A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.

Answers

Answer 1

We are are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.242895 in first simulation and between 0.1948 and 0.2732 in second simulation.

A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.

A 95% confidence interval gives us a range of values that we are 95% confident contains the true proportion of wins that the new game strategy will produce in the long run. To construct the confidence interval for each simulation, we can use the following formula:

CI = p ± 1.96 * sqrt(p * (1 - p) / n)

where p is the sample proportion of wins, n is the number of trials, and 1.96 is the z-score corresponding to a 95% confidence level.

For the first simulation, p = 212 / 1000 = 0.212 and n = 1000, so the confidence interval is:

CI = 0.212 ± 1.96 * sqrt(0.212 * (1 - 0.212) / 1000)

CI = (0.1812, 0.2428)

This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.2428.

For the second simulation, p = 235 / 1000 = 0.235 and n = 1000, so the confidence interval is:

CI = 0.235 ± 1.96 * sqrt(0.235 * (1 - 0.235) / 1000)

CI = (0.1948, 0.2732)

This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1948 and 0.2732.

In general, larger sample sizes lead to narrower confidence intervals. In this case, both confidence intervals overlap, indicating that the two simulations are consistent with each other. This gives us additional confidence in the estimated proportion of wins using the new strategy.

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Answer 2

Answer:

the confidence interval for the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.

Step-by-step explanation:

got it right on the test :)


Related Questions

Do the equations 1/5 + 2= 6 and 1/5(x +2)= 6 represent the same situation? Explain

Answers

No, the equations 1/5 + 2 = 6 and 1/5(x + 2) = 6 do not represent the same situation.

About the equationThe first equation, 1/5 + 2 = 6, is a simple arithmetic equation that can be solved to find the value of the variable. The second equation, 1/5(x + 2) = 6, is an algebraic equation that can be solved to find the value of the variable x.

To solve the first equation, we can subtract 2 from both sides to get 1/5 = 4, and then multiply both sides by 5 to get 1 = 20.

This equation is not true, so there is no solution. To solve the second equation, we can multiply both sides by 5 to get x + 2 = 30, and then subtract 2 from both sides to get x = 28.

This is the solution to the equation. So, while both equations contain the same numbers and operations, they represent different situations and have different solutions.

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Below are the dimensions for a US postal office box that you are wrapping as a gift.

Explain how to find the surface area of this box. You may explain using words or numerically.

also there is a 12in 2in and 8in on it

Answers

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Surface area

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Area = length x breadth

To find the surface area of the postal box, we first find the area of each sides of the box and add them together.

Top and bottom area = L x B = 12 x 8 = 96inches² x 2 = 192inches²

Front and back areas = L x B = 12 x 2 = 24inches² x 2 = 48inches²

Area of the sides = L x B = 8 x 2 = 16inches² x 2 = 32inches²

Total surface area will be 192 + 48 + 32 = 272inches²

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What is the test of nonverbal intelligence?

Answers

A test of nonverbal intelligence is a type of cognitive assessment that measures an individual's ability to solve problems and think abstractly without the use of language.

Unlike traditional intelligence tests that rely heavily on verbal abilities such as vocabulary, reading, and verbal reasoning, nonverbal intelligence tests use visual-spatial and abstract reasoning tasks that do not require the use of language.

Nonverbal intelligence tests can be particularly useful for individuals who have language or communication difficulties, such as those with speech and language disorders, or those who are non-native speakers of the language in which the test is administered. They can also be used to assess individuals who have difficulty with traditional tests due to visual or hearing impairments.

Examples of nonverbal intelligence tests include Raven's Progressive Matrices, the Naglieri Nonverbal Ability Test (NNAT), and the Universal Nonverbal Intelligence Test (UNIT). These tests typically involve completing visual pattern recognition and completion tasks, spatial reasoning tasks, and other nonverbal problem-solving tasks.

