Answer:
A. Pr(8) = 1/10
B. Pr(odd) = 1/2
C. Pr(even) = 1/2
D. Pr(less than 6) = 1/2
E. Pr(prime) = 2/5
F. Pr(3 or 8) = 1 / 5
G. Pr(8, 9 or 10) = 3/10
H. Pr(greater than 9) = P(10) = 1/10
Step-by-step explanation:
We assume a FAIR 10-faced die, meaning there is an equal probability of throwing any one of the ten numbers.
With 10 possible outcomes each with equal probability, the probability of throwing any number is 1/10.
(It is preferable to work with fractions in probability because fractions are exact numbers, while decimals can often be rounded, or truncated).
A. Pr(8) means probability of throwing an 8, therefore Pr(8) = 1/10
B. Pr(odd) there are 5 odd number from 1 to 10, so Pr(odd) = 5/10 = 1/2
C. Pr(even) there are 5 even number from 1 to 10, so Pr(even) = 5/10 = 1/2
D. Pr(less than 6) there are 5 numbers less than 6 (between1 to 10),
so Pr(less than 6) = 5/10 = 1/2
E. Pr(prime) (remember that 1 is not prime)
A prime number is an integer not divisible by any number except one and itself.
Between 1 to 10, the four prime numbers are 2,3,5,7
therefore Pr(prime) = 4/10 = 2/5
F. Pr(3 or 8)
(3 or 8) make 2 successful outcomes out of 10, so Pr(3 or 8) = 2/10 = 1 / 5
G. Pr(8, 9 or 10)
similarly, (8,9 or 10) make three successful possible outcomes out of 10, so
P(8,9 or 10) = 3/10
H. Pr(greater than 9)
there is only one successful outcome, namely "10" out of 10 possible outcomes. So
P(greater than 9) = P(10) = 1/10
1. please explain what’s a “die” all I know was “dice” but dice is 6 sided yea?
A die is singular for dice, which can take up any number of faces. With a 10-faced solid, we can make a 10-faced die numbered 1 to 10.
2. and please explain the answer... I’m international student so I still need some explanation for the questions and answers thank you
See solutions above.
Answer:
Remember that standard probabilities are defined as the ratio between the number of favorable cases, and the total number of possible events.
In this case, we have a 10-sided die, which means its faces are numbered from 1 to 10, which gives us 10 total number of possible events. In other words, the denominator of the ratio is going to be 10.
Now we're able to find each probability.
(A) Probability of getting an 8:[tex]P_{8} =\frac{1}{10}=0.10[/tex]
The numerator is 1 because there's only one number 8 in the die, that means the number of favorable cases is 1, and, as we said before, the total number of possible events is 10.
(B) Probability of getting an odd number:[tex]P_{odd} =\frac{5}{10}=0.5[/tex]
The numerator is 5 because there are 5 odd numbers from 1 to 10. In other words, there are 5 favorable cases to this probability.
(C) Probability of getting an even number:[tex]P_{even}=\frac{5}{10}=0.5[/tex]
There are 5 even numbers from 1 to 10, that's why we had the same probability.
(D) Probability of getting a number less than 6:We know that there are only 5 numbers less than 6 for this die.
[tex]P_{<6}=\frac{5}{10}=0.5[/tex]
(E) Probability of getting a prime number:A prime number is such that it can be divided only by itself and the unit. So, there are four prime numbers from 1 to 10, which are 2, 3, 5, 7.
[tex]P_{prime}=\frac{4}{10}=0.4[/tex]
(F) Probability of getting 3 or 8:When we are going to find the probability of an event "or" another, we must sum those favorable cases.
[tex]P_{3 \ or \ 8} =\frac{1+1}{10}=\frac{2}{10}=0.2[/tex]
(G) Probability of getting 8, 9, or 10:In this case, we need to some all three favorable cases. The die has only one 8, one 9 and one 10. So, the probability is
[tex]P_{8,9,10}=\frac{1+1+1}{10}=\frac{3}{10} =0.3[/tex]
(H) Probability of getting a number greater than 9:We know that there's only one number greater than 10 on such die.
[tex]P_{>10}=\frac{1}{10}=0.1[/tex]
Lastly, "die" refers to this special 10-sided dice. In other problems, you can find "a die" with more faces even. But, in general, "die" refers to a dice.
how to do this question plz
Answer:
[tex]=3/4[/tex]
Step-by-step explanation:
[tex]\frac{4\sqrt{18}}{16\sqrt{2}}[/tex]
First, simplify the fraction:
[tex]=\frac{\sqrt{18}}{4\sqrt2}[/tex]
Now, simplify the radical in the numerator (the radical in the denominator cannot be simplified:
[tex]\sqrt{18}=\sqrt{9\cdot2}=\sqrt{9}\cdot\sqrt{2}=3\sqrt{2}[/tex]
Substitute:
[tex]=\frac{3\sqrt{2}}{4\sqrt{2}}[/tex]
The radicals cancel:
[tex]=3/4[/tex]
in which table does y vary inversely with x?
Answer:
Table B
Step-by-step explanation:
Note that for y to vary inversely as x, an increase in x will cause a decrease in y. Therefore, by careful observation of tables A, B, C, and D, we would notice the following:
In table C:
As x increases from 1 to 2 to 3, y also increases from 26 to 52 to 78. Which means that an increase in x causes an increase in y. This is not an inverse variation.
In table D:
As x increases from 1 to 2 to 3, y also increases from -7 to -1 to 6. Which means that an increase in x causes an increase in y. This is also not an inverse variation.
We are left with options A and B
If y varies inversely as x, the following relationship must hold:
[tex]y \alpha \frac{1}{x}\\y = \frac{k}{x}[/tex]
Where k is a constant of proportionality
considering option B:
When x = 1, y = 36
36 = k/1
k = 36 * 1
k = 36
when x = 2, y = 36/2
y = 18
when x = 3, y = 36/3
y = 12
These tally with all that is indicated in the table. Option B is an inverse variation
Which geometric model using algebra tiles represents the factorization of x2 – 5x + 6? An algebra tile configuration. 4 tiles are in the Factor 1 spot: 1 is labeled + x and 3 are labeled negative. 3 tiles are in the Factor 2 spot: 1 is labeled + x and 2 are labeled negative. 12 tiles are in the Product spot: 1 is labeled + x squared, 5 are labeled negative x, and 6 are labeled +. An algebra tile configuration. 3 tiles are in the Factor 1 spot: 1 is labeled + x and 2 are labeled negative. 3 tiles are in the Factor 2 spot: 1 is labeled + x and 2 are labeled negative. 11 tiles are in the Product spot: 1 is labeled + x squared, 4 are labeled negative x, and 6 are labeled +. An algebra tile configuration. 3 tiles are in the Factor 1 spot: 1 is labeled + x and 2 are labeled negative. 3 tiles are in the Factor 2 spot: 1 is labeled + x and 2 are labeled negative. 11 tiles are in the Product spot: 1 is labeled + x squared, 4 are labeled negative x, and 6 are labeled +.
Answer:
Step-by-step explanation:
The factorization of x² - 5x + 6 can be determined thinking critically about two numbers, that if we multiply those two numbers together it will result into a value of +6 and if we add those numbers together , we will have -5
The numbers are -3 and -2 ; if we multiply -3 and -2 , we have = 6
If we add -3 + (-2) ; we have,
-3-2 = -5
Now the factorization of
x² - 5x + 6 = 0 is as follows.
x² - 3x - 2x + 6
By factorization,
x(x - 3) - 2 (x - 3) = 0
(x - 2) or (x-3) = 0
Now, using An algebra tile configuration. The diagrammatic expression showing how an algebraic tile configuration should looks like can be found in the attached image below.
Hint:
Let represent ,
1 = x² tile
-5 = - x tiles
6 = 1 tiles
Answer:
The answer is the first tile choice.
Step-by-step explanation:
The slope-intercept form of the equation of a line that passes through point (-3, 8) is y=-2/3x+6. What is the point-slope form of the
equation for this line?
Answer:
b. y - 8 = -2/3(x + 3)
Step-by-step explanation:
Well point-slope form takes one point in this case (-3,8) and puts it into the equation.
