute the values:

m = (9-3) / (1-0)

m = 6/1

m = 6

The equation of the line into slope intercept form is equal to

y = mx + c

where

m is the slope

b is the y-intercept

In this problem we have

m = 6

b = 3 ---->  the y-intercept is the point B

Substitute the values:

y = 6x + 3

Step -2

Find the equation of the inequality

we know that:

The solution is the shaded area above the dashed line

so, the inequality is equal to

y > 6x + 3

rewrite

-6x + y > 3

6x - y < -3

Step 3

Using a graphing tool

The x-intercept is the point

The y-intercept is the point

The slope of the dashed line is positive, the graph in the attached figure.

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a) His distances after each jump are given as follows:

b) He will jump exactly 16 meters.

In a geometric sequence, each term is obtained by the multiplication of the previous term by the common ratio.

In this problem, the sequence is given as follows:

8, 4, 2, ...

The common ratio is of:

q = 2/4 = 4/8 = 0.5.

Then the next jumps are given as follows:

The sum of the elements of an infinite geometric sequence is given as follows:

[tex]S = \frac{a_1}{1 - q}[/tex]

In which [tex]a_1[/tex] is the first element.

Hence for this problem, the sum is of:

S = 8/(1 - 0.5) = 16 meters.

Which means that he will reach exactly the desired distance.

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At year-end, Factory Overhead is debit of $34000.

What is profit and loss?

A profit and loss (P&L) statement could be a monetary report that has a outline of a company’s revenue, expenses and profit. It provides investors and alternative interested parties an insight into however an organization is working and whether or not it's the flexibility to get a profit.

Main Body:

Estimated total overhead costs = $456,000

Estimated direct labor costs = $2,280,000

Actual overhead costs= $422,000

Actual direct labor costs= $1,940,000

To calculate the factory overhead, we need to first calculate Estimated overhead rate.

Estimated overhead rate = Estimated total overhead costs / Estimated direct labor costs

= $456,000 / $2,280,000

= 0.2

= 20%

Therefore;

Actual Factory overhead = Actual direct labor cost × application rate

= $1,940,000 × 20%

= $388,000

We can get the balance in the overhead account as shown below;

Balance = Actual overhead cost - Actual cost that should be applied

= $422,000 - $388,000

= $34,000 (Debit).

Hence there is debit of $34000.

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The scale model of the sports arena has a height of 12 inches.

Unit rate is the amount of something at a rate of one amount to another amount.

If 2 inches = 30 feet, then a sports stadium's height is 180 feet.

A man can walk 6 kilometers in 2 hours.

A man can cover 3 miles by walking in an hour.

A machine can cut 10 potatoes in five minutes.

A machine can cut two potatoes in a minute.

30 feet equals 2 inches.

Add 30 to both sides.

1 foot equals 2/30 inches.

1 foot equals 2/30 inches today.

Add 180 to both sides.

180 feet equals 180 x 2/30 inches.

6 × 2 inches times 180 feet.

12 inches equal 180 feet

Since the height of the sports stadium is 180 feet, 2 inches would equal 30 feet.

The scale model of the sports arena has a height of 12 inches.

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The two errors that Sterling made in the proof include:

In this case, it should be noted that the step 6. statement must be that LEO is equal to NEO. This is due to the substitution property of equality.

The substitution property of equality states that one value can be substituted for another in an expression or equation and the result will be the same. If the values of x and y are equal, then x and y can be substituted for one another.

Also, the step 7 should be that OLE is identical to ONE. The reason is due to the angle-side-angle postulate. According to the AAS Postulate, if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another, the triangles are congruent.

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Answer:

yes youre right it is point D

Step-by-step explanation:

Answer: exact form is 24/5, decimal form is 4.8 and mixed number form is 4 4/5

Step-by-step explanation:

Answer:

4 4/5 (simplified)

Step-by-step explanation:

Using reciprocals:

4 divided by 5/6 = 4 x 6/5

= 24/5 = 4 4/5

To check: 4 4/5 x 5/6 = 4

You can use the same method for similar problems

A pivot in every row means that the linear system A x=b has at least one solution, for every b.

If every column has a pivot, then the linear system A x=b has at most one solution.

If both hold (which can happen only if A is a square matrix), we get that the system A x=b has unique solution for every b.

A pivot in every row is equivalent to A having a right inverse, and equivalent to the columns of A spanning

[tex]$\mathbb{R}^m$ ( $m$[/tex] is the number of rows).

A pivot in every column is equivalent to A having a left inverse, and equivalent to the columns of A being linearly independent

A pivot means fundamentally changing the direction of a business when you realize the current products or services aren't meeting the needs of the market. The main goal of a pivot is to help a company improve revenue or survive in the market, but the way you pivot your business can make all the difference.

The first nonzero item of each row in a matrix in row-echelon form is known as a pivot, and the columns in which pivots appear are known as pivot columns.

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The probability of event A and event B of the independent events will be 0.05.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the conditional probability is given as,

P(A and B) = P(A) x P(B)

Event A and event B are independent events. The probability of event A is 0.50 and the probability of event B is 0.10.

Then the probability of event A and event B of the independent events is given as,

P(A and B) = P(A) x P(B)

P(A and B) = 0.50 x 0.10

P(A and B) = 0.05

The probability of event A and event B of the independent events will be 0.05.

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Answer:3.71 miles

Step-by-step explanation: