The gallons after 8 hours will be 3400 gallons.
How to illustrate the expression?Expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations.
In this case, the reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours.
Therefore, the gallons after 8 hours will be:
= 200 + 400(8)
= 200 + 3200
= 3400 gallons.
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In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
70
Step-by-step explanation:
Solve x2 + 4x = 1 for x by completing the square.
x = −3
x = −1
x equals plus or minus square root of 5 minus 2
x equals plus or minus square root of 5 plus 2
Using the completing square method, the value of (C) x = ±√5 - 2.
What is completing the square method?A quadratic polynomial of the form ax2+bx+c can be transformed to the form in elementary algebra by using the "completing the square" method for certain values of h and k.
In other words, the quadratic expression is completed by inserting a perfect square trinomial.
So, we have:
x² + 4x = 1
The x-coefficient terms must be divided by two:
4/2 = 2
Square:
2² = 4
Add 4 on both sides as follows:
x² + 4x + 4 = 1 + 4
x² + 4x + 4 = 5
Transform into perfect squares:
(x + 2)² = 5
Both sides of the square root:
x + 2 = ±√5
x = ±√5 - 2
Therefore, using the completing the square method, the value of (C) x=±√5-2.
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Complete question:
Solve x2 + 4x = 1 for x by completing the square.
a. x = −3
b. x = −1
c. x equals plus or minus the square root of 5 minus 2
d. x equals plus or minus square root of 5 plus 2
Answer:
is c correct?
Step-by-step explanation:
A racetrack charges $85 for each seat in the lower section, $60 for each seat in the upper sections, and $35 for field tickets. There are three times the amount of seats in the upper section as compared to the lower section. The revenue from selling all 22,800 seats is $948,000. How many seats are in the upper section of the racetrack?
Using a system of equations, the number of seats in the upper section of the racetrack is 3,600.
What is a system of equations?A system of equations, also called simultaneous equations, is two or more equations solved concurrently.
We can use any of the following methods to solve simultaneous equations:
GraphicalSubstitutionEliminationMatrix.In this situation, after forming the equations, we can use substitution and elimination methods to solve them.
Racetrack charge per lower seat = $85
Racetrack charge per upper seat = $60
Racetrack charge per field ticket = $35
Let lower seats = x
Let upper seats = 3x
Let field tickets = y
4x + y = 22,800 ... Equation 1
y = 22,800 - 4x ...Equation 3
85x + 60(3x) + 35y = 948,000
85x + 180x + 35y = 948,000 ... Equation 2
Substitute Equation 3 in Equation 2 to eliminate y:
85x + 180x + 35(22,800 - 4x) = 948,000
85x + 180x + 798,000 - 140x = 948,000
125x = 948,000 - 798,000
125x = 150,000
x = 1,200
Determining the number of seats:
Seats in the Lower section = 1,200
Seats in the Upper section = 3,600 (1,200 x 3)
Field tickets, y = 22,800 - 4x
y = 22,800 - 4(1,200)
= 18,000
Check:
85x + 180x + 35y = 948,000
85(1,200) + 180(1,200) + 35(18,000) = 948,000
102,000 + 216,000 + 630,000 = 948,000
948,000 = 948,000
Thus, based on simultaneous equations, there are 3,600 seats in the upper section of the racetrack.
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Need Awnser asap
Right Awnser gets branliest
Answer:
x1,y16 is the rate of change
Step-by-step explanatI subtracted 13-32 which gives me 16, then I added 16 to 32 to be sure and it gave me 48 so the change on the Y axis is going up by 16 and x axis is going up by 1
What is 0.6 divided by 10
Answer: 0.06
Step-by-step explanation:
Is 5x-8+7y=y-6 linear or nonlinear
Answer:
Step-by-step explanation:
The equation 5x-8+7y=y-6 is linear because it contains only terms with the variables x and y raised to the power of 1. In a linear equation, the highest power of any variable is 1. Nonlinear equations contain exponents that are higher than 1 on one or more variables.
