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In order to find the center of the circunscribed circle, we can use the midpoint theorem because the center point is in the middle of any two vertices
that is, if we take points (9,23) and (8,16) the midpoint C is given as
[tex]C=(\frac{8+9}{2},\frac{16+23}{2})[/tex]which gives
[tex]C=(8.5,19.5)[/tex]So the center of the circle is the point (8.5,19.5)
On the other hand, the radius is equal to the distance from any vertex to the center. If we take the vertex (8,16), we get
[tex]r=\sqrt[]{(8.5-8)^2+(19.5-16)^2}[/tex]which gives
[tex]\begin{gathered} r=\sqrt[]{0.5^2+3.5^2} \\ r=\sqrt[]{0.25+12.25} \\ r=\sqrt[]{12.5} \\ r=3.5355 \end{gathered}[/tex]so, the radius measure 3.54 units.
Now, lets prove that the answer are correct. In order to do that, we can choose the other vertices and apply the same procedure as above.
So the vertices are (5,20) and (12,19). Again, the center is the midpoint between these points and is given as
[tex]\begin{gathered} C=(\frac{5+12}{2},\frac{20+19}{2}) \\ C=(\frac{17}{2},\frac{39}{2}) \\ C=(8.5,19.5) \end{gathered}[/tex]which is the same center as above.
Now, the distance from the center to vertec (5,20) is
[tex]\begin{gathered} r=\sqrt[]{(8.5-5)^2+(20-19.5)^2} \\ r=\sqrt[]{3.5^2+0.5^2} \\ r=\sqrt[]{12.25+0.25} \\ r=\sqrt[]{12.5} \\ r=3.5355 \end{gathered}[/tex]which is the same radius obtained above. Then, the answers are correct.
Related Questions
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95%confidence intervals for the population mean Interpret the results and compare the widths of the confidence intervals. Ifconvenient, use technology to construct the confidence intervals.A random sample of 40 home theater systems has a mean price of $126.00. Assume the population standard deviation is$18.60Construct a 90% confidence interval for the population mean.
Answers
Solution
Given the following below
[tex]\begin{gathered} \bar{x}=\text{ \$126}.00 \\ n=40 \\ \sigma=\text{ \$18.60} \\ At\text{ 90\% the critical z is }\pm1.645 \end{gathered}[/tex]To find the 90% confidence interval, the formula is
[tex]\bar{x}\pm z\frac{\sigma}{\sqrt[]{n}}[/tex]Substituting values into the formula above
[tex]126\pm1.645\frac{18.6}{\sqrt[]{40}}[/tex]Solve the above
[tex]\begin{gathered} 126+_{}1.645\frac{18.6}{\sqrt[]{40}}=130.84\text{ (two decimal places)} \\ 126-1.645\frac{18.6}{\sqrt[]{40}}=121.16\text{ (two decimal place)} \end{gathered}[/tex]At 90% confidence interval, the population mean will be between 121.16 and 130.84 (121.16, 130.84)
consider a right triangle with acute angle of measure 0 and cos 0 = 4/5 use Pythagorean identity to write an equation that can be used to find Sim 0 is ( + ( 4/5 = 1
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3. In television shows you may watch, scientists may patterns of data (growth of zombies, bacteria, etc). Below is a table that shows the number of zombies over a 4 day period. Days 0 1 2 3 4 # of zombies 2 8 32 128 512 *** a) What is the initial value? b) ** What is the growth/ decay factor?
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We are given a table that shows the number of zombies over a 4 day period.
a) What is the initial value?
The initial value means an initial population that is the number of zombies at day 0
From the table, we see that the initial population is 2
Initial value = 2
b) What is the growth/decay factor?
The growth/decay factor can be found by finding the ratio of the consecutive terms
r = 512/128 = 4
r = 128/32 = 4
r = 32/8 = 4
r = 8/2 = 4
As you can see, we have got the same ratio.
Since the ratio is greater than 1 then it is a growth factor.
If it was less than 1 then it would have been a decay factor.
