Answer:
Its the Segmant addition postulate :)
Step-by-step explanation:
Answer:
C) Transitive property
Step-by-step explanation:
If two values are equal and either of the two values is equal to the third value,
then all the three values are equal.
EG: a=b and b= c, then
a = b= c
1/8 + -3/16 how do you solve this?
Answer:
-1/16
Step-by-step explanation:
Answer: 1/8 + -3/16 = -1/16
Step-by-step explanation:
First, multiply the numerator and denominator of 1/8 by 2.
1/8 + -3/16
1 x 2 = 2
8 x 2 = 16
2/16 + -3/16
Next, turn the + and - into one -.
2/16 + -3/16
2/16 - 3/16
Finally, solve 2/16 - 3/16! We will get a negative number.
2/16 - 3/16 = -1/16
1/8 + -3/16 = -1/16
42−(2c+4)=4(c+6)+c what is the value of C
What is the volume of this 3 dimensional figure
Answer: 2496in³
Step-by-step explanation:
To find volume, multiply the numbers by length, width, and height.
In this case, 24 is the length, 8 is the width, and 13 is the height.
24 × 8 × 13 = 2496 inches ³ (cubed).
Answer:
option C 2496
Step-by-step explanation:
you multiply 13 by 24 by 8
what is the slope of the line graphed below?
Answer:
5
Step-by-step explanation:
the gradient is 5
change in Y over change in X
Which of the following assumptions is necessary to apply a goodness-of-fittest? Multiple Choice The population must be normally distributed The data are measured with a nominal or ordinal scale. The population variance must be known The population mean must be known
The assumption necessary to apply a goodness-of-fit test is that the data are measured with a nominal or ordinal scale.
Goodness-of-fit tests are used to determine whether an observed frequency distribution of categorical data fits an expected theoretical distribution. They compare the observed frequencies with the expected frequencies based on a specified distribution. The data being analyzed using a goodness-of-fit test are typically categorical, such as counts or proportions in different categories or groups.
Therefore, the correct answer is: The data are measured with a nominal or ordinal scale.
Know more about nominal or ordinal scale here:
https://brainly.com/question/29674527
#SPJ11
42,133,285,612 in scientific notation (round to two digts after the decimal)
To do this, move the decimal in such a way that there is a non-zero digit to the left of the decimal point. The number of decimal places you shift will be the exponent by 10. If the decimal is shifted to the right the exponent will be negative. If the decimal is shifted to the left, the exponent will be positive. So,
Then as the point moved 10 places to the left you have
\(4.21\times10^{10}\). Constructed Response. Be sure to answer all parts of the constructed response.
Miles, Hayden, and Dubem are going to have a paint battle. Miles fills his wall at a rate of
12 wall in 9 minutes, Hayden can fill his wall at 15 wall in 313 minutes, and Dubem can cover 49 wall in 638 minutes.
Part A Place the students in order from fastest to slowest, in terms of who has the fastest water filling rate.
1.
2.
3.
Part B Explain how you determined the fastest rate.
Placing the students in order from fastest to slowest, in terms of who has the fastest water filling rate is;
1. Miles
2. Dubem
3. Hayden
The way the fastest rate is determined is by finding the unit rates
What is the unit rate of work done?A unit rate (or unit ratio) is a ratio that describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.
Now, from the question, the rate would clearly be number of walls filled per minute.
1) Mills fills his wall at a rate of 12 wall in 9 minutes. Thus;
Mills unit rate = 12/9 = 4/3 walls filled per minute = 1.333 walls filled per minute
2) Hayden can fill his wall at 15 wall in 313 minutes. Thus;
Hayden's unit rate = 15/313 walls filled per minute = 0.0479 walls filled per minute
3) Dubem can cover 49 wall in 638 minutes. Thus;
Dubem's unit rate = 49/638 walls filled per minute = 0.0768 walls filled per minute
Looking at the decimal unit rates, we can see that fastest to slowest in order are;
1. Miles
2. Dubem
3. Hayden
The way I knew who was faster was to look at the decimal values of their unit rates and it is seen that Miles covered the most part of wall in one minute
Read more about Unit Rate of work at; https://brainly.com/question/19493296
#SPJ1
What is the value of a+b-2 c for a=3, b=1 , and c=-3 ?