Conrad Savings Bank has a $50 overdraft fee. On Friday, Mr. McQuire deposited his paycheck of $332 for a total
account balance of $750. The next morning, his wife wrote a check for $1,183.15 for a new refrigerator and stove.
The check cleared the bank by the end of the day. What is the current balance in the McQuire's account?
Answer: -433.15
Step-by-step explanation:
he's id debt and has to pay off the 433.15 later on.
Answer:
The McQuires' account is currently overdrawn by $483.15.
Step-by-step explanation:
If the McQuires' account balance was $750 on Friday and they wrote a check for $1,183.15 on Saturday, then the balance would be 750 - 1,183.15 = -$433.15 after the check cleared. Since the bank charges a $50 overdraft fee, the final balance in the McQuires' account would be -$433.15 - $50 = -$483.15. The McQuires' account is currently overdrawn by $483.15.
an engineer says a pipe should be 7/10 centimeters long. The pipe is 9/10 centimeter long. How much of the pipe needs to be cut off? write an equation.
Answer: x = 9/10 - 7/10
Step-by-step explanation:
An area code has three digits. How many different area codes are possible
Answer:
1000
Step-by-step explanation:
If any of the digits 0-9 can be used then there are 10^3 possible codes.
10^3 = 1000
Problems 14 and 15 pertain to the following situation: a woman buys 20 one-dollar lottery tickets per month. The probability of any ticket being a winning ticket is 0.10 or 10%.
14. The probability that in any one month at least three of the tickets that the woman buys are winning tickets is about?
15. The average number of winning tickets that the woman buys each month is about?
The required probability is P(X≥3) =0.3234
The average number of winning tickets that the woman buys each month is 2.
The binomial probability distribution is a discrete type of probability distribution with two parameters, n, and p. The probability mass function of the distribution is used to get the required probability. The average value of the winning number is the expected value of the binomial distribution.
The probability mass function of the binomial distribution is defined as:
[tex]P(X=x)=\frac{n}{x} p^{x} (1-p)^{n-x} , x =0,1,2,3,....,n.[/tex]
Given that,
n = 20
p = 0.10
The required probability is P(X≥3)
P(X≥3) = 1-P(X<3)
P(X≥3)= 1-P(X=0)-P(X=1)-P(X=2)
P(X≥3)= 1- 0.1216- 0.270- 0.285
P(X≥3) = 0.3234
The mean of the distribution is defined as μ=n*p= 20*0.10= 2
The average number of winning tickets that the woman buys each month is 2.
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URGENT!!!!
Find z such that 7% of the area under the standard normal curve lies to the right of z.
The value of z such that 7% of the area under the standard normal curve lies to the right of z is approximately -0.4
How to find z such that 7% of the area under the standard normal curve lies to the right of z?
To find the value of z such that 7% of the area under the curve lies to the right of z, we need to find the value of z such that 43% of the area lies to the left of z.
This value of z is known as the 43rd percentile of the standard normal curve.
We can use a table of the standard normal distribution, also known as the z-table, to find the value of z corresponding to the 43rd percentile.
According to the z-table, the value of z corresponding to the 43rd percentile is approximately -0.4
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The length of a rectangular poster is 8 more inches than three times its width. The area of the poster is 256 square inches. Solve for the dimensions (length and width) of the poster
The dimensions are
inches ___ by ____ inches.
When the area of the poster is 256 square inches, the measurements are 32 inch and 8 inch.
What is area?The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.
Here,
let length be l and width be w.
l=3w+8
l*w=256
(3w+8)*w=256
3w²+8w=256
3w²+32w-24w-256=0
3w(w-8)+32(w-8)=0
(3w+32)(w-8)=0
w=-32/3, 8
w=8 inch
l=3*8+8
l=32 inch
The dimensions for the poster are 32 inch and 8 inch when area of the poster is 256 square inches.
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Is there anyone that can help me with a finance question?
Answer:
Yes, there are many people who can help you with a finance question. Some of the people who can help you include: financial advisors, accountants, financial planners, and financial analysts. Additionally, there are many online resources available such as personal finance forums, websites, and blogs.