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Hal sold a box of 30 books at a yard sale for a total of $62.16. He sold the paperback books for $1.78 each and sold the hardcover books for $2.51 each.
Which system of equations can be used to determine the number of $1.78 paperback books, x, and the number of $2.51 hardcover books, y, that were
sold at the yard sale?

Answers

Answer:

Step-by-step explanation:

Let x be the number of $1.78 paperback books and y be the number of $2.51 hardcover books that were sold. The total number of books is x + y = 30 and the total amount of money earned is $62.16. The cost of the paperback books is x * $1.78 and the cost of the hardcover books is y * $2.51.

So, we have the following system of equations:

x + y = 30 (the total number of books is 30)

x * $1.78 + y * $2.51 = $62.16 (the total amount of money earned is $62.16)

This system of equations can be used to determine the number of $1.78 paperback books and the number of $2.51 hardcover books that were sold at the yard sale.

Is -9(k-5+2k-8) and -27k+117 equivalent expressions

Answers

-9(k-5+2k-8) and -27k+117 are equivalent expressions since the solution of -9(k-5+2k-8) = -27k+117.

What are equivalent expressions?

Equivalent expressions are algebraic expressions that produce the same answer when being simplified. They are said to be a similar expression for whatsoever process used to solve the expression, either by substitution of values or applying mathematical property, they tend to produce equivalent expressions at the end. The equality sign is used between two algebraic expressions that are said to be equivalent.

Given that:

= -9(k-5+2k-8)  

Open brackets

= -9k + 45 - 18k + 72

= -27k + 117

Therefore, we can say  -9(k-5+2k-8) and -27k+117 equivalent expressions are equivalent expressions.

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What is the median of the data set? 9, 3, 10, 12, 4, 5, 12, 2 enter your answer in the box.

Answers

The median of the given standard data set 9, 3, 10, 12, 4, 5, 12, 2 will be calculated approximately to 7. So , the median of the dataset is 7.

The median is a measure of central tendency that gives us an idea of where the "middle" of a data set lies. In other words, it gives us a value that separates the data set into two equal parts, with half of the values being above the median and the other half being below the median.

To find the median of a data set, the first step is to arrange the values in ascending or descending order. This makes it easier to identify the middle value(s) in the data set.

If the data set has an odd number of values, then there is a single middle value and that value is the median. For example, if we have the data set: 1, 2, 3, 4, 5, the median would be 3 because it is the middle value in the ordered set.

If the data set has an even number of values, then there are two middle values and the median is the average of those two values. For example, if we have the data set: 1, 2, 3, 4, 5, 6, the median would be the average of 3 and 4, which is (3 + 4) / 2 = 3.5.

So, in the case of the data set: 9, 3, 10, 12, 4, 5, 12, 2, we arrange the values in ascending order: 2, 3, 4, 5, 9, 10, 12, 12. Since there are 8 values, which is an even number, there are two middle values: 5 and 9. The median is the average of these two values, which is (5 + 9) / 2 = 7.

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You deposit $1000 in a savings account that earns 5% annual interest compounded yearly.
(a) Write an exponential equation to determine when the balance of the account will be $1500.
(b) Solve the equation.

Answers

The balance of the account will be 1500 in a period of 8.31 years.

What is Compound Interest?

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

(a) The final amount in a compound interest is,

A = P(1 + [tex]\frac{r}{n}[/tex] )^ (nt), where,

A : Final amount

P : Principal amount

r : Rate of interest

t : Time in years

n : number of times compounded in a year

Given A = $1500, P = $1000, r = 0.05, n = 1

The equation is,

1500 = 1000 (1 + 0.05)^t

(b) 1500 = 1000 (1 + 0.05)^t

1500 / 1000 = (1.05)^t

1.5 = (1.05)^t

Taking logarithm on both sides,

㏒ (1.5) = t ㏒ (1.05)         [since ㏒ (a)ᵇ = b ㏒ (a)]

t = ㏒ (1.5) / ㏒ (1.05)

t = 8.31 years

Hence the amount will be $1500 in 8.31 years.

