The standard deviation of the return on Portfolio1 invested 40% in Stock 1 and 60% in Stock 2 is 0.83%.
To calculate the expected return of Portfolio1, we can use the formula:
Expected return of Portfolio1 = (Weight of Stock 1 x Rate of return of Stock 1) + (Weight of Stock 2 x Rate of return of Stock 2)
Using the given information, we have:
Expected return of Portfolio1 = (0.4 x 3%) + (0.6 x 8%) = 1.2% + 4.8% = 6%
Therefore, the expected return of Portfolio1 invested 40% in Stock 1 and 60% in Stock 2 is 6%.
To calculate the standard deviation of the return on Portfolio1, we need to calculate the variance first. The variance formula for a portfolio is:
[tex]Variance of Portfolio1 = (Weight of Stock 1)^2 x Variance of Stock 1 +[/tex][tex](Weight of Stock 2)^2 x Variance of Stock 2 + 2 x Weight of Stock 1[/tex] [tex]x Weight of Stock 2 x Covariance between Stock 1 and Stock 2[/tex]
The covariance between Stock 1 and Stock 2 can be calculated using the formula:
[tex]Covariance between Stock 1 and Stock 2 = Correlation between Stock 1[/tex] and[tex]Stock 2 x Standard deviation of Stock 1 x Standard deviation of Stock 2[/tex]
The correlation between Stock 1 and Stock 2 is not given, so we assume it to be 0. This means that the returns of Stock 1 and Stock 2 are not correlated with each other.
Using the given information, we have:
Variance of Stock 1 = (0.2 x (3% - 6%)^2) + (0.8 x (10% - 6%)^2) = 0.68%
Variance of Stock 2 = (0.2 x (2% - 6%)^2) + (0.8 x (8% - 6%)^2) = 1.44%
Covariance between Stock 1 and Stock 2 = 0 x SQRT(0.68%) x SQRT(1.44%) = 0
Using these values, we can calculate the variance of Portfolio1:
Variance of Portfolio1 = (0.4)^2 x 0.68% + (0.6)^2 x 1.44% + 2 x 0.4 x 0.6 x 0 = 0.696%
Finally, the standard deviation of Portfolio1 can be calculated by taking the square root of the variance:
Standard deviation of Portfolio1 = SQRT(0.696%) = 0.83%
Therefore, the standard deviation of the return on Portfolio1 invested 40% in Stock 1 and 60% in Stock 2 is 0.83%.
Learn more about deviation here:
https://brainly.com/question/31835352
#SPJ11
Triangle DEF is congruent to triangle UVW. The length of side DE is 6 cm, EF is 7.5 cm, and DF is 5 cm. What is the length of side VW?
The length of side VW is 7.5 cm
What is the length of side VW?The given parameters are:
DE is 6 cm, EF is 7.5 cm, and DF is 5 cm
Since the two triangles are congruent, then it means that:
D corresponds to UE corresponds to VF corresponds to WSo, we have:
VW= EF
The side EF is
EF = 7.5 cm
So, we have:
VW = 7.5 cm
Hence, the length of side VW is 7.5 cm
Read more about congruent triangles at:
https://brainly.com/question/12413243
#SPJ1
The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers?
If x represents the first number, then which of the following equations could be used to solve the problem?
69 = 7x - 8
x = 6x - 8
69 = 6x - 8
Answer:
[tex]69 = 6x - 8[/tex]
Step-by-step explanation:
All 3 numbers must sum to 69, so we can draw out the second option [tex]x = 6x - 8[/tex]
Let the first number be x, adding 5x to the first x would give you 6x for the sum of the first and third numbers, therefore you can remove [tex]69 = 7x - 8[/tex] from your considerations as it includes 7x not 6x.
This leaves you with the one final answer [tex]69 = 6x - 8[/tex]
If the area of the rectangle avove is 180 spuare inches, then x =
Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.
Hence, option A is the correct answer.
This question is incomplete, the missing diagram is uploaded along this answer below.
What is the value of x?Area of a rectangle is expressed as; A = l × b
Given that;
Length of the rectangle l = 20inBreadth b = xArea A = 180in²A = l × b
180in² = 20in × x
x = 180in² / 20in
x = 9in
Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.
Hence, option A is the correct answer.
Learn more about area of rectangle here: brainly.com/question/12019874
#SPJ1
please give the answer
The function can be solved as follows:
f(6 + 4) = 25f(6) - f(4) = 20f(6 - 4) = 1f(6) - f(4) = 6f(6) . f(4) = 91How to solve function?f(x) = 3x - 5
Therefore, the function can be solved as follows:
f(6 + 4) = f(10) = 3(10) - 5 = 25
f(6) + f(4) = 3(6) - 5 + (3(4) - 5)
f(6) - f(4) = 13 + 7
f(6) - f(4) = 20
f(6 - 4) = f(2) = 3(2) - 5 = 6 - 5 = 1
f(6) - f(4) = 3(6) - 5 - (3(4) - 5)
f(6) - f(4) = 18 - 5 - (12 - 5)
f(6) - f(4) = 13 - 7
f(6) - f(4) = 6
f(6.4) = f(24) = 3(24) - 5 = 72 - 5 = 67
f(6) . f(4) = (3(6) - 5 ) (3(4) - 5)
f(6) . f(4) = (18 - 5)(12 - 5)
f(6) . f(4) = (13)(7) = 91
learn more on function here: https://brainly.com/question/9390144
#SPJ1
A table showing gallons of solution, acid concentration, and amount of acid. the first row shows 10 percent acid, and has the entries, 0.5, 0.10, and 0.10 times 0.5. the second row shows 35 percent, and has the entries, g, 0.35, and 0.35 g. the third row shows. mixture, and has the entries, g plus 0.5, 0.15, and 0.15 left parenthesis g plus 0.5 right parenthesis. eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution. which equation can you use to determine how many gallons of the 35% acid solution eli should add?
The number of gallons of the 35% acid solution eli should add is; 0.125 gallons
How to Simplify Basic Algebra?From the given table, since Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution, then we can say that;
(0.10)(0.5) + 0.35g = 0.15(g + 0.5)
where g is number of gallons
Now, for us to determine how many gallons of the 35% acid solution eli should add, we will solve the word problem earlier to get;
(0.10)(0.5) + 0.35g = 0.15(g + 0.5)
⇒ 0.05 + 0.35g = 0.15g + 0.075
⇒ 0.35g - 0.15g = 0.075 - 0.005
⇒ 0.2g = 0.025
g = 0.025/0.2
g = 0.125 g
Read more about Algebra Simplification at; https://brainly.com/question/723406
#SPJ1
PLS HELP ASAP
42. Use the graph below to answer all questions. Assume the graph is incremented by one.
Does the graph represent a function? How do you know?
What is the domain?
What is the range?
What is the maximum?
What is the minimum?
Identify the intervals where the graph is increasing. What does this mean in the context of the problem?
Identify the intervals where the graph is decreasing. What does this mean in the context of the problem?
See below for the solution to each question
Is the graph a function?Yes, the graph is a function.
This is because all x values have different y values
The domainThis is the set of input values of the graph.
From the graph, we have
x = 0 to x = 17
Hence, the domain is [0, 17]
The rangeThis is the set of output values of the graph.
From the graph, we have
y = 0 to y = 10
Hence, the range is [0, 10]
The maximumThis is the maximum point on the graph.
From the graph, we have
Maximum = (12, 10)
The minimumThis is the minimum point on the graph.
From the graph, we have
Minimum = (0, 0)
The increasing intervalsThese are the intervals where the y values increase as x increase.
