Answer:
a. A linear pattern exists in the data.
b. The parameters for the line that minimizes MSE for this time series are as folows:
ß1 = Estimated slope = 1.4567
ß0 = Estimated intercept = 4.7165
Also, we have:
MSE = Mean squared error = 0.4896
c. Forecast for year 10 is 19,280.
Step-by-step explanation:
a. What type of pattern exists in the data?
Note: See Sheet1 of the attached excel file for the line graph.
From the line graph, it can be observed that a linear pattern exists in the data.
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
Note: See Sheet2 of the attached excel file for all the calculations to obtain the following:
Sample size = 9
Total of X = 45
Total of Y = 108
Mean of X = Total of X / Sample size = 45 / 9 = 5
Mean of Y = Total of X / Sample size = 108 / 9 = 12
SSxx = Total of (X - Mean of X)^2 = 60
SSyy = Total of (Y - Mean of Y)^2 = 130.74
SSxy = Total of (X - Mean of X) * (Y - Mean of Y) = 87.40
Therefore, we have:
ß1 = Estimated slope = SSxy/SSxx = 87.4 / 60 = 1.4567
ß0 = Estimated intercept = Mean of Y – (ß1 * Mean of X) = 12 - (5 * 1.4567) = 4.7165
Therefore, the parameters for the line that minimizes MSE for this time series are as folows:
ß1 = Estimated slope = 1.4567
ß0 = Estimated intercept = 4.7165
Regression equation which also used in the attached excel is as follows:
Y = ß0 + ß1X =
Y = 4.7165 + 1.4567X …………………. (1)
SSE = Sum of squared error = Total of (Y - Y*)^2 = 3.4273
Therefore, we have:
MSE = Mean squared error = (SSE/(n-2)) = (3.4273 / (9 - 2)) = 0.4896
c. What is the forecast for year 10?
This implies that X = 10
Substitute X = 10 into equation (1), we have:
Y = 4.7165 + (1.4567 * 10) = 19.28
Since it is 1,000s, we have:
Y = 19.28 * 1,000 = 19,280
Therefore, forecast for year 10 is 19,280.
Andrea's Sequoia gets 12 miles per gallon while driving in the city, and 20 miles per gallon while on the highway. The last time she filled up the car it took 16 gallons of gas, and she had driven 280 miles since the previous fill-up. How many miles of that 280 were city driving?
Answer:
60miles
Step-by-step explanation:
if they drove x miles in the city and y miles on the highway then you know that
x + y = 280
x/12 + y/20 = 16
x + 12y/20 = 16*12 = 192
8y/20 = 88
y = 220
x = 280-y = 280-220 = 60
Write the point-slope form of an equation of the line through the points (-4, 7) and (5,-3).
0
A. Y+4= -1; (1 – 7)
B.Y-5 = = 10 (x+3)
OC. y +3 = = 10 (2+5)
D. y - 7= -5° (x+4)
Answer:
Step-by-step explanation:
There are two possible equations, but neither matches the the choices you listed. The choices seem to have several typographical errors.
Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 =(-10/9)(x + 4).
How to estimate the point-slope form of an equation of the line through the points (-4, 7) and (5,-3)?Slope
[tex]$= \frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]
= (-3 - 7) / (5 - (-4))
= -10/9
The point-slope equation for the line of slope -(10/9) that passes through the point (5, -3).
y + 3 = (-10/9)(x - 5)
Point slope equation for the line of slope -(10/9) that passes through the point (-4, 7)
Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 = (-10/9)(x + 4).
Therefore, the correct answer is y - 7 = (-10/9)(x + 4).
To learn more about the equation of a line refer to:
https://brainly.com/question/11751737
#SPJ2
Determine whether the following relationship is a linear inequality or not
1. Y < 3
2. x ≥ 6
3. x² > -3
4. x -3 > 1/2
5. xy + 5 ≤ 7
Answer:
What is a linear inequality ? A linear inequality has the same condition as a linear equality, but instead of the equal sign, we have for example this one ≤ wish means less than or equal to.
But what are the condition of a linear equality ? There are many ways of writing linear equations but they usually have constants (like "2" or "c") and must have simple variables (like "x" or "y") BUT the variables (x and y) on a linear equation do NOT have Exponents (like the 2 in x²) and square roots,
1. y < 3
Yes, this is a linear inequation. Frequently, the term linear equation refers implicitly to the case of just one variable (here y).
2. x ≥ 6
Yes.
3. x² > - 3
No, remember the rule the variable (here x) must not have exponents.
4. x - 3 > 1/2
Yes.
5. xy + 5 ≤ 7
This one is nice. If both x and y are variables then the answer is no, it's not a linear inequation. Why ?The linear equation is a sum of terms like "Ax" where x is a variable, and A is a number or a constant. On the other hand if x or y was a constant (like e or π), it could be treated as a number and the whole expression would become linear.
