Year (X) =2000 2001 2002 2003 2004
Cost in Dollars(Y) = 56.25 74.30 122.75 200.00 308.50
The table shows the cost of a game from 2000 to 2004, which has been increasing in a quadratic fashion. Let x = 0 in 2000, and find the best-fit quadratic equation. What will game cost in 2010?
A) $417
B) $746
C) $960
D) $1,586
Answers
Answer-
The best-fit quadratic equation is [tex]y=14.9786x^2+3.1057x+56.2771[/tex] and the game cost in 2010 will be $1586
Solution-
Plotting a table taking year as input variable and cost as output variable.
X= year - 2000
Y= cost in dollar.
Quadratic equation formula,
[tex]y=ax^2+bx+c[/tex]
[tex]a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]
[tex]b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]
[tex]c=\frac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}[/tex]
Where,
[tex]\sum xx=\sum x^2-\frac{(\sum x)^2}{n}[/tex]
[tex]\sum xy=\sum xy-\frac{\sum x\sum y}{n}[/tex]
[tex]\sum xx^2=\sum x^3-\frac{\sum x\sum x^2}{n}[/tex]
[tex]\sum x^2y=\sum x^2y-\frac{\sum x^2\sum y}{n}[/tex]
[tex]\sum x^2x^2=\sum x^4-\frac{(\sum x^2)^2}{n}[/tex]
Putting the values, we get
[tex]a=14.9786,b=3.1057,c=56.2771[/tex]
Putting these in the quadratic equation,
[tex]y=14.9786x^2+3.1057x+56.2771[/tex]
In order to get the cost of game in 2010, we can put x=10 to get the value of y or the cost of game.
[tex]y(10)=14.9786(10)^2+3.1057(10)+56.2771=1585.1941 \approx 1586[/tex]
Related Questions
willie wants to save for a new racing bike. if he deposits $250 in a saving account at 4% simple annual interest, what willis balance be after 3 years?
A.15
B.30
C.265
D.280
Answers
A=p (1+rt)
A future value?
P present value 250
R interest rate 0.04
T time 3years
A=250×(1+0.04×3)
A=280
Hope it helps!
A vertical plane intersects the three-dimensional object in the image and divides the object into equal halves. What is the shape of the cross section?
Thank you :)
Answers
It will look a lot like how the object looks from the side.
The best answer is D, the last image.
Answer:
Option 4 is correct .
Step-by-step explanation:
Given : A three dimensional figure
To Find : What is the shape of the cross section?
Solution :
If we intersects the three-dimensional object in the image and divides the object into equal halves by vertical plane then we can see the attached figure what the output will be .
We can see that if we see the cross section from the side then it looks like the fourth one
So, Option 4 is correct .
12 is 30% of blank plz give the right answer
Answers
A friend creates an IRA (Individual retirement account) with an APR of 6.25%. She starts the IRA at the age of 25 and deposits $50 at the end of each month. How much will her IRA contain when she retires at the age of 65?
Answers
so
A = [P (1 + i/n)^nt - 1 ] / (i/n)
A = [50 (1 + 0.0625 / 12)^12*40 - 1] / (0.0625 / 12)
A = $106,596
answer
$106,596
(y3 - 4y2 + 7y - 6) ÷ (y - 2)
Answers
(2y-6)/(y-2)
2(y-3)/2(y/2-2)
(y-3)/(y/2-2)
Greg is 5 feet three inches tall and weighs 260 pounds. greg is ________.
Answers
(99 POINTS AVAILABLE)
When three or more lines intersect at one point, the point of intersection is called the ____________.
Answers
Luis makes $23.10 per hour at his job for the first 40 hours he works each week. if he works more than 40 hours, then luis makes $34.65 per hour. if luis works 46 hours in one week, how much does he earn?a.$1,062.60b.$1,097.25c.$1,131.90d.$1,593.90
Answers
Answer:
correct answer is C. Just took the test.
A scatter plot has been created with a line of best fit that matches the equation y = 11x + 340. Using this line of best fit, determine the output value when the input is 10. Do you think this matches a point on the scatterplot? Why or why not?
Answers
y = 11(10) + 340
y = 110 + 340
y = 450
For the second part of that question, do you think this matches a point on the scatterplot.....more than likely this is a NO, as generally speaking a line of best fit doesn't pass through many of the data points that it uses to create the equation for the line, so I'd say probably not.
Hope this helps.
Brian
for the function:
f(x) = -3x^4
complete the table of values using at least 5 points.
x -2 -1 0 1 2
f(x)
Answers
Doing so, we get:
[tex]f(-2)=-3(-2)^4=-3(16)=-48\\ f(-1)=-3(-1)^4=-3(1)=-3\\ f(0)=-3(0)^4=0\\ f(1)=-3(1)^4=-3(1)=-3\\ f(2)=3(2)^4=-3(16)=-48[/tex]
Write 3 ½% as a fraction
Answers
Answer:
7/200
Step-by-step explanation:
3.5% = 3.5/100 = (3.5/100)×(2/2) = 7/200
_____
The % symbol is a shorthand way to write "/100", so 3.5% = 3.5/100.
