Given the circumference of equation \(\bf{x^{2}+y^{2}-2x+4y-4=0}\), find the center and the radius.
Answers
We will convert the general equation to the ordinary form \left \(\bf{( x-h \right )^{2}+\left ( y-k \right )^{2}=r^{2}}\); For this we follow the following steps:
We rewrite the equation by ordering the x and y and we complete the perfect square trinomials:
\(\bf{x^{2}-2x+1+y^{2}+4y+4=4+1+4 }\)
Factor the perfect square trinomials:
\(\bf{(x-1)^{2}+(y+2)^{2}=9 }\\\bf{ \ \ \ \ \Rightarrow \ C(1,-2) y \ r=3 }\)
Related Questions
Posterior probabilities are _____.
a. simple probabilities
b. conditional probabilities
c. joint probabilities
d. marginal probabilities
Answers
The selling price of a $10,000 5-year bond will be less than $10,000 if the A. Coupon rate is less than the market interest rate B. Coupon rate is greater than the market interest rate C. Coupon rate is equal to the market interest rate D. Maturity date is less than 5 years
Answers
The correct answer is A. The selling price of a bond is affected by the coupon rate and the market interest rate.
If the coupon rate is less than the market interest rate, investors will not be interested in buying the bond because they can get a higher return elsewhere. This results in the selling price of the bond being less than its face value of $10,000.
The selling price of a $10,000 5-year bond will be less than $10,000 if the:
A. Coupon rate is less than the market interest rate
This is because when the coupon rate (the interest paid by the bond) is lower than the market interest rate, investors would prefer to invest in other options that offer a higher return. Therefore, to attract buyers, the bond's selling price would be discounted to compensate for the lower coupon rate.
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The length of a Train A is 480 m and it takes 2 minutes to cross a tunnel of length 1,320 m. The length of a Train B, which is slower than Train A, is 420 m. Both the trains start at the same time from the opposite directions. If the difference between their speeds is 18 km/h, find the time they take to cross each other. (Enter only the number)
Answers
Answer: 52.94
Step-by-step explanation:
Length of train A = 480m
Tunnel length = 1320m
Time taken to cross tunnel = 2 mins = 120sec
Length of train B = 420m
Train B is slower than train A
Difference between their speed = 18km/hr
18km/hr = (18×1000)/3600 = 5m/s
Speed of train A :
Speed = distance / time
Speed = 1320 / 120 = 11m/s
Therefore, speed of train B :
(11 - 5)m/s = 6m/s
Relative speed of the two trains is therefore;
(Speed of A + speed of B)
Note : they are moving in opposite direction
( 11 + 6)m/s = 17m/s
Therefore time taken to cross each other :
(Sum of the length of both trains / relative speed of the trains)
Time taken = (480m + 420m) / (17m/s)
Time taken = 900m / 17m/s
Time taken = 52.94s
(4pts)
Show all Work!!!!
1)
The sum of four consecutive integers is -18. What are the four integers?
(Use a let statement)
Answers
Answer:
-4.5
Step-by-step explanation:
this the work, -4.5-4.5-4.5-4.5
adam, benin, chiang, deshawn, esther, and fiona have internet accounts. some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. each of them has the same number of internet friends. in how many different ways can this happen?
Answers
(a) Therefore, the range of possible values for "x" is 1 to 5. (b) Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31. Therefore, there are 31 different ways this can happen
To find the number of different ways this can happen, we can consider the number of internet friends each person can have. Since each person has the same number of internet friends, let's denote that number as "x". We can then create equations based on the given information:
1. Some, but not all, of them are internet friends with each other: This means that at least two people are internet friends with each other, but not everyone is friends with each other. This implies that the minimum number of internet friends any person can have is 1, and the maximum number is 5 (since there are 6 people in total).
Therefore, the range of possible values for "x" is 1 to 5.
2. None of them has an internet friend outside this group: This means that each person's internet friends must be within this group of 6 people. So, the number of internet friends each person can have is limited to the remaining 5 people.