Therefore, the growth factor is 4
Initial value = 2
Growth factor = 4
Given the following frequency table of values, is the mean, median, or mode likely to be the best measure of the center for the data set?ValueFrequency271280290300310320330340350360370380391402411425432442453Select the correct answer below:ModeMeanMedian
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The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
On the given dataset, if we ignore the outlier of the dataset, all those measures are going to be similar, but since we have a high frequency on the middle of our dataset and the presence of an outlier value, the most likely to describe the center of the dataset is the mode.
help me with this question please
Answers
Answer: 56
To solve this problem, we will use the formula for Combination which goes by
[tex]_{}C(n,r)=^nC_r=_nC_r=\frac{n!}{r!(n-r)!}[/tex]From the problem, we know that:
n = 8
r = 3
Since there are a total of 8 different movie soundtracks and we only need 3.
Substituting it on the formula,
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex][tex]C(8,3)=\frac{8!}{3!(8-3)!}[/tex][tex]C(8,3)=56[/tex]Therefore, there are 56 possible selections of movie soundtracks at the music store.
Quadrilateral EFGH has the given measurements. EF = 8 units FG = 15 units GH = 8 units EH = 15 units FH = 17 units EG = 17 units What conclusion can be made from the given information? A. The quadrilateral is both a parallelogram and a rectangle. B. The quadrilateral is a parallelogram, but not a rectangle. C. The quadrilateral is a rectangle, but not a parallelogram. D. The quadrilateral is neither a parallelogram nor a rectangle.
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A conclusion which can be made from the given information about quadrilateral EFGH is that: A. the quadrilateral is both a parallelogram and a rectangle.
What is a quadrilateral?A quadrilateral can be defined as a type of polygon that has four (4) sides, four (4) vertices, four (4) edges and four (4) angles.
The types of quadrilateral.In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapeziumIn this scenario, we can reasonably infer and logically deduce that quadrilateral EFGH is both a parallelogram and a rectangle because the length of its diagonal are equal and it has adjacent sides of equal of length.
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Which of the following are solutions to the equation below?
Check all that apply.
9x – 64 = 0
A. 8
B.
_ c.
C D.
3
F.
ო/დ
I
დო
3
J E. -8
დო
3
8
Answers
Answer:
C -8/3
F 8/3
Step-by-step explanation:
9x² - 64 = 0
==> 9x² = 64
==> x² = 64/9
x = ±√(64/9) = ±√64/√9 = ±8/3
write the word sentence as an equationa number w divided by 5 equals 6
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a number : w
A number w divided by 5: w/5
equals (=) 6
[tex]\frac{w}{5}=6[/tex]you are 37 years old and have accumulated $150,000 in your savings account. you intend to add a fixed amount each month for twenty years. for the first five (5) years you add $100 at the end of each month. then $ 200 at the end of the month for the remaining time. given that the account pays an interest rate of 6% per year compounded monthly, how much money will you have at age 58 in your savings account?
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At age 58, the investor will have (Future Value) $571,816.64 in their savings account after accumulating $150,000 and then adding $100 monthly for five years and $200 monthly for fifteen years.
How is the future value at age 58 computed?The future value at age 58 can be computed in two tranches.
The first step is to compute the future value using the present value of the accumulated funds in addition to the periodic monthly investments.
The second step computes the future value using the present value of the funds after 5 years in addition to the periodic monthly savings.
Future Value at the end of the first 5 years:N (# of periods) = 60 months (5 x 12)
I/Y (Interest per year) = 6%
PV (Present Value) = $150,000
PMT (Periodic Payment) = $100
FV = $209,304.53
Sum of all periodic payments = $6,000 (60 x $100)
Total Interest = $53,304.53
Future Value at the end of the remaining years:N (# of periods) = 180 months (12 x 15 years)
I/Y (Interest per year) = 6%
PV (Present Value) = $209,304.53
PMT (Periodic Payment) = $200
Results:
Future Value (FV) = $571,816.64
Sum of all periodic payments = $36,000 ($200 x 180 months)
Total Interest = $326,512.11
Thus, you will have $571,816.64 as the future value in your savings account when you turn 58.
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Given: BC = EC, CA = CD Prove: BA= DE
PLEASE HELP ASP!
Answers
Answer:
hope it helps
Step-by-step explanation:
The scatterplot shows the number of cars and trucks sold by 10 differentemployees at a car and truck dealership during a month.How many employees sold more trucks than cars?
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Let's us tabulate the data that is on the scatterplot.
As you can see in the fourth column, "Sold More Trucks than Cars?", some rows say "Yes" and some say "No".
