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
__
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
Compare areas: the side of a square is 14 m long. If all four size increased by 5, how my how much is the area increase?
The areas from _____ m^2 to _____ m^2, which is an increase of _____ m^2.
Answers
9514 1404 393
Answer:
196361165Step-by-step explanation:
The original side length is 14 m, so the area is (14 m)² = 196 m².
The longer side length is 14 m + 5m = 19 m, so the area is (19 m)² = 361 m².
The increase in area is ...
361 m² -196 m² = 165 m²
The area increases from 196 m² to 361 m², which is an increase of 165 m².
Answer:
The areas from 196 m² to 361 m², which is an increase of
165 m²
PLEASE HURRY
A public radio station raised 25% more during this year's fund-
raiser than it raised last year. If p represents the amount raised
by last year's fund-raiser, which expression represents the
amount raised this year?
Answers
Answer:
1.25p
Step-by-step explanation:
p = amount raised last year
amount raised this year = p +(25% of p)
=1 p+0.25p
=p(1+0.25)
=1.25p
A container has a volume of 3.6 m3 . Convert the volume into cm3 .
Answers
Answer: 3 600 000 cm³
Step-by-step explanation: 1 m³ = 1000 dm³ = 1 000 000 cm³
Reflect (2.5,4.5) in the x-axis.
Answers
9514 1404 393
Answer:
(2.5, -4.5)
Step-by-step explanation:
Reflection in the x-axis changes the sign of the y-coordinate
(x, y) ⇒ (x, -y)
(2.5, 4.5) ⇒ (2.5, -4.5)
Type the correct answer in the box log's
Answers
Answer:
log(7) will be the correct answer.
Step-by-step explanation:
[tex]\text{\frac{14}{3}}+\text{log}(\frac{11}{5})-\text{log}(\frac{22}{15})[/tex]By using law of logarithm to solve the given expression,
1). [tex]\text{log}(m)+\text{log}(n)=\text{log(mn)}[/tex]
2). [tex]\text{log(m)}-\text{log(n)}=\text{log}(\frac{m}{n})[/tex]
By applying these rules, we can simplify the given expression,
[tex]\text{log}(\frac{14}{3})+\text{log}(\frac{11}{5})-\text{log}(\frac{22}{15})[/tex]
[tex]\text{log}(\frac{14}{3})+\text{log}(\frac{11}{5})-\text{log}(\frac{22}{15})=\text{log}(\frac{\frac{14}{3}\times \frac{11}{5}}{\frac{22}{15}})[/tex]
[tex]=\text{log}(\frac{\frac{154}{15}}{\frac{22}{15}})[/tex]
= [tex]\text{log}(\frac{154}{15}\times \frac{15}{22})[/tex]
= log(7)
Therefore, log(7) will be the correct answer.
What should be included in a financial plan to protect assets?
Answers
Which property can be used to solve the equation?
d/10=12
A. addition property of equality
B. subtraction property of equality
C. multiplication property of equality
D. division property of equality
Answers
Answer:
C
Step-by-step explanation:
You are dividing, if you think about it every time I do it is the opposite of your equation. Plus you are supposed to multiply on both sides to get the value of d.
Hall and rey are seeing who can make the most money working their new summer jobs. Rey made $154.21 in the first month. If hall finishes the summer with $313.06, how many hours at a rate of $8.04 per our, does rey need to work to make more than hall
Write an inequality that represents the situation using x to represent the hours
Answers
Answer:
x564.99
Step-by-step explanation:
What is the perimeter of the shaded part of this??
Answers
Answer:
18.9cm ( I rounded of and used Π as 3.14)
Step-by-step explanation:
P=distance all round
=1\2ΠD +Πd
see you have to calculate the upper length of the circle , since its half u multiply by a half. And since its not fully shaded the two semi circles are now included as the lower part of the whole shape. so you add them too. (I hope I'm making sense)
Mike, Tania, Bill, and Rachael each took many samples from the same
population of students. The number of students in each sample is shown in
the table. Which person's sampling distribution is most likely to closely
approximate the population distribution?
Person taking samples Students in each sample
Mike
79
Tania
23
Bill
37
Rachael
51
A. Tania
B. Mike
C. Bill
D. Rachael
Answers
Answer: Mike!
Step-by-step explanation:
In the book Chances: risk and odds in Everyday Life, author James Burke says that approximately 57% of the general US population wears glasses or contacts. If two people are chosen at random from the US population, what is the probability that both wear glasses or contacts?