You can also have fun and write :
xy ≤ 2
for y > 0 we write:
x ≤ 2/y
x ≤ 2[tex]y^{-1}[/tex]
and then simply say exponents are not allowed so not a linear inequation.
Which of these numbers are greater than 24? Check all that apply.
O A. 12
B. 15
O C. 42
D. 41
E. 13
D F. 18
Answer:
A, B, E, F
Step-by-step explanation:
24>12, 24>15, 24>13, 24>18, 24<42, 24<41
What is the image of (3, -12) after a dilation by a scale factor of į centered
at the origin?
Answer:
9 is. ................m.m..mk
Probability of picking a blue marble and a yellow marble when 2 marbles are picked (without replacement) from a bag containing 4 blue and 4 yellow marbles
Answer:
9/49
Step-by-step explanation:
that is the procedure above
You $12 for a day, and plan to spend your time feeding the Lorakeets. $2 per feed (f), and drinking ICEE's (I), $4 each. What is the equation for the total number f times you can feed the lorakeets and icees you can drink with your total amount of money you brought?
Answer: 85 i think
Step-by-step explanation:
Which expression is equivalent to square root 216x3y6z12?
Answer:
hello mateee ;)
Step-by-step explanation:
lets go step by step...
216 cub root = 6
x^3 cube root = 3/3 = power 1 = x
y^6 cube root = 6/3 = power 2 = y^2
z^12 cube root = 12/3 = power 4 = z^4
final ans becomes 6x y^2 z^4 hence option a is correct
glad for brainliest <3
please help me with this on the image
Answer:
we will then have to also multiply the y with three so the answer is B and that's ( ×3)
Find the missing side length in the image below
where are parabolas on your hand?
parabolas are there on my hand palms and it must be there on your hands too but why are you asking this question?
I need help with this please
Answer:
its the 1st one
Step-by-step explanation:
they need to know what the Total
Answer:
English; 12
French; 9
Both; 7
Step-by-step explanation:
28 - 19 = 9, therefore there are only 9 students who can only speak French
28 - 16 = 12, therefore there are only 12 students who can only speak English
12 + 9 = 21, then subtract 21 from the 28 total students
28 - 21 = 7, therefore there are only 7 students who can speak both
2 6 + 3 * 4 2 + 7 * - 2 /
Answer:
26 + 3 x 42 + 7 x -2 = 138
Step-by-step explanation:
Ok bud, first step we must convert our symbols (Makes it easier to solve)
26 + 3 x 42 + 7 x -2
* subsitutes for multiplication.
I recommend using PEMDAS at times:
1 - Parentheses
2 - Exponents and Roots
3 - Multiplication
4 - Division
5 - Addition
6 - Subtraction
Yet again your numbers were spaced out could they be exponents? if so:
3x^{42}+7x+24
Our answer would round to 24 but he equation was not put in a valid or straight forward way.
total mass vs. numbers of cd and numbers of cd
Answer: Choice A) M = 0.25n + 100
=============================================================
Explanation:
For now, I'll treat n as x, and M as y.
In other words,
x = number of CDsy = total mass in kgLet's select two points from this graph. I'll pick (200,150) and (400,200)
The slope of the line through those points is
m = (y2-y1)/(x2-x1)
m = (200-150)/(400-200)
m = 50/200
m = 0.25
Now we'll use the point (x,y) = (200,150) along with that slope value to find the y intercept b
y = mx+b
150 = 0.25*200+b
150 = 50+b
150-50 = b
100 = b
b = 100
You could also use (x,y) = (400,200) and you should get the same b value.
In fact, any other point from this graph works as well.
------------------------------
Since m = 0.25 and b = 100, we go from y = mx+b to y = 0.25x+100
This then translates over to M = 0.25n + 100 which is choice A
To help verify this, let's say we plugged in n = 100
M = 0.25*n + 100
M = 0.25*100 + 100
M = 25 + 100
M = 125
Which is confirmed by what the graph shows. I'll let you check the other points as well.
A bacteria culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.
(a) Find the initial population. P(0) = 80 )ãbacteria
(b) Find an expression for the population after t hours. r(t) = 180( 125(6 Plt) =180(125(2))-
(c) Find the number of cells after 7 hours. (Round your answer to the nearest integer.) P(7)=72.358- bacteria
(d) Find the rate of growth after 7 hours. (Round your answer to the nearest integer.) P(7) 2x bacteria/hour
(e) When will the population reach 200,000? (Round your answer to one decimal place.) hours
Answer:
a) P(0) = 80
b) [tex]P(t) = 80(2.2361)^t[/tex]
c) 22,363 cells.
d) The rate of growth after 7 hours is of 18,000 bacteria per hour.
e) 9.7 hours.