From the graph, we have
Increasing intervals = (0, 5) ∪ (10, 12) ∪ (14, 15)
The decreasing intervalsThese are the intervals where the y values decrease as x increase.
From the graph, we have
Decreasing intervals = (7, 10) ∪ (12, 14) ∪ (15, 17)
The constant intervalsThese are the intervals where the y values remain unchanged as x changes.
From the graph, we have
Constant intervals = (5, 7)
Read more about functions at
https://brainly.com/question/1600302
#SPJ1
Calculate x for each of the following right angled triangles.
Give your answer as a simplified surd (or integer).
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
(a) x = 6.5 cm (b) x = 10 cm(c) x = 7 cm(d) x = 7.9 cmStep-by-step explanation:
To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..
Formula :(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2
(h)^2 = (p)^2 + (b)^2
therefore,(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.
by formula,→ h^2 = p^2 + b^2
→ (x)^2 = (√12)^2 + (√30)^2
→ x^2 = 12 + 30
→ x^2 = 42
→ x = √42
→ x = 6.480...
→ x = 6.5 cm. (approx)
___________________________(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.
by formula,→ h^2 = p^2 + b^2
→ (√300)^2 = (x)^2 + (√200)^2
→ 300 = x^2 + 200
→ x^2 = 300 – 200
→ x^2 = 100
→ x = √100
→ x= 10 cm.
___________________________(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.
by formula,→ h^2 = p^2 + b^2
→ (√66)^2 = (x)^2 + (√17)^2
→ 66 = x^2 + 17
→ x^2 = 66 – 17
→ x^2 = 49
→ x = √49
→ x = 7 cm.
___________________________(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.
by formula,→ h^2 = p^2 + b^2
→ (x)^2 = (2√3)^2 + (5√12)^2
→ x^2 = 12 + 50
→ x^2 = 62
→ x = √62
→ x = 7.874...
→ x = 7.9 cm. (approx)
___________________________Hope it helps you!!pls i need help on this quick pls
Answer:
Answer should be 15
Step-by-step explanation:
25 divided by 15 is 1.6666666667 so if use that multiply 9 you'll get 15.
Answer:
Step-by-step explanation:
A^2 + B^2=C^2
30^2 -25^2= 16.5
answer= 16.5
Order the set of numbers from least to greatest: -
--5, -√26.-31
6
Answer:
-31, /~26, -5, 6
Step-by-step explanation:
Convert the exponential to a logarithmic form: 10 ^ 4 = 10000
Answer:
10^4 = 10 × 10 × 10 × 10
= 10000
DOES ANYONE KNOW THE ANSWER
Answer:
D. none
Step-by-step explanation:
we only know about the right angle at the bottom right.
that is not enough information.
we always need 3 pieces of confirmed information of each triangle to be able to say that the 2 triangles are indeed of the same shape and size.
like the other answer options would indicate :
SAS : side - angle - side.
2 sides and the enclosed angle. if we know they are equal, then the rest of the triangles follow automatically.
SSS : all 3 sides. with 3 defined sides there is only one possible shake and size for that triangle.
HL : Hypotenuse and a leg of a right-angled triangle (also 3 pieces of information - 2 sides and the right angle).
since we have only the right angle and nothing else, we cannot prove that the triangles are congruent.
The hotel staff is decorating the lobby by placing one row of string lights along the outer edge of the rectangular ceiling. A member of the staff maps the ceiling on a coordinate grid as shown, where each unit represents 1 meter.
The length of string used to decorate the ceiling = 40.5 meters.
According to the statement
we have given that the hotel staff is decorating the lobby by placing one row of string lights along the outer edge of the rectangular ceiling.
And the coordinates of rectangular ceiling is A(5,16), B(17,10), C(14,4), D(2,10).
And we have to find the total length for string is used to decorate the rectangular ceiling.
We know that the Total length of string = Area of the rectangular ceiling.