Step-by-step explanation:
If 1+3+5+7+…+49 =625, what is 2+4+6+8+…+50?
If 1+3+5+7+…+49 =625, then the value of 2+4+6+8+…+50 = 650.
What is arithmetic series?
A series of numbers called an arithmetic progression or sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Here, we have
Given: 1+3+5+7+…+49 =625
We have to find the value of 2+4+6+8+…+50.
Here, we calculate the sum of all even numbers and we get
2+4+6+8+…+50 = 650
Hence, if 1+3+5+7+…+49 =625, the value of 2+4+6+8+…+50 = 650.
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You brought popular game on sale for $20 and want to sell it on eBay. You want to mark up the toy 60%. What did you sell it for?
The better your time management skills are, the more work you are able to do is an example of a Continuous correlation Biserial correlation O Positive correlation O Negative correlation
The time management skill and amount of work done is an example of positive correlation.
Correlation or dependency pertains to any statistical link involving two random variables or bivariate data, whether causal or not. Although the term "correlation" can refer to any form of link, in statistics it is most usually used to refer to the degree to which two variables are statistically linearly associated.
The link between the heights of parents and their children, as seen in the enough that demand curve, and the correlation between the price of an item and the quantity of items that buyers are willing to acquire are examples of dependent phenomena.
The Pearson product-moment correlation coefficient (PPMCC), sometimes known as "Pearson's correlation coefficient," is the most commonly used measure of two-value dependency.
It is computed by dividing the covariance ratio of the two variables in our numerical dataset by the square root of their variances. The covariance of the two variables is simply divided by the product of their standard deviations in mathematics. The coefficient was calculated by Karl Pearson from Francis Galton's similar but slightly different idea.
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which graph represents the equation y =1/3 x + 2
The graph of the equation y = (1/3)x + 2 is passing through points
(3, 3) and ( -3, 1).
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A linear equation y = (1/3)x + 2.
Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.
When x = 3, y = 3 ⇒ (3, 3).
When x = - 3, y = 1 ⇒( -3, 1).
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In AUVW, m/U = (3x - 10)°, m/V = (6x + 5)°, and m/W = (4x - 10)°. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
You have ∆UVW with angles U=(3x-10)°, V=(6x+5)°, and W=(4x-10)°, and you want to know the value of x.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
U +V +W = 180°
(3x -10)° +(6x +5)° +(4x -10)° = 180°
13x -15 = 180 . . . . . . . divide by °, collect terms
13x = 195 . . . . . . . add 15
x = 15 . . . . . . . divide by 13
The value of x is 15.
In the last 24 days, it rained 18 days. What is the ratio of rainy days to total days written as a percent?
The ratio of rainy days to total days written as a percent will be 75%.
How to illustrate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.
Since in the last 24 days, it rained 18 days.
Number of rainy days = 18.
Number of total days = 24
The ratio of rainy days to total days written as a percent will be:
= Number of rainy days / Total days × 100
= 18/24 × 100
= 3/4 × 100
= 75%
Therefore, the ratio is 3:4 which is 75%.
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What is the approximate perimeter of this triangle?
Answer:
163.6 in---------------------------
Given:
a = 56 in,m∠A = 55°.Find the missing sides:
56/b = tan 55° ⇒ b = 56 / tan 55° = 39.21 in,56/c = sin 55° ⇒ c = 56 / sin 55° = 68.36 in.Perimeter is:
56 + 68.36 + 39.21 = 163.57 ≈ 163.6 inHeight (in inches) Mean Minimum Q1 Median Q3 Std Dev 4.21 Maximum 79 68.2 67 , 71 , Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches. Height (in inches) Q3 Mean 68. 2 Std Dev .21 Minimum 62 4 Q1 63 Median 67 Maximum 79 Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches. (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches.
Standard deviation will be √3.3516 .
To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².
After that , we have to calculate the Xbar by using
Xbar = ∑fiXi / N
for which we need the value of fi , Xi and N
N = 100
fiXi = 6478
we have calculated the values from the given data ,
Therefore ,
Xbar = 6478 / 100
= 64.78
Var(X) = αx² - ∑fiXi² / N - (Xbar²)
= 419980 / 100 - (64.78)²
= 4199.80 -4196.4484
=3.3516
Thus,
standard deviation ax = √var(X)
= √3.3516
Therefore , the standard deviation will be √3.3516
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Your class council determined that its profit from the upcoming homecoming dance is directly
related to the ticket price for the dance. Looking at past dances, the council determined that the
profit p can be modeled by the function p(t) = -1212 + 480t + 30, where t represents the price of
each ticket. What should be the price of a ticket to the homecoming dance to maximize the
council's profit?
The price of a ticket to the homecoming dance to maximize the council's profit is 4830.
Define vertex?A vertex is a location in geometry where two or more curves, lines, or edges converge. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.The vertex of an angle is the point around which it is measured, and the vertex angle is the angle that corresponds to a particular vertex.A face is a flat surface, an edge is a straight line connecting two faces, and a vertex is the corner of the shape.Given: a= -12, b = 480Vertex t= -b/2at= -480/2(-12) = 20Therefore, $20 per ticket.p(20) = -12(20) pow 2 + 480(20) + 30= 4830To learn more about vertex refer to:
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Answer:
$2 each ticket
Step-by-step explanation:
I don't really know how it's 2, but it's in the vertex of the graph. I just got my test back which the answer was 2. I'm sorry if you expected reasoning but I only got an answer. You can make a table for the equation and then see that 2 results in the highest profit though. 2 being substituted for t equates to the greatest profit.
Lucy wants to buy a small car. She speaks to her bank and they offer her a loan of £5000 over 5 years at a simple interest rate of 5%. How much simple interest will Lucy have to pay back in total?
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
What is simple interest?To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest. Most loans with simple interest rates are auto loans and short-term personal loans.
A = $6,250.00
I = A - P = $1,250.00
Formula: A = P(1 + rt)
First, convert R percent to r decimal, which is equal to 5%/100 or 0.05 per year.
Fixing our equation
A = 5000(1 + (0.05 × 5)) = 6250 \sA = $6,250.00
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
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find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius r.
The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
Now, According to the question:
The given sphere is of radius R.
Let h be the height and r be the radius of the cylinder inscribed in the sphere.
We know that:
Volume of cylinder
V = [tex]\pi R^2h[/tex] .....(1)
In right Triangle OBA
[tex]AB^2 + OB^2 = OA^2[/tex]
[tex]R^2 + \frac{h^2}{4} = r^2[/tex]
So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]
Putting the value of [tex]R^2[/tex] in equation (1), We get
V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]
V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex] ....(2)
dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)
For, Stationary point, dV/dh = 0
[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0
[tex](r^2 - \frac{3h}{4} )[/tex] => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]
Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]
[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex] = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0
Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]
Maximum volume is :
[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]
[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
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A punter kicks a football. Its height h, in yard, t seconds after the kick is given by the equation h(t)=-4.9t^2+18.24t+0.8. The height of an approaching blocker's hand is modeled by the equation h(t)=-1.43t+4.26, using the same time. Can the blocker knock down the punt (do they intersect)? If so, at what point will that happen (the point of intersection)?
Part 1
[tex]-4.9t^2 +18.24t+0.8=-1.43t+4.26\\\\-4.9t^2 +19.67t-3.46=0\\\\\Delta =(19.67)^2 -4(-4.9)(-3.46)=319.0929 > 0[/tex]
Therefore, the blocker can knock down the punt.
Part 2
Using the quadratic formula,
[tex]t=\frac{-19.67 \pm \sqrt{319.0929}}{2(-4.9)}\\\\t \approx 0.18437, 3.82992[/tex]
Considering the graphs, it is clear to take the smaller solution. Thus, the point of intersection is [tex](0.18437, h(0.18437))=\boxed{(0.18437, 3.99635)}[/tex].