So this is point slope form,
[tex]y -y_{1} = m(x - x_{1} )[/tex]
The 2 negatives in the -y and -x means you have to change the number to a negative to a positive to a negative.
We plug in (-3,8) to the equation.
y - 8 = m(x + 3)
Well we change the -3 to a 3 because of the negative.
So with the given slope -2/3 we plug that in for m.
y - 8 = -2/3(x + 3)
Thus,
answer choice b is correct.
Hope this helps :)
Consider the right triangle. Determine whether each equation is correct. Select yes or no for each question.
Step-by-step explanation:
Given
Opp=8
Adj=6
Hyp=10
Answer
1)Sin<A=Opp/Hyp
8/10=4/5... Yes
2)Cos<A=Opp/Adj
8/6=4/3... No
Given
Opp=6
Adj= 8
Hyp= 10
Answer
1)Sin<B= Opp/Hyp
6/10=3/5... No
2)Cos<B= Opp/Adj
6/8=3/4... No
Hope this helps ❤❤❤
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that
Answer:
The triangle has two sides that are equivalent and the angle where the two meet are also equivalent.
In other words, two sides and the angle between them are congruent.
Hope this helps, if it does please give me brainliest, it will help me a lot :)
Have a good day
Answer:
A on edge
Step-by-step explanation:
PLEASE HELP FAST
answers:
A.) RT and plane RSU
B.) RS and plane UR
C.) RS and plane RSU
D.) SR and plane UT
Answer:
RS and plane RSU
Step-by-step explanation:
I think not to sure
5.
Evaluate x(-y + z) for x = 3, y = 3, and z = 1.
10
-8
12
-6
Answer:
-6
Step-by-step explanation:
x(-y + z)
Let x= 3 y =3 and z =1
3( -3+1)
Parentheses first
3 ( -2)
Then multiply
-6
Answer:
Hello! The answer to your question is -6
Steps will be provided below.
Step-by-step explanation:
This is how to solve your question:
Question:
Evaluate x(-y + z) for x = 3, y = 3, and z = 1.
Answer and how to solve:
The answer is -6 because....
If you do the steps correctly it will be...
Do the Parentheses first.
3x-(2)
Now you just multiply and you will get your answer.
Which will give you -6
SO THE ANSWER TO YOUR QUESTION IS -6
⭐️Hope this helps! :) ⭐️
Have a wonderful day! :D
Ten turns of a wire are helically wrapped around a cylindrical tube with outside circumference 4 inches and length 9 inches. The ends of the wire coincide with ends of the same cylindrical element. Find the length of the wire. (a) 41 inches (b)36 inches (c) 40 inches (d) 90 inches
Answer:
b) 36 inches
Step-by-step explanation:
Length of the wire = Outside circumference of the cylindrical tube * length of the cylinder
= 4 * 9
= 36 inches
Length of the wire will be same to the surface area of the cylinder
Surface area of cylinder = circumference * length
Suppose the probability that a randomly selected man, aged 55 - 59, will die of cancer during the course of the year is StartFraction 300 Over 100 comma 000 EndFraction . How would you find the probability that a man in this age category does NOT die of cancer during the course of the year?
Answer:
The probability that a man in this age category does NOT die of cancer during the course of the year is 0.997.
Step-by-step explanation:
Suppose the probability of an event occurring is [tex]P_{i}[/tex].
The probability of the given event not taking place is known as the complement of that event.
The probability of the complement of the given event will be,
[tex]1 - P_{i}[/tex]
In this case an events X is defined as a man, aged 55 - 59, will die of cancer during the course of the year.
The probability of the random variable X is:
[tex]P (X) = \frac{300}{100000}=0.003[/tex]
Then the event of a man in this age category not dying of cancer during the course of the year will be complement of event X, denoted by X'.
The probability of the complement of event X will be:
[tex]P(X')=1-P(X)[/tex]
[tex]=1-0.003\\=0.997[/tex]
Thus, the probability that a man in this age category does NOT die of cancer during the course of the year is 0.997.
