A 210∘ arc has a length of 42π. Find the radius of the circle.

Answers

Answer 1

Answer:

20

Step-by-step explanation:


Related Questions

how to pass a multiple choice math test without studying?

Answers

Answer:

Imposible!

Step-by-step explanation:

When it comes to passing a multiple choice math test without studying, it is important to understand that studying and preparation are key factors in achieving success. However, if you find yourself in a situation where you haven't had the opportunity to study, there are still some strategies you can employ to increase your chances of passing the test. Familiarize yourself with the format of multiple choice questions, read the questions carefully, eliminate obviously incorrect options, use the process of elimination, make educated guesses, and manage your time effectively. While these strategies may improve your chances of passing the test, it is important to note that studying and preparation are essential for long-term success in mathematics.

When it comes to passing a multiple choice math test without studying, it is important to understand that studying and preparation are key factors in achieving success. However, if you find yourself in a situation where you haven't had the opportunity to study, there are still some strategies you can employ to increase your chances of passing the test.

Familiarize yourself with the format of multiple choice questions: Understanding how multiple choice questions are structured can help you approach them more effectively. Pay attention to the number of options, the way the questions are phrased, and any patterns you notice.Read the questions carefully and eliminate obviously incorrect options: Take your time to read each question carefully and eliminate any options that are clearly incorrect. This can help you narrow down your choices and increase your chances of selecting the correct answer.Use the process of elimination to narrow down your choices: If you're unsure about the correct answer, use the process of elimination. Cross out options that you know are incorrect, which will increase your chances of selecting the right answer.Make educated guesses based on your understanding of the topic: Even without studying, you may have some prior knowledge or understanding of the topic. Use this knowledge to make educated guesses when you're unsure about the correct answer.Manage your time effectively: Multiple choice tests are often timed, so it's important to manage your time effectively. Pace yourself and ensure you have enough time to answer all the questions.

While these strategies may improve your chances of passing the test, it is important to note that studying and preparation are essential for long-term success in mathematics.

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Quantitative research only works if: a You talk to the right number of people b You talk to the right type of people c You ask the right questions and analyze the data you get in the right way d All of the above .

Answers

Quantitative research only works ,The correct answer is d) All of the above.

Quantitative research involves collecting and analyzing numerical data to draw conclusions and make generalizations about a population. To ensure the validity and reliability of the research findings, all three factors mentioned in the options are crucial.

Firstly, talking to the right number of people is important to achieve a representative sample size. The sample should be large enough to provide sufficient statistical power and reduce the margin of error. It helps in generalizing the findings to the larger population.

Secondly, talking to the right type of people is essential to ensure that the sample is representative of the population of interest. The sample should include individuals who are relevant to the research objectives and possess the characteristics or attributes that are being studied.

Lastly, asking the right questions and analyzing the data in the right way are essential components of quantitative research. The questions should be designed to gather the necessary information and measure the variables of interest accurately. The collected data should be analyzed using appropriate statistical techniques to derive meaningful insights and draw valid conclusions.

By considering all these factors together, quantitative research can effectively generate reliable and valuable findings.

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Please I need answers for these two asap! Please explain your answer I will mark brainliest!!!

Please I need answers for these two asap! Please explain your answer I will mark brainliest!!!
Please I need answers for these two asap! Please explain your answer I will mark brainliest!!!

Answers

Answer:

Triangle ABC is congruent to triangle DCB because of the Side-Side-Side theorem

Step-by-step explanation:

Triangle ABC is congruent to triangle DCB because of the Side-Side-Side theorem this is the answer cause it expalins the way to do it

f(x)=23x−1 and g(x)=−4x+6.

What transformation occurs from function f to function g?


a horizontal stretch by a factor of −6

a horizontal translation 6 units left

a vertical translation 6 units down

a horizontal compression by a factor of −6

Answers

The transformation occurs from function g is a vertical translation 6 units down.

What is Transformation?

A function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f : X → X.

Given:

g(x) = 4x + 6

g(x) = 0

4x + 6=0

x= -6/4

Now,

f(-6/4) = 2 - 1

=-1

By seeing g(x), we can say that  function g is a vertical translation 6 units down.