And area of rectangular ceiling = L*B
So, Length of rectangular ceiling = A+B
Length of rectangular ceiling = (17-5) + (16-10)
Length of rectangular ceiling = (12+6)/2
Length of rectangular ceiling = 9.
So,
Breadth of rectangular ceiling = B+C
Breadth of rectangular ceiling = (17-14)+(10-4)
Breadth of rectangular ceiling = (3+6) /2
Breadth of rectangular ceiling = 4.5
So, the length of string used = 4.5*9
the length of string used = 40.5 meters.
The length of string used to decorate the ceiling = 40.5 meters.
Learn more about Length here https://brainly.com/question/1972490
Disclaimer: This question was incomplete. Please find the full content below.
Question:
The hotel staff is decorating the lobby by placing one row of string lights along the outer edge of the rectangular celling. A member of the s⊥aff maps the celling on a coordinate grid as shown, where each unit represents . What is the approximate length of string lights the staff needs to decorate the ceiling?
A 20.25 meter
B. 35 meter
C. 40.5 meter
D. 14 meter
#SPJ4
Consider the function shown on the graph.
45-
12
9.
6
3
-13.
999
-6-
-9
-12-
-15-
(3, 0)
23
(8, 15)
((7,0)
5 6 7 8 9
X
Which function does the graph represent?
Of(x) = (x+3)(x + 7)
Of(x)=(x-3)(x-7)
Of(x)=3(x-3)(x-7)
Of(x)= 11(x+3)(x + 7)
Answer:
(c) f(x) = 3(x -3)(x -7)
Step-by-step explanation:
The correct function can be chosen by looking at the x-intercepts and the behavior around the vertex.
X-interceptsThe graph crosses the x-axis at x=3 and x=7. Each x-intercept x=p gives rise to a factor (x -p). These two x-intercepts mean the function will have factors ...
(x -3)(x -7) . . . . . . . . eliminates choices A and D
Vertex behaviorThe vertical scale factor of the quadratic is easily found by looking at the function behavior near the vertex. Specifically, the scale factor is the change in y-value at a distance of 1 unit either side of the vertex.
Here, the y-value at the vertex (x=5) is -12. The y-value at x=4 and x=6 is -9, three units up from the value at the vertex. This means the vertical scale factor (leading coefficient) is 3. (This eliminates choice B.)
EquationPutting these observations together, we have determined the equation of the function to be ...
f(x) = 3(x -3)(x -7) . . . . . . matches choice C
What is the solution to the inequality?
A. y > 32
B. y > 2
C. y < 2
D. y < 32
[tex]\textbf{Heya !}[/tex]
✏[tex]\bigstar\textsf{Given:-}[/tex]✏
An inequality [tex]\sf{-\cfrac{y}{4}+7 > -1}[/tex]✏[tex]\bigstar\textsf{To\quad find:-}[/tex]✏
y -- ?▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
✏[tex]\bigstar\textsf{Solution\quad steps:-}[/tex]✏
First, subtract both sides by 7:-
[tex]\sf{-\cfrac{y}{4} > -1-7}}[/tex]
[tex]\sf{-\cfrac{y}{4} > -8}[/tex]
Now multiply both sides by 4:-
[tex]\sf{-y > -8*4}[/tex]
[tex]\sf{-y > -32}[/tex]
last step:-
[tex]\sf{y < 32}[/tex]
`hope it was helpful to u ~
[tex] \implies \: \sf{ - \dfrac{y}{4} \: + \: 7 \: > \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 7 \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 8} \\ \\ \implies \: \sf{ \cancel- \: \dfrac{y}{4} \: > \: \cancel- \: 8} \\ \\ \implies \: \sf{ \dfrac{y}{4} \: < \: 8} \\ \\
\implies \: \sf{ y \: < \: 8 \times 4} \\ \\ \implies \: \bf{ y \: < \: 32}[/tex]
18. The area of a right triangle is 30 cm². The length
of one leg of the triangle is 5 cm. What is the
length of the other leg?