In how many ways can 6 commercials be played in 6-time slots in a 1-hour program?
Answer:
6
Step-by-step explanation:
I think the answer is 6
Be nice and answer my question
Answer:
look below
Step-by-step explanation:
hi
Any answers on this?
Answer:
40
Step-by-step explanation:
We're given an angle that forms a linear pair, and we're given an isosceles triangle. The angle to the right of 110 is 70, since they have to add up to 180. Since this is an isosceles triangle (denoted by the two dashes), we know that the other base angle has to be 70. 70 + 70 = 140; all angles add up to 180 so 180 - 140 = 40 degrees.
Answer:
40 degrees
Step-by-step explanation:
Since this is an isosceles triangle the 2 bottom angles are congruent
The bottom angles will be 70 degrees bc the exterior angle is 110 and 180-110=70
Because a triangle adds up to 180 degrees you need to use the equation 70 + 70 + x = 180 and you should get x = 40 degrees
A local high school has 1250 students in grades 9 through 12. Twenty-eight percent of the students in the school are in the ninth grade. One-half of the ninth-grade students ride the bus to school. How many ninth-grade students ride the bus?
Answer:175
Step-by-step explanation:
1. Turn 28% into a decima: 0.28
2. Multiply 1250 by 0.28 to get the amount of ninth grade students:350
3. Half the amount of ninth grade students:175
Answer:
The answer is 175
Step-by-step explanation:
Because I read the problem carefully and identified that the explanation is way too long so I am gonna make this short and easy for you. I am correct, just Trust me :)
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1650 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week? Firstcar:gallons= Secondcar:gallons=
Answer:
First car: 30 gallons
Second car: 35 gallons
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
Total gas consumption was 65:
x+y=65
Where:
x = gallons consumed by the first car
y = gallons consumed by the second car
The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas, the two cars went a combined total of 1650 miles:
x 20+y 30 = 1650
The system is:
x+y=65 (1)
x 20+y 30 = 1650 (2)
Isolating y on (1)
y = 65-x
Replacing y= 65-x on (2):
x 20+(65-x)30 = 1650
20x +1,950-30x= 1650
20x-30x= 1650-1950
-10x= -300
x= -300/-10
x = 30 gallons
Back to (1)
y =65-x
y =65-30
y= 35 gallons
Feel free to ask for more if needed or if you did not understand something.
Which of the following shows the polynomial below written in descending order ?
Answer:
A. 4x¹¹ + x⁷ + 3x³ - 5x + 9
Step-by-step explanation:
order the exponents from largest to smallest. variables always come first; therefore, -5x before 9
1) In rectangle ABCD, AE is perpendicular on diagonal BD, BE=3DE and AC∩BD={O}.
1. DE/EO=?
2. If BD=8√2 inches, find out the lenght of AE
3. Calculate the measure of angle AOD.
2) In rectangle MNPQ, MA⊥NQ, A∈NQ, MA∩PQ={B}. If AN measures 12 inches, AQ=27 inches, calculate the lenght of MA and MB.
Please help me with these. Or at least with one of them.
Answer:
to be honest I'm not sure how to do
Real solutions please WILL GIVE BRAINLIEST
Answer:
the answer is A=2
Step-by-step explanation:
a real solution is a solution that uses real numbers. This equation has 2 real solutions.
Answer:
A. 2 real solutions
Step-by-step explanation:
One graph is a parabola and 1 graph is a straight line and they intersect twice.
Find side AC and round your answer to the nearest hundredth, help please.
Answer:
Step-by-step explanation:
Side AC is the side opposite the reference angle of 70 degrees while side BC is the side adjacent to the reference angle. AB is the hypotenuse since it is across from (or opposite) the right angle. The trig ratio that uses the sides opposite from and adjacent to the reference angle is the tangent. Setting up to solve for AC:
[tex]tan(70)=\frac{?}{3}[/tex] and
3tan(70) = ? so
? = 8.24
Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Round all answers using one decimal place.