Answers
Answer:
[tex]Pr = 32.49\%[/tex]
Step-by-step explanation:
Given
Let E represents the event of wearing glasses or contacts.
So;
[tex]P(E) =57\%[/tex]
Required
The probability that selected 2 wears glasses
This is calculated as:
[tex]Pr = P(E)\ and\ P(E)[/tex]
[tex]Pr = P(E)\ *\ P(E)[/tex]
[tex]Pr = 57\% * 57\%[/tex]
[tex]Pr = 0.57 * 0.57[/tex]
[tex]Pr = 0.3249[/tex]
[tex]Pr = 32.49\%[/tex]
Is 2/9 a perfect square
Answers
PLEASE HELP!!!!!! I WILL MARK YOU BRAINIEST
Answers
Answer:
Measure of angle b is 42 degrees
Step-by-step explanation:
Since angle b is part of a right angle, we can see that part of the right and blue is 48 degrees, and the other part is b. So, we can do 90-48 to get 42 degrees.
Answer:
42
Step-by-step explanation:
since one of the lines for angle b makes a 90° angle all you have to do is subtract 48 from 90 and that is your answer
According to the AAA Foundation for Traffic Safety's American Driving Survey, U.S. drivers spend.
on average, 51 minutes behind the wheel each day. A researcher believes this is an overstatement.
To investigate, a random sample of 75 drivers were selected. The study revealed that the mean
time behind the wheel for the sample of 75 drivers was 46.4 minutes with a standard deviation of
18.8 minutes. Is there convincing evidence that the mean time behind the wheel for all U.S. drivers
is less than 51 minutes? Use a = 0.01.
Answers
Answer:
The pvalue of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.
Step-by-step explanation:
U.S. drivers spend on average, 51 minutes behind the wheel each day.
This means that at the null hypothesis we test that:
[tex]H_{0}: \mu = 51[/tex]
Is there convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes?
This means that the alternate hypothesis is:
[tex]H_{a}: \mu < 51[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
51 is tested at the null hypothesis:
This means that [tex]\mu = 51[/tex]
The study revealed that the mean time behind the wheel for the sample of 75 drivers was 46.4 minutes with a standard deviation of 18.8 minutes.
This means that [tex]n = 75, X = 46.4, \sigma = 18.8[/tex]
Value of the test-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{46.4 - 51}{\frac{18.8}{\sqrt{75}}}[/tex]
[tex]z = -2.12[/tex]
Pvalue of the test:
The pvalue of the test is the probability of finding a sample mean less than 46.4, which is the pvalue of z when X = 46.4.
Looking at the z-table, z = -2.12 has a pvalue of 0.017.
Decision:
The pvalue of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.
No, there isn't convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes.
Given the following data:
Mean = 51.Number of drivers = 75 drivers.Sample mean (mean time) = 46.4 minutes.Standard deviation = 18.8 minutes.What is a null hypothesis?A null hypothesis ([tex]H_0[/tex]) can be defined the opposite of an alternate hypothesis ([tex]H_a[/tex]) and it asserts that two (2) possibilities are the same.
For the null hypothesis, we would test that:
[tex]H_o : \mu =51[/tex]
For the alternate hypothesis, we would test that:
[tex]H_a : \mu < 51[/tex]
The test statistics would be calculated with this formula:
[tex]Z=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.[tex]\delta[/tex] is the standard deviation.n is the number of drivers.Substituting the given parameters into the formula, we have;
[tex]Z=\frac{46.4\;-\;51}{\frac{18.8}{\sqrt{75} } }\\\\Z=\frac{-4.6}{\frac{18.8}{8.6603} }\\\\Z=\frac{-4.6}{2.1708 }[/tex]
Z = -2.12.
What is a p-value?In Statistics, a p-value also known as the probability value is the probability which occurs when the null hypothesis ([tex]H_0[/tex]) is true of obtaining a sample mean that is at least as unlikely as what is observed by a researcher or scientist.
From the z-table, a z-score of -2.12 corresponds to or has a p-value of 0.017. Therefore, the p-value for this test is 0.017 > 0.01.
In conclusion, there isn't convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes.
Read more on null hypothesis here: https://brainly.com/question/14913351
Use the point-slope form to write an equation of a line through the given points.