(A) 6 cm
(B) 12 cm
(C) 18 cm
(D) 24 cm
Answer:
12
Step-by-step explanation:
The area of a triangle is calculated with the following formula:
[tex]\frac{1}{2} *b*h[/tex] (b: base, h: height (or legs))
We can use this formula to find the length of the other leg:
30 = [tex]\frac{1}{2} *b*h[/tex] multiply both sides with 2 to get rid of fraction
60 = b*h one of the leg's length is given as 5 so
60 = 5*h divide both sides by 5
12 = h is the length of the missing leg.
Suppose the shipping weight of your cheese shop's customized gift baskets is asymmetrically distributed with unknown mean and standard deviation. For a sample of 70 orders, the mean weight is 57 ounces and the standard deviation is 7.1 ounces. What is the lower bound of the 90 percent confidence interval for the gift basket's average shipping weight
The lower bound of the 90% confidence interval for the gift basket's average shipping weight is 55.605.
Given mean weight of 57 ounces ,sample size 70 ,confidence level 90% and standard deviation of 7.1 ounces.
We have to find the lower bound of the confidence interval for the gift's basket's avrage shipping weight.
We can easily find the confidence interval and its lower bound through theformula of margin of error.
Margin of error is the difference between real values and calculated values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the critical value of confidence level
σ is standard deviation,
n is the sample size
We have to first find the z value for 90% confidence level which is 1.645.
Margin of error=1.645*7.1/[tex]\sqrt{70}[/tex]
=11.6795/8.3666
=1.395
Lower bound of the confidence interval = Mean - margin of error
=57-1.395
=55.605.
Hence the lower bound of the confidence interval for the gift basket's average shipping weight is 55.605.
Learn more about margin of error at https://brainly.com/question/10218601
#SPJ4
Sam is rowing a boat away from a dock. The graph shows the relationship between time and Sam’s distance from the dock. Evaluate the function for an input of 6.
Answer:
See below
Step-by-step explanation:
Go across the 'x' axis to '6'....then go UP to the graph to find y = 60
after 6 minutes he has rowed 60 meters
The function of f(x) = 3x + 6,000 represents the amount of money a tablet is being sold for, where x is the number of tablets being manufactured. The function g(x) = 20x - 400 represents the cost of production, where x is the number of tablets being manufactured. The function g(x) = 20x - 400 represents the cost of production, where x is the number of tablets being manufactured. What is (f - g)(300)? Explain.
A. $1,300 is the cost of manufacturing 300 tablets
B. $12,500 is the cost of manufacturing 300 tablets.
C. $1,300 is the profit made from 300 tablets.
D. $12,500 is the profit made from 300 tablets.
Answer:
(f - g)(300) = $1,300 is the profit made from 300 tablets
Step-by-step explanation:
(f - g)(300) is the profit made from 300 tablets
(f - g)(x) = (3 x + 6,000) - (20 x - 400)
- Simplify it
(f - g)(x) = 3 x + 6,000 - 20 x + 400
- Add like terms
(f - g)(x) = -17 x + 6,400
Substitute x by 300
(f - g)(300) = -17(300) + 6,400
(f - g)(300) = -5,100 + 6,400
(f - g)(300) = $1,300
The profit is $1,300
HELP ASAP!!
Select the two values of x that are roots of this equation.
x²+2x-5=0
A. x--1+2√√6
B. x=-1+√6
C. x=-1-√6
D. x=-1-2√6
Answer:
Step-by-step explanation:
hello:
here an solution
Solve the system of equations using substitution. 6x=−6y−30−3x−3y=15
The system of equation have an infinite solution.
How to solve system of equation?6x = -6y - 30
-3x -3y = 15
Therefore, let's rearrange the system of equations.
6x + 6y = -30
-3x - 3y = 15
multiply equation(ii) by 2
6x + 6y = -30
-6x - 6y = 30
add the equations
0 = 0
Since 0 = 0 for any value of x, the system of equations has infinite solutions.
learn more on equations here: https://brainly.com/question/14943216
#SPJ1
A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 123 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
The height of package is 34 inches.
According to the statement
we have given that the perimeter of cylinderical package is 123 inches.
and we have to find the volume of this package.
So,
According to the perimeter
2(Pi)r + h = 123
and then
h = 123 - 2(Pi)r
then the volume become
V = (Pi) r^2h
V= (Pi) r^2 * [ 123 - 2(Pi)r ] = 123 (Pi) r^2 - 2(Pi)r^3
then differentiate it
dV/dr = 246(Pi) r - 6(Pi)r^2
Now take
r(246(Pi) - 6(Pi)r) = 0
then neglect r=0 and then find another value of r.
r = 246(Pi) / 6(pi)
here r=41 then
h = 123 - 2(Pi)r
h = 123 - 2(3.14)41
h = 123 - 2(Pi)r
Then put the value of r then h = 34 inches.
So, The height of package is 34 inches.
Learn more about Volume here https://brainly.com/question/1972490
#SPJ4
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes
respectively: (a) 3 /2 and 5
The quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3 /2 and 5 is 2x² - 3x + 10
What is a quadratic polynomial?A quadratic polynomial is a polynomial of the form ax² + bx + c
How to find the quadratic polynomial?For any given quadratic polynomial we have
x² - (sum of zeros)x + (products of zeros) = 0
Given that the sum and product of its zeroes respectively 3/2 and 5,
We have that
sum of zeroes = 3/2 and product of zeros = 5Substituting the values of the variables into the equation, we have
x² - (sum of zeros)x + (products of zeros) = 0
x² - (3/2)x + (5) = 0
x² - (3/2)x + (5) = 0
Multiplying through by 2, we have
2 × x² - 2 × (3/2)x + 2 × (5) = 0 × 2
2x² - 3x + 10 = 0
So, the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3/2 and 5 is 2x² - 3x + 10
Learn more about quadratic polynomial here:
https://brainly.com/question/7784687
#SPJ1
What is the equation of the line that passes through (4,11) and is perpendicular to the line with the following equation
Your question is incomplete. please read below for the missing content
y = -3/4x + 14 is the answer.
y = 4/3x+ 7...slope here is 4/3. A perpendicular will have a negative reciprocal slope. All that means is to flip the slope and change the sign.
4/3....flip it....3/4....change the sign....-3/4. So our perpendicular equation has to have a slope of -3/4
y = mx + b
slope(m) = -3/4
(4,11)...x = 4 and y = 11
now we sub and find b, the y int
11 = -3/4(4) + b
11 = - 3 + b
11 + 3 = b
14 = b
so ur line is : y = -3/4x + 14
The perpendicular line has the opposite slope of the reciprocal, so the slope of the line you want to find is 1/2. Inserting the given points into the equation y = 1 / 2x + b and solving b yields b = 6. Therefore, the linear equation is y = ½x + 6. When relocated, it becomes –x / 2+. y = 6.
Q) What is the equation of the line that passes through the point (4,11) and is perpendicular to the line with the following equation y = 4/3x + 7
Learn more about the equation of perpendicular line here:https://brainly.com/question/7098341
#SPJ4
Can someone help me please
The domain of the function will therefore be 0≤x<∞
Domain of a functionDomain of a function are the independent value for which a function exists. Given the function below;
f(x) = [tex]\sqrt[4]{x}[/tex]
Since the value in the root cannot be negative hence the domain of the function will be all positive real numbers.
The domain of the function will therefore be 0≤x<∞
Learn more on domain here: https://brainly.com/question/25959059
#SPJ1
I need this problem solved
Answer:
AP = 12, and FQ = 8
Step-by-step explanation:
The proportion between AB:FG and AP:FQ is the same.