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An employee who receives a weekly salary of $300 and a 4% commission is paid according to the formula y = 0.04s + 300, where s represents the total weekly sales. Make a table to show an employee's weekly salary for weekly sales of $3,000, $2,340, and $4,675.

Answers

The weekly salary for weekly sales of $3,000, $2,340, and $4,675 of the employee is $420, $393.6 and $487 respectively.

Table is attached

What is commission?

A commission is the extra pay to the person in the form of incentives.

Given that, an employee who receives a weekly salary of $300 and a 4% commission is paid according to the equation y = 0.04s + 300, where s represents the total weekly sales.

We are asked to find and make a table for employee's weekly salary for weekly sales of $3,000, $2,340, and $4,675.

We are given values of s,

so, weekly salary for weekly sales of $3,000

y = 0.04(3000)+300

= $420

Weekly salary for weekly sales of $2,340

y = 0.04(2340)+300

= $393.6

Weekly salary for weekly sales of $4,675

y = 0.04(4675)+300

= $487

Hence, the weekly salary for weekly sales of $3,000, $2,340, and $4,675 of the employee is $420, $393.6 and $487 respectively.

Table is attached

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The base of s is the triangular region with vertices (0, 0), (8, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles.

Answers

The volume of the triangular solid is 128/3 cubic units.

The cross-sections of the triangular solid along the y-axis are equilateral triangles with side length equal to the width of the triangular base at that y-coordinate. The width of the triangular base at y = h is equal to 8 - 4h/4. So, the side length of the equilateral triangle at y = h is 8 - 4h/4.

Let's call the height of the equilateral triangle at y = h as "x". Then, using the Pythagorean theorem, we can find the relationship between x and the side length:

x^2 = (8 - 4h/4)^2 - (x/2)^2

Expanding and simplifying the right-hand side:

x^2 = 64 - 16h + h^2/16 - x^2/4

Multiplying both sides by 4:

4x^2 = 256 - 64h + h^2 - x^2

Solving for x^2:

3x^2 = 256 - 64h + h^2

Taking the square root of both sides:

x = √(256 - 64h + h^2)/√3

So, the height of the equilateral triangle at y = h is equal to x = √(256 - 64h + h^2)/√3.

The volume of the triangular solid can be found by integrating the cross-sectional area over the height of the triangular base:

V = (1/3) ∫[0, 4] x^2(y) dy

= (1/3) ∫[0, 4] (√(256 - 64h + h^2)/√3)^2 dh

= (1/3) ∫[0, 4] (256 - 64h + h^2)/3 dh

Evaluating the definite integral:

V = (1/3) * [(256h/3 - 32h^2/2 + h^3/3) |_0^4]

= (1/3) * [(256/3 * 4 - 32/2 * 4^2 + 4^3/3) - (256/3 * 0 - 32/2 * 0^2 + 0^3/3)]

= (1/3) * (256 - 128 + 64/3)

= 128/3.

Correct Question :

The base of s is the triangular region with vertices (0, 0), (8, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles. What is the volume of the triangular solid.

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PLEASSEEEEEE HELPPPPP ASAPPP IM SO SORRY BUT THIS IS THE LAST ONE FOR TODAY I THINKK
Solve for x and y

Answers

The value of x and y in the right triangle are as follows:

x = 15√3 units

y = 30 units

How to find the side of a right triangle?

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles of a right angle triangle is 180 degrees.

The side x and y can be found using trigonometric ratios,

tan 60° = opposite / adjacent

tan 60° = x / 15

cross multiply

x = 15 tan 60°

x = 15 × √3

x = 15√3 units

Let's find y as follows:

cos 60° = adjacent / hypotenuse

cos 60° = 15 / y

cross multiply

y = 15 / cos 60

y = 15 ÷ 1 / 2

y = 15(2)

y = 30 units

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If there are roughly 4500 bacterial in a culture, and the number of bacteria doubles each hour, the number N
of bacteria after t
hours can be found using the formula N=4500(2^t)
. About how long will it take the culture to grow to 80,000 bacteria?