To find the value of a+b-2c, we substitute the given values of a, b, and c into the expression.
a = 3
b = 1
c = -3
Substituting these values into the expression, we get:
3 + 1 - 2(-3)
Now, we simplify the expression by performing the operations in the correct order:
= 3 + 1 + 6
= 10
Therefore, the value of a+b-2c, when a = 3, b = 1, and c = -3, is 10.
To know more about find the value visit:
https://brainly.com/question/22137601
#SPJ11
what is the height of ABC is 30 centimeters, what is the length of a side of this triangle in the centimeters?
Since each triangle is a right triangle we can apply trigonometric functions:
Sin a = opposite side / hypotenuse
Where;
a = angle = 60° ( we are looking at the bottom left one)
Opposite side = 30 cm
Hypotenuse = AB
Replace:
Sin60 = 30 / AB
Solve for AB
AB = 30 / sin 60
AB = 34.64 cm
find the second derivative of y= 4x^2sinx
Answer:
\(y'' = 8\sin(x) + 16x\cdot \cos(x) - 4x^2 \cdot \sin(x)\)
Step-by-step explanation:
Given the function:
\(y=4x^2 \cdot \sin(x)\)
We can find its derivative, or instantaneous slope, by applying the power rule and using the common derivative of the trigonometric function sine within the product rule.
Here are the relevant formulas:
product rule: \(\left(\dfrac{}{} f(x) \cdot g(x) \dfrac{}{} \right)' = f(x)\cdot g'(x) + g(x) \cdot f'(x)\)power rule: \((x^a)' = ax^{a\, - \, 1}\)derivative of sine: \((\sin(x))' = \cos(x)\)First, we can find the derivative of each of the function's factors [ which I will label \(f(x)\) and \(g(x)\) ].
\(f(x) = 4x^2\)
↓ applying the power rule \((x^a)' = ax^{a\, - \, 1}\)
\(f'(x) = 4(2x^{2-1})\)
\(\bold{f'(x) = 8x}\)
⎯⎯⎯⎯⎯⎯⎯
\(g(x) = \sin(x)\)
↓ applying the common derivative \((\sin(x))' = \cos(x)\)
\(\bold{g'(x) = \cos(x)}\)
Now, we can apply the product rule using these values of \(f'(x)\) and \(g'(x)\).
\(\left(\dfrac{}{} f(x) \cdot g(x) \dfrac{}{} \right)' = f(x)\cdot g'(x) + g(x) \cdot f'(x)\)
\(y' = 4x^2 \cdot \cos(x) + \sin(x) \cdot 8x\)
\(\boxed{y' = 4x^2 \cdot \cos(x) + 8x \cdot \sin(x)}\)
To find the second derivative of the function, we have to take the derivative of the derivative. We can apply the same concepts from the previous step, but also with the sum/difference rule.
sum/difference rule: \(\left(\dfrac{}{}f(x) \pm g(x)\dfrac{}{}\right)' = f'(x) \pm g'(x)\)derivative of cosine: \((\cos(x))' = -\sin(x)\)↓ applying the sum/difference rule to the function's derivative
\(y'' = \left(\dfrac{}{}4x^2 \cdot \cos(x)\dfrac{}{}\right)' + \left(\dfrac{}{}8x \cdot \sin(x)\dfrac{}{}\right)'\)
↓ applying the product rule to each derivative
\(y'' = \left(\dfrac{}{} 4x^2 \cdot (-\sin(x)) + \cos(x) \cdot 8x \dfrac{}{}\right) + \left(\dfrac{}{} 8x \cdot \cos(x) + \sin(x) \cdot 8 \dfrac{}{}\right)\)
↓ combining like terms
\(\boxed{y'' = 8\sin(x) + 16x\cdot \cos(x) - 4x^2 \cdot \sin(x)}\)
Examine the relation. { ( − 2 , − 2 ) , ( − 2 , 4 ) , ( − 1 , 1 ) , ( 1 , 0 ) , ( 1 , 1 ) , ( 3 , 3 ) , ( 3 , − 2 ) } Is the relation a function, and what is the range? function; range { − 2 , − 1 , 1 , 3 } function; range { − 2 , − 1 , 1 , 3 } function; range { − 2 , 0 , 1 , 3 , 4 } function; range { − 2 , 0 , 1 , 3 , 4 } not a function; range { − 2 , − 1 , 1 , 3 } not a function; range { − 2 , − 1 , 1 , 3 } not a function; range { − 2 , 0 , 1 , 3 , 4 }
The given relation is not a function, and the range is {−2, 0, 1, 3, 4}. In a function, each input (x-value) can only be associated with a single output (y-value).