--> 9:6 = AP:FQ
I'll say that FQ is x and AP is x+4 (since AP is 4 longer than FQ)
--> 9:6 = x+4:x
--> 6(x+4) = 9x
--> 6x + 24 = 9x
--> 24 = 3x
--> x = 8
Since AP= x+4 and FQ= x. AP becomes 12 and FQ becomes 8.
Move the sliders to set the values of r, h, and k, and record at least three different sets of data. also record the equations of the corresponding circles.
The equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
The question seems incomplete and complete question given in the image !!!!
A circle is the set of all points in a plane at a given distance (called the radius) from a given point (called the center.)
We know that the general equation for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where ( h, k ) is the center and r is the radius.
According to the question
The equation of circle given is [tex]x^2+y^2=1[/tex]
Center at origin
i.e
(h,k) = (0,0)
and radius = 1 unit
Now ,
By changing changing center (h,k) and radius of equation it will give following equations
h k r equation of circle
0 1 3 [tex](x-0)^2+(y-0)^2=3^2[/tex]
2 2 3 [tex](x-2)^2+(y-2)^2=3^2[/tex]
1 1 1 [tex](x-1)^2+(y-1)^2=1^2[/tex]
-2 -1 2 [tex](x+2)^2+(y+1)^2=2^2[/tex]
3 2 1 [tex](x-3)^2+(y-2)^2=1^2[/tex]
-5 1 3 [tex](x+5)^2+(y-1)^2=3^2[/tex]
Hence, the equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
Learn more about general equation for a circle here
brainly.com/question/10618691
#SPJ4
Three less than a number x is more than 15. an inequality that represents this word sentence is
Answer:
x - 3 > 15
Step-by-step explanation:
Which is the best first step to factor….?
Answer:
A
Step-by-step explanation:
By using greatest common factor you are able to take a 2 out of all the numbers
Which of the following is equal to m^5/2, for all value of m?
The equivalent expression is:
[tex](m^5)^{1/2} = \sqrt{m^5}[/tex]
Which is the one in option A.
How to identify the equivalent expression?
Here we start with the expression:
[tex]m^{5/2}[/tex]
Now, remember that:
[tex]\sqrt{x} = x^{1/2}[/tex]
[tex](x^a)^b = x^{a*b}[/tex]
if we define a = 5 and b = 1/2, we get:
[tex]m^{5/2} = (m^5)^{1/2}[/tex]
Using the first property, we get:
[tex](m^5)^{1/2} = \sqrt{m^5}[/tex]
Then we conclude that the correct option is A.
If you want to learn more about equivalent expressions:
https://brainly.com/question/2972832
#SPJ1
a. Use the properties of right triangles and AABC to prove the Law of Sines.
b. Find the length of BC, rounded to the nearest tenth of a unit.
In your final answer for parts A and B, Include all of the necessary steps and calculations.
The Law of sines defines that in a triangle, (Sin A)/a = (Sin B)/b = (Sin C)/c and as per law of sines the length of BC is 24.
The given triangle is ΔABC, we split the given triangle into two right-angled triangle ΔABD and ΔBCD.
In the triangle ΔABD,
sin θ = opposite side/hypotenuse
sin A=BD/AB
BD=(sin A)/AB
And in the triangle ΔBCD,
sin θ = opposite side/hypotenuse
sin B=BD/BC
BD=(sin B)/BC
Hence, BD=(sin A)/AB=(sin B)/BC
Let say, (sin A)/a=(sin B)/b
As per law of sine, (sin A)/a=(sin B)/b
Then,
(sin 46°)/a=(sin 31°)/17
a=(17 × sin 46°)/(sin 31°)
a=23.74
a=24
Hence, the value of BC, rounded to the nearest tenth of a unit is 24.
Learn more about law of sine at
https://brainly.com/question/13983159
#SPJ1