Let's take a look at Employee No.1. Employee No.1 sold 4 trucks and sold 2 cars. Therefore, employee no.1 was able to sell more trucks than cars and thus, the answer to the fourth column is "Yes."
The same is done for all the employees.
In the end, there are 6 employees who were able to sell more trucks than cars.
Please help me find what X equals for question 3.
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The value of the missing variable x in the given triangle is; x = 15
What is the missing angle?
We know that sum of angles on a straight line is 180 degrees. That means the angle on the horizontal line of (9x + 16)° inside the triangle will be;
180 - (9x + 16)°
Now, we know that sum of angles in a triangle is 180 degrees. Thus;
180 - (9x + 16)° + 5x - 14 = 90
180 - 4x - 30 = 90
150 - 4x = 90
150 - 90 = 4x
60 = 4x
x = 60/4
x = 15
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please help me out thanks
Answers
According to the solving the matrix will be BF = [tex]\left[\begin{array}{ccc}4&0&-3\\15&9&6\end{array}\right][/tex]
What is the matrix?A matrix is a rectangular array as well as table of characters, numbers, or expressions that is set up in rows and columns to represent a mathematical object or a characteristic of one. As an illustration, consider a matrix containing two rows as well as three columns..
What does matrix actually mean?In the field of optics, matrices are employed to model refraction and reflection. Quantum mechanics, electrical circuits, and resistor conversion all benefit from the usage of matrices. In electric circuits, matrices are utilized to solve equations relating to the AC network.
According to the given data:B = [tex]\left[\begin{array}{ccc}2&-1&2\\3&-1&-2\end{array}\right][/tex]
F = [tex]\left[\begin{array}{ccc}3&1&1\\-2&-2&1\\-2&-2&-2\end{array}\right][/tex]
Now solving for BF:
B = [tex]\left[\begin{array}{ccc}2&-1&2\\3&-1&-2\end{array}\right][/tex] x F = [tex]\left[\begin{array}{ccc}3&1&1\\-2&-2&1\\-2&-2&-2\end{array}\right][/tex]
BF = [tex]\left[\begin{array}{ccc}6+2-4&2+2-4&2-1-4\\9+2+4&3+2+4&3-1+4\end{array}\right][/tex]
BF = [tex]\left[\begin{array}{ccc}4&0&-3\\15&9&6\end{array}\right][/tex]
According to the solving the matrix will be BF = [tex]\left[\begin{array}{ccc}4&0&-3\\15&9&6\end{array}\right][/tex].
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if 2 blams equal 15 droms and 5 droms equals 28 klegs, how many klegs are in a blam?
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2 blams ----------------- 15 droms
5 droms ----------------- 28 klegs
1 blam ------------------ ? klegs
5 droms ------------------- 28 klegs
15 droms -------------------- x
x = (15 x 28) / 5
x = 84 klegs
2 blams ------------------------- 84 klegs
1 blam --------------------------- ? klegs
x = (1 x 84)/2
x = 42 klegs
There are 42 klegs in 1 blam
Hey, I am looking for a answer to this, I need a simple answer! It is for 25 points! Please and thank you, enjoy your day!
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what is i^30?A. -iB. -1c. 1D.i
Answers
Answer
Explanation
Given:
[tex]i^{30}[/tex]we can rewrite the expression as follows:
[tex][/tex]Step 2: In the question above, find (using the method of your choice—formula, or graphing calculator function, or Excel, or app) the value of the test statistic t, to two places after the decimal point.
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From the question given,
The formula to find the test statistics mean is given below as,
[tex]t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]Where,
[tex]\begin{gathered} \bar{x}\text{ is the population mean} \\ \mu\text{ is the sample mean} \\ \sigma\text{ is the standard deviation } \\ n\text{ is the }sample\text{ size} \end{gathered}[/tex]Given the values of the above below,
[tex]\begin{gathered} \bar{x}=2.27\text{ mins} \\ \mu=2.98\text{ mins} \\ \sigma=0.98\text{ mins} \\ n=20 \end{gathered}[/tex]Substituting the values into the formula of test statistics t above,
[tex]\begin{gathered} t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}} \\ t=\frac{2.27-2.98}{\frac{0.98}{\sqrt[]{20}}}=\frac{-0.71}{\frac{0.98}{4.472}}=-\frac{0.71}{0.219}=-3.242 \\ t=-3.24\text{ (two decimal places)} \end{gathered}[/tex]Hence, the test statistics, t = -3.24 ( two decimal places)
what is the value of (mn)(8)? m(8)=15 n(8)=10
A. 25
B. 150
C. 88
D. 1,510
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Answer: I believe the answer would be B
Step-by-step explanation: Multiply m(8) and n(8) together to get (mn)(8) and you would get 150.