Find the Probability of, A King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.
As per the given data,
we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
We know that,
Probability(Event) =Number of Favorable Outcomes/Total number of
Outcomes = x/n.
Total number of Outcomes is 52 (given)
So, we will calculate Number of Favorable Outcomes as follows:
The total no. of King in deck of card is 4
The total no. of queen in deck of card is 4.
The total no. of ace in deck of card is 4.
The total no. of jack in deck of card is 4.
Therefore, the number of favorable outcomes is 4+4+4+4= 16
Now, putting values in the above stated formula of probability, we get:
Probability= 16/52=4/13
Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.
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Say that we have three voters deciding among seven candidates, a, b, c, d, e, f, g. Their preference orderings are as follows.
1 2 3
(Best) c f g
a b b
e c c
g g d
b a e
d d f
(W orst) f e a
a. Find the top cycle.
b. For each candidate in the top cycle, write down an agenda (a sequence of majority rule
votes) that makes that candidate win (you can write the agenda as a tree).
c. Say that the voters use the Borda count system (each voter gives 6 points to their first
choice, 5 points to their second choice, and so on) to decide among the candidates. Which
candidate wins?
d. Is the Borda count winner also the Condorcet winner?
e. Which candidate does the worst in the Borda count?
f. Say that the person who does worst in the Borda count (your answer in part e. above) is
embarrassed about their poor performance, and tries to convince another candidate to drop
out so that they are no longer the worst person. If a candidate drops out, there would be
six candidates, and hence in the Borda count system, each voter gives 5 points to their first
choice, 4 to their second choice, and so forth. If a candidate drops out, is it possible for the
person who was originally the worst to no longer be the worst? If so, which candidate should
drop out? If not, please explain why not.
A. The top cycle in this case is a -> b -> c -> a.
B. The agenda that wins the candidate is:
First vote:
a vs b -> a wins
Second voice:
versus. c -> a wins
The agenda that Candidate B wins is:
First vote:
b vs c -> b wins
Second Voice:
b vs a -> b wins
The agenda that Candidate C wins is:
First vote:
c vs a -> c wins
Second Voice:
c vs b -> c wins
C. Using the Borda count system, the candidates' scores are as follows:
a:
18 points (6 points from voter 1, 4 points from voter 2, and 8 points from voter 3)
b:
18 points (4 points from voter 1, 6 points from voter 2, and 8 points from voter 3)
c:
18 points (6 points from voter 1, 8 points from voter 2, and 4 points from voter 3)
d:
12 points (8 points from voter 1, 4 points from voter 2, and 0 points from voter 3)
e:
12 points (4 points from voter 1, 8 points from voter 2, and 0 points from voter 3)
f:
12 points (8 points from voter 1, 0 points from voter 2, and 4 points from voter 3)
g:
6 points (4 points from voter 1, 0 points from voter 2, and 2 points from voter 3)
Therefore, candidates a, b, and c tie for first place with 18 points each.
D. No, the Borda count winner is not the Condorcet winner, because the Condorcet winner is the candidate who would win in a majority rule vote against every other candidate. In this case, candidate c is the Condorcet winner, because c beats a and b in majority rule votes.
E. The candidate with the worst score in the Borda count is g of 6 points.
F. If a candidate fails, the original worst candidate may no longer be the worst. In this case, if candidate g fails, the remaining candidates will have the following results:
a:
15 points (Voters 1 to 5 points, Voters 2 to 4 points, Voters 3 to 6 points)
b:
15 points (Voters 1 to 4 points, Voters 2 to 5 points, Voters 3 to 6 points)
c:
15 points (Voters 1 to 5 points, Voters 2 to 6 points, Voters 3 to 4 points)
Day:
10 points (voters 1 to 6 points, voters 2 to 4 points, voters 3 to 0 points)
e:
10 points (voters 1 to 4 points, voters 2 to 6 points, voters 3 to 0 points)
f:
10 points (voters 1 to 6 points, voters 2 to 0 points, voters 3 to 4 points)
In this case, g's 6-point score is not included in the calculation, so candidate g is no longer last.