Please do not make into a fraction because I can’t use a fraction as an answer. Rewrite using a negative exponent.
1/(xy)^1
Answers
David bought a used car for $3,000 and later sold it for $1,000. What was the approximate percent decrease in the price of the car?
Answers
When four basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name.
P(shoot free throws in alphabetical order) = _____
Answers
The total number of possibilities of drawing their names is given by permutation.
4P4 = 24
The total possibility of drawing their names in alphabetical is only 1.
Therefore the probability is:
P = 1 / 24
P = 0.0417
Therefore there is about 4.17% chance that it will be in alphabetical order
What is 2(6+5•2)=5(4-2•5)
Answers
..................................
Answer: Not true
Step-by-step explanation: 2(16)=5(-6)
32=-30
This is not true
The formula for the area of a triangle is a=1/2bh. solve the formula for h. a triangle has a base of 7cm and an area of 28cm squared. what us it's height
Answers
Divide by 7 on both sides giving you
4=1/2h
Multiply by 2 on both sides giving you
h=8
Therefore, the height is 8cm.
Answer: 8 cm
Step-by-step explanation:
Given : The formula for the area of a triangle is [tex]a=\dfrac{1}{2}bh[/tex]
If a triangle has a base of 7 cm and an area of 28 cm squared.
The substitute the values of b = 7 and a = 28 in the above formula, we get
[tex]28=\dfrac{1}{2}(7)h[/tex]
Divide 7 and multiply 2 on on both sides, we get
[tex]h=\dfrac{28\times2}{7}=4\times2=8\ cm[/tex]
Hence, the height of triangle = 8 cm
Staci is attending a music festival. The ticket to the festival costs 87.96. Staci plans to purchase 30.00 t-shirts from the event for close friends. She is taking 200.00 to the festival . What is the maximum number of t-shirts Staci can purchase?
Answers
Ticket cost : $87.96
T-shirt cost per piece: $30.00
The first thing Staci needs to do is to deduct the cost of the ticket from her money.
$200 - 87.96 = $112.04
Stacy has the extra amount of 112.04 to purchase t-shirts. Since, each t-shirt costs $30. To know the number of shirts she can buy, she must divide the difference by 30.
$112.04 / $30 = 3.73
Based from the quotient, Stacy can buy 3 t-shirts.
$30 * 3 = $90 total cost of the tshirts.
$112.04 - 90 = $22.04
After buying the ticket and 3 tshirts, Staci has an excess of $22.04 from her $200.
Hope this helped
Final answer:
Staci can purchase a maximum of 3 T-shirts after buying her festival ticket, given she brings $200.00 and each T-shirt costs $30.00.
Explanation:
To calculate the maximum number of T-shirts Staci can purchase at the music festival, we can follow these steps:
Subtract the cost of the festival ticket from the total amount of money Staci is taking to the festival. This will give us how much money she has left for the T-shirts.
Divide the remaining amount by the cost of one T-shirt to find out the maximum number of T-shirts she can buy.
So for the first step:
Staci has $200.00 and the ticket costs $87.96, leaving her with $200.00 - $87.96 = $112.04.
For the second step:
Each T-shirt costs $30.00, so we divide $112.04 by $30.00, which gives us 3.734.
Since Staci cannot buy a fraction of a T-shirt, we round down to the nearest whole number, which is 3.
Therefore, the maximum number of T-shirts Staci can purchase is 3.
what is 63 as the product of prime factors in ascending order?
Answers
Prime factors of 63 are : 3, 3, 7
As 3 repeats and 3 is smaller than 7 so, when we write this in ascending order as the product of these, we write in such a way;
63 = 3 x 3 x 7 = 3² x 7
Now 3² = 9 and 9 is greater than 7,so,
63 = 7 x 9
C(x) = 0.5x+70 find the domain and range
Answers
Lets find F^(-1) if
y=-2x+1
I’m not sure if the F^(-1)=1+x/2
Answers
[tex]\bf y=-2x+1\qquad \boxed{x}=-2\boxed{y}+1\implies x-1=-2y \\\\\\ \cfrac{x-1}{-2}=y\implies \cfrac{1-x}{2}=\stackrel{f^{-1}}{y}[/tex]
[tex]y=-2x+1[/tex]
To find [tex]f^{-1}[/tex], we solve for [tex]x[/tex].
[tex]y-1=(-2x+1)-1[/tex] (subtract 1 from both sides)
[tex](y-1)/(-2)=(-2x)/(-2)[/tex] (divide both sides by -2)
That gives us
[tex]x= \frac{y-1}{-2} [/tex]
Now that we have a way of mapping [tex]y[/tex] back to [tex]x[/tex], all we do is swap the domain and range, and we have
[tex]f^{-1}(x)= \frac{x-1}{-2} [/tex]
While catching fireflies, you and a friend decide to have a competition. after mm minutes, you have (3m+13)(3m+13) fireflies and your friend has (4m+6)(4m+6) fireflies.
a. how many fireflies are caught each minute during the competition?
Answers
To find for the number of fireflies caught in a minute, we simply look at the equation. The equation is linear and takes the form y = slope * x + b
where slope is also equivalent to the fireflies caught each minute.