However, in the given relation, we can see that for the input value of -2, there are two different output values: -2 and 4. This violates the definition of a function, making the relation not a function. The range of a relation or function refers to the set of all possible output values. By examining the given relation, we can observe that the y-values -2, 0, 1, 3, and 4 are present. These are the distinct output values from the relation, and therefore, the range of the relation is {−2, 0, 1, 3, 4}.
Learn more about range of a relation here: brainly.com/question/29503017
#SPJ11
working simultaneously and independently at an identical constant rate, four machines of a certain type can produce a total of x units of product p in 6 days. how
A) 24 machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days..
Let's analyze the given information and use it to determine the number of machines required to produce 3x units of product P in 4 days.
We are told that 4 machines can produce a total of x units of product P in 6 days. This means that the rate at which these 4 machines produce the product is x/(4 * 6) units per day.
To find the number of machines required to produce 3x units of product P in 4 days, we can set up a proportion based on the rates:
(x units / (4 machines * 6 days)) = (3x units / (N machines * 4 days))
Simplifying the proportion:
1/(4 * 6) = 3/(N * 4)
Multiplying both sides by 4:
1/24 = 3/N
Cross-multiplying:
N = 24/1
N = 24
Therefore, the number of machines required to produce 3x units of product P in 4 days is 24.
The answer is option A. 24.
Correct Question :
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8
To learn more about rate here:
https://brainly.com/question/13753548
#SPJ4
The general term of a sequence if Tn = 2n, what will be its 50th term?
Answer:
100
Step-by-step explanation:
Given:
Tn = 2n
Where,
n = nth term
what will be its 50th term?
Tn = 2n
T(50) = 2(50)
= 100
T(50) = 100
Therefore,
The 50th term = 100
An auditing software can identify 63.7% of misreporting issues in accounting ledgers. Let X be the number of accounting misreporting transactions identified by the software among 50 randomly selected transactions for the last 3 months.
Determine the probability that no misreported transactions are found.
Determine the probability that less than 10 misreported transactions are found.
Determine the probability that at least half of the transactions are misreported.
If the firm applying the auditing software as a test run finds no misreporting, it will receive a $200 compensation, but if there are less than 10 misreported transactions it will have to pay a fee of $50, and if the misreported transactions represent more than half of the transactions then the fee will be $100. Determine the expected monetary gain (assuming that the auditing software is correct when identifying a misreporting).
The auditing software can identify 63.7% of misreporting issues in accounting ledgers. The probability that no misreported transactions are found is 1 - 63.7% = 36.3%. The probability that at least half of the transactions are misreported is 1 - P(X 25) = 1 - P(X 24) P(X 24) = _(i=0)24 (50C_i) (0.363)i (1 - 0.363)(50 - i) 0.0001. The expected monetary gain is approximately -$49.8.