dilate triangle LMN by a scale factor of four using the origin as the center of dilation label the image triangle LMN and give the coordinates for each of the vertices
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Let's begin by listing out the information given to us:
3 What is the length of the missing leg? 15 m I meters
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Answer
The length of the missing leg = 12 m
Explanation
The triangle presented is a right angled triangle because one of its angles is equal to 90 degrees.
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
Hypotenuse side = 15 m
a = 9 m
b = d = ?
a² + b² = (hyp)²
9² + d² = (15)²
81 + d² = 225
d² = 225 - 81
d² = 144
d = √144
d = 12 m
Hope this Helps!!!
Answer:
We'd use the pythagorean theorem to solve for the other leg's length. As the image suggests, we'd use the theorem,
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
If one leg is 9 , that's our a value.
If the hypotenuse is 15 , that's our c value.
Now we just have to find the b value.
Plugging in the variables,
[tex] {9}^{2} + {b}^{2} = {15}^{2} [/tex]
[tex] {9}^{2} = 81 \\ {15}^{2} = 225 \\ 81 + {b}^{2} = 225[/tex]
Subtract 81 from both sides.
[tex] {b}^{2} = 144[/tex]
Square root both sides.
[tex] \sqrt{ {b}^{2} } = b \: and \: \sqrt{144 = 12 } [/tex]
so b = 12
Multiply.Simplify your answer as much as possible. 3v5 .6y.2y4v4
Answers
Solution
[tex]3v^5(6y)2y^4v^4[/tex]For this case we can do the following:
[tex](3\cdot6)\cdot(v^{5+4})\cdot(y^{1+4})=18v^9y^5[/tex]And then the solution for this case would be:
18v^9 y^5
Drag and drop the answers into the boxes to correctly complete the statement.
A sequence of transformations that maps ABC to A'B'C' is a ______ followed by a _______
reflection across the x-axis
rotation of 180 degrees about the origin
translation 2 units right
rotation of 90 degrees counterclockwise about the origin
Answers
A sequence of transformations that maps ABC to A'B'C' is a Rotation of 90° counterclockwise about the origin followed by a Translation of 2 units right.
This is further explained below.
What is Translation?Generally, The purpose of translation is to convey the meaning of a text written in one language into another language using texts written in those respective languages.
In conclusion, A rotation of 90 degrees anticlockwise around the origin, followed by a translation of 2 units right, is the sequence of transformations that maps ABC to A'B'C'.
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This net represents an unfolded box. 4 in. 4x5=7 WXI- 2 sov 6 in. n 1 yo 10 in. sa 14 Sau What is the total surface area, in square inches, of this box?
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The total surface area will be given by:
[tex]A=2A1+2A2+2A3[/tex]Where:
[tex]\begin{gathered} A1=40in^2 \\ A2=24in^2 \\ A3=6\cdot4=60in^2 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} A=2\left(40\right)+2\left(24\right)+2\left(60\right) \\ A=80+48+120 \\ A=248in^2 \end{gathered}[/tex]Answer:
248 in²
3) A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles. What is the actual area of the park? Show how you know. (From Unit 1, Lesson 12)
Answers
Given:
Length of the park, l=4 inches
Width of the park, w=6 inches.
Here, 1 inch is equal to the 30 miles.
To find the actual area of the park:
Area of the park is, A=lw
That is,
[tex]\begin{gathered} A=4\times6 \\ =24\text{ inches} \end{gathered}[/tex]In miles,
[tex]\begin{gathered} A=24\times30 \\ =720\text{ miles} \end{gathered}[/tex]Hence, the area of the park in miles is 720 miles.
Marcia bought a dozen roses for $16.38 (including tax). If tax was 5%, what was the cost of the roses before tax?