So the equation of you and your friend is: (where y is the total fireflies caught)
you:
y = 3 m + 13
your friend:
y = 4 m + 6
So the fireflies caught each minute is:
you: 3
your friend: 4
So a total of 7 fireflies each minute combined
The length of a rectangle is 4 inches more than its width. the perimeter of the rectangle is 32 inches. what is the length of the rectangle
Answers
2(10+6) =32
What is an equation of the line in slope-intercept form? m = 2 and the y-intercept is (0, 3)
Answers
y=2x+3
y = mx + c
m represents the gradient and c represent where the line intercept y-axis
The y-intercept happens when the value of x-coordinate is 0, so the coordinate is (0, c)
We have, m = 2 and c = 3
The equation of the line is: y = 2x + 3
bh+hr=25
solve for h and r
Answers
h(B + r) = 25
Divide b+r
h = 25/ b + r
Subtract bh:
hr = -bh + 25
Divide h:
r = -bh/h + 25/h
Simplify:
r = -b + 25/h
Hope this helps!
To solve for h and r in the equation bh + hr = 25, isolate one variable, solve for h using division, and solve for r by expanding the equation. There is no unique solution for h and r in terms of each other.
Explanation:To solve for h and r in the equation bh + hr = 25, we need to isolate one variable on one side of the equation. Let's solve for h first:
bh + hr = 25
Factor out h from the left side of the equation:
h(b + r) = 25
Divide both sides by (b + r) to solve for h:
h = 25 / (b + r)
Now, let's solve for r. Replacing h in the original equation:
bh + hr = 25
b(25 / (b + r)) + r(25 / (b + r)) = 25
Multiply both sides by (b + r) to get rid of the denominators:
25b + 25r = 25(b + r)
Expand the equation:
25b + 25r = 25b + 25r
As we can see, the equation is an identity, meaning any value of r will satisfy it. Therefore, there is no unique solution for r in terms of h, and vice versa.
Learn more about Solving equations here:https://brainly.com/question/14410653
#SPJ3
What type of angles are 6 and 8?
Answers
Y -2 > -11 what is the answer to this
Answers
The blade of a circular saw rotates at a rate of \2500 revolutions per minute. what is the linear velocity in miles per hour of a point on the tip of the outer edge of a 7 and one fourth7 1 4 inch diameter blade?
Answers
The linear velocity of a point on the tip of the outer edge of the circular saw blade is 0.429 miles per hour.
Explanation:To find the linear velocity of a point on the tip of the outer edge of the circular saw blade, we can use the formula:
Linear velocity = 2 * π * radius * angular velocity
Where the radius is half of the diameter. Given that the diameter is 7 1/4 inches, the radius is 7 1/4 / 2 = 3 5/8 inches or 3.625 inches. Converting this to feet, we get 3.625 / 12 = 0.302 feet. To convert the angular velocity from revolutions per minute to radians per second, we multiply by 2 * π / 60. Substituting these values into the formula, we get:
Linear velocity = 2 * π * 0.302 * (2500 * 2 * π / 60) = 37.699 feet per minute.
To convert this to miles per hour, we divide by 5280 (since there are 5280 feet in a mile) and multiply by 60 (since there are 60 minutes in an hour):
Linear velocity = (37.699 / 5280) * 60 = 0.429 miles per hour.
The graph of a line goes up and to the right when
Answers
Answer: When the coefficient of X is positive!
Marla has a pet hamster. The hamster makes 3 laps around her cage every minute.
What line represents the situation?
Line a
Line b
Line c
Line d
Answers
Let
x-------> the time in minutes
y------> the number of laps
we know that
In this problem the linear equation represent a direct variation and the slope is equal to
[tex]m=3\frac{laps}{minute}[/tex]
so
the equation of the line is
[tex]y=3x[/tex]
For [tex]x=1\ minute[/tex]
the value of y is equal to
[tex]y=3*1=3\ laps[/tex]
Plot the point [tex](1,3)[/tex] in the graph
therefore
the answer is
The solution is the line b
see the attached figure to better understand the problem
Alberto, Carlos and Maria share an inheritance of $54000 in the ratio of 3: 4: 5
What fraction of the the money does Alberto get?
Answers
12x=54000
X=4500
Now im not sure which is alberto but if they are in the order as listed he would be 3.
So alberto = 3x
Alberto= $13500
Alberto gets [tex]\( \frac{1}{4} \)[/tex] of the inheritance.
To find out the fraction of the money Alberto gets, we first need to find out how much of the total inheritance each part of the ratio represents.
The total parts in the ratio are [tex]\(3 + 4 + 5 = 12\)[/tex].
Alberto's share is [tex]\(3\)[/tex] parts out of [tex]\(12\)[/tex].
So, Alberto's share of the inheritance is [tex]\( \frac{3}{12} \)[/tex] of the total amount.
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is [tex]\(3\)[/tex]:
[tex]\( \frac{3}{12} = \frac{1}{4} \)[/tex]
Therefore, Alberto gets [tex]\( \frac{1}{4} \)[/tex] of the inheritance.