To find the number of different ways this can happen, we need to sum up the possible values of "x" and calculate the corresponding combinations. For "x = 1", we choose 1 person out of 5 remaining people, giving us C(5, 1) = 5. For "x = 2", we choose 2 people out of 5 remaining people, giving us C(5, 2) = 10.
Similarly, for "x = 3", "x = 4", and "x = 5", we have C(5, 3) = 10, C(5, 4) = 5, and C(5, 5) = 1 respectively. Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.
Therefore, there are 31 different ways this can happen
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Someone help me with this pls
Answers
Answer:
C
Step-by-step explanation:
\((a^{-2}*8^{7})^2 = a^{-2*2}*8^{7*2} = a^{-4}*8^{14}\)
the normal distribution is an example of select one: a. a smooth curve showing data from a population. b. a bar graph showing data from a population. c. a histogram showing data from a sample. d. a polygon showing data from a sample.
Answers
The correct answer is histogram showing data from a sample
What is meant by Normal distribution?Normal distribution: Normal distribution is also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, the normal distribution appears as a "bell curve".
it is asked about the normal distribution is an example of
the correct option is c
i.e., Answer is histogram showing data from a sample
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the mean wait time for a drive-through chain is 193.2 seconds with a standard deviation of 29.5 seconds. what is the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds? (write answer round to whole number like 91%).
Answers
The probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.
To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means is approximately normal for large sample sizes.
First, we need to calculate the standard error of the mean (SEM) using the formula
SEM = standard deviation / sqrt(sample size)
SEM = 29.5 / sqrt(45) = 4.4
Next, we can standardize the sample mean using the formula
z = (x - μ) / SEM
where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.
For the lower limit, we have
z = (185.7 - 193.2) / 4.4 = -1.70
For the upper limit, we have
z = (206.5 - 193.2) / 4.4 = 3.02
We can use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.
The probability of z being between -1.70 and 3.02 is approximately 0.9429 or 94%. Therefore, the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.
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WORTH 100 POINTS. WILL GIVE BRIANLIEST. Six contestants on a reality TV show were stunned to find their lowest scoring colleague was
“murdered”.
You must figure out the crime before the murderer strikes again. The question is Whodunnit?
And how… The Player, Last Known Whereabouts and Method that are left unaccounted for --
is the solution.
• Use this sheet to show your work (2nd page) and solve the mystery (1st page).
o You will need to submit these two pages for credit as your Unit 5 Part 2.
• Use the “Clues” PDF to find the clues to solve the mystery.
SHOW YOUR WORK ON WHY OR WHY. WILL GIVE BRAINLIEST.
Answers
Answer:
8 The victim wasn't mauled by a cougar - Clue 1
20 Dr. Alpha was in the kitchen cooking - Clue 2
-12 The victim had no venomous bites - Clue 3
72 Miss Beta was at the movie theater - Clue 4
14 The victim wasn't electrocuted - Clue 5
14 Coach Omega was sleeping at the atrium - Clue 6
-8 The murder did not include a firearm - Clue 7
-12 Mrs.Gamma was doing yoga at the gym - Clue 8
169 The murder wasn't drowning - Clue 9
-274 Mr.Epsilon was swimming laps at a pool - Clue 10
is what i know, i will figure out in a bit! :D
Step-by-step explanation:
There are 3 students to 1 adult on a field trip. You need to find the number of adults needed for 24 students. What would
the second ratio of the proportion look like If the first proportion is as follows?
3 students
1 adult
O
Х
24 students
O
24 students
Х please just answer
o
3
o
Answers
Answer:
6
Step-by-step explanation:
Answer:
24students:X
Step-by-step explanation:
I didnt really understand but this is my best answer
find the critical value(s) and rejection region(s) for the type of z-test with level of significance . include a graph with your answer. right-tailed test, a=0.03.
Answers
Answer:
c
Step-by-step explanation:
The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.
The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88 OR Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.
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Given the tunction g(x) = 4x - 5, compare and contrast g(2) and g(-4). Choose the statement that is true concerning these two values.