(−3, 2) and (3, 4)
Answers
Answer:
y-2=1/3(x+3)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-2)/(3-(-3))
m=2/(3+3)
m=2/6
simplify
m=1/3
y-y1=m(x-x1)
y-2=1/3(x-(-3))
y-2=1/3(x+3)
300 paper cups in a dispenser the cups are taken from dispenser at rate at rate of 40 cups per hour
Answers
Answer:
i dont know i dont understand the question
Show
that (2+√3)(2-√3)(5+root2)
(5-root2) is rational number.
Answers
Answer:
(2+3)(2−3)(5+2)(5−2)=>(22−(3)2)(52−(22))=>(4−3)(25−2)=>(1)(23)=>23
(5-√2)=(2^2-√3^2)(5^2-√2^2)=(4-3)(25-2)=23 and 23 is rational number
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags. A 22 bag sample had a mean of 408 grams with a standard deviation of 14. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled
Answers
Answer:
i think it is 451 i believe
5/x=7/x-4
pls help me with this problem if u help i willl heart and follow you
Answers
Answer:
5/x = 7/x-4
5(x-4) = 7(x)
5x - 20 = 7x
5x - 7x = 20
-2x = 20
x = -20/2 = -10
In ΔKLM, m = 480 cm, k = 360 cm and ∠L=29°. Find the area of ΔKLM, to the nearest square centimeter.
Answers
Answer:
The answer is=
41887.551
solve it : x² *dy/dx = -2y
Answers
Answer:
r= -sec(θ) x ∛2
θ=0
Step-by-step explanation:
Which of the following is the measure of an acute angle?
A. 89°
B. 270°
C. 97°
D. 122°
Answers
Answer:
A
Step-by-step explanation:
An acute angle is an angle that is less than 90 degrees.
Answer:
Step-by-step explanation:
A
max is a 22 year old planning to retire at age 67 he is i vesting in a mutual fund and hopes to earn the average inflation adjusted stock market return of 7% anually. If max deposits $200 per month into this fund, how much can he expect to have when he retires? Show work
Answers
Based on the calculation below, the amount Max can be expected to have when he retires is $758,518.94.
How to calculate the future value (FV)?The amount he will be expected to have when he retires can be calculated using the formula for calculating the future value of an ordinary annuity as follows:
FV = D * (((1 + r)^n – 1) / r) ……………………………….. (1)
Where;
FV = Future value or the expected amount when he retires = ?
D = Monthly deposit = $200
r = monthly average inflation adjusted stock market return = 7% / 12 = 0.07 / 12 = 0.00583333333333333
n = number of months = (67 - 22) * 12 = 540
Substituting the values into equation (1), we have:
FV = $200 * (((1 + 0.00583333333333333)^540 – 1) / 0.00583333333333333)
FV = $758,518.94
Learn more about future value here: https://brainly.com/question/14586629.
#SPJ1
How is the graph of the parent quadratic function transformed to produce the graph of y--(2x+6)2+3?
O The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated
up 3 units
O The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated
up 3 units
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up
3 units
O The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up
3 units
Answers
Answer: a
Step-by-step explanation:
just took the test
12. Find the measure of angle x.
13. Find the measure of angle x.
Answers
Answer:
x=21
x=122
Step-by-step explanation:
Answer:
x= 21
x=122
I hope this will help you.
What is the solution to the equation?
19 + 13x = 32
Record your answer in the boxes
below.
00000.00
+/-
I give brainleist
Answers
Answer:
the answer is x=1
Step-by-step explanation:
minus 19 on both sides
then divide by 13 on both sides
Need ASAP
Gabe spent 26 days traveling in Europe. How many hours did he spend traveling in Europe?
Answers
Answer:
624hours
Step-by-step explanation:
There are 24 hours in a day, so multiply the amount of days by 24 to find the amount of hours:
26 x 24 = 624hours
What is the product of 2.416 and 10^5? *
Answers
2.416x10^5
Or
241600
Both are correct the second is just in expanded form
MARK ME BRAINLIEST PLEASE
Answer:
241600
Step-by-step explanation:
Which expressions are equivalent to 16^(3/2)?
Answers
Answer:
16^(3/2)=64
Step-by-step explanation:
what is the equation for the volume of a cylinder? I think is v=pi × r^2 * h just asking for clarification
Answers
Answer:
V=pi multiplied by r^2 times height
Step-by-step explanation: