There are 720 ways that the 3 homes could be chosen if the order of visiting is considered. There are 120 ways that the 3 homes could be chosen if the order of visiting is not important.
What is permutation?A permutation is the arrangement or ordering of a finite set of an element.
From the information given:
If there are 10 homes in the desired price range listed in the area:
Then:
n = 10 and r = 3So, the number of ways of choosing 3 out of 10 (without replacement) and arranging is:
[tex]\mathbf{^nP_r= \dfrac{n!}{(n-r)!}}[/tex]
[tex]\mathbf{^nP_r= \dfrac{10!}{(10-3)!}}[/tex]
[tex]\mathbf{^nP_r= \dfrac{10\times 9\times 8 \times 7!}{(7)!}}[/tex]
= 720 ways
Now, the number of ways of choosing 3 out of 10 if the order of visiting is not important is the combination of the elements and it can be computed as:
[tex]\mathbf{^nC_r= \dfrac{n!}{(n-r)!r!}}[/tex]
[tex]\mathbf{^{10}C_3= \dfrac{10!}{(10-3)!3!}}[/tex]
[tex]\mathbf{\implies \dfrac{10\times 8\times 9 \times 7!}{(7)! \times 3\times 2}}[/tex]
[tex]\mathbf{\implies \dfrac{10\times 8\times 9}{6}}[/tex]
= 120 ways
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The total interest on a discounted loan is $80. If James received $880 into his bank account on drawdown, and the loan lasts for 6 months, what is the (simple) interest rate? Give your answer as a percentage to the nearest tenth of a percent.
With the use of formula, the interest rate is 18.2%
How can Simple Interest be Calculated ?The Interest is the product of the principal, time and the rate in percentage. That is, I = PTR / 100
Where
P is the Principal = $880T is the time = 6 months = 0.5 yearR is the rate = ?I is the interest = $80Substitute all the parameters into the formula
80 = (880 x 0.5R)/100
cross multiply
8000 = 440R
R = 8000/440
R = 18.2%
Therefore, the (simple) interest rate is 18.2%
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if the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y-intercept of the regression line to three decimal places. x2,3,4,5,6 y73,77,85,101,133
A. log(y) =-1.706x + 0.064
B. log(y) =-0.064x + 1.706
C. log(y) = 1.706x + 0.064
D. log(y) = 0.064x + 1.706
The regression equation is (d) log(y) = 0.064x + 1.706
How to determine the regression equation?The table of values is given as:
x 2 3 4 5 6
y 73 77 85 101 133
Calculate the logarithm of the y values.
So, we have:
x 2 3 4 5 6
log(y) 1.86 1.89 1.93 2 2.12
Next, we enter the above values in a regression calculator.
From the calculator, we have the following summary:
Sum of X = 20Sum of Y = 9.8Mean X = 4Mean Y = 1.96Sum of squares (SSX) = 10Sum of products (SP) = 0.63The regression equation is then represented as:
log(y) = bx + a
Where:
b = SP/SSX = 0.64/10 = 0.064
a = MY - bMX = 1.96 - (0.064*4) = 1.706
So, we have:
log(y) = 0.064x + 1.706
Hence, the regression equation is (d) log(y) = 0.064x + 1.706
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Let [tex]K[/tex] be a circle with centre [tex]O[/tex]. A second circle [tex]L[/tex] passes through [tex]O[/tex] and cuts [tex]K[/tex] at two other points [tex]A[/tex] and [tex]B[/tex]. Let [tex]P[/tex] be a point on arc [tex]AOB[/tex] and extend line segment [tex]BP[/tex] to intersect [tex]K[/tex] at a second point [tex]Q[/tex]. Prove that the bisector of angle [tex]APQ[/tex] passes through [tex]O[/tex].
The bisector of angle APQ passes through O and this is illustrated below.
How to illustrate the information?From the information given, the center is O. and the circle passes through O and cuts at K.
In this case, it should be noted that the circles are equal according to the SAS test.
Here, AOB + APQ = 180° (Linear pair)
2AOB = 180
AOB = 90.
Therefore, the bisector of angle APQ passes through O.
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Pls help! Geometry
Find the area
3 red balls, 4 white balls, and 1 green ball are in a bag. Balls are drawn without replacement. Find the probability that the red balls can be drawn before the green ball is drawn.
The probability that the red balls can be drawn before the green ball is drawn is 3/8.
What is Probability?The probability is the measure of the likelihood of an event to happen.
Given:
red balls= 3
white balls = 4
green balls = 1
So, Probability of red balls
=3/8
Probability of green balls
=1/7
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2. Marjorie wants to subdivide a rectangular plot of land measuring 600 m by 720 m
into equal square lots. What is the side length of the largest possible square lot
she can use? Show the prime factorization results to support your answer.
the largest length of the squares will be 120m.