Answers

To grow 80000 bacteria, it will take 4.152 hours.

What is exponential function?

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Given,

Initial number of bacteria = 4500

Number of bacteria get doubled each hour

Function for population growth of bacteria is given by

N = 4500(2ˣ)

x is time in hours

Future population is N = 80000

Then

80000 = 4500(2ˣ)

800 = 45 . 2ˣ

taking log on both sides

log 800 = log (45 . 2ˣ)

log(mn) = log m + log n and log mⁿ = nlogm

log800 = log45+ x log2

2.9030 = 1.653 + x . 0.3010

x = (2.9030 - 1.653)/0.3010

x = 4.152

Hence, it will take 4.152 hours to grow 80000 bacteria.

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In ΔVWX, w = 680 inches, m∠X=15° and m∠V=116°. Find the length of W, to the nearest 10th of an inch

Answers

Answer:

  W = 680 in

Step-by-step explanation:

You want the length of side w in ∆VWX, where w = 680 in, X = 15°, and V = 116°.

Reading

As written, this seems to be a problem in reading comprehension. You are asked for one of the values that is given in the problem statement:

  W = 680 inches

__

Additional comment

The attachment shows the solution of the triangle. In this, we have used ∆ABC ≅ ∆VWX.

What is the image point of (5,1) after translation right 5 units and down 2 units

Answers

The image point after the translation would be (10, - 1).

What is translation of image?The translation of image is the movement of image across the dimensional plane. It can be either horizontally {rightwards or leftwards) or vertically {upwards or downwards}.

Given is the coordinate point of (5, 1).

We can write the translation rule as -

(x, y) → (x + 5, y - 2)

We can write the image point as -

(5, 1) → (5 + 5, 1 - 2)

(5, 1) → (10, - 1)

Therefore, the image point after the translation would be (10, - 1).

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answer the question. if you get it correct ill give it 5 stars and the brainiest.

Answers

(x^2 - 7x - 18)/(x + 2) = x - 9 can be simplified by multiplying both sides of the equation of x + 2. The new equation is x^2 - 7x - 18 = x^2 - 7x - 18. Therefore the equation's solution is all real numbers.

What is one tenth more than 13.7?

Answers

The value of the number one-tenth more than 13.7 is 13.8.

What is a decimal number?

In geometry, a polygon is a type of plane figure and is defined as a closed polygonal chain made up of a finite number of straight-line segments. A region that is enclosed by a bounding plane, a bounding circuit, or both are referred to as a polygon. The portions of a polygonal circuit are referred to as its edges or sides.

Given that numbers are one-tenth and 13.7.

More means add two numbers.

One-tenth = 1/10

The number one-tenth more than 13.7 is

1/10 + 13.7

= 0.1 + 13.7

= 13.8

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please help me on this

Answers

B. 5/12

B. 5/12

B. 5/12

B. 5/12

B. 5/12

B. 5/12

B. 5/12

Answer: B

Step-by-step explanation:

Here's how to subtract 3/12 from 4/6:

4/6−3/12

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 4 by 12, and get 48.

Then we multiply 3 by 6, and get 18.

Next we give both terms new denominators -- 6 × 12 = 72.

So now our fractions look like this:

48/72−18/72

Step 2

Since our denominators match, we can subtract the numerators.

48 − 18 = 30

So the answer is:

30/72

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

30/72÷ 2 =15/36

Let's try dividing by 2 again...

Nope! So now we try the next greatest prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

15/36÷ 3 =5/12

Let's try dividing by 3 again...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

No good. 7 is larger than 5. So we're done reducing.

There you have it! The final answer is:4.6−3/12=5/12

Help ASAP WILL GIVE BRAINILEST

Answers

Answer:

My friend didn't factorise the x in 4xy out.

