A shopkeeper earns Rs. 380 in the first week, Rs. 660 in the second week and Rs. 860 in the third week. Earning is the quadratic function of number of week for which the earning is found. a. Find the quadratic function that fits the data
Answers
9514 1404 393
Answer:
e(w) = -40w^2 +400w +20
Step-by-step explanation:
A graphing calculator or spreadsheet can do the quadratic regression and help you find the formula. Here earnings (e) as a function of weeks (w) can be expressed by ...
e(w) = -40w^2 +400w +20
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Further development
There are a couple of other ways you can go at this. One is to write equations for a, b, c using the standard form quadratic.
aw^2 +bw +c = e
a +b +c = 380 . . . . . . for week 1
4a +2b +c = 660 . . . for week 2
9a +3b +c = 860 . . . for week 3
The solution of this system of equations will give the coefficients of the quadratic. Your graphing calculator or any of several web sites can solve these equations for you.
__
Consider the differences between quadratic values for w = 1, 2, 3.
e2 -e1 = (4a +2b +c) -(a +b +c) = 3a +b
e3 -e2 = (9a +3b +c) -(4a +2b +c) = 5a +b
Then the second differences are ...
(e3 -e2) -(e2 -e1) = (5a +b) -(3a +b) = 2a
In the given set of numbers, the first differences are ...
660 -380 = 280 . . . . . . . call this d1
860 -660 = 200
And the second difference is ...
200 -280 = -80 . . . . . . . call this d2
From the above, we know that 2a = -80 ⇒ a = -40
and 3a +b = 280 = 3(-40) +b ⇒ b = 400
Finally, a+b+c = 380 = -40 +400 +c ⇒ c = 20
Then the generic solution is ...
a = d2/2
b = d1 -3a
c = e1 -a -b . . . . . where e1 is the first-week's earnings
Related Questions
Vhat is the domain of the function y = In {-x+3/2}
Answers
Answer:
(-∞,3/2),{xIx<3/2}
Step-by-step explanation:
Using inverse function concepts, the correct option is:
B. Domain: x < -2 Range: y> 3
What is domain?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in
here, we have,
we know that,
The domain of a function is the set that contains all possible input values.
The range of a function is the set that contains all possible output values.
In the inverse function, input and output are exchanged, thus, domain and range are also exchanged.
For the original function, the domain is x > 3 and the range is y < -2.
Thus, for the inverse function, the domain is x < -2 and the range is y > 3, which means that option B is correct.
learn more on domain at :
brainly.com/question/24603090
#SPJ7
Complete question:
The domain of a function h(x) is x > 3, and the range is y2 -2. What are the domain and range of its inverse function, h-1(x)?
A. Domain: x>3 Range: y2 -2
B. Domain: x2 -2 Range: y> 3
C. Domain: x>-2 Range: y> 3
D. Domain: x2 3 Range: y> -2
VX
What is the measure of _c?
148
С
42
90°
42
48
O 42°
O 48°
O 90°
180°
Answers
Answer:
48
Step-by-step explanation:
One nice, reliable thing about triangles is that their interior angles will ALWAYS add up to 180 degrees. So, if one angle is 43 degrees and the other angle is 48 degrees, we can see that
180 - 43 - 48 = 89
Now, the tricky part: how to determine which type of triangle this is.
An acute triangle is one in which all interior angles are less than 90 degrees. An isoceles triangle is one in which two of the interior angles are the same, while the third is different. An obtuse triangle is one in which one of the interior angles is greater than 90 degrees. A right triangle is one in which one of the interior angles is equal to 90 degrees.
We distinguish between these different types because they each have useful, but different, properties.
By these definitions, it is clear that the triangle in question is acute.
A rocket is launched from atop a 74-foot cliff with an initial velocity of 113 ft/s. The height of the rocket above the ground at time t is given by h=16t^2+113t+74. When will the rocket hit the ground after it is launched? Round to the nearest tenth of a second.
Answers
9514 1404 393
Answer:
7.7 seconds
Step-by-step explanation:
The solution is given by the quadratic formula.
For ax² +bx +c = 0, the roots are ...
x = (-b±√(b²-4ac))/(2a)
We want the positive root, so ...
x = (-113 -√(113² -4(-16)(74)))/(2(-16)) = (113 +√17505)/32 ≈ 7.6658
The rocket will hit the ground about 7.7 seconds after it is launched.
Write the polynomial in factored form as a product of linear factors:
p(a) = a^3 + 3a^2+ 9a + 27
zeros of polynomial.
Answers
Answer:
Step-by-step explanation:
p(A) = a^3 + 3a^2 + 9a + 27
put brackets around the 1st and second terms and another set around the 3rd and 4th
P(a)= (a^3 + 3a^2) + (9a + 27)
Using the distributive property, pull out the common factor for each of the 2 terms that contain the brackets.
P(a) = a^2 ( a + 3) + 9(a + 3)
Let a + 3 = x
P(a) = a^2x + 9x
Put brackets around these 2 terms
P(a)= x(a^2 + 9)
Substitute a + 3 for x
P(a) = (a + 3) ( a^2 + 9)
You have 42 peaches and want to share them equally with 6 people. How many peaches will each person get? Please be sure to write your answer in a complete sentence.
Answers
Answer:
7
Step-by-step explanation:
I did the math on a calculator
Which expression has a value of 39?
A 24 X 2 - 8 + 42 divided by 8 - 6
B 24 X 2 - 8 + 42 divided by (8 - 6)
C 24 X (2 + 8) + 42 divided by 8 - 6
D 24 X 2 - (8 + 42) divided by 8 - 6
Answers
Answer:
A
Step-by-step explanation:
48 - 8 +5.25-6 = 39.25
b 48 -8 + 21 = 61
c 240+5.25-6= 239.25
d 48 -50/8 - 6 = 35.75
Anyone know how to do this people are answering the question but aren’t choosing two anwsers
Answers
Answer:
Option B and Option D are the two answers
what is 2x10^4 in standard notation
Answers
Answer:
I love Math anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
100 POINTS AND BRAINLIEST IF YOU USE EXPLANATION
What type of table or graph do you use to help you make a histogram?
A.
a dot plot
B.
a frequency table
C.
a circle graph
D.
a bar graph
Answers
Answer:
B
Step-by-step explanation:
Answer:
D. a bar graph
Step-by-step explanation:
a bat graph because it keeps track of data that changes over time
Find the area of this parallelogram, top= 14 left= 11 right = 10
Answers
Answer:
140 cm^2
Step-by-step explanation:
Formula for area of a Parallelogram: base*height
14 cm * 10cm = [tex]140 cm^{2}[/tex]
what is another ratio that is equivalant to 5:3 and 10:6?
Answers
Answer:
5:3 = 10:6
10:6 = 20:12 or 5:3
y is inversely proportional to the square of p, can be written as: y = O True O False
Answers
Answer:
False
Step-by-step explanation:
It should be ∝ .. if that’s what your asking
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answers
Answer:
Angles and XWY and STR
Step-by-step explanation:
These two angels are alternate exterior angels because:
- They are on different sides of the transversal (the line intersecting the two parallel lines)
- They have the same angle measure
- They are exterior, meaning they are on the outside, not inside (interior)
Hope this helps!!! :)
which is most likely the next step in the series?
Answers
Answer: the correct answer is a
Step-by-step explanation:
Tell whether the statement is true or false.
{ {4, 16, 24, 7, 37} = (37, 16, 7,42,4}
Answers
Answer:
false
Step-by-step explanation:
i dont understand kinda
but if you add it,
88<106
so false
The Athens-Clarke Country Wildlife Resource Center wanted to encourage wildlife preservation efforts among students in its summer camp. In the past, it would run a particular curriculum, then gauge students' interest in wildlife preservation in a test at the end of the camp. Historically, the average on this final test to gauge preservation interest was 35.3 (out of 100).
Last summer, the resource Center created a new curriculum focusing on campers interacting directly with wildlife to promote preservation efforts. This included efforts in species dentrication handling of wild animals, and directoration of animals in habitat The Resource Center considers the collection of 40 to be a random samping from the population of campers they will encounter They need your help to determine whether this new curriculum Improves impressions about witte preservation. For their 40 scores at the end of lut summer, they found a sample mean of 26.58 and a standard deviation of 3.18.
Required:
What are the null and alternative trypotheses?
Answers
Answer:
H0 : u ≤ 0.353
Ha: u > 0.353
Step-by-step explanation:
The null and alternate hypotheses are formulated by the given claim. The claim is mostly set as the alternate hypothesis and the opposite of the alternate hypothesis is the null hypothesis.
In this question the given statement is the average on this final test to gauge preservation interest was 35.3 (out of 100). This can be used as the null hypothesis.