What is the side length of the largest possible square lot she can use?
The largest possible length will be equal to the greatest common factor between the dimensions of the rectangular plot, so we need to find the GCF between 600 and 720.
If we decompose both numbers, we get:
600 = 2*2*2*3*5*5
720 = 2*2*2*2*3*3*5
Then the greatest common factor is: (2*2*2*3*5) = 120
So the largest length of the squares will be 120m.
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Thomas traveled north 24 miles and then 15 miles west. Find the shortest distance between the start and end points. 15 miles O 24 miles 28.3 miles 32.8 miles Thomas traveled north 24 miles and then 15 miles west . Find the shortest distance between the start and end points . 15 miles O 24 miles 28.3 miles 32.8 miles
The distance between the start and end points is 28.3 miles.
How to find the distance?
Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_2 -y_1)^2}[/tex]
Here the initial point is (0mi, 0mi).
If we define the north as positive y-axis and east as the positive x-axis, after that Thomas travels 24 miles north and 15 miles west his new position is:
(-15mi, 24mi).
The distance is then:
[tex]d = \sqrt{(-15mi - 0mi)^2 + (24mi - 0mi)^2} = 28.3mi[/tex]
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John missed 4 problems on a test but did 75% of them correctly. How many problems
were there in the test?
Answer:
16
Step-by-step explanation:
he missed 25%
if 4 = 25% then 16 questions total
4*4=16 and 25% * 4 = 100%
Answer: 16 problems
Step-by-step explanation:
First find out how many John got wrong. 100%-75%=25%. Then do cross multiplication: 4*100=25x; 400=25x. Divide 25 on both sides and... BOOM! you get 16 problems.
Determine if the given ordered triple is a solution of the system.
(4, -5, -4)
4x + 2y + z = 2
5x - 4y - z = 44
3x + y + 4z = -9
Answer:
It is.
Step-by-step explanation:
(x, y, z) => (4, -5, -4)
substitute 4 in x, -5 in y & -4 in z for all the equations in the system.
4x + 2y + z = 2
4(4) + 2(-5) - 4 = 2
2 = 2
5x - 4y - z = 44
5(4) - 4(-5) - (-4) = 44
44 = 44
3x + y + 4z = -9
3(4) + (-5) + 4(-4) = -9
-9 = -9
All equations therefore agree with the ordered triple.
find x and y
pls help
Angles on straight line = 180
110 + 5x = 180 degrees
-110
5x. = 70
÷ 5
x. = 14
5 x 14 = 70
Angles in triangle = 180
70 + 40 = 110
So, the missing angle inside the triangle is 70
Now to find y, use angles on straight line = 180
2y + 70 = 180
- 70
2y = 110
÷2
y = 55 degrees
Hope this helps!
Pls help! Geometry
What is the total cost of material for bunny costumes?
Answer: $201.81
Step-by-step explanation:
The total amount of faux fur required is [tex]6(3.1)=18.6[/tex] square yards.
Multiplying this by $10.85 per square yard, we get the total cost is [tex](18.6)(10.85)=\$201.81[/tex]
What is the value of "y" that satisfies the expression below?
1 y + 12 = 6 ( 1 y + 1 )
Round your answer to 2 decimal points (i.e. #.##)
Answer:
1.20Step-by-step explanation:
1y + 12 = 6 (1y + 1)
1y + 12= 6y + 6
12 - 6 = 6y - 1y
6 = 5y
y = 6/5
y = 1.2
I don't what you meant by rounding to 2 decimal points so my answer is
1.20Need answer & explanation! Please & thank you!
Answer: the correct is x=1,
Step-by-step explanation:
Graph each side of the equation. The solution is the x-value of the point of intersection.
x=1
Answer:
1
Step-by-step explanation:
you can plug it in and it gives you 3-1 which results in 2 as the question asks for
Which composition of transformations maps figure EFGH to figure E"F"G"H"?
a reflection across line k followed by a translation down
a translation down followed by a reflection across line k
a 180° rotation about point G followed by a translation to the right
a translation to the right followed by a 180° rotation about point G
The composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.
What is the transformations rule that was used here?A transformation is a rule that is used to manipulate the position of a point of geometric figure.
And from the figure, we can see that a translation is used, because of the movement of EFGH to figure E"F"G"H" which occurred in the same direction.
Hence, composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.
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Find the demand function for the marginal revenue function. Recall that if no items are sold, the revenue is 0.
R'(x) = 599 - 0.21sqrt(x)
What is the integral that is needed to solve the problem and the demand function?