Given that an auditing software can identify 63.7% of misreporting issues in accounting ledgers. Let X be the number of accounting misreporting transactions identified by the software among 50 randomly selected transactions for the last 3 months.Probability that no misreported transactions are found:X follows a binomial distribution with n = 50 and p = 1 - 63.7% = 36.3%.P(X = 0) = (1 - p)^n = (1 - 0.637)^50 ≈ 0.0002Probability that less than 10 misreported transactions are found:
P(X < 10) = P(X ≤ 9)P(X ≤ 9)
= P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 9)P(X ≤ 9)
= ∑_(i=0)^9 (50C_i ) (0.363)^i (1 - 0.363)^(50 - i) ≈ 0.99
Probability that at least half of the transactions are misreported:
P(X ≥ 25)P(X ≥ 25)
= P(X > 24)P(X > 24)
= 1 - P(X ≤ 24)P(X ≤ 24)
= ∑_(i=0)^24 (50C_i ) (0.363)^i (1 - 0.363)^(50 - i) ≈ 0.0001
Expected monetary gain:Let Y be the amount of money that the firm gets to earn or pay. The probability distribution of Y can be shown below:Outcomes: $200, -$50, -$100
Probabilities: P(X = 0), P(0 < X < 10), P(X ≥ 25)P(X = 0)
= 0.0002P(0 < X < 10)
= 0.99 - 0.0002 = 0.9898P(X ≥ 25)
= 0.0001E(Y)
= ($200 x P(X = 0)) + (-$50 x P(0 < X < 10)) + (-$100 x P(X ≥ 25))E(Y)
= ($200 x 0.0002) + (-$50 x 0.9898) + (-$100 x 0.0001)≈ -$49.8
Therefore, the expected monetary gain is approximately -$49.8.
To know more about probability Visit:
https://brainly.com/question/31828911
#SPJ11
A robot can complete 7 tasks in 2/3
hour. What is the unit rate for hours per task
Answer:
2/21 hours per task.
Step-by-step explanation:
2/3 / 7 hours per task
= 2/21.
Please answer the question in the picture below
Thank you!
Answer:
Question 23: 39
Question 24: 10
Question 25: Airline B
Question 26: 20 to 50
Step-by-step explanation:
NEED HELP NOWW!! TYY FIRST HELPFUL QUESTION GETS 90 COIN THINGYSSSS
A theme park wants to know which new ride option is the most appealing to customers. Which sampling method produces an unbiased, representative sample of the population?
1) Survey the first 250 customers in line for the theme park in August.
2) Survey every 30th customer to enter the theme park.
3) Survey the first 80 teenagers to enter the theme park.
4) Survey 100 randomly selected parents in the theme park.
Option 4 - Survey 100 randomly selected parents in the theme park - produces an unbiased, representative sample of the population because it selects individuals randomly from the population.
This ensures that everyone in the population has an equal chance of being selected for the survey, which minimizes bias and produces a sample that is more representative of the entire population. The other options may introduce bias because they only survey specific groups of customers or use a non-random sampling method.
To obtain an unbiased, representative sample of the population in the theme park, the best sampling method would be option 2) Survey every 30th customer to enter the theme park. This approach, called systematic sampling, reduces potential bias and provides a more diverse sample compared to the other options.
To know about population visit:
https://brainly.com/question/27991860
#SPJ11
Senor Pena found some change on the floor while cleaning a classroom. He found a total of 6 coins that consisted of quarters and nickels. If the total change was $1.30, how many of each coin did he find?
Answer:
There are 5 quarters and 1 nickel
Step-by-step explanation:
Let Q and N be the numbers of Quarters and Nickels that Senor Pena found, respectively.
The value of each coin is $0.25 for quarters and $0.05 for each nickel
The total of $1.30 would be the result of:
1) Quarters: $0.25*Q, and
2) Nickels: $0.05*N
So we can write: $0.25*Q + $0.05*N = $1.30
We also know he found 6 coins, so:
Q + N = 6
We have two equations and two unknowns. We can use substitution to find the answer.
Rearrange the second equation to isolate one of the two variables. lets isolate Q:
Q = 6-N
We can use this definition of Q in the first equation by substitution:
$0.25*Q + $0.05*N = $1.30
$0.25*(6-N) + $0.05*N = $1.30
Leaving off the $ signs for clarity:
0.25(6-N) + 0.05N = 1.30
1.5 - 0.25N + 0.05N = 1.30
-0.2N = -0.20
N = 1
There is 1 nickel
Since Q = 6-N, Q = 5
There are 5 quarters and 1 nickel
CHECK
Do 5 quarters and 1 nickel add to $1.30?
5*($0.25) + 1*($0.05) = $1.30?
$1.25 + $0.05 = $1.30 YES
A marathon is about 26 miles long. Which of these shows how to convert 26 miles to feet?