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Books in the clearance section at Reading Central Bookmart cost $5.00 for paperbacks and $9.00 for hardbacks. Which inequality best describes the number of paperback books, p, and the number of hardback books, h, that can be purchased for $45.00 or less?
A.
5p + 9h < 45
B.
5p + 9h < 45
C.
9p + 5h > 45
D.
9p + 5h < 45

Answers

The inequality best describes the number of paperback books 'p' and the number of hardback books 'h' that can be purchased for $45.00 or less

is 5p + 9h ≤ 45.  

What are inequalities and their types?

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Two types of books paperbacks are represented by 'p', and hardbacks are represented by 'h'.

Also, we can only buy two types of books for $45 or less.

Therefore, The inequality representing the context is,

5p + 9h ≤ 45.  (As the cost van be $45 or less not only less)

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8.
Out of total population of 50,000, only 28,000 read Newspaper and 23,000 read
magazines while 4,000 read both. How many of them do not read any paper ?​

Answers

the answer is in the picture

8.Out of total population of 50,000, only 28,000 read Newspaper and 23,000 readmagazines while 4,000

You are studying a population of mountain bighorn sheep. There are currently 170 individuals and the intrinsic growth rate is 0.2 per year. Assuming exponential growth, approximately what will the population size be in 4 years

Answers

The population size of mountain bighorn sheep after four years will be approximately 374 individuals.

The intrinsic growth rate of a population is the highest possible growth rate without any environmental or other constraints. Exponential growth is a growth pattern that arises when a population increases in size by a set percentage each year. Exponential growth is one method of modeling population growth and is defined by an accelerating growth rate over time.

The mountain bighorn sheep has an intrinsic growth rate of 0.2 per year, and the formula used to estimate the population size after a given number of years is P = P0ert. In this equation, P0 is the initial population size, P is the final population size, e is Euler's number, r is the intrinsic growth rate, and t is the time in years.

Therefore, to calculate the population size of mountain bighorn sheep after four years, we can use the equation as follows: P = P0ert. By substituting the values given in the problem into the equation, we obtain P = 170 x e^(0.2 x 4). Simplifying the equation yields P = 170 x e^0.8, and rounding this number yields P ≈ 373.96.

Hence, the population size of mountain bighorn sheep after four years will be approximately 374 individuals.

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Use the matrix calculator to find the area of this
triangle:
(-7,3)
(5,0)
(-4,-3)
A=
DONE

Answers

Answer:

63/3 or 31.5

Step-by-step explanation:

use the formula A(B-C) +B(C-A)+C(A-B) /2

Then you will substitute the values

-7(0+3) +5(-3-3)-4(3-0)/2

Do the algebra = 63/3 or 31.5

hope that helped cheers

A sail boat traveled 9000 meters in 30 minutes.


On average how many meters did the sailboat travel

Answers

The sailboat traveled an average of 18,000 meters per hour based on the given information that it traveled 9000 meters in 30 minutes.

Given that a sailboat traveled 9000 meters in 30 minutes, we can find the average meters traveled by the sailboat. The average meters traveled by a sailboat can be calculated by dividing the total distance covered by the sailboat with the total time taken.

This can be done as follows:

Average meters traveled = Total distance / Total time

Total distance traveled by the sailboat = 9000 meters

Total time taken by the sailboat to travel this distance = 30 minutes = 0.5 hours

Average meters traveled = 9000 / 0.5 = 18,000 meters per hour

Therefore, on average, the sailboat traveled 18,000 meters per hour.

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) The value of shares, t years after their floatation on the stock market, is modelled by V=10e 0.09t
Find the initial value of these shares and values after 5 years, 10 years and 12 years, respectively. Round your answer to two decimal places. [9 marks] During a recession, a firm's revenue declined continuously so that the total revenue (TR) in t years' time is modelled as TR=10e −0.19t
(in million dollars) Calculate the current revenue and revenue in 5 years' time. After how many years the revenue of this firm is going to drop to $1 million? Round your answer to two decimal places.

