The standard deviation for the dataset is 28.89.
What is the standard deviation?
When we measure diversity in a data set, it is called standard deviation. We have to calculate the variance first. The square root of variance gives the standard deviation. The formula to calculate standard deviation is:
s= [tex]\sqrt{\frac{(x1-xm)^{2} + (x2-xm)^{2} +........+ (xn-xm)^{2} }{n-1} }[/tex]
First, we will calculate the mean of the data, xm
[tex]xm=\frac{18+22+39+48+77+89}{6}[/tex]
[tex]=48.83[/tex]
Then, we will calculate the following:
[tex](x1-xm)^{2}=(18-48.83)^{2} \\\\(x2-xm)^{2}=(22-48.83)^{2} \\\\(x3-xm)^{2}=(39-48.83)^{2} \\\\(x4-xm)^{2}=(48-48.83)^{2} \\\\(x5-xm)^{2}=(77-48.83)^{2} \\\\(x6-xm)^{2}=(89-48.83)^{2} \\[/tex]
The summation comes out to be 4174.83.
Therefore, the standard deviation becomes = [tex]\sqrt{\frac{4174.83}{5} }[/tex]
=28.89
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The following amounts are taken from Parker Company's contribution margin income statement: Net operating income, $30,000; Fixed expenses, $90,000; Sales, $200,000; and CM ratio, 60%. What is the company's degree of operating leverage?
Multiple Choice
A)0.25
B)0.60
C)1.25
D)4.00
A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. Thus, option D is correct.
How to solve for degree of operating leverage?The degree of operating leverage (DOL) formula is:
DOL = Contribution Margin / Net Operating Income
We can calculate the contribution margin using the CM ratio:
Contribution Margin = Sales x CM ratio
Contribution Margin = $200,000 x 0.60
Contribution Margin = $120,000
Now we can calculate the DOL:
DOL = Contribution Margin / Net Operating Income
DOL = $120,000 / $30,000
DOL = 4.00
Therefore, the company's degree of operating leverage is 4.00.
The answer is (D) 4.00.
Step-by-step explanation:
Identify the relevant values from the problem statement:
Net operating income = $30,000
Fixed expenses = $90,000
Sales = $200,000
CM ratio = 60%
Calculate the contribution margin using the CM ratio:
Contribution Margin = Sales x CM ratio
Contribution Margin = $200,000 x 0.60
Contribution Margin = $120,000
Use the contribution margin and net operating income to calculate the degree of operating leverage:
DOL = Contribution Margin / Net Operating Income
DOL = $120,000 / $30,000
DOL = 4.00
Interpret the result:
A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. This indicates that the company has a high degree of operating leverage, which means that it is more sensitive to changes in sales volume. In other words, small changes in sales can have a big impact on the company's profitability.
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A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. Thus, option D is correct.
How to solve for degree of operating leverage?The degree of operating leverage (DOL) formula is:
DOL = Contribution Margin / Net Operating Income
We can calculate the contribution margin using the CM ratio:
Contribution Margin = Sales x CM ratio
Contribution Margin = $200,000 x 0.60
Contribution Margin = $120,000
Now we can calculate the DOL:
DOL = Contribution Margin / Net Operating Income
DOL = $120,000 / $30,000
DOL = 4.00
Therefore, the company's degree of operating leverage is 4.00.
The answer is (D) 4.00.
Identify the relevant values from the problem statement:
Net operating income = $30,000
Fixed expenses = $90,000
Sales = $200,000
CM ratio = 60%
Calculate the contribution margin using the CM ratio:
Contribution Margin = Sales x CM ratio
Contribution Margin = $200,000 x 0.60
Contribution Margin = $120,000
Use the contribution margin and net operating income to calculate the degree of operating leverage:
DOL = Contribution Margin / Net Operating Income
DOL = $120,000 / $30,000
DOL = 4.00
Interpret the result:
A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. This indicates that the company has a high degree of operating leverage, which means that it is more sensitive to changes in sales volume. In other words, small changes in sales can have a big impact on the company's profitability.
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Emily took an airplane trip. Her plane flew and equal numbers of miles each hour. Let m stand for the miles flown each hour. Write an equation to represent one way you can find how many miles Emily’s plane flew each hour.