Step-by-step explanation:

15x-20xy= 5x(3-4y)

Which equation represents a proportional relationship?
A. y = 4x+1
B. y = 5x²
C. y=9

Answers

B. y = 5x² represents a proportional relationship.

In a proportional relationship, the ratio of the dependent variable (y) to the independent variable (x) is constant. In this equation, as x increases, y also increases by a constant factor (5 times x). This indicates that the two variables are proportional to each other.

In A. y = 4x + 1 and C. y = 9, there is no constant ratio between y and x, so they do not represent proportional relationships.

Consider the graphs of the following lines.
3x - 5y = 2
3x + 5y = -2
Find the slope m of each line.
3x - 5y = 2
m₁ =
3x + 5y = -2
m2 =
8.6A.
4

Answers

Slope of lines 3x - 5y = 2 and 3x + 5y = -2 are m₁ = 3/5 and m₂ = -3/5 respectively.

What is slope of the line?

The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. Therefore, the change in y-coordinate for a change in x-coordinate can be written as

Line slope is a measure of the steepness or direction of a line in the coordinate plane.  

m = Δy/Δx

where,m is the slope

Given,

equations of the line

3x - 5y = 2

Moving 3x to RHS
-5y = -3x + 2

y = (3/5)x - 2/5

comparing with slope intercept equation of the line y = mx + c

slope m₁ = 3/5

Now, equation

3x + 5y = -2

moving 3x to RHS

5y = -3x - 2

y = (-3/5)x - 2

comparing with slope intercept equation of the line y = mx + c

slope m₂ = -3/5

Hence, m₁ = 3/5 and m₂ = -3/5 are slope of lines 3x - 5y = 2 and 3x + 5y = -2 respectively.

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solve for x 3x-6 x-2

Answers

Answer:

x=46

Step-by-step explanation:

this is how you set up the problem

3x-6+x-2=180

then you combine like terms

4x-6-6=180

then combine like terms again

4x-4=180

then you have to get 4 to the other side

4x-4=180

+4 +4

which leaves you with 4x=184

which you then divide both sides by 4

which leaves you with

x=46

I hope this helps you!!!

Answer:

x=46 =))))))))))))))))))))))))))))))))))(((()((((()()(

What is the result of multiplying the first equation by −3
and adding to the second equation?
5x−2y=−2
3x+y=12
A. −10x+8y=15
B.−12x+7y=18
C. 12x+7y=18
D.8x−y=10

Answers

Answer:i got u mate

The answer is a _10×+8y=15

Step-by-step explanation:

Sam drive 965 mile from city A to city b ,Rita drive 1,041 mile from city C To city B

Answers

Sam travels on the highway for approximately 1.4 hours.

We know that Sam's total travel time is 1.5 hours plus the time he spends on the highway, which we'll call "x" hours. So his total travel time can be represented as:

Total travel time = 1.5 + x

We also know that the total distance he travels is 140 miles. We can use the formula:

distance = rate x time

to set up two equations, one for his travel on city roads and one for his travel on the highway. Let's start with the city roads:

distance = rate x time

distance = 35 mph x 1.5 hours

distance = 52.5 miles

So Sam travels 52.5 miles on city roads, which means he still has to travel:

140 miles - 52.5 miles = 87.5 miles

on the highway. Now we can set up an equation for his travel on the highway:

distance = rate x time

87.5 miles = 65 mph x x hours

Solving for x, we get:

x = 87.5 miles / (65 mph)

x ≈ 1.35 hours

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I have solved the question in general, as the given question is incomplete:

The complete question is:

Sam is driving a distance of 140 miles from his house to visit Melissa. Sam takes city roads , on which can he travel an average of 35 mph for a total of 1.5 hours . Sam also takes the highway , on which he travels an average of 65 mph for a total of x hours . approximately how long does Sam travels on the highway , to the nearest tenth of an hour ?