Answers

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Interpreting data (Box & Whisker & Histogram) & Review Systems
For questions 1-4 use the graph below to answer the following questions/problems.



1. What is the value of the third quartile shown on the box-and-whisker plot?
2. Determine the interquartile range? Determine the range?
3. How many people were surveyed?
12
4. What is the type of average you can find? Find that average.

Answers

The type of average that can be found is the median. The median is the middle value of the data set when the values are arranged in order. In this case, the median is 11, as shown by the line inside the box.

What is value ?

Value is the relative worth, merit, or importance of something. It is subjective and can be determined by a variety of factors, including personal preferences, beliefs, and economic forces. Value is a concept that can be applied to many different aspects of life, including economic goods, personal relationships, and objects. Value is determined by how much someone is willing to pay for something or how much someone needs something. In economics, value is determined by the market, which is based on supply and demand. In personal relationships, value is determined by the mutual respect, trust, and understanding between two people. In objects, value is determined by the sentiment and meaning it holds for the owner. Ultimately, value is a perception of worth, and its true value is subjective.

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what is the length of a car if the length on the scale model car is 17 centimeters and the scale is 2 centimeters colon 50 centimeters?

Answers

If the length on the scale model car is 17 cm and the scale is 2 cm colon 50 centimeters the length of a car  is 425 cm

To find the length of the actual car, we can use the given scale ratio. The scale ratio is 2 centimeters colon 50 centimeters, which means that for every 2 centimeters on the scale model car,

it represents 50 centimeters on the actual car.
We can set up a proportion to solve for the length of the actual car.

Let's call the length of the actual car "x". The length on the scale model car is given as 17 centimeters.
Using the proportion, we have:
2 cm / 50 cm = 17 cm / x
To solve for x, we cross-multiply:
2 cm × x = 50 cm × 17 cm
2x = 850 cm
Divide both sides by 2 to isolate x:
x =  850/ 2

x = 425 cm
Therefore, the length of the actual car is 425 centimeters.

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Based on the given scale and the length of the scale model car, the length of the actual car is 425 centimeters. The scale model car is 17 centimeters long, and the scale is 2 centimeters colon 50 centimeters.

To find the length of the actual car, we can set up a proportion.

Let's label the length of the actual car as "x".

Using the scale, we can write the proportion:

    2 cm (scale model car) / 50 cm (actual car) = 17 cm (scale model car) / x cm (actual car)

To solve for x, we can cross multiply:

    2 cm * x cm = 50 cm * 17 cm

=> 2x = 850 cm

Dividing both sides of the equation by 2:

    x = 425 cm

Therefore, the length of the actual car is 425 centimeters.

In conclusion, based on the given scale and the length of the scale model car, the length of the actual car is 425 centimeters.

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Suppose a circle is divided into congruent slices. Match each number of slices with the

resulting central angle measure of each slice.

2

[ Choose ]

3

[ Choose ]

4.

[ Choose ]

5

[Choose ]

6

[ Choose1

>

8

[ Choose ]

Answers

26 skate and with wunno when ask what about the gc and the park to park in

Answer:

Think of it like this each circle has 360 degrees so take 360/2 360/3 and so on and see what you get

Step-by-step explanation:

PLSSS HELP IMMEDIATELY!!!! i’ll give brainiest, if u don’t provide just a link! answer choices: (4,6) , (0,1) , (0,0) , (5,4)

PLSSS HELP IMMEDIATELY!!!! ill give brainiest, if u dont provide just a link! answer choices: (4,6) ,

Answers

Answer:

try (4,5)

Step-by-step explanation:

that is where the points meet I think it is that I am not sure sorry if it is wrong

Sorry the lines aren’t even but this should be correct
PLSSS HELP IMMEDIATELY!!!! ill give brainiest, if u dont provide just a link! answer choices: (4,6) ,

When conducting a scientific investigation, how many variables should be tested?.

Answers

An experiment usually has three kinds of variables: independent, dependent, and controlled. The independent variable is the one that is changed by the scientist.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.