The value of g(2) is larger than the value of g(-4).
The value of g(2) is smaller than the value of g(-4).
The value of g(2) is the same as the value of g(-4).
The values of g(2) and g(-4) cannot be compared.
Answers
g(-4)=4•(-4)-5=-21
So the answer is the value of g(2)is smaller than the value of g(-4)
A 258-inch board is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.
Answers
Answer:
43in
Step-by-step explanation:
Let the length of the pieces be x and y
Since the total length is 258in, then;
x+y = 258... 1
If One piece is five times the length of the other, then x = 5y ....2
Substitute 2 into 1
From 1:
x+y = 258
5y+y = 258
6y = 258
y = 258/6
y = 43
Since x = 258-y
x = 258-43
x = 215
Hence the length of the shorter piece is 43in
A consumer charges a $2,530. 16 purchase on a credit card. The card has a daily interest rate of 0. 42%. If the balance is paid off at the end of 30 days, how much interest will the consumer pay? a. $0. 32 b. $3. 19 c. $31. 88 d. $318. 78.
Answers
The interest the customer would pay is $318.78.
Interest can be described as the cost of borrowing. It is the amount of money a borrower has to pay to the lender.
Interest = amount borrowed x interest rate
Daily interest = $2,530.16 x 0.42%
$2,530.16 x 0.0042 = 10.63
Monthly interest = 10.63 x 30 = $318.80
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1
The coefficient of x2 in the expansion of 2x +1 by 3 whole square
Answers
Answer:
1 +6 x + 12 x 2 + 8x 3
Explanation:
We must use our knowledge of the binomial expansion:
Method 1:
We can use:
(
x
+
1
)
n
=
1
+
n
x
+
n
(
n
−
1
)
2
!
x
2
+
n
(
n
−
1
)
(
n
−
2
)
3
!
x
3
+
...
Substituting
n
=
3
and
x
for
2
x
⇒
(
2
x
+
1
)
3
=
1
+
(
3
⋅
2
x
)
+
3
⋅
2
2
!
⋅
(
2
x
)
2
+
3
⋅
2
⋅
1
3
!
⋅
(
2
x
)
3
=
1
+
6
x
+
12
x
2
+
8
x
3
Method 2:
We can use:
(
A
+
B
)
n
=
A
n
+
(
n
1
)
A
n
−
1
B
1
+
(
n
2
)
A
n
−
2
B
2
+
...
Letting
A
=
2
x
and
B
=
1
for this circumstance:
(
2
x
+
1
)
3
=
(
2
x
)
3
+
(
3
1
)
(
2
x
)
2
(
1
)
+
(
3
2
)
(
2
x
)
1
(
1
)
2
+
(
3
3
)
(
2
x
)
0
(
1
)
3
=
8
x
3
+
12
x
2
+
6
x
+
1
Step-by-step explanation:
a rectangular board is 1300 millimeters long and 800 millimeters wide. what is the area of the board in square meters? do not round your answer.
Answers
A rectangular board is 1300 millimeters long and 800 millimeters wide. Then, the area of the board in square meters is 104 m².
Determine the area of the boardThese are the specified parameters:
Length of the board (l) = 1300 mm
Breadth of the board (b) = 800 mm
The area of a rectangular board
A = l × b
= 1300 mm × 800 mm
= 1040000 mm²
The area of the board in square meters
To convert mm² to m², divide mm² by 10000.
Therefore
A = 1040000 mm²
= 1040000 : 10000 m²
= 104 m²
So, the area of the board in square meters is 104 m².
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To make a bow out of ribbon, Carrie needs 1
1
4
yards of ribbon. If Carrie bought 8
3
4
yards of ribbon at a sale, how many bows could she make?
Answers
Answer:
7 bows
Step-by-step explanation:
I will assume that the numbers are \(1\frac{1}{4}\) and \(8\frac{3}{4}\). To find the answer, we can do:
\(8\frac{3}{4} / 1\frac{1}{4}\\ = \frac{35}{4} / \frac{5}{4} \\= \frac{35}{4} * \frac{4}{5}\\= \frac{35}{5}\)
= 7 bows
Which box-and-whisker plot matches the data?
23, 32, 20, 13, 27, 36, 29, 38, 23, 15, 30, 18
A. A box-and-whisker plot is shown above a number line that spans from 10 to 40. It is marked in increments of 2.The box extends from between 18 and 20 to between 30 and 32. There is a division and a point between 26 and 27. The left whisker extends from a point between 12 and 14 to a point between 18 and 20. The right whisker extends from a point between 30 and 32 to 36.
B. A box-and-whisker plot is shown above a number line that spans from 10 to 40. It is marked in increments of 2.The box extends from between 18 and 20 to 32. There is a division and a point between 26 and 27. The left whisker extends from a point between 12 and 14 to the box between 18 and 20. The right whisker extends from 32 to a point between 36 and 38.
C. A box-and-whisker plot is shown above a number line that spans from 10 to 40. It is marked in increments of 2.The box extends from between 18 and 20 to between 30 and 32. There is a division and a point between 22 and 24. The left whisker extends from a point between 12 and 14 to the box between 18 and 20. The right whisker extends from the box between 30 and 32 and extends to 38.
D. A box-and-whisker plot is shown above a number line that spans from 10 to 40. It is marked in increments of 2.The box extends from 18 to a point between 30 and 32. There is a division and a point at 24. The left whisker extends from 12 to 18. The right whisker extends from the box at a point between 30 and 32 to 36.
20 / 23
19 of 23 Answered
Answers
Answer:
Option C
Step-by-step explanation:
Given the data set, 23, 32, 20, 13, 27, 36, 29, 38, 23, 15, 30, 18, to find out which box-and-whisker plot matches the data, let's work out the 5-number summary needed for constructing a box plot.
The five-number summary includes the min, Q1, median, Q3 and max value.
Let's find them.
First, order the data set from the least to the largest
13, 15, 18, 20, 23, 23, 27, 29, 30, 32, 36, 38
Min = 13
Max = 38
Median = (23 + 27) ÷ 2 = 50 ÷ 2 = 25
Q1 = (18 + 20) ÷ 2 = 38 ÷ 2 = 19
Q3 = (30 + 32) ÷ 2 = 62 ÷ 2 = 31
The box-and-whiskers plot will have the description given in option C.
It will look like the box plot shown in the attachment below.
If the diagonal of a rectangle measures 60 inches and one side measures 48 inches, what is the length of the other side of the rectangle?
Answers
Answer:
36
Step-by-step explanation:
Using pythag, 60^2 - 48^2 = 3600 - 2304, which is 1296, whose square root if 36. This is also a 3-4-5 triangle.
Answer:
36
Step-by-step explanation:
60 power 2 minus 48 power 2 under square root = 36
(a) We would like to know if Intel's stock and Southwest Airlines' stock have similar rates of return. To find out, we take a random sample of 50 days, and record Intel's and Southwest's stock on those same days.
Answers
Thus, to determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can use a statistical analysis of the daily rate of return for each stock over a 50-day period. However, the small sample size means that we must be cautious when interpreting the results.
To determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can conduct a statistical analysis using the sample data collected. The sample size of 50 days is relatively small, so we must be cautious when interpreting the results.
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Simplify the expression. #1-2
Answers
Answer: 1/2
Step-by-step explanation:
(3x + 4)(x + 2x + 3)
Answers
Answer:
9x^2 + 21x + 12
Step-by-step explanation:
(3x+4)(x+2x+3)
Combine x and 2x to get 3x.
(3x+4)(3x+3)
Apply the distributive property by multiplying each term of 3x+4 by each term of 3x+3.
9x^2 + 9x + 12x + 12
Combine 9x and 12x to get 21x.
9x^2 + 21x + 12
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
Answer:
A, B, F
- The radius of the circle is 3 units
- The center of the circle lies on the x-axis
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9
Step-by-step explanation:
The first option is correct because the standard equation of the circle is:
\((x - 1)^{2} + {y}^{2} = 9\)
making the radius equal to 3.