Given the parabola f(x)=-(x-8)^2+5, describe three transformations which would transform the graph of y=x^2 into the graph of f(x). Give both the transformations and the order.

Answers

The transformations and the order are a shift of 8 units left and 5 units up

How to determine the transformations and the order.

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

f(x) = (x - 8)^2 + 5

The parent function is given as

y = x^2

When these functions are compared, we  have

y = x^2 is shifted right by 8 units and shifted up by 5 units to get f(x)

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Graph the angle -4pi/3 in standard position

Answers

The angle -4π/3 in its standard position is added as an attachment

How to plot the angle in its standard position

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

Angle = -4π/3

The coordinates of this point can be found by using the formula for converting from polar to rectangular coordinates:

x = cos(-4π/3)

y = sin(-4π/3)

So, we have

x = -0.5

y = 0.86

As an ordered pair, we have

(0.86, -0.5)

This means that we plot (0.86, -0.5)

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Find the area of this rectangle please help!

Answers

I got 9 7/9 by using a calculator

If the prism is surrounded by a fluid, what is the maximum index of refraction of the fluid that will still cause total internal reflection within the prism?.

Answers

The maximum index of refraction of the fluid that will still cause total internal reflection within the prism is nf = n/sinΘc.

Total internal reflection is a phenomenon in which light passes through a medium with a higher index of refraction and bounces back into the same medium instead of exiting it. This is possible when the angle of incidence is greater than the critical angle of the material.

In the case of a prism surrounded by a fluid, the maximum index of refraction of the fluid that will still cause total internal reflection within the prism can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two materials.

The critical angle of the prism can be calculated as the angle at which the sine of the angle of refraction becomes equal to 1. The critical angle can be calculated using the equation:

sinΘc = 1/n

where n is the index of refraction of the prism.

The maximum index of refraction of the fluid can then be found by rearranging Snell's law and substituting the critical angle into the equation:

nf = n/sinΘc

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I NEED HELP ASAP Please and Thank You!

Answers

An exponential decay function that shows the relationship between y and t is y = 16,000 (0.74)^t.

What is an exponential decay function?

An exponential decay function is one of the two types of exponential functions, including an exponential growth function.

Exponential functions are depicted as y = abˣ, where "a" is a constant, b is the base and x is the variable exponent.

The purchase value of a car = $16,000

Annual decreasing rate in value = 26%

Decayed value after 1 year = 0.74 (1 - 26%)

Let the number of years after the purchase = t

Let the resale value of the car after t years = y

Exponential Function:

Resale value after t years, y = 16,000 x (1.074)^t

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If 1/5+1/5=a/5 then a=

Answers

Answer: a = 2 because 1 + 1 = 2

Step-by-step explanation:

What is the area for 5ft 10 1/2 ft

Answers

The area of this rectangular figure is equal to 52 1/2 feet.

How to calculate the area of a rectangle?

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.

Substituting the given points into the area of rectangle formula, we have the following;

Area of rectangular figure = 5 × 10 1/2

Area of rectangular figure = 5 × 21/2

Area of rectangular figure = 105/2

Area of rectangular figure = 52 1/2 feet.

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How many of the numbers have three digits in monotone (i. E. , non-increasing or non-decreasing) order?

Answers

There are a total of 198 numbers with three digits in monotone order.

For non-decreasing order, we can choose any three digits from 0-9, and arrange them in increasing order. The total number of ways to do this is 10 choose 3, which is 120. For non-increasing order, we can choose any three digits from 1-9, and arrange them in decreasing order. The total number of ways to do this is 9 choose 3, which is 84. However, we have double counted the numbers that are all the same digit, such as 111, 222, etc. There are 9 of these numbers, so we need to subtract them from our total.

So the total number of numbers with three digits in monotone order is 120 + 84 - 9 = 198.

Therefore, there are 198 numbers with three digits in monotone order.

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