The variable you alter, regulate, or change in an experimental study to examine its effects is known as an independent variable. It is named "independent" because it is unaffected by any other study variables.

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URGENT!!!!! LAST TWO QUESTIONS!!!!!!! WILL GIVE BRANLIEST!!!AT LEAST TAKE A LOOK!!!!!! PLS HELP!!! 1. A cartographer wants to create a map of Seattle. He has designed a key/legend for the map indicating that 1 cm equals 2 miles. If the distance between Woodland Park Zoo and the Seattle Aquarium is 5.2 miles, how long is the distance going to be on the map? A) 2.6 cm B) 8.2 cm C) 6 cm D) 10.4 cm 5. What similarity property, if any, can be used to show that the following two triangles are similar. A) SAS B) SSS C) AA D) Not enough information given

URGENT!!!!! LAST TWO QUESTIONS!!!!!!! WILL GIVE BRANLIEST!!!AT LEAST TAKE A LOOK!!!!!! PLS HELP!!! 1.

Answers

Answer:

1. 5.2 / 2 = 2.6 cm

2. Since 2 angles are congruent the answer is AA.

Karen has $600. She spent $240 on clothes. What percentage of money did she have left?

Answers

Answer: She had 60% of the money left

Step-by-step explanation:

240/600=0.4

0.4 = 40%

100%-40%=60%

Answer:

60%

Step-by-step explanation:

LETS MAKE IT INTO A FRACTION

FIRST LETS CALCULATE HOW MUCH SHE SPENT

=240/600

WE CAN SIMPLIFY BY DIVIDING THE EQUATION BY 10

=24/60

LETS DIVIDE BY 6

=4/10

DIVIDE BY 2

=2/5

NOW LETS CALCULATE HOW MUCH SHE HAS LEFT

THE EASIEST WAY IS TO SUBTRACT

5/5-2/5=3/5

3/5 IS ALSO EQUAL TO 60/100

SO KAREN HAS 60% OF HER MONEY LEFT

HOPE I HELPED

PLS MARK BRAINLIST

(DESPERATELY TRYING TO LEVEL UP)

        ✌

anyone know the answer??

anyone know the answer??

Answers

The measure of the indicated angle to the nearest degree can be found to be A. 51 degrees .

How to find the angle ?

The cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle .

In this case , the adjacent side is 17 and the hypotenuse is 27 . This means that the angle can be found to be :
Cos ( angle ) = Adjacent / Hypotenuse

Cos ( angle ) = 17 / 27

Angle = Cos ⁻ ¹ ( 17 / 27 )

Angle = 50. 98 degrees

Angle = 51 degrees

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what is the slope of y-intercept of the linear function shown (-6,0),(2,-2)

Answers

Answer:y=2x−6

Step-by-step explanation:

Give your answer in simplest form.

Give your answer in simplest form.

Answers

Answer:

The answer is -1

Step-by-step explanation:

PLEASE MARK BRAINLIEST IT WILL HELP SM

And if you are looking for more help go to math-way

Answer is 1
Start to solve in the brackets first and then do the exponents and then do the rest
In short ur bedmas
Where
B means brackets
E means exponent
D division
M multiple
A addition
S subtract

Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 2 42% compounded monthly. The annual percentage yield is

Answers

The Annual Percentage Yield (APY) in this situation is approximately 2.454%.

To find the Annual Percentage Yield (APY) in this situation, use the formula:

\(APY = (1 + r/n)^n - 1\)

where:

- r is the annual interest rate (APR) expressed as a decimal,

- n is the number of compounding periods per year.

In this case, the APR is 2.42% or 0.0242 (expressed as a decimal), and the interest is compounded monthly, so there are 12 compounding periods per year (n = 12).

Substituting these values into the formula,

\(APY = (1 + 0.0242/12)^{12} - 1\)

Calculating this expression:

\(APY = (1 + 0.002017)^{12} - 1\)

  \(= (1.002017)^{12} - 1\)

   ≈ 0.02454 or 2.454%

Therefore, the Annual Percentage Yield (APY) in this situation is approximately 2.454%.

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HELP . I'm not sure what the range is.

HELP . I'm not sure what the range is.

Answers

Answer:

y<-1

Step-by-step explanation:

This exponential function will never approach y=-1, but it goes "under" the line of -1, so it is y<-1

the student lockers at olympic high are numbered consecutively beginning with locker number 1. the plastic digits used to number the lockers cost two cents a piece. thus, it costs two cents to label locker number 9 and four cents to label locker number 10. if it costs $137.94 to label all the lockers, how many lockers are there at the school?

Answers

The number of lockers in the school, given that each locker costs two cents, would be 2, 001 lockers.

How to find the number of lockers ?

The number of lockers can be found by finding the cost of the first 9 lockers to be :

= 2 x 9 lockers

= 18 cents

The next 90 lockers till 99 locker:

= 4 x 90

= $ 3.60

Then 100 lockers till 999 lockers :

= 6 cents  x 900

= $ 54

Then 1, 000 lockers to 1, 999 lockers :

= 8 cents x 1, 000

= $ 80

This gives :

= 0. 18 + 3. 60 + 54 + 80

= $ 137. 78

We are left with 16 cents to reach $ 137. 94 which means that there are 2 more lockers with 4 digits:

= 1, 999 + 2

= 2, 001 lockers

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A bag contains​ red, green, and blue marbles. One dash fourth of the marbles are​ red, there are one half as many blue marbles as green​ marbles, and there are 6 fewer red marbles than green marbles. Determine the number of marbles in the bag in these two approaches.

Answers

The bag contains a total of r + g + b = 18 + 24 + 12 = 54 marbles.

The bag contains a total of r + g + b = 18 + 12 + 6 = 36 marbles.

Let's denote the number of red, green, and blue marbles by r, g, and b, respectively.

The following information:

r = 1/4(r + g + b) (one-fourth of the marbles are red)

b = 1/2 g (there are half as many blue marbles as green marbles)

r = g - 6 (there are 6 fewer red marbles than green marbles)

These equations to form a system of equations and solve for the values of r, g, and b.

Here's one approach:

First, we can simplify the equation r = 1/4(r + g + b) by multiplying both sides by 4 to get:

4r = r + g + b

Then, we can substitute b = 1/2 g and r = g - 6 into the above equation to get:

4(g - 6) = (g - 6) + g + (1/2)g

Simplifying and solving for g, we get:

g = 24

Using this value of g, we can find the values of r and b as follows:

r = g - 6 = 18

b = 1/2 g = 12

The bag contains a total of r + g + b = 18 + 24 + 12 = 54 marbles.

Alternatively, we can use a slightly different approach:

We know that the fraction of red marbles is 1/4 of the total number of marbles, so we can write:

r = (1/4)(r + g + b)

Multiplying both sides by 4, we get:

4r = r + g + b

Subtracting r from both sides, we get:

3r = g + b

We also know that there are half as many blue marbles as green

marbles, so we can write:

b = (1/2)g

Substituting b = (1/2)g into the above equation, we get:

3r = (3/2)g

Multiplying both sides by 2/3, we get:

g = (2/3)r

We also know that there are 6 fewer red marbles than green marbles, so we can write:

r = g - 6

Substituting g = (2/3)r into the above equation, we get:

r = (2/3)r - 6

Solving for r, we get:

r = 18

Using this value of r, we can find the values of g and b as before:

g = (2/3)r = 12

b = (1/2)g = 6

The bag contains a total of r + g + b = 18 + 12 + 6 = 36 marbles.

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Give an actual answer please

Rhett decides to build a square room for his movie and music collection. If the area of the room is 4x2 + 28x + 49 square feet, what is the length of one side of the room?
(7x + 2) feet
(2x + 7) feet
(2x − 7) feet
(7x − 2) feet

Answers

Hello There!!

Your best answer choice will be is A.

(2x + 7) feet.

Because, All you have to do for this problem is factor the equation. I would be hard to explain on this so I recomment you watch a video on it. If you did not know how to factor, you could have muliplied each of the answers by themselves to determine the correct answer because it is a square.

Hope This Helps!!