The center is at (-1,0), therefore it lies on the x-axis.
And lastly, the last option is correct because both options have the radius of 3.
Karen wants to advertise how many chocolate chips (in grams) are in each Big Chip cookie at her bakery. She randomly selects a sample of 13 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 60.3 and a standard deviation of 37.5. What is the 98% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? O 32.4<< 88.2 O 12.4 < x < 108.2 46.5< < 74.1 21.5<<99.1 O 15.3<< 105.3
Answers
The 98% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is approximately 32.4<< 88.2
How to construct a confidence interval for the mean number of chocolate chips per cookie?To construct a confidence interval for the mean number of chocolate chips per cookie, we can use the t-distribution since the sample size is small (n = 13) and the population standard deviation is unknown.
Given that the sample mean is 60.3 and the sample standard deviation is 37.5, we can calculate the standard error (SE) as:
\(SE = s / \sqrt(n)\)
where s is the sample standard deviation and n is the sample size.
\(SE = 37.5 / \sqrt(13) \approx 10.41\)
To calculate the margin of error, we multiply the standard error by the t-score corresponding to a 98% confidence level with n-1 degrees of freedom.
With n-1 = 12 degrees of freedom, the t-score can be obtained from a t-table or calculator. For a 98% confidence level, the t-score is approximately 2.681.
Margin of Error = t * SE = 2.681 * 10.41 ≈ 27.92
Finally, we can construct the confidence interval by subtracting and adding the margin of error to the sample mean:
CI = sample mean ± margin of error
CI = 60.3 ± 27.92
Therefore, among the answer choices provided, the closest option is "32.4 << 88.2."
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if 3/8 of a pizza cost $5, how much would a full pizza cost? (Be sure to write your answer in the form of money)
Answers
$13.35 rougly around that
3. Find the inverse of the given function.
f(x) = - x-17 over 12
Answers
Given :-
A function f(x) = - (x -17)/12To Find :-
The inverse of the function .Solution :-
The given function is ,
\(\longrightarrow\) f(x) = -(x-17)/12
Replace y with f(x) ,
\(\longrightarrow\) y = -(x-17)/12
Interchange x and y ,
\(\longrightarrow\) x = -(y-17)/12
Solve for y ,
\(\longrightarrow\) 12x = -y +17
\(\longrightarrow\) y = -12x +17
Replace y with f-¹(x) ,
\(\longrightarrow\sf \ f^{-1}(x)= -12x +17\)
Hence the required answer is -12x +17.
PLS HELP I WILL GIVE BRAINLIEST
HELP ASAP
Answers
10 procent
Step-by-step explanation:
150 / 150 = 10
Answer:10%
Step-by-step explanation:
19 points
Why did those sympathetic to slavery in Union Border States such as Kentucky and Delaware not support the Emancipation Proclamation?
Answers
Answer:
Those sympathetic to slavery in Union border states, such as Kentucky and Delaware, did not support the Emancipation Proclamation because it granted freedom to slaves if their home southern states did not join the Union by January 1, 1863.
Missouri, Maryland, Kentucky and Delaware were slave holding border states and not in rebellion from the Union so the Proclamation did not effect their slaves. But, the area of the border states were closely linked to the South and held political, economic, geographic, and social connections to the Southern (and Northern) states. This led border states to not support the Emancipation Proclamation.
Step-by-step explanation:
Which of the following equations of a line is NOT written in standard form?
A. 3x + 2y = 8
B. -9x – 4y = 17
C. x + y = 10
D. y = 6x
Answers
Step-by-step explanation:
None of the options are written as standard except option D.
Answer:
D. y = 6x
Step-by-step explanation:
Edge 2022
Twice the sum of x
and 5 equals 3.
Answers
⇛2x + 5 = 3
⇛2x = 5 - 3
⇛2x = 2
⇛x = 2/2
⇛x = 1
Answer:
1
Step-by-step explanation: