Answer: x^2 - 2x + y^2 - 6y + 10 = 0.
Step-by-step explanation: The power station is located 1 mi west and 3 mi north of the center of town, which means that it is located at the point (1, 3) on the coordinate plane. The power outage affected all homes and businesses within a 5 mi radius of the power station, which means that the furthest points from the station affected by the power outage are located on a circle with a radius of 5 mi.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values for the center of the circle (h, k) = (1, 3) and the radius r = 5, the equation of the circle consisting of the furthest points from the power station affected by the power outage is:
(x - 1)^2 + (y - 3)^2 = 5^2
This simplifies to:
x^2 - 2x + 1 + y^2 - 6y + 9 = 25
Combining like terms, the equation becomes:
x^2 - 2x + y^2 - 6y + 10 = 0
This can be written in standard form as:
x^2 - 2x + y^2 - 6y + 10 = 0
Therefore, the equation of the circle consisting of the furthest points from the power station affected by the power outage is x^2 - 2x + y^2 - 6y + 10 = 0.
approximate fy(3,5)fy(3,5) using the contour diagram of f(x,y)f(x,y) shown below.
The approximation of [tex]f_x(3,5)[/tex] using the contour diagram of f(x, y) is [tex]-\frac{2}{3}[/tex]
As per the given data we have determine the value of approximation of [tex]f_x(3,5)[/tex] using the contour diagram of f(x, y).
A contour or a contour line may be defined as the line of intersection of a level surface with the surface of ground.
This means every point on a contour line has the same altitude as that of the assumed intersecting surface.
The set of the curves f(x, y)=c
From the given contour plot the curves intersects with the line y = 5 are f( x, y ) = 12 and f (x, y) = 10
f(x, y) = 12 intersects the line y = 5 at the point x = 3
So, f(3,5) = 12
f(x, y) = 10 intersects the line y = 5 at the point x = 6
so, f(6,5) = 10
[tex]$f_x(3,5)= \lim _{h \rightarrow 0} \frac{f(3+h, 5)-f(3,5)}{h}$[/tex]
Where approximate h = 3
[tex]f_x(3,5) & =\frac{f(3+3,5)-f(3,5)}{3}[/tex]
[tex]=\frac{f(6,5)-f(3,5)}{3}[/tex]
[tex]=\frac{10-12}{3}[/tex]
[tex]f_x(3,5) & =\frac{-2}{3}[/tex]
Therefore the answer is [tex]-\frac{2}{3}[/tex].
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Approximate [tex]f_x(3,5)[/tex] using the contour diagram of f(x, y) shown below.
Diagram attached at the end of solution
need help with this question
Answer:
y = -6x - 4
Step-by-step explanation:
Slope intercept form:
y = mx + b
m is the slope
b is the y-intercept
To find the slope, you take two points from the line and plug them into the following equation:
[tex]\frac{y2-y1}{x2-x1}[/tex]
Let's use (0, -4) and (-2, 8):
[tex]\frac{8-(-4)}{-2-0} = \frac{12}{-2}=-6[/tex]
So m = -6
We know that the y-intercept (b) is -4, so we can plug everything into the equation:
y = -6x - 4
How is h = 20 different than h < 20?
Answer:
h = 20 mean h can only be 20
h < 20 means h can only be a number that is smaller than 20, can't be exactly 20
Step-by-step explanation:
h = 20
This means the variable h can only be 20; it can't be lower or higher than 20.
h < 20
This means the variable h can only be smaller than 20; this means the number can only be below 20 and can't be exactly 20.
how many elements if a coin is tossed 10 times start and end with different faces and have a total of 4 tails
A total of 112 combinations are possible out of all possible combinations when a coin is tossed 10 times and having total of 4 tails and have different start and end faces.
For the given question we have 2 conditions:
condition 1:
when the start turn have head face then the end turn must have tails face as it is given that start and end have different faces.
so in this case 1st and last position is fixed so we have exactly 8 positions.
and given that out of 10 times there must be total of 4 tails and we discussed that last face already have tail face so now out of 8 available positons we have exactly 3 tails in it and rest 5 must be heads.
so we have 8 available positions and we can select any 5 out of them and the number of ways of selection of this is = 8 combination 5 = [tex]8_C__5[/tex] =56 ways
conditon 2:
when the start turn have tail face then the end turn must have head face as it is given that start and end have different faces.
so in this case 1st and last position is fixed so we have exactly 8 positions
and given that out of 10 times there must be total of 4 tails and we discussed that first face already have tail face so now out of 8 available positons we have exactly 3 tails in it and rest 5 must be heads.
so we have 8 available positions and we can select any 5 out of them and the number of ways of selection of this is =8 combination 5 = [tex]8_C__5[/tex] =56 ways
so total number of ways is = no. of ways condition 1+ no. of ways condition 2 = 56 +56 = 112 ways
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1. Name the inequality that is graphed. If you need use <= and >= (Use the attached photo)
2. Solve for t.
2t +7 > -3(t+1)
3. Graph (or describe the graph--give the starting point, if it is open or closed and if the graph points to the right or left)
-3y>6
4. (same instructions as #3)
y/2 <-3
5. (same instructions as #3)
4y 3x -1
1) The inequality used in graph is;
⇒ x > -2
2) The solution for t will be;
⇒ t > - 2
3) The graph of - 3y > 6 is shown in figure.
4) The graph of y/2 < - 3 is shown in figure.
5) The graph of 4y > 3x - 1 is shown in figure.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Now,
1) By the graph, we get;
The solution of the graph is,
⇒ x > - 2
Thus, The used inequality is '>'.
2) The inequality is,
⇒ 2t + 7 > - 3 (t + 1)
Solve for t as;
⇒ 2t + 7 > - 3t - 3
⇒ 2t + 3t > - 3 - 7
⇒ 5t > - 10
⇒ t > - 2
3) The inequality is,
⇒ - 3y > 6
⇒ - y > 2
⇒ y < - 2
4) The inequality is,
⇒ y/2 < - 3
⇒ y < - 6
5) The inequality is,
⇒ 4y > 3x - 1.
Thus, The graph of 4y > 3x - 1 is shown in figure.
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A high school environmental science class decides to spend one day each week cleaning a river by collecting discarded
plastic water bottles. Each week, the class collects half as many bottles as the previous week.
If the number of bottles collected in the first week is 256, which function models the number of bottles, B, collected
during week n?
The function that models the number of bottles, B, collected during week n is; B(n) = 256(¹/₂)ⁿ⁻¹
How to solve Geometric Sequence?The formula for the nth term of a geometric sequence is;
aₙ = arⁿ⁻¹
where;
a is first term
r is common ratio
n is position of term
We are given that;
a = 256 bottles
r = ¹/₂
Thus;
B(n) = 256(¹/₂)ⁿ⁻¹
Thus, we conclude that B(n) represents the required function.
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Liam's family has completed 40% of a trip. They have traveled 15 miles.
How far is the trip?
The number of miles the whole trip is 15 miles
What is the trip's length?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
The number of miles the whole trip is 15 miles.Given that, Liam's family has completed 40% of a trip.
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of miles be x.
so, 40% of x=30
⇒ 40/100 ×x=30
⇒ 0.4x=30
⇒ x=30/0.4
⇒ x=12 miles
Therefore, the number of miles the whole trip is 15 miles.
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CAN YOU PLEASE HELP ME I AM IN GRADE 12 I NEED SOLVE THIS QUESTION
WHATS 1+1=
Answer:
2
Step-by-step explanation:
1 + 1 = 2
I hope my answer helps you :)
Answer:
2 or Window
Step-by-step explanation:
1 + 1 = 2
OR
1 + 1 = WINDOW!
Write the
equation of the line that
passes through the point (3,-1) and has a slope of
2
Answer:
y = 2x - 7
Step-by-step explanation:
y = mx + b
m is known (m=2):
y = 2x + b
Since one point is known (3,-1), you can solve for b:
-1 = 2(3) + b
b = -7
So the equation is:
y = 2x - 7
A local petting zoo allows visitors to feed the goats food pellets. The petting zoo starts the month with 525.25 pounds of food pellets. Each week, the workers track the amount of food pellets given out and any food pellet deliveries.
Week 1 = -164 1/2
Week 2 = -189.75
Week 3 = 355 7/8
Week 4 = -200 3/16
How many pounds of food pellets will the petting zoo have left at the end of the month? Write your answer as a mixed number in simplest form.
__ pound(s)
Answer:
326 11/16 pounds----------------------------
Add up all the numbers to get the end of month figure.
Convert mixed fractions to sum of whole and fractions, then combine whole numbers and fractions, bringing all to common denominator of 16.
525.25 - 164 1/2 - 189.75 + 355 7/8 - 200 3/16 = 525 + 1/4 - 164 - 1/2 - 189 - 3/4 + 355 7/8 - 200 3/16 = (525 - 164 - 189 + 355 - 200) + (4/16 - 8/16 - 12/16 + 14/16 - 3/16) = 327 + (- 5/16) = 327 - 5/16 = 326 11/16 poundswhich of the following is true about sampling distributions? 1 point sampling distributions get closer to normality as the sample size increases. sampling distribution of the mean is always right skewed since means cannot be smaller than 0. sampling distributions are always nearly normal. shape of the sampling distribution is always the same shape as the population distribution, no matter what the sample size is.
A correct statement about sampling distributions is: Sampling distributions of means get closer to normality as the sample size increases.
The correct answer is an option (A)
In this question we have been given few statements.
We need to select a correct statement about sampling distributions.
We know that the sampling distribution is nothing but a probability distribution that is obtained through repeated sampling of a specific population.
Also according to central limit theorem, sampling distribution of means approaches normal when the sample size increases.
Therefore Sampling distributions of means get closer to normality as the sample size increases.
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What is the length of the midsegment of a trapezoid whose vertices are I(-3, -5), J(8, -5), K(3, -9), and L(-3, -9)?
Answer:
the answer will be 4.75 units
Step-by-step explanation:
explained
The midsegment of a trapezoid is a line segment that connects the midpoints of the nonparallel sides of the trapezoid. To find the length of the midsegment, we need to first find the midpoints of the sides IJ and KL.
The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. We can find the midpoint of a line segment by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.
The coordinates of the endpoints of the side IJ are (-3, -5) and (8, -5), so the midpoint of this side is:
((-3 + 8)/2, (-5 + (-5))/2) = (2.5, -5)
The coordinates of the endpoints of the side KL are (-3, -9) and (3, -9), so the midpoint of this side is:
((-3 + 3)/2, (-9 + (-9))/2) = (0, -9)
To find the length of the midsegment, we can use the distance formula to find the distance between the two midpoints:
sqrt((2.5 - 0)^2 + (-5 - (-9))^2) = sqrt(2.5^2 + 4^2) = sqrt(6.25 + 16) = sqrt(22.25) = 4.75
Therefore, the length of the midsegment of the trapezoid is approximately 4.75 units.
According to the 2000 u.s. census, 7 out of every 25 homes are heated by electricity. at this rate, predict how many homes in a community of 12,000 would be heated by electricity. a. 6,725 homes b. 3,100 homes c. 3,360 homes d. 4,020 homes
The number of homes in a community of 12, 000 which would be heated by electricity, given the rate of houses heated, is c. 3,360 homes
How to find the number of houses ?To find the number of homes in the community which would be heated by electricity, first find the percentage of homes that are heated according to the U.S. Census :
= Number of houses heated / Total number
= 7 / 25
= 28 %
When given a community of 12, 000 homes therefore, the number of homes which would be heated are:
= Percentage of houses heated x Community size
= 28 % x 12, 000
= 3,360 homes
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Answer:
c. 3,360 homes
Step-by-step explanation:
Use this model to determine the answer.
What is 6÷1/3?
Answer:
18
Step-by-step explanation:
[tex]6/ 1/3[/tex] =
6 x 3
18
ten distinct points are chosen on a circle. a line segment is drawn between every pair of chosen points. how many line segments are drawn?
Answer:
45
Step-by-step explanation:
You want to know the number of line segments that can be drawn between pairs of points in a group of 10 distinct points.
SolutionFrom the first point, 9 segments can be drawn.
From the second point 8 more segments can be drawn. (The segment to the first point has already been counted.)
From the third point, 7 more segments can be drawn. The total number of segments will be the sum of integers from 1 through 9:
9(10)/2 = 45
45 line segments can be drawn.
__
Additional comment
This is identical to the "handshake" problem: the number of handshakes in a group of 10 people if each shakes hands with all the others.
Find the sum of the first 75 terms for the following sequence:
bn = {-10, -6, -2, 2, ... }
Answer: The sum of the first 75 terms for the following sequence is 10,200
Step-by-step explanation: To find the sum of the first 75 terms for the following sequence, we have to first find the 75th term for which the formula used here will be,
[tex]a_{75\\} = a_{1} + (n-1)d\\ = -10 + (74-1)(4)\\ = -10 + 292\\ = 282[/tex]
So, the 75th term of this arithmetic progression is 282
Now we will find the sum of the first 75 terms,
[tex]S_{n} = n(a_{1} + a_{75} )/ 2\\ =75(-10 + 282)/2\\ =75(272)/2\\ =20400/2\\ =10200[/tex]
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ANSWER FOR THE POINTS. THE PERFECT 1
Answer:
60
Step-by-step explanation:
Let x = number of people at the party.
0.9x wore red dresses.
2/25x wore green dresses.
rest of people wore white dresses
The rest of the people is
x - 0.9x - 2/25 x
x - 0.9x - 0.08x = 15
0.02x = 15
x = 750
0.9x = 675 (red)
2/25 x = 60 (green)
0.02x = 15 (white)
Answer: 60
Increase by
50%
Decrease by
5%
A number went into this machine and 57 came out.
What number went in?
Answer:
40
Step-by-step explanation:
Using the distance formula, what is the distance of C (-4, -2) and D (3, 5)?
15
45
9.8
22
4 tons of fertilizer cost $7,440.00. What is the price per pound?
Answer:
The correct answer would be 0.94 per pound.
Step-by-step explanation:
Mr. Montenegro is ordering tennis shirts for his Holub tennis team. He pays a delivery fee of $18. He also pays $12 each shirt ordered. Which equation can be used to find y, the total cost Mr. Montenegro pays in dollars when x shirts are ordered?
Answer:
y = 18 + 12x
Step-by-step explanation:
To find the total cost Mr. Montenegro pays in dollars when x shirts are ordered, we can use the equation y = 18 + 12x, where y is the total cost in dollars and x is the number of shirts ordered. This equation takes into account the delivery fee of $18 and the cost of each shirt, which is $12. Therefore, we can use the equation y = 18 + 12x to find the total cost Mr. Montenegro pays when he orders x shirts.
A hostel has food provisioned for 30 days to serve 80
people. If 40 more men join the hostel, the same provision
would have last for how many days?
Answer: 20 days
Step-by-step explanation:
First, we find the food provisioned for 1 man will last for how many days
Take 80 times 30 = 2400 days
Now we know that 40 more joined
80 + 40 = 120 serve
So, we take 2400 divided by 120 = 20 days
find f. f '(t) = 16 1 + t2 , f(1) = 0
If the given function is f '(t) = 16/(1 + t²), the value of the function f will be f = 16 tan (t) - 24.8.
It is described as a particular kind of relationship with a set domain and range. Every value in the domain has a specific relationship with one value in the range, according to the function.
Given that,
f '(t) = 16/(1 + t²)
f(1) = 0
In order to find f integrate the function,
f = ∫(16/(1 + t²)) dt
f = 16 ∫1/(1 + t²) dt
f = 16 tan t + C
As, f(1) = 0
0 = 16 tan 1 + C
C = - 16(1.55) = -24.8
Thus, the value of function is f = 16 tan (t) - 24.8.
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ifty percent of the people that use the internet buy their clothes exclusively online. find the probability that only of internet users buy their clothes exclusively online. round to three decimal places.
The answer is 0.109, or choice B. The probability that only six of 8 Internet users buy their clothes exclusively online is 0.109.
The probability that only 6 out of 8 Internet users buy their clothes exclusively online can be calculated using the binomial distribution. The probability of a single Internet user buying their clothes exclusively online is 0.5, and the probability of an Internet user not buying their clothes exclusively online is 0.5.
The probability of 6 out of 8 Internet users buying their clothes exclusively online can be calculated using the formula:
P(X=6) = (8 choose 6) * (0.5)^6 * (0.5)^2
Plugging in the values, we get:
P(X=6) = (8 choose 6) * (0.5)^6 * (0.5)^2
= 28 * (0.5)^6 * (0.5)^2
= 28 * (0.015625) * (0.25)
= 0.109
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Complete Question:
Fifty percent of the people that use the Internet buy their clothes exclusively online. Find the probability that only six of 8 Internet users buy their clothes exclusively online. Round to three decimal places. explain answer in 100 words.
A. 0.750
B. 0.109
C. 0.438
D. 0.004
Which statement about determining the quotient 12÷1/4 is true?
A. Because 3×1/4=12, 12 divided by 1/4 is 3.
B. Because 24×1/4=12, 12 divided by 1/4 is 24.
C. Because 16×1/4=12, 12 divided by 1/4 is 16.
D. Because 48×1/4=12, 12 divided by 1/4 is 48.
Answer:
D
Step-by-step explanation:
If 48 times 1/4 is 12, 12 divided by 1/4, the inverse operation, is 48.
a machine uses electrical switches that are known to have a 3% fail rate for each use. the machine uses three switches, and each switch is independent. (a) how many outcomes are there in the sample space?
There can be 8 possible outcomes present in the sample space
The probability that one switch is not working is 3% or 0.03
We need to find the number of possible outcomes in the sample space that can be possible
The first switch can be working or not
The second switch might be working or not
so does the third switch, it might be working or not working
And each switch is independent to one another
The number of outcomes can be
2 x 2 x 2 = 8
Therefore, the number of outcomes are there in the sample space is 8
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Using long division, determine the decimal expansion of 5/8
Answer: Solution: 0.625
Step-by-step explanation: First, you have to set up the fraction as a division problem, so we have to remember that when making a fraction to a decimal, the numerator becomes the dividend, and the denominator becomes the divisor, which the dividend goes inside the bracket, and the divisor goes outside the bracket. Now, you would divide as usual, and get 0.625. I hoped this helped! NOTE: I put in an attachment to show what I'm talking about.
Answer:
Step-by-step explanation: do 5÷8 and u get 0.625
. the volume of a cube is increasing at a rate of 10 cm3 ymin. how fast is the surface area increasing when the length of an edge is 30 cm?
The surface area of the cube is increasing at a rate of 49 cm²/min.
If the length of an edge of a cube is l cm.,
its volume V is l3 and surface area A is 6l2.
Differentiating V=l3 w.r.t. time,
we get,
dV/dt = 3l2dldt
dV/dt=10 cm3min,
when l=90
dl/dt=103×902
=12430
As A=6l2
dA/dt =12l×dldt
=12×90×12430
=49 cm2min
The total number of cubic units that a cube occupies in three dimensions is its volume. Six faces, twelve edges, and eight vertices make up the three-dimensional shape of a cube. Therefore, the area encircled by a cube's six faces is considered to equal its volume.
It differs from 2D shapes in that it adds a third dimension, known as height or thickness, in addition to length and breadth.
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how many bit strings of length 12 contain a) exactly three 1s? b) at most three 1s? c) atleastthree1s? d) an equal number of 0s and 1s?
bit strings of length 12 contain a) exactly three 1s is 220 b) at most three 1s is 2700 c) atleastthree1s is 220 d) an equal number of 0s and 1s is 66.
a) To calculate the number of bit strings of length 12 containing exactly three 1s, we can use the combination formula. The formula is nCr, where n is the total number of bits (12) and r is the number of 1s (3).The solution is 12C3 = 220.
b) To calculate the number of bit strings of length 12 containing at most three 1s, we can use the summation formula. The formula is sum of nCr, where n is the total number of bits (12) and r is the number of 1s (3). So, the answer is (12C0 + 12C1 + 12C2 + 12C3) = 2700.
c) To calculate the number of bit strings of length 12 containing at least three 1s, we can use the combination formula. The formula is nCr, where n is the total number of bits (12) and r is the number of 1s (3). The solution is 12C3 = 220.
d) To calculate the number of bit strings of length 12 containing an equal number of 0s and 1s, we can use the combination formula. The formula is nCr
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Joan' income i $390 per week. She ave 20% of her weekly alary. How much doe he ave each week?
Joan saved a total of $78 from her $390 weekly income each week.
What is percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. Percentage means 1 part from hundreds and represented by the symbol '%'. Percentages have no dimensions. Therefore, it is called a dimensionless number.
Percentage = (value/total value)× 100
We have, Joan's income = $390/week
Saving = 20% from her weekly salary.
We have to calculate how much does she save each week. Joan save 20% of her weekly income (i.e $390). let Joan saved $x each week from her sallary. The saved income in dollars each week by Joan i.e ($x) is equals to 20% of 390
x =( 20/100)× 390
=> x = 390/5
=> x = 78
Hence, Joan saves $78 each week.
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