StartFraction 26 miles Over 1 EndFraction times StartFraction 1 foot Over 5,280 miles EndFraction
StartFraction 26 miles Over 1 EndFraction times StartFraction 1 mile Over 5,280 feet EndFraction
StartFraction 26 miles Over 1 EndFraction times StartFraction 5,280 feet Over 1 mile EndFraction
StartFraction 26 miles Over 1 EndFraction times StartFraction 5,280 miles Over 1 foot EndFraction
Answer:
26 miles * 5280 ft/ 1 mile
Step-by-step explanation:
We know there are 5280 ft in 1 mile
26 miles * 5280 ft/ 1 mile
Answer:
C
Step-by-step explanation:
Carly spends 9 hours each day working at her job. What percentage of her day does she spend at work?
Answer:
37.5%
Step-by-step explanation:
divide 9 by 24 and you get .375 abd then move 2 decimal places to the left to get a percentage
Answer:
Step-by-step explanation:
I know this is probably wrong but
I think she spends 37.8% of her day at work. 100% is the maximum for percentages. 100/24=about 4.2
9x4.2=37.8
Estimate the bending strength of beams by bending 10 beams untll they break and recording the force at which the beams broke.
The bending strength of beams by bending 10 beams untll they break will be estimated as-
The ten beams that were evaluated.The breaking force of each beam. It is quantitative.What is bending strength?Flexural strength is a material property that refers to the highest stress in a material well before yielding in a bending test. It is also recognized as bending strength or transverse rupture strength.
Some key features regarding the bending strength are-
When a specimen, typically a beam or rod, is bent, it is subjected to a variety of stresses throughout its depth. The stress will be at the maximum compressive stress on the inside of the bend, while it will be at its maximum tensile stress on the opposite side.The extreme fibres are the specimen's inner and outer edges. Tensile stress is what causes most materials to fail before compressive stress. This is caused by small surface defects of varying sizes that grow under tensile stress.Flexural strength is defined as the maximum tensile stress value under bending before the beam and rod fails.
To know more about Flexural strength, here
https://brainly.com/question/14434715
#SPJ4
Which relationships have the same constant of proportionality between
�
yy and
�
xx as the following graph?
Options A and C have the same constant of proportionality between y and x as the given graph.
What is graph?Rather than using values variable, theoretical physicists assess and illustrate claims using graphs. Typically, a graph point shows the relationship between several distinct objects. A graph is a particular kind of transportation system formed up of both groups and lines. The channels or borders should be fastened with glue. The numbers 1 through 4 and also the characters 2.5, certain individuals.
The graph shows a linear relationship between x and y, where as x increases, y also increases at a constant rate. The slope of the line is positive, which means that y increases as x increases.
To find relationships with the same constant of proportionality between y and x as the given graph, we need to look for equations that represent a straight line with a positive slope.
From the given options, two equations that represent a straight line with a positive slope are:
A) 6y = 8x (or y = 4/3 x)
C) y = 2x + 4
Therefore, options A and C have the same constant of proportionality between y and x as the given graph.
To know more about graphs visit:
brainly.com/question/11950136
#SPJ1
you roll a 6-sided die with faces numbered 1 through 6, and toss a coin what is the probability of rolling a 2 or getting heads
Answer:
2/3
Step-by-step explanation:
You have 6 possible outcomes. Getting 1 outcome is 1/6. You have 2 possible outcomes. Getting 1 outcome is 1/2.
Add 1/2 and 1/6 to get 2/3
Help?? The answer isn't -1026 btw i already guessed :(
Answer:
153
Step-by-step explanation:
12² - 3 [ 4(\(\frac{1}{4}\) - \(1^{8}\) ) ] ← evaluate the inside part of the bracket
= 144 - 3 [ 4(\(\frac{1}{4}\) - 1) ]
= 144 - 3 [ 1 - 4 ]
= 144 - 3(- 3)
= 144 + 9
= 153
(1 point each) Provide S-expressions for extracting the atom "jim" from each of the following: a) (he is dead jim) b) (captain (((jim) kirk )) ) c) (((((spock) asked) jim) if) he was all right) d) (after (looking at the (lizard man) ((((jim))) asked for warp 9)))) e) (append (star (trek)) (jim))
a) (first 'jim' '(he is dead jim)) S-expression
b) (first (first (first 'jim' '(captain (((jim) kirk))))))
c) (second (third (fourth (first 'jim' '((((spock) asked) jim) if) he was all right)))))
d) (third (second (fourth (fourth 'jim' '(after (looking at the (lizard man) ((((jim))) asked for warp 9)))))))
e) (third (second (append (star (trek)) '(jim))))
To extract the atom "jim" from each S-expression, we use the following approach:
a) In the expression '(he is dead jim)', we can directly extract the atom "jim" by using the 'first' function: (first 'jim' '(he is dead jim)).