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Tax amount = 5% of $16.38
[tex]\begin{gathered} =\frac{5}{100}\times16.38=0.819\approx0.82 \\ \text{The actual cost of the roses before tax = 16.38-0.82= \$15.56} \end{gathered}[/tex]What’s the correct answer answer asap for brainlist
Answers
Answer:
I would say B, because the entire purpose and main theme of The Interlopers is to show the futility and uselessness of feuds and arguments, and that sometimes its best to just live and let live, just to keep it short.
i) Hence solve cosec 3y ÷ cot 3y + tan 3y = 0.5 for 0
[tex] \leqslant y \leqslant \pi \: radians \: giving \: your \: your \: am \\ answer \: in \: terms \: of \: \pi[/tex]
Answers
The value of y is π/9 or 7π/9 for the range 0 ≤ y ≤ π.
cosec 3y /( cot 3y + tan 3y) = 0.5
Trigonometry formula is:
cosec Ф = 1/ sin Ф
cot Ф = cos Ф/ sinФ
tan Ф = sinФ/ cos Ф
[tex]\frac{\frac{1}{sin 3y} }{\frac{cos 3y}{sin 3y} +\frac{sin 3y}{cos 3y} }[/tex] = 0.5
[tex]\frac{\frac{1}{sin 3y} }{\frac{cos 3y^{2} + sin 3y^{2} }{sin 3y cos 3y} }[/tex] = 0.5
sin² 3y + cos ² 3y = 1
1/ sin 3y × sin 3y cos 3y = 0.5
cos 3y = 0.5 = 1/2
cos π/ 3 = 1/2
For 0≤ y ≤π
0 ≤3y ≤ 3π
So 3y = 2kπ + π/3 , k = 0, 1
y = π/ 9 or 7π/ 9
Therefore the value of y is π/9 and 7π/ 9 for the given range.
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The builder of a parking garage wants to build a ramp at an angle of 16 degrees covers a horizontal span of 55 feet. How long will the actual ramp be? Round yoursolution to four decimal places.
Answers
Let's draw the ramp to better understand the problem:
For us to be able to determine how long the ramp will be, we will be using the Cosine Function.
We get,
[tex]\text{ Cosine }\Theta\text{ = }\frac{\text{ b}}{\text{c}}[/tex][tex]Cosine(16^{\circ})\text{ = }\frac{55}{x}[/tex][tex]x\text{ = }\frac{55}{Cosine(16^{\circ})\text{ }}[/tex][tex]\text{ x = }\frac{55}{0.9612616959}[/tex][tex]x=57.216468974668940618504468175387[/tex][tex]\text{ x }\approx\text{ 57.2165 feet}[/tex]Therefore, the answer is 57.2165 feet.
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 1.6 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N([],[])b. What is the median recovery time?daysc. What is the Z-score for a patient that took 5.7 days to recover? []d. What is the probability of spending more than 4.5 days in recovery? []e. What is the probability of spending between 3.5 and 4.3 days in recovery? []f. The 85th percentile for recovery times is []
Answers
Part B
What is the median recovery time?
Remember that
For a normal distribution, mean = median = mode
so
The median is 4 days
Part C
What is the Z-score for a patient that took 5.7 days to recover?
Remember that
z =(x - μ)/σ
where
μ=4 days
σ=1.6 days
X=5.7 days
substitute
z=(5.7-4)/1.6
z=1.0625
Part D
What is the probability of spending more than 4.5 days in recovery?
z =(x - μ)/σ
μ=4 days
σ=1.6 days
x=4.5 days
Find out z
z=(4.5-4)/1.6
z=0.3125
using a z-score table values
P(X>4.5)=0.3773
Part E
What is the probability of spending between 3.5 and 4.3 days in recovery?
For x=3.5 -------> z=(3.5-4)/1.6=-0.3125
For x=4.3 -----> z=(4.3-4)/1.6=0.1875
using a z-score table values
P(3.5 < X < 4.3)=0.1970
Part F
Remember that
If your score is in the 85th percentile, it means that 85% of the scores are below your score and 15% are above your score
using a z-score table values
the value of Z=1.036
Find out the value of x
1.036=(x-4)/1.6
solve for x
x=5.6576 days
what is 126945 rounded to the nearest hundred thousand
Answers
To the nearest hundred thousand, we must first determine the number in the hundred thousand position. This is the digit 1. Now consider the number next to it. This is 2. Since two is not up to 5, we would round off all other nuber to zero.
Hence to the nearest hundred thousand, 126,945 is 100,000