An equation to represent one way you can find how many miles Emily’s plane flew each hour is y = 182x.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Assuming the variable m represent the miles flown each hour, an equation for the number of miles Emily’s plane flew each hour can be calculated as follows;
y = kx
y = (2184/12)x
y = 182x
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Complete Question:
Emily took an airplane trip. Her plane flew an equal number of miles each hour. Write an equation to represent one way you can find how many miles Emily's plane flew each hour.
Use this to help you:
Air travel time: 12 hours
Destination: 2,184 miles
Please help meee!! I will give brainliest and 5 stars!
NO || PR using the converse of the Triangle Proportionality Theorem are not parallel.
What is Triangle Proportionality Theorem?The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
Conversely, if a line divides two sides of a triangle proportionally, then it is parallel to the third side.
In this problem, we are given a right triangle NQM, where line PR intersects the sides NM and QM at points P and R, respectively. We are also given that NM = 16, PM = 12, RM = 6, and QR = 8. We want to verify that NO || PR.
To do this, we will use the converse of the Triangle Proportionality Theorem. We know that PR divides NM proportionally, so we need to show that it also divides QM proportionally.
Using the ratios of corresponding side lengths of similar triangles, we can write:
PM / RM = PN / RN
Substituting the given values, we get:
12 / 6 = PN / (16 - 6)
2 = PN / 10
PN = 20
Similarly, we can write:
QR / RM = QN / RN
Substituting the given values, we get:
8 / 6 = QN / (16 - 6)
4 / 3 = QN / 10
QN = 40 / 3
Now we can check if PR divides QM proportionally:
PM / QN = 12 / (40 / 3) = 9 / 5
PN / RM = 20 / 6 = 10 / 3
Since these ratios are not equal, we can conclude that PR does not divide QM proportionally.
Therefore, by the converse of the Triangle Proportionality Theorem, we can conclude that NO is not parallel to PR.
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Graph the image of the triangle after a rotation 90° counterclockwise around the origin.
Answer:
The answer you're looking for is: (4, -9), (6, -9), (4, -1)
Step-by-step explanation:
When translating an image 90º counterclockwise you go one quadrant to the right and use the scale factor: (x, y) --> (y, -x).
When using this scale factor you switch the x and y coordinates and also make sure that x is the opposite operation, it doesn't always mean it's going to be negative.
In this case points (-9, -4), (-9, -6), and, (-1, -4) were translated to (4, -9), (6, -9), (4, -1) accordingly.
I hope this was helpful!
d(t) = 16t2 -23t + 18
Answer:
t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32
Step-by-step explanation:
Solve for t:
16 t^2 - 23 t + 18 = 0
Divide both sides by 16:
t^2 - (23 t)/16 + 9/8 = 0
Subtract 9/8 from both sides:
t^2 - (23 t)/16 = -9/8
Add 529/1024 to both sides:
t^2 - (23 t)/16 + 529/1024 = -623/1024
Write the left hand side as a square:
(t - 23/32)^2 = -623/1024
Take the square root of both sides:
t - 23/32 = (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32
Add 23/32 to both sides:
t = 23/32 + (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32
Add 23/32 to both sides:
Answer: t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32
Question 3
Mr Dladla wants to open a training company, he will be training Learnerships and
ABET. He plans to operate at South Gate Mall with the total Market share of 4500
customers per month. He knows that he can only expect 50% of the market share for
the year.
His selling price will be R500 and the cost of running his course in R300. His training
company opens 20 days per month.
(10)
3.1 Calculate his gross profit per day and thereafter
Answer:
To calculate Mr. Dladla's gross profit per day, we first need to calculate his total revenue and total cost per month:
Total revenue per month = Selling price x Expected market share per month
Total revenue per month = R500 x (50% of 4500 customers) = R112,500
Total cost per month = Cost per course x Number of courses per month
Total cost per month = R300 x 20 days = R6,000
Gross profit per month = Total revenue per month - Total cost per month
Gross profit per month = R112,500 - R6,000 = R106,500
To calculate his gross profit per day, we can divide the gross profit per month by the number of days the training company opens per month:
Gross profit per day = Gross profit per month / Number of days per month
Gross profit per day = R106,500 / 20 days = R5,325 per day
Therefore, Mr. Dladla's gross profit per day is R5,325.
Step-by-step explanation:
Select if the statement is true or false.
Absolute value can equal a negative number.
true or false?