Step-by-step explanation:
A bacteria culture grows with a constant relative growth rate.
This means that the population is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial population and r is the growth rate, as a decimal.
After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.
This means that in 6 hours, the population went from 400 bacteria to 50,000 bacteria. We use this to find r. So
[tex]50000 = 400(1+r)^6[/tex]
[tex](1+r)^6 = \frac{50000}{400}[/tex]
[tex](1+r)^6 = 125[/tex]
[tex]\sqrt[6]{(1+r)^6} = \sqrt[6]{125}[/tex]
[tex]1 + r = 125^{\frac{1}{6}}[/tex]
[tex]1 + r = 2.2361[/tex]
So
[tex]P(t) = P(0)(2.2361)^t[/tex]
(a) Find the initial population. P(0)
We have that P(2) = 400. We use this to find P(0). So
[tex]P(t) = P(0)(2.2361)^t[/tex]
[tex]400 = P(0)(2.2361)^2[/tex]
[tex]P(0) = \frac{400}{(2.2361)^2}[/tex]
[tex]P(0) = 80[/tex]
So
[tex]P(t) = 80(2.2361)^t[/tex]
(b) Find an expression for the population after t hours.
[tex]P(t) = 80(2.2361)^t[/tex]
(c) Find the number of cells after 7 hours.
This is P(7). So
[tex]P(7) = 80(2.2361)^7 = 22363[/tex]
22,363 cells.
(d) Find the rate of growth after 7 hours.
We have to find the derivative when t = 7. So
[tex]P(t) = 80(2.2361)^t[/tex]
[tex]P^{\prime}(t) = 80\ln{2.2361}(2.2361)^t[/tex]
[tex]P^{\prime}(7) = 80\ln{2.2361}(2.2361)^7 = 18000[/tex]
The rate of growth after 7 hours is of 18,000 bacteria per hour.
(e) When will the population reach 200,000?
This is t for which [tex]P(t) = 200000[/tex]. So
[tex]P(t) = 80(2.2361)^t[/tex]
[tex]200000 = 80(2.2361)^t[/tex]
[tex](2.2361)^t = \frac{200000}{80}[/tex]
[tex](2.2361)^t = 2500[/tex]
[tex]\log{(2.2361)^t} = \log{2500}[/tex]
[tex]t\log{2.2361} = \log{2500}[/tex]
[tex]t = \frac{\log{2500}}{\log{2.2361}}[/tex]
[tex]t = 9.7[/tex]
So 9.7 hours.
Trên tập hợp số thực cho quan hệ tương đương T như sau: m, n : mTn ⇔ m^3-n^3= m-n . Tìm lớp tương đương của 0 và lớp tương đương của 2021
Answer:
where are u from bro?
Step-by-step explanation:
I didn't understand your language.
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to thegiven statistics and confidence level. Round the margin of error to four decimal places.1)99% confidence; n
Answer:
[tex]E = 0.0158[/tex]
Step-by-step explanation:
Given
[tex]n = 5900[/tex]
[tex]x = 1770[/tex]
[tex]CI = 99\%[/tex]
Required
The margin of error (E)
First, calculate proportion p
[tex]p = x/n[/tex]
[tex]p = 1770/5900[/tex]
[tex]p = 0.3[/tex]
Given that:
[tex]CI = 99\%[/tex]
Calculate the alpha leve;
[tex]\alpha = 1 - CI[/tex]
[tex]\alpha = 1- 0.99[/tex]
[tex]\alpha= 0.01[/tex]
Divide by 2
[tex]\alpha/2= 0.01/2[/tex]
Subtract from 1
[tex]1 - \alpha/2= 1 - 0.01/2[/tex]
[tex]1 - \alpha/2= 0.995[/tex]
The corresponding z value is:
[tex]z =2.576[/tex]
So, the margin of error is:
[tex]E = z * \sqrt{p * (1 - p)/n}[/tex]
So, we have:
[tex]E = 2.576 * \sqrt{0.3 * (1 - 0.3)/5600}[/tex]
Using a calculator, we have:
[tex]E = 0.01577471394[/tex]
Approximate
[tex]E = 0.0158[/tex]
Pls Help! I'll mark the correct answer brainliest <3
A new computer virus is infecting computers and handheld devices connected to the internet. The number of devices affected by the virus n, in thousands, as a function of t days after it was discovered is n(t)=235(1.24)t. Interpret the rate of change within the context of this situation.
a) The number of devices infected with the virus increases by 24% each day.
b) The number of devices infected with the virus increases by 24% each hour.
c) The number of devices infected with the virus decreases by 76% each day.
d) The number of devices infected with the virus is 235,000 when the virus was discovered.
Answer:
The number of devices infected with the virus increases by 24% each day.
Step-by-step explanation:
Have a nice day! ♡
plzzzzzzzz helllllllppppppppp
Answer:
C
Step-by-step explanation:
He want's the bookshelf to be 1.5 feet taller than 1/4 of the height of his plant
If his plant's height is p, 1/4 of it's height would be 1/4p
As he wants the bookshelf to be 1.5 feet taller than this, the height should be
1.5 + 1/4p, which can also be written as p/4 + 1/5
Answered by g a u t h m a t h
Answer:
1/4p +1.5
Step-by-step explanation:
p = plant stand
The bookshelf is 1/4 the height of the plant stand plus 1.5 ft
1/4p +1.5
Find the fractal dimension of the object.
Answer:
maaqqqf aku ngak tau soal jawaban in
3. A toy car is traveling with a velocity of 4 m/s and has a mass of 1120g. What is the car's
kinetic energy?
if k = p+2q/3 , find the value of p when k=7 and q=3
Answer:
p = 5
Step-by-step explanation:
hopefully it is clear and understandable :)
Find the solution of the exponential equation, as in Example 1. (Enter your answers as a comma-separated list.)
e1 − 3x = e4x − 3
x=_______
Answer:
Hello,
Very bad written!!!
Step-by-step explanation:
[tex]e^{1-3x}=e^{4x-3}\\\\1-3x=4x-3\\\\7x=4\\\\\boxed{x=\dfrac{4}{7} }\\[/tex]
Hi there!i am confused about this equation. Please help to solve this.
Answer:
Step-by-step explanation:
Short of taking 3 hours to type out the way that I did this, let me just tell you the process. Square both sides and multiply to distribute. You end up with radicals still, so square both sides again and multiply to distribute. What you end up with is a 6th degree polynomial that has to be factored. What I got in the end were these zeros:
x = 21.41917943
x = 1.306542114+/-7186864435i
x = -1.066667927
x = 1.28038353
x = 1.28038353
x = -.2459792634
will give someone a brainlyest pls help! thank you
Answer:
D.
Step-by-step explanation:
5/4=1.25, -2[tex]\sqrt{2}[/tex] = -2.828
Therefore,
1.25 (5/4), 1.04, -0.34, -2.828 (-2[tex]\sqrt{2}[/tex]), -17
(x+7)(x-6) Find the product.ddddddddddddd
Answer:
x^2 + x - 42
Step-by-step explanation:
use the distributive property:
(x+7)(x-6) = x^2 + x - 42
Answer: x^2 + x - 42
Step-by-step explanation:
if 10x=1/0.001 find the value of x
[tex]\\ \sf\longmapsto 10x=\dfrac{1}{0.001}[/tex]
Turn over the decimal[tex]\\ \sf\longmapsto 10x=\dfrac{1}{\dfrac{1}{1000}}[/tex]
[tex]\\ \sf\longmapsto 10x=1000[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{1000}{10}[/tex]
[tex]\\ \sf\longmapsto x=100[/tex]
THE DISTANCE OF A PARTICLE FROM
IT'S STARTING POINT AT TIME T
SECONDS IS GIVEN BY S= 80T - 1672.
WHAT IS THE VELOCITY OF THE
PARTICLE AFTER 2 SECONDS?
Answer:
the answer will be 3.........
An Experiment to investigate the relation between two physical quantities was performed where 10 data pairs were collected. You are to perform regression analysis to describe the relation between the two quantities using a polynomial. What are the possible values for the order of that polynomial?
a) from 0 to 10
b) from 1 to 9
c) from 1 to 10
d) Any integer
Answer:
d). Any Integer.
Step-by-step explanation:
Regression analysis is characterized as the statistical method that is employed to determine the association between a dependent, as well as, the independent variable(one or more). It
As per the question, the probable values for the arrangement of a polynomial would be 'any integer' in order to determine the relationship among the different variables(the two physical quantities). Since a regression analysis helps in knowing the factors that influence the other and the factors that do not affect much in order to reach a reliable conclusion. Thus, any of the values can be examined to examine the association among them. Hence, option d is the correct answer.
Which of the proportions below could be used to convert 2500 kilograms to grams?
A. 1000/1 = x/2500
B. 100/1 = x/2500
C. 1/100 = x/2500
D. 1/10 = x/2500
Answer:
A. 1000/1 = x/2500
Step-by-step explanation:
1000 g = 1 kg
Using ratios
1000 g x g
------------ = --------------
1 kg 25 00 kg
Answer:
A. 1000/1 = x/2500
Step-by-step explanation:
KHD - DCM
Kilo - Hecta - Deca - Base - Deci - Centi - Mili
*When moving from left to right, each spot you pass multiplis your number by 10.
2500 kilo → x grams (base)
Proportions:
grams/kilos = x/2500
*For every 1 kilo, there is 1000 grams.
1000/1 = x/2500