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A sinusoidal function whose period is π2
, maximum value is 10, and minimum value is −4 has a y-intercept of 10.
What is the equation of the function described?
Responses
f(x)=7cos(4x)+3
f ( x ) = 7 cos ( 4 x ) + 3
f(x)=7sin(4x)+3
f ( x ) = 7 sin ( 4 x ) + 3
f(x)=7cos(4πx)+3
f ( x ) = 7 cos ( 4 π x ) + 3
f(x)=7sin(4πx)+3
The equation of the function described as; y = 7 sin ( 4x + π/2 ) + 3
The general equation of the sine curve can be written as;
y = a sin ( nx + α ) + b
where : a is the amplitude, n = 2π/period, b = shift in the direction of y
α°= shift in the direction of x
We are Given period = π/2 the maximum value is 10, the minimum value is −4 and y-intercept of 10.
Thus,
a = (maximum - minimum)/2 = (10 - -4)/2
a = 7
n = 2π/period = 2π/(π/2)
n = 4
b = maximum - a = 10 - 7
b= 3
To find α as y-intercept = 10
y = 10 at x = 0
Substitute in the general function;
y = a sin ( nx + α ) + b
10 = 7 sin ( 4*0 + α ) + 3
Thus, we have;
sin α = 1
α = π/2
So, the equation of the function described is;
y = 7 sin ( 4x + π/2 ) + 3
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look at attached photo
The correct answer is A) y = 9000x + 65,000.
Find a linear equation that models the value of the house after x years?The correct answer is A) y = 9000x + 65,000.
This is an equation in slope-intercept form, where "y" is equal to the value of the house after x years, "9000x" is the slope (or rate of change) of the equation, and 65,000 is the y-intercept (or the initial value of the house). The equation can be derived from the given information.The initial value of the house is 65,000, so the y-intercept must be 65,000. To find the slope, we can use the formula "rise/run", or change in y/change in x.The house has increased in value by 54,000 ($119,000 - $65,000) over 6 years (change in x), so the slope must be 9000 (54,000/6).
The equation y = 9000x + 65,000
models the value of the house after x years, where y is the value of the house,
9000x is the slope of the equation,
and 65,000 is the y-intercept.
This equation can be used to calculate the value of the house after any given number of years.To learn more about linear equation in slope-intercept form refer to:
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Use the extended Euclidean algorithm to find the greatest common divisor of 3,984 and 588 and express it as a linear combination of 3,984 and 588.
Step 1: Find
q1
and
r1
so that
3,984 = 588 · q1 + r1,
where
0 ≤ r1 < 588.
The greatest common divisor is 12. The linear combination of 3984 and 588 is given by 12 = 61×588 - 9×3984.
The extended Euclidean algorithm is an algorithm to compute integers x and y such that: ax+by=gcd(a,b)The extended Euclidean algorithm can be viewed as the reciprocal of modular exponentiation.
By reversing the steps in the Euclidean algorithm, it is possible to find these integers x and y. The whole idea is to start with the GCD and recursively work our way backwards. This can be done by treating the numbers as variables until we end up with an expression that is a linear combination of our initial numbers.
First use Euclid's algorithm to find the GCD:
3984 = 588 ×6 + 456
588 = 456×1 +132
456= 132 ×3 + 60
132 = 60×2 +12
60 = 12×5+0
The last non-zero remainder is 12.
Thus, the greatest common divisor is 12.
Now we use the extended algorithm:
12 = 132 +(-2)×60
= 132 + (-2)×(456 + (-3)×132))
= (-2)×456 + 7×132
= (-2)×456 + 7×(588 +(-1)×456))
= 7×588 + (-9)×(3984 +(-6)×588))
= 61×588 + (-9)×3984
Thus, a = -9 and b = 61.
Thus, the linear combination of 3984 and 588 is given by 12 = 61×588 - 9×3984.
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