Answer:

(2x+7)

Step-by-step explanation:

4x^2 + 28x + 49

This is a perfect square trimonial

a^2 + 2ab + b^2 =  (a+b)^2

(2x)^2 + 2 * 2x*7 + 7^2

( 2x+7)^2


Evaluate
(9n +8m)
—————
2j
when n = 4, m = -2 and j = 5
2j

Answers

Answer:

2

Step-by-step explanation:

Let n= 4, m= -2 and j= 5(9n + 8m)/2j= 9(4) + 8(-2)/2(5)= 36 + (-16)/10= 20/10= 2

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

In a post office, the mailboxes are numbered from 1 to 4,500. These numbers represent О А categorical dataO B quantitative data O C e ither categorical or quantitative data. O D since the numbers are sequential, the data is quantitative.

Answers

The numbers on the mailboxes could be considered either categorical or quantitative data. The correct Option is C: Either categorical or quantitative data.

The numbers on the mailboxes can be considered either categorical or quantitative data, depending on the context in which they are being used.

If the numbers are simply labels for the mailboxes, with no inherent numerical value or order, then they can be considered categorical data. In this case, the numbers would be treated as labels for the different categories or groups, rather than as measurements with numerical significance.

On the other hand, if the numbers are being used to represent a quantity or a position in a sequence, then they can be considered quantitative data. For example, if the numbers represent the physical location of the mailbox within a building, or the order in which mail is sorted and delivered, then they can be treated as numerical measurements.

Therefore, without further context, the numbers on the mailboxes could be considered either categorical or quantitative data.

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Heather drove 441 miles in 7 hours.
At the same rate, how many miles would she drive in 5 hours?

Answers

Answer:315

Step-by-step explanation:

441 divide by 7 then what u get multiply by 5

8. Find the probability of each set of independent events.
flipping a tail on a coin and spinning a 5 on a spinner with sections of
equal area numbered 1-5.
a) 1/2
c) 1/5
b) 1/7
d) 1/10

8. Find the probability of each set of independent events.flipping a tail on a coin and spinning a 5

Answers

Answer:

Step-by-step explanation:

8. Find the probability of each set of independent events.flipping a tail on a coin and spinning a 5

there is an island containing two types of people: knights who always tell the truth, and knaves who always lie. as you arrive at the island, you are approached by three natives, a, b, and c. a says: if b is a knight then c is a knave. b says: if c is a knight then a is a knave. c says: if a is a knight then b is a knave.

Answers

There are two valid solutions

1. A is a knight, B is a knight, and C is a knave.

2. A is a knave, B is a knave, and C is a knight.

In this scenario, we have three natives on the island: A, B, and C. It is known that knights always tell the truth, while knaves always lie. Let's analyze the statements made by each native:

A says: "If B is a knight, then C is a knave."

B says: "If C is a knight, then A is a knave."

C says: "If A is a knight, then B is a knave."

To determine the true identities of A, B, and C, we need to examine the consistency of their statements.

Let's consider the possibilities:

1. If A is a knight:

  - A's statement would be true.

  - B and C's statements would also need to be true.

  - This implies that B is a knight and C is a knave.

2. If A is a knave:

  - A's statement would be false.

  - B and C's statements would also need to be false.

  - This implies that B is a knave and C is a knight.

Now let's evaluate these possibilities:

1. If A is a knight, B is a knight, and C is a knave:

  - A's statement is true, as B is a knight and C is a knave.

  - B's statement is true, as C is indeed a knave.

  - C's statement is false, as A is a knight, not a knave.

  - This configuration is consistent with the rules.

2. If A is a knave, B is a knave, and C is a knight:

  - A's statement is false, as B is not a knight.

  - B's statement is false, as C is a knight.

  - C's statement is true, as A is indeed a knave.

  - This configuration is consistent with the rules.

Therefore, there are two valid solutions:

1. A is a knight, B is a knight, and C is a knave.

2. A is a knave, B is a knave, and C is a knight.

These solutions are consistent with the statements made by A, B, and C, considering the behavior of knights and knaves on the island.

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