Answer:
False
Step-by-step explanation:
The absolute value of a number is defined as its distance from zero on the number line. Distance is always a non-negative quantity, so the absolute value of a number can never be negative.
Therefore, the absolute value of any number, whether positive or negative, is always a non-negative value.
Amira has 27 feet of ribbon to make 5 braided bracelets.How much ribbon goes to each bracelet
27 ÷ 5 = 5.4
∴ 5.4 feet of ribbon goes to each bracelet.
Can someone help me with this math problem, ASAP?
Answer: [tex]\sqrt{\text{x}-7}-10[/tex]
Work Shown:
[tex]f(\text{x}) = \sqrt{\text{x}-6}-10\\\\f(\text{x}-1) = \sqrt{\text{x}-1-6}-10\\\\f(\text{x}-1) = \sqrt{\text{x}-7}-10[/tex]
Explanation:
I replaced each copy of x with x-1. Then I combined like terms. Doing this will shift the graph 1 unit to the right.
3x + 12y = −8 in intercept form
Answer:
y=-1/4x-2/3
Step-by-step explanation:
34.6°C =°F (round the answer to the nearest tenth).
● 4.7
● 32.3
● 30.3
● 94.3
● None are correct
Answer:
94.3/C
Step-by-step explanation:
Hope this helps!
By first calculating the size of angle LMN,
calculate the area of triangle MNL.
You must show all your working.
I
+
M
4.8 cm
Answer cm²
38/43 Marks
L
8
7.2 cm
38°
14%
Not drawn
to scale
N
The area of triangle MNL is approximately 10.44 cm².
What is the sine rule?
The sine rule, also known as the law of sines, is a formula used in trigonometry to find the lengths of the sides and the measure of the angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:
[tex]a/sin A = b/sin B = c/sin C[/tex]
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides. The sine rule can be used to find the length of a side of a triangle or the measure of an angle if the other two sides and the included angle are known, or if two sides and the angle opposite one of them are known.
To find the area of triangle MNL, we need to first calculate the length of side NL using the sine rule:
sin(38°) / NL = sin(90°) / 4.8
NL = sin(38°) / sin(90°) * 4.8
NL = sin(38°) * 4.8
NL ≈ 2.9 cm
Now we can find the area of the triangle using the formula:
[tex]Area = (1/2) * base * height[/tex]
[tex]Area = (1/2) * 7.2 * 2.9[/tex]
Area ≈ 10.44 cm²
Therefore, the area of triangle MNL is approximately 10.44 cm².
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The same video is uploaded to a different website.There are also 100 views in day one ,but 400 views on day 2and 1,600 views on day 3.explain how the explicit and rescursive formula change .
The explicit formula of the geometric sequence is given as follows:
[tex]a_n = 100(4)^{n-1}[/tex]
The recursive formula of the geometric sequence is given as follows:
f(n + 1) = 4f(n).f(1) = 100.What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio (q). In other words, a geometric sequence is a sequence where each term is a fixed multiple of the previous term.
The explicit formula of the sequence is given as follows:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
For the recursive formula, we just take the first term and each consecutive term is the previous term multiplied by the common ratio.
There are 100 views in day one, hence the first term is given as follows:
[tex]a_1 = 100[/tex]
The number of viewers is multiplied by 4 each day, hence the common ratio is given as follows:
q = 4.
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Let D= Ф(R), where Φ(u,v)= (u^2, u+v) and R= [1,9] x [0,5]. Calculate \int \: \int \: _D ydA
The value of the double integral of y over D is 160.
The region D is defined as the image of the rectangle R under the transformation Φ(u,v) = (u², u+v). To find the integral of y over D, we need to express y as a function of u and v, and then compute the double integral in terms of u and v.
From the definition of Φ, we have:
u² = x
u + v = y
Solving for v in terms of u and y, we get:
v = y - u
Substituting this expression for v into the second equation, we get:
y = u + (y - u) = y
Therefore, y does not depend on u, and we can write:
y = f(v) = v + u
The integral of y over D can then be written as:
∫∫D y dA = ∫∫R f(v) |J| dA
where J is the Jacobian of the transformation Φ.