H0 : u ≤ 0.353
The claim is also given which is To test whether the new curriculum Improves impressions about witte preservation.
against the claim Ha: u > 0.353
Therefore it will be a one tailed test.
Speedy crawled 5/9 yards. Slimy crawled 4 times as far as speedy. How far did slimy crawl?
Answers
Answer:
2 2/9 yards or 20/9 yards
Step-by-step explanation:
Slimy went 4 times as much as Speedy did so that means 5/9 x 4 yards which is the same thing as 5 x 4/9 so 5 x 4/9 equals 20/9 or 2 2/9 so Slimy crawled 2 2/9 yards.
In the figure below, m2 1=(x-12)° and mZ2 =5xº.
Find the angle measures.
Answers
Answer:
15 165
Step-by-step explanation:
m1 + m2 = 180
x-18 +5x = 180
6x = 198
x = 33
m1 = 15
m2 = 165
This week Andres will practice with his band for 1 1\2 hours Monday, 1 3\4 hours on Tuesday, and 2 hours Wednesday. Next week Andre will practice with his band for the same number of hours on Monday Tuesday Wednesday. What was the total number of hours Andre will practice with his band over these 6 days?
A: 5 1/4 hours
B: 10 1/2 hours
C: 4 1/4 hours
D: 8 1/2 hours
Answers
Answer:
Step-by-step explanation:
Jill is flying a kite that has a 30ft. long string. If Jill is 5.4 ft. tall and her arm is making a 31-degree angle with the ground, how high is the kite in the air?
Answers
Answer:
20.85ft
Step-by-step explanation:
height of kite = person's height + vertical component of kite at the angle
= 5.4ft + 30sin31
=20.85ft
Kathy bought 5 pencils for the price of $6.30. Which equation represents r, the cost, in dollars, of each pencil?
A.r=6.30+5
B.r = 6.30÷5
C.r=6.30×5
D.r=6.30−5
Answers
9514 1404 393
Answer:
B. r = 6.30÷5
Step-by-step explanation:
The cost per pencil is found by dividing the cost by the number of pencils.
Here, the cost is $6.30 and the number of pencils is 5. Then the cost per pencil (r) is ...
r = 6.30 ÷ 5
3.The probability of drawing a pearl bead out of a bag of mixed beads is 2/3. What is the probability of drawing a bead which is NOT pearl?
Answers
Answer:
1_2/3
=1/3 or 0.33
Step-by-step explanation:
Probability is not more than 1..
Find the area of the composite figure
Answers
Then we would work out the area of the square and the triangle
Area of a square = length x width
Area of a triangle = 1/2 base x height
Area of a square = 10 x 15 = 150
Area of a triangle = 1/2 15 x 5 = 37.5
(5 is the height of the triangle as you do 15-10 to work out the height of just the triangle
To get the total area we just combine both areas using addition
37.5+150=187.5
Answer:187.5ft squared
Hope this helped
How many pairs of glasses can we make with the foil beads and how many foil beads will be left over ?
Answers
Answer:
I hate to break it, but you ain't giving any information or numbers
11-square root of x where x=64
Answers
Write the log equation as an exponential equation. You do not need to solve for x. log(5x+2)=3
Answers
Answer:
So happy you are with brainly
Step-by-step explanation:
34
An expression is shown below:
2x3y + 8xy − 4x2y − 16y
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Plz help, give good answer and get brainlest!!
Answers
Answer:
2y is greatest common factor
Add and subtract the second term to the expression and factor by grouping.
2y(x−2)(x2+4) is the factor
Step-by-step explanation:
Answer:
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
answer:
2y(x³+4x-2x²-8)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
answer:
2y(x³+4x-2x²-8)
2y(x³-2x²+4x-8)
2y(x²(x-2)+4(x-2))
2y(x²+4)(x-2)
can you please help me out if you know this answer
Answers
Step-by-step explanation:
A strike in bowling meant all 10 pins knocked down.
In this case, there is only 1 strike
Find the missing angle in the triangle,
x°
36°
111°
Answers
Answer:
33°
Step-by-step explanation:
you add the two numbers together and subtract from 180° to get your answer
PLEASE HELPPP! I'LL GIVE BRAINLEST
Answers
Answer:
Thats easy C:
2 and 3 at the same time
Step-by-step explanation:
3x2=6 or if you dived 6/2=3
Also one thing when doing markup or profit(I think thats how you spell it if not im srry my spelling is very bad lol) you dived it
Have a good day :D