Answer:
[tex]Side\ B = 6.0[/tex]
[tex]\alpha = 56.3[/tex]
[tex]\theta = 93.7[/tex]
Step-by-step explanation:
Given
Let the three sides be represented with A, B, C
Let the angles be represented with [tex]\alpha, \beta, \theta[/tex]
[See Attachment for Triangle]
[tex]A = 10cm[/tex]
[tex]C = 12cm[/tex]
[tex]\beta = 30[/tex]
What the question is to calculate the third length (Side B) and the other 2 angles ([tex]\alpha\ and\ \theta[/tex])
Solving for Side B;
When two angles of a triangle are known, the third side is calculated as thus;
[tex]B^2 = A^2 + C^2 - 2ABCos\beta[/tex]
Substitute: [tex]A = 10[/tex], [tex]C =12[/tex]; [tex]\beta = 30[/tex]
[tex]B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30[/tex]
[tex]B^2 = 100 + 144 - 240*0.86602540378[/tex]
[tex]B^2 = 100 + 144 - 207.846096907[/tex]
[tex]B^2 = 36.153903093[/tex]
Take Square root of both sides
[tex]\sqrt{B^2} = \sqrt{36.153903093}[/tex]
[tex]B = \sqrt{36.153903093}[/tex]
[tex]B = 6.0128115797[/tex]
[tex]B = 6.0[/tex] (Approximated)
Calculating Angle [tex]\alpha[/tex]
[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]
Substitute: [tex]A = 10[/tex], [tex]C =12[/tex]; [tex]B = 6[/tex]
[tex]10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha[/tex]
[tex]100 = 36 + 144 - 144 *Cos\alpha[/tex]
[tex]100 = 36 + 144 - 144 *Cos\alpha[/tex]
[tex]100 = 180 - 144 *Cos\alpha[/tex]
Subtract 180 from both sides
[tex]100 - 180 = 180 - 180 - 144 *Cos\alpha[/tex]
[tex]-80 = - 144 *Cos\alpha[/tex]
Divide both sides by -144
[tex]\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}[/tex]
[tex]\frac{-80}{-144} = Cos\alpha[/tex]
[tex]0.5555556 = Cos\alpha[/tex]
Take arccos of both sides
[tex]Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)[/tex]
[tex]Cos^{-1}(0.5555556) = \alpha[/tex]
[tex]56.25098078 = \alpha[/tex]
[tex]\alpha = 56.3[/tex] (Approximated)
Calculating [tex]\theta[/tex]
Sum of angles in a triangle = 180
Hence;
[tex]\alpha + \beta + \theta = 180[/tex]
[tex]30 + 56.3 + \theta = 180[/tex]
[tex]86.3 + \theta = 180[/tex]
Make [tex]\theta[/tex] the subject of formula
[tex]\theta = 180 - 86.3[/tex]
[tex]\theta = 93.7[/tex]
Find the eigenvalues and eigenvectors of A geometrically over the real numbers ℝ. (If an eigenvalue does not exist, enter DNE. If an eigenvector does not exist, enter DNE in any single blank.) A = 0 −1 1 0 (counterclockwise rotation of 90° about the origin)
Answer:
The eigen values obtained are not real and thus according to the notation in the question, the eigen values DNE in R
Step-by-step explanation:
Here, we are to find the eigen value and the eigen vector of matrix A over the real numbers R
Please kindly check attachment for complete solution and explanation
A movie theater sells up to 10 tickets at a time online. what is the domain of this graph?
Answer:
i will say c
Step-by-step explanation:
c
Answer:
B. Whole numbers from 0 to 10
Step-by-step explanation:
this is a dot graph, so only those dots, whole numbers of tickets, are valid input, that is, domain of the graph.
HALP !Find the next term of the series: -3 + -1 + 1 + ...
Answer:
3
Step-by-step explanation:
We are adding 2 each time
-3 +2 = -1
-1 +2 = 1
To get the next term add 2
1 +2 = 3
Answer: 3
Step-by-step explanation:
What the correct answer now
Answer:
11
Step-by-step explanation:
The Law of Cosines is useful when you have two sides of a triangle and the angle between.
v^2 = w^2 +u^2 -2wu·cos(V)
v^2 = 6^2 +16^2 -2·6·16·cos(27°)
v^2 = 292 -171.0733
v ≈ 10.9966
v ≈ 11
The ratio of Ed’s cars to Pete’s cars was 5:2 at first. After Ed gave 30 cars to Pete, they had an equal amount of cars each. How many cars did they have altogether?
Answer:
Step-by-step explanation:
The two have a total of 5+2 = 7 "ratio units" so have a total of 140 cars.
can you mark me as brainliest?
Please Answer ASAP! (NO EXPLANATION NEEDED!) <3
volume=l1*l2*l3
=8*15*20=2400cm^3
Volume = length x breadth x height = 20 x 15 x 8 = 2400 sq cm
For water to be a liquid, its temperature must be within 50 Kelvin of 323 Kelvin. Which equation can be used to determine the minimum and maximum temperatures between which water is a liquid? |323 – 50| = x |323 + 50| = x |x – 323| = 50 |x + 323| = 50
Answer:
Mark as BRAINLIEST plz
|x-323|<50: answer
Step-by-step explanation :
For water to be a liquid, the temperature must be within 50 Kelvin of 323 K.
So, the range of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323.
The equation that can be used to determine the maximum temperature at which water is a liquid can be given by : x < 323 + 50
The equation that can be used to determine the minimum temperature at which water is a liquid can be given by : x > 323 - 50
So the resultant equation can be written as :
|x-323|<50
The solution of inequality equation is | x - 323 | < 50
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the temperature of the water be = x Kelvin
Now , the equation will be
For water to be in the liquid state, the temperature must be within 50 kelvin (K) of 323 K
So , the value of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323
Substituting the values in the inequality equation , we get
For maximum temperature ,
x should be 50 more than 323 and
For minimum temperature ,
x should be 50 less than 323
So ,
The inequality relation is
x > 50 + 323 be equation (1)
x < 323 - 50 be equation (2)
So , the modulus function is expressed as
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
Therefore , the value is | x - 323 | < 50
Hence , The solution of inequality equation is | x - 323 | < 50
To learn more about inequality equations click :
https://brainly.com/question/11897796
#SPJ6
Find the value of x in the data given below if the mean is 2. The values are 2, 4, 1, 1, x, 3, 2
Answer:
[tex]\boxed{x=1}[/tex]
Step-by-step explanation:
[tex]mean=\frac{sum \: of \: terms}{number \: of \: terms}[/tex]
[tex]2=\frac{2+4+1+1+x+3+2}{7}[/tex]
[tex]2=\frac{13+x}{7}[/tex]
[tex]14=13+x[/tex]
[tex]x=1[/tex]
 Shelby baked 48 cookies with 6 scoops of flower. how many scoops of flour does Shelby need in order to bake 64 cookies? Solve using unit rates.
Answer:
8 scoops of flour
Step-by-step explanation:
It asks for you to solve using unit rates so we need to find out the rate of how much flour you need to bake a single cookie since the question is about how many scoops of flour Shelby needs to bake 64 cookies.
So first, do 6/48, which is 1/8.
It takes 1/8 scoop of flour to bake one cookie.
Unit rate: 1/8 scoop of flour per cookies.
Now, we can multiply 1/8 by 64 since 64 is the number of cookies Shelby needs and 1/8 is the amount of flour for one single cookies. 1/8 * 64 = 8.
Shelby needs 8 scoops of flour to bake 64 cookies
I need an answer asap. I really would like some help with this
Answer:
(x + 4)² + (y + 1)² = 4
Step-by-step explanation:
From the graph attached,
Extreme ends of the diameter of the circle,
(-4, 1) and (-4, -3)
Center of the circle = Midpoint of the diameter
Center = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
= [tex](\frac{-4-4}{2},\frac{1-3}{2})[/tex]
= (-4, -1)
Radius of the circle = Distance between the center and extreme end
= 2 units
Since standard equation of the circle is,
(x - h)² + (y - k)² = r²
where (h, k) is the center and 'r' is the radius of the circle
By substituting the values in the standard equation,
(x + 4)² + (y + 1)² = 2²
(x + 4)² + (y + 1)² = 4