The Jacobian of Φ is given by:
J = ∂(x,y)/∂(u,v) =
| 2u 1 |
| 1 1 |
The determinant of J is:
|J| = 2u - 1
Substituting this expression for |J| and the expression for f(v) into the integral, we get:
∫∫D y dA = ∫∫R (v + u)(2u - 1) dudv
To evaluate this integral, we can integrate first with respect to u and then with respect to v:
∫∫D y dA = ∫[0,5]∫[1,9] (v + u)(2u - 1) dudv
= ∫[0,5] [(v+9)³/3 - (v+1)³/3] dv
= [(5+9)⁴/12 - (1+9)⁴/12]
= 480/3
= 160
Therefore, the value of the double integral of y over D is 160.
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Complete question:
Let D= Ф(R), where Φ(u,v)= (u², u+v) and R= [1,9] × [0,5].
Calculate [tex]\mathrm{\int \: \int \: _D ydA}[/tex]
13. Sameen wants to build a fence around a rectangular area of her yard. The graph shows the area y in square feet that she can surround with the fencing that she has, where x is the width in feet of the rectangle.
We can write the quadratic equation as -
y = - (x - 25)² + 625
What is the general form of a quadratic equation?The general form of a quadratic equation is -
y = ax² + bx + c
where -
a, b and c are constants.
Given is that Sameen wants to build a fence around a rectangular area of her yard. The graph shows the area {y} in square feet that she can surround with the fencing that she has, where the breadth is width {x} in feet of the rectangle.
The given coordinates on the parabola are -
(8, 336)
(42, 336)
(25, 625)
Here, the point (25, 625) represents the vertex (h, k) of the parabola.
We can write the equation of parabola as -
y = a(x - h)² + k
y = a(x - 25)² + 625
For the point (8, 336), we can write -
336 = a(8 - 25)² + 625
336 - 625 = a(8 - 25)²
a(8 - 25)² = - 289
a(- 17)² = -289
a = -289/289
a = -1
So, we can write the quadratic equation as -
y = - (x - 25)² + 625
Therefore, we can write the quadratic equation as -
y = - (x - 25)² + 625
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y=4x=6 how many soluations does it have?
The line goes through the point and has a slope of 4, a y-intercept of -6, and a slope of 4. (0, 6).
What is a good example of a line's slope?The proportion of the increase in the y-value to the change inside the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) and Q := (4,1) on the line.
What does slope mean?A line's slope is how steeply it slopes form LEFT to RIGHT. Divide the rise, or vertically increase, by the run, or horizontally start changing, to get the line's gradient.
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The complete question is:
X in graphs the equation y = 4x - 6.
Select all statements about Xin's graph that are true.
a. The graph is a curved line.
b. The line passes through the origin.
c. The line passes through the point (0, 6).
d. The slope of the line is 4.
e. The y-intercept of the line is -6.
I need help, please its due today
Answer:??? Bio?
Step-by-step explanation:give a good expample
The cost of 4 concert tickets is $95.80. How much is the cost of one ticket
Compare center and variations of histograms 1 questions with part A, B, C, D PLEASE HELP ME 40 POINTS SUPER EASYY
The requried (a) median for the chocolate candy and nonchocolate candy sales are $3040 and $1566.5 respectively. (b) The range for the chocolate candy sales, the range is ($1941, $3454). For the non-chocolate candy sales, the range is (from 1,096 dollars to 2,892 dollars).
What is a histogram?A histogram is a graphical representation of the distribution of a set of numerical data. It consists of a set of rectangles, where the area of each rectangle is proportional to the frequency (or count) of the observations falling within a particular interval, called a bin.
Here,
A. The interval for the median for each data set can be found by arranging the data in ascending order and finding the middle value. For the chocolate candy sales, the median falls in the interval of 2800-3,099 dollars. While for the Nonchocolate candy, it falls under 1300 -1599
The median for the chocolate candy sales = $3040
The median for the Nonchocolate candy sales = $1566.5
B. The range for each data set can be found by subtracting the minimum value from the maximum value. For the chocolate candy sales, the range is ($1941, to $3454). For the non-chocolate candy sales, the range is (from 1,096 dollars to 2,892 dollars).
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write two monomials with the quotient:
[tex]24 {a}^{2} {b}^{5} [/tex]
Answer:
Two monomials with the quotient 24a2b5 are:
12a b³
48a³ b²
Step-by-step explanation:
Which function describes this graph?
The function describes this graph is y = x² + 9x + 18.
What is Graph?In mathematics, a graph is defined as a graphical representation or diagram that organises facts or values. The graph's points frequently reflect the relationship between two or more things.