b) In the expression '(captain (((jim) kirk)))', we need to nest the 'first' function three times to access "jim" in the nested structure: (first (first (first 'jim' '(captain (((jim) kirk)))))).
c) In the expression '((((spock) asked) jim) if) he was all right)', we use the 'first' function four times and then use the 'second' function to access "jim": (second (third (fourth (first 'jim' '((((spock) asked) jim) if) he was all right))))).
d) In the expression '(after (looking at the (lizard man) ((((jim))) asked for warp 9))))', we use the 'first' function four times and then use the 'third' and 'second' functions to access "jim": (third (second (fourth (fourth 'jim' '(after (looking at the (lizard man) ((((jim))) asked for warp 9))))))).
e) In the expression '(append (star (trek)) (jim))', we use the 'append' function to combine '(star (trek))' and '(jim)', and then use the 'third' and 'second' functions to access "jim": (third (second (append (star (trek)) '(jim)))).
Learn more about: S-expression
brainly.com/question/28027362
#SPJ11
starting at the point (0,0 how many ways are there to get to the point 7 4) if you have to pass through the point (1,1) and each step can only be in a positive direction. (i.e. to the right or up)?
Thus, there are two ways to get from (0,0) to (7,4) passing through (1,1) and only taking steps in a positive direction.
To get from (0,0) to (7,4) passing through (1,1) and only taking steps in a positive direction, we can break down the problem into smaller steps.
First, we need to get from (0,0) to (1,1). This can only be done with one step, either going right or up.
Then, we need to get from (1,1) to (7,4). We can do this by taking six steps to the right and three steps up. However, we need to make sure that we always pass through (1,1).
One way to ensure this is to take three steps to the right, then one step up to (2,2), and then three more steps to the right and two steps up to (7,4).
Therefore, there are two ways to get from (0,0) to (7,4) passing point through (1,1) and only taking steps in a positive direction:
1. One step to the right and then three steps to the right, one step up, three more steps to the right, and two steps up.
2. One step up and then two steps to the right, three steps to the right and one step up to (2,2), and then three more steps to the right and two steps up to (7,4).
Know more about the positive direction
https://brainly.com/question/11301920
#SPJ11
batco, a company that sells batteries, claims that 99.5% of their batteries are in working order. how many would you expect to buy, on average, to find one that does not work?
To find one machine that does not work, you expected to buy 200 machines on average.
What is division?One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.
A company named Batco sells batteries.
And Batco claims that 99.5% of their batteries are in working order.
That means, 100 - 99.5 = 0.5% of their machines have defect.
0.5 as a fraction of 100% is 0.005.
To find the one machine that does not work;
Divide 1 by fraction of machines not working,
1 / 0.005
= 200
Therefore, you need to buy 200 machines.
To learn more about the division;
https://brainly.com/question/13263114
#SPJ1
Find the area of the rectangle and the triangle independently. What is the ratio comparing the area of the triangle to the area of the rectangle? (Must be in Reduced Form)
Answer:
hello your question is incomplete attached below is the complete question
answer : 2
Step-by-step explanation:
Area of rectangle = \((\frac{b}{h}) (\frac{h}{2})\)
Area of triangle = \(\frac{1}{2}bh\)
therefore the ratio of the area of the triangle to the area of the rectangle
= \(\frac{\frac{1}{2} bh}{\frac{b}{2}*\frac{h}{2} }\) = 2
−5x + 8 ≤ −2x + 23 was solved by dividing each side of the inequality by −3 in the last step. Is there another way to solve this inequality so that you can avoid dividing by a negative number? Explain.
Answer:
x≥−5
Step-by-step explanation:
DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!
Answer:
\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)
\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)
So the equation of the circle is
\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)