The integral that is needed to solve the demand function is R(x) = 599x - 0.14[tex]x^{3/2}[/tex]
What is Demand Function?A demand function describes the mathematical relationship between the quantity demanded and one or more determinants of the demand, as the price of the good or service, the price of complementary and substitute goods, disposable income, etc.
Here, given differential equation;
R'(x) = 599 - 0.21[tex]\sqrt{x}[/tex]
we can also write this as;
[tex]\frac{d}{dx}R(x) = 599 - 0.21\sqrt{x}[/tex]
[tex]d R(x) = (599 - 0.21\sqrt{x} ) dx[/tex]
On integrating both sides, we get
[tex]\int\ d R(x) = \int\ (599 - 0.21\sqrt{x} ) dx[/tex]
R(x) = [tex]599x - 0.21 X \frac{2}{3}x^{3/2}[/tex] + C
R(x) = 599x - 0.14[tex]x^{3/2}[/tex] + C ...........(i)
Also given, at x = 0, R(x) = 0, Put these values in equation (i), we get
0 = 0 - 0 + C
C = 0
Put the value of C in equation (i), we get
R(x) = 599x - 0.14[tex]x^{3/2}[/tex]
Thus, the integral that is needed to solve the demand function is R(x) = 599x - 0.14[tex]x^{3/2}[/tex]
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which graph shows the system of inequalities y<-1/3x+1 and y≤2x-3
The graph of the system of inequalities can be seen below.
Which graph shows the solution for the system?
Here we have the inequalities:
y < -(1/3)*x + 1
y ≤2x-3
To graph the first inequality, we need to graph the line -(1/3)*x + 1 with a dashed line (because the symbol < was used) and shade the region below that line.
For the second inequality we need to graph the line 2x-3 with a solid line this time, and again, shade the region below the line.
The graph of the system is shown in the image below.
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What is the slope of the line that passes through the points (-6, -6) and (-9,-5)? Write your answer in simplest form. What is the slope of the line that passes through the points ( -6 , -6 ) and ( -9 , -5)?
Answer:
[tex]y=-\frac{1}{3}x -8[/tex]
Step-by-step explanation:
1) Write down the standard form of an equation of a line and the formula to find m.
[tex]y=mx+b[/tex]
[tex]m=\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
2) Find m using the formula then substitute it into [tex]y=mx+b[/tex].
[tex]m=\frac{-5 - (-6) }{-9 - (-6)}\\m=\frac{-5 +6 }{-9 +6}\\m=\frac{1}{-3} \\m=-\frac{1}{3}[/tex]
So, [tex]y=-\frac{1}{3}x +b[/tex].
3) Find b by substituting a pair of coordinates the line goes through.
[tex]-6=-\frac{1}{3}(-6) +b\\-6=2+b\\-6 - 2=b\\-8=b[/tex]
4) Substitute b into [tex]y=-\frac{1}{3}x +b[/tex] to get your final answer.
[tex]y=-\frac{1}{3}x -8[/tex]
What is the equation of the line AB, if it passes through (-4,0), and is parallel to the line
-x - 4y = 1?
Rewriting the equation of the given line in slope-intercept form,
[tex]-x-4y=1\\\\-4y=x+1\\\\4y=-x-1\\\\y=-\frac{1}{4}x-\frac{1}{4}[/tex]
From this, we know the slope of the given line is -1/4.
Since parallel lines have the same slope, we know the line whose equation we want to find has a slope of -1/4.
Substituting into point-slope form,
[tex]y=-\frac{1}{4}(x+4)\\\\\boxed{y=-\frac{1}{4}x-1}[/tex]
PLEASE HELP
a marine biologist tags 50 fish at lake ness and releases them. five days later, he captures 75 fish and finds that 3 of them are tagged. assuming the population of fish has remained constant over the five days and that this sample is an accurate representation of the portion of the fish in the lake that are tagged, how many fish are in the lake?
Pls Help (question is in pic)
1. If the function holds true, in what year would the cost of mailing a first class letter reach 60 cents.
2. In 2007, the cost of mailing a first-class letter was 41 cents. Has the inflation rate stayed constant since 1991?
Based on the function given, the year when the cost of mailing a first class letter would reach 60 cents is 2007.
If the cost of mailing a first-class letter is 41 cents, then the inflation rate has not stayed constant.
What year does the cost reach 60 cents?0.60 = 0.29 (1.046)^t
0.60 / 0.29 = (1.046)^t
log (2.07) = t x log (1.046)
t = 16 years
Added to 1991:
= 1991 + 16
= 2007
The cost of mailing a first-class ticket was 41 cents however which means that inflation was not constant.
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please help! :(
Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get?
a. 4^2 - 3^3
b. 3^3 + 4^2
c. 4 - 3^3
d. 3^3 - 4^2
e. 3^2 - 4^3
Answer:
d.
Step-by-step explanation:
k gets 3^3
a gets 4^2
subtract 3^3-4^2=d.
A system of three linear equations in three variables is inconsistent. how many solutions to the system exist? none one three infinitely many
None solutions to the system exist.
Given statement: A system of three linear equations in three variables is inconsistent.
Concept: If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables. (The “three variables” are the x, the y, and the z.) The numbers a, b, and c are called the coefficients of the equation.
We know that if a system has no solution, then it is known as inconsistent.
[If there are one, two, or an infinite number of solutions to the system, then it is called consistent.]
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y = x² + 3
y = x + 5
Answer:
x^2-x-2=0
Step-by-step explanation:
x^2+3=x+5
x^2-x-2=0
The diameter of a sphere is
a chord that passes through the center of the sphere.
a fixed point equidistant from all points on the surface of the sphere.
a line segment from the center point to a point on the sphere.
a three-dimensional circle in which all points are equidistant from a fixed point.
The diameter of a sphere is a chord that passes through the centre of the sphere.
We need to complete the given statement.
What is the diameter of the sphere?The diameter of a sphere is the maximum distance between two antipodal points on the surface of the sphere. If is the radius of a circle or sphere, then. The ratio of the circumference of a circle or great circle of a sphere to the diameter.
A chord of a sphere is a segment whose endpoints are on the sphere. A diameter is a chord that contains the centre.
Therefore, the diameter of a sphere is a chord that passes through the centre of the sphere.
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HELP ME! what is the measure of the supplement of each angle? 165°
Answer:
15
Step-by-step explanation:
Supplementary angles add to 180 degrees
Let the supplement be x
x+165 = 180
x +165-165= 180-165
x = 15
The supplement is 15
Answer:
Hello! The answer is 15°.
Step-by-step explanation:
Supplementary angles add up to 180°.
To find the measure of each angle, we can now set up an equation because we have the total that supplementary angles add up to:
x + 165 = 180
Now, we can subtract 165 from both sides to get x by itself:
x + 165 = 180
-165 -165
This leaves us with:
x = 15
can i have the x,y,z for this question? THanks!
Answer:
x=4, y=-2, p=14
Step-by-step explanation:
First simplify the LHS:
[tex]LHS = (16p^8)^\frac{3}{2} \times (216p^{-3})^{-\frac{2}{3}}[/tex]
[tex]= 64 p^{12} \times \frac{1}{36} p^{2}[/tex]
[tex]=\frac{16}{9}p^{14}[/tex]
[tex]=\frac{2^4}{3^2}p^14\\=2^43^{-2}p^{14}[/tex]
Hence x=4, y=2, p=14
Write a proportion for the statement.
40 is to 10 as 32 is to 8.
Hi! ⋇
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
All proportions have this form:
[tex]\sf{\dfrac{a}{b}=\dfrac{c}{d}}[/tex], Where [tex]\sf{\dfrac{a}{b}}[/tex] is equal to [tex]\sf{\dfrac{c}{d}}[/tex].
If [tex]\sf{\dfrac{a}{b}\neq\dfrac{c}{d}}[/tex], it's not a proportion.
_________________________
Here we have two pairs of numbers:
40,10 and 32,8.
Written As a proportion, they look like :
[tex]\sf{\dfrac{40}{10}=\dfrac{32}{8}}[/tex]
Hope this made sense to you :)
[tex]\it{Calligrxphy}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Select the properties of a square? please answer, I'm desperate
Answer:
all are the properties of square
Step-by-step explanation:
all are correct
Tony makes a table to use as a quick reference guide:
Cookies baked (y) is a function of number of batches (x).
Use the table tool to answer the question.
How many cookies will Tony have if he bakes 10 batches more than the maximum number of batches in the table?
Enter the correct answer.
Tony will have 486 cookies if he bakes 10 batches more.
Take two points from table: (8, 234), (9, 252)
Find slope:
[tex]slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow slope \ (m) : \dfrac{252-234}{9-8} = 18[/tex]
This determines that one batch of cookies has 18 cookies.
So, if he bakes 10 more batches:
(10 × 18) = 180 cookies
Total cookies he then will have:
306 cookies + 180 cookies = 486 cookies.
What's the sum Sn of the first n terms of this given sequence?
1, 1+2, 1+2+3, 1+2+3+4, ...
The kth term is 1+2+3+ ... +k =
(I also attached a picture of the question. Thanks!)
Answer: [tex]\frac{k(k+1)}{2}[/tex]
Step-by-step explanation:
This is a standard formula.