Given:
We can see from the Graph touches the x axis at -6 and -3.
So, the factors of function are (x +6) and (x+ 3).
Then, the function represented by the graph is
y = (x+ 6) (x + 3)
y = x² + 6x + 3x + 18
y = x² + 9x + 18
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42 + z= 131
what is z?
Answer:
z=89
Step-by-step explanation:
42+z=131
take 42 away from both sides
z= 89
Answer:
z = 89
Step-by-step explanation:
42 + z = 131
z = 131 - 42
z = 89
How many sixths does it take to make the same amount as 1/3
Answer: Two 1/6
Step-by-step explanation:
It takes two 1/6 to make the same amount as 1/3 because 1/6 is half of 1/3, so all it takes is two 1/6 to make 1/3.
Answer:
1/3 is equal to 2/6, so it takes 2 sixths to make the same amount as 1/3.
WW
the same area without any on
square? How many such squares can the rectangle be cut into?
15 In the figure below, point B is the corner of street ABC. If streetlights are to be
installed along one side of the street with equal distance between the lights, and a
streetlight must be installed at points A, B and C, at least how many streetlights
can be installed along the street?
1625 m
B
1170 m
The minimum number of streetlights that can be installed along the street is 1641 + 1182 = 2823.
Describe Distance?In Euclidean geometry, the distance between two points is defined as the length of the shortest path between them. This is often referred to as the "straight-line distance" or "Euclidean distance." It is calculated using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The total distance between A and C is the sum of the distances AB and BC:
AC = AB + BC = 1625 + 1170 = 2795 m
Since we need to install streetlights at points A, B, and C, there will be two segments of the street with streetlights:
From A to B, which has a distance of 1625 m
From B to C, which has a distance of 1170 m
We want to install streetlights along each segment with equal distance between the lights. Let's call the distance between each pair of adjacent streetlights "d".
For the first segment, there will be "n" streetlights, so the total distance covered by the streetlights will be (n-1)d. Similarly, for the second segment, there will be "m" streetlights, and the total distance covered by the streetlights will be (m-1)d.
The total distance covered by the streetlights should be equal to the distance AC, so we have:
(n-1)d + (m-1)d = AC
Substituting the values we know, we get:
1624d + 1169d = 2795
2793d = 2795
d = 2795/2793
d ≈ 0.999
We can round down to 0.99 to ensure that we don't have more streetlights than necessary.
Therefore, the distance between each pair of adjacent streetlights should be 0.99 m. To find the minimum number of streetlights required, we can divide the distance of each segment by 0.99 and round up to the nearest integer:
For the first segment: ceil(1625/0.99) = 1641
For the second segment: ceil(1170/0.99) = 1182
So the minimum number of streetlights that can be installed along the street is 1641 + 1182 = 2823.
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You find the communication system to get in touch with your team leader on the
surface, but all except one of the wires for the communication system have been
disconnected. You know that you can reconnect the wires by matching equivalent
expressions (hint: evaluate each expression to check which ones match). After you
match all of the equivalent expressions, you can use them to find the code word!
A3 is already connected.
A-8-(-3)-7
B-8-3-(-7)
C 8-(+3)-7
D-8-(-3)-(-7)
E 8-(-7)-3
S
8+7+(-3)
-8+3+7 2
-8+3+(-7) 3
8+(-3)+(-7) 4
-8+(-3)+7 5
The equivalent expressions are A3, B2, C3, D4 and E5.
What is expression in math?Expression in math is a combination of numbers, symbols, and operations that represent a value or a relationship between values. Expressions are used to represent relationships between numbers, variables, and other mathematical objects. Expressions are the basic building blocks of algebra and calculus, and allow us to solve problems and describe relationships between different quantities. Expressions help us to understand math better, as they allow us to express complex ideas in concise, clear, and concise form.
Once the wires are connected by matching the equivalent expressions, the code word is 8+7+(-3).
This is happening because in order to unlock the communication system, you need to match the equivalent expressions in order to find the code word. By evaluating each expression, you can determine which of the expressions are equivalent and then connect the wires accordingly. By connecting the wires, you can then find the code word which will unlock the communication.
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Can you help on this fast
The table that shows proportional relationship is x = 1,3,4,5 and y = 50, 150, 200,250 ( table 1).
What is proportionality?The term proportionality describes any relationship that is always in the same ratio. The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.
To determine the proportionality the ratio of x toby must be thesame Ina table
in table 1
x/y = 1/50 = 3/150 = 4/200 = 5/250 = 1/50
table 1 show proportional relationship
in table 2
3/1.5 is not equal to 7/3 , therefore table 2 does not show proportional relationship
in table 3
1/1.5 is not equal to 3/6 , therefore table 3 does not show proportional relationship
therefore the table that show proportional relationship is table 1
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A survey of 1,033 tourists visiting Orlando was taken. Of those surveyed:
256 tourists had visited the Magic Kingdom
267 tourists had visited Universal Studios
52 tourists had visited both the Magic Kingdom and LEGOLAND
75 tourists had visited both the Magic Kingdom and Universal Studios
82 tourists had visited both LEGOLAND and Universal Studios
33 tourists had visited all three theme parks
93 tourists did not visit any of these theme parks
How many tourists only visited the LEGOLAND (of these three)?
There are 509 tourists only visited the LEGOLAND (of these three).
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, To find the number of tourists who only visited LEGOLAND, we need to subtract the tourists who visited LEGOLAND and another theme park from the total number of tourists who visited LEGOLAND.
Calculation:
First, we can find the total number of tourists who visited LEGOLAND:
Total = Tourists who visited only LEGOLAND + Tourists who visited LEGOLAND and another park
Hence, Total = (Total visitors to LEGOLAND) - (Tourists who did not visit any of the parks)
Total = 1,033 - (256 + 267 + 75 + 93 - 52 - 82 - 33)
Total = 1033 - 260
Total = 509
Hence, There are 509 tourists only visited the LEGOLAND (of these three).
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Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)? A. x2 + y2 + 41 = 0 B. x2 + y2 − 41 = 0 C. x2 + y2 + x + y − 41 = 0 D. x2 + y2 + x − y − 41 = 0
The general form of the equation for the given circle centered at O(0, 0) is B. x² + y² - 41 = 0.
What is Circle?A circle is a round, two-dimensional shape with all points on its boundary equidistant from its center.
Since the center of the circle is O(0,0), the equation of the circle will have the form x² + y² + ax + by + c = 0. To find the values of a, b, and c, we can use the fact that point B(4, 5) lies on the circle. Substituting the coordinates of B into the equation and simplifying, we get:
4² + 5² + a4 + b5 + c = 0
16 + 25 + 4a + 5b + c = 0
41 + 4a + 5b + c = 0
We now have one equation with three variables, so we need more information. Since the center of the circle is (0,0), we know that the distance from the center to any point on the circumference is equal to the radius of the circle. The distance between points (0,0) and (4,5) is the length of the line segment joining them, which can be found using the distance formula:
[tex]\sqrt{(4-0)\² + (5-0)\²} = \sqrt{(16+25) }= \sqrt{41}[/tex]
Therefore, the radius of the circle is √(41). We can use this fact to eliminate one of the variables in the equation we derived earlier. Since point (0,0) lies on the circle, we can substitute its coordinates into the equation to get:
41 + 0a + 0b + c = 0
c = -41
Now we can substitute this value of c back into the equation we derived earlier to get:
41 + 4a + 5b - 41 = 0
4a + 5b = 0
Finally, we have two equations with two variables, which we can solve to get:
a = -5/4
b = 4/5
Substituting these values into the equation of the circle, we get:
x² + y² - 5x/4 + 4y/5 - 41 = 0
Multiplying by 20 to eliminate fractions, we get:
20x² + 20y² - 25x + 16y - 820 = 0
Simplifying, we get:
x² + y² - 25/4x + 4/5y - 41 = 0
Which is equivalent to:
x² + y² - 41 = 0
So the answer is B. x²+ y² - 41 = 0.
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Please help with this math question!
On evaluating the expression (1 - 1i) + (3 + 2i), the value for a and b are 4 and 1 respectively.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
To evaluate the expression (1 - 1i) + (3 + 2i), we simply add the real parts and the imaginary parts separately -
(1 - 1i) + (3 + 2i)
= (1 + 3) + (-1i + 2i)
= 4 + i
The value for a is obtained as 4
The value for b is obtained as 1.
Therefore, the result is 4 + i, which is in the form a + bi.
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If Catlain had 3 apples and Josh had 75% more apples than Catlain. How many apples did Josh have?
Answer:
5 apples
Step-by-step explanation: