Answer:
build linear model
When modeling scenarios with linear functions and solving problems involving quantities with a constant rate of change, we typically follow the same problem solving strategies that we would use for any type of function.
fitting linear models to data
A professor is attempting to identify trends among final exam scores. His class has a mixture of students, so he wonders if there is any relationship between age and final exam scores. One way for him to analyze the scores is by creating a diagram that relates the age of each student to the exam score received.
distinguish between linear and nonlinear relations
As we saw in the cricket-chirp example, some data exhibit strong linear trends, but other data, like the final exam scores plotted by age, are clearly nonlinear. Most calculators and computer software can also provide us with the correlation coefficient, which is a measure of how closely the line fits the data.
use a linear model to make predictions
Once we determine that a set of data is linear using the correlation coefficient, we can use the regression line to make predictions. As we learned previously, a regression line is a line that is closest to the data in the scatter plot, which means that only one such line is a best fit for the data.
key concepts
1. Scatter plots show the relationship between two sets of data.
2. Scatter plots may represent linear or non-linear models.
3. The line of best fit may be estimated or calculated using a calculator or statistical software.
4. Interpolation can be used to predict values inside the domain and range of the data, whereas extrapolation can be used to predict values outside the domain and range of the data.
glossary
correlation coefficient
1. a value, r, between –1 and 1 that indicates the degree of linear correlation of variables or how closely a regression line fits a data set.
extrapolation
1. predicting a value outside the domain and range of the data
Step-by-step explanation:
Jade wants to build a raised garden bed in her backyard. The garden measures 9 feet in length by 6 feet in width by 4 feet in depth. The cost to purchase soil to fill the raised garden bed is $12 per cubic yard. How much will it cost to purchase soil for Jade’s raised garden?
Answer:
$864
Step-by-step explanation:
4x^2 - y^2 - 2x- y
Factorise each of the following expressions completely
Answer:
(2x + y)(2x - y - 1)
Step-by-step explanation:
4x² - y² - 2x - y
4x² - y² is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
4x² - y²
= (2x)² - y²
= (2x - y)(2x + y)
expression is now
(2x - y)(2x + y) - (2x + y) ← factor out (2x + y) from each term
= (2x + y)(2x - y - 1)
A tank that is 20% full contains 125 gallons of water. How many gallons would be needed to fill the entire tank? How many gallons are there if thetank was 30% full? What percent of the tabk is full if tgerd are 500 gallons?
Answer:
625
Step-by-step explanation:
becuase 20% is equivilant to 1/5 you need to multiply by 5 to get 1t or full.
part b: 187.5
part c: 125 gallons is 25%. this is because you can fit 4 of it into one 500 gallon tank
Answer:
625 gal, 187.5 gal, 80%
Step-by-step explanation:
[tex]\frac{125}{x}[/tex]=[tex]\frac{20}{100}[/tex] 125*100/20=625
[tex]\frac{x}{625}=\frac{30}{100}[/tex] 30*625/100=187.5 or 625*.3=187.5
[tex]\frac{500}{625}=\frac{x}{100}[/tex] 500*100/625=80
Visible light waves that our eyes see as the color red have a wavelength of about 6.7 x 10-7 meters. What is the frequency of these waves? The speed of light is 3.0 x 10 8 m/s. [v = 1f]
The frequency of these visible light waves that our eyes see is equal to [tex]4.47\times 10^{-14}\;Hz[/tex]
What is wavelength?Wavelength refers to the distance between two (2) successive crests (troughs) of a wave.
How to calculate frequency.Mathematically, the frequency of a wave is given by this formula:
[tex]F = \frac{V}{\lambda}[/tex]
Where:
F is the frequency of a wave.V is the speed of a wave.[tex]\lambda[/tex] is the wavelength of a wave.Substituting the given parameters into the formula, we have;
[tex]F=\frac{3 \times 10^8}{6.7 \times 10^{-7}} \\\\F=4.47\times 10^{-14}\;Hz[/tex]
Read more on frequency here: https://brainly.com/question/19250621
The seats in a movie theater are arranged so that each row has 6 more seats than the row in front of it. If the first row has 24 seats, how many seats are in the 6th row?
a. 30
b. 48
c. 54
d. 60
Answer:
54 seats
Step-by-step explanation:
To make it easier, I'll put it like this.
Row | Seats
1 | 24
2 | 30
3 | 36
4 | 42
5 | 48
6 | 54
(Add 6, because each row has 6 more seats than the row in front of it.)
So, the 6th row has 54 seats.
Hope this helped !
pls help ill give 15 brainliest and 5 starts question is down below
Answer:
1 is 9 sq units
2 is 12
3 is 24cm^2
Step-by-step explanation:
solve: 15x = 180.75
please and thanks
Answer:
x = 12.05
Step-by-step explanation:
Given:
15x=180.75
Divide both sides by 15
15x 180.75
------ = --------
15 15
x = 12.05
Hence, x = 12.05
~lenvy~
Answer:
12.05
Step-by-step explanation:
Divide both sides by the same term
15x/15 = 180.75/15
180.75/15
= 12.05
Hence, x = 12.05
Check Answer:
15(12.05) = 180.75
[RevyBreeze]
The graph of g is a translation 2 units left of the graph of f(x) = x−−√x. What is the domain of g? A. all real numbers B. x ≥ −2 C. x ≥ 0 D. x ≥ 2
4 units left means change in x
y=x√x+2So
Solve for domain
x+2≥0x≥-2Domain=[-2,oo)Option A
The domain of g is x ≥ -2, which is option B.
What is Translation?Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.
Given that,
the graph of g is a translation 2 units left of the graph of f(x) = x√x.
When f(x) is translated k units to the left, the new function will be f(x + k).
So the new function g is,
g(x) = (x + 2) √(x + 2)
In order for the function to be defined, the part inside the square root must be greater than or equal to 0.
x + 2 ≥ 0
x ≥ -2
Hence the domain is x ≥ -2.
Learn more about Translation here :
https://brainly.com/question/29288435
#SPJ3
what is pi and why do we need it
Answer:
Pi is used to find the area and circumference of a circle. Pi can be used to find an area by multiplying the radius of the circle squared times pi.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Is my answer correct?
Answer:
No, not all of them are correct.
Step-by-step explanation:
The first one that u picked is incorrect. The second one is correct. And so it the third. I'm not so sure about the last one but pls MARK BRAINLIEST IF IT IS CORRECT
Identify the key characteristics of the exponential function.
y =
2(1)"
Answer:
2x1 mabe
Step-by-step explanation:
im just doing that because they are next to eatch other but im in 6 grade so if i get it wrong dont blame me
Sam has a cylindrical storage container 7 inches tall with a radius of 5 inches. How much cat litter will fit in the container? Round your answer to the nearest tenth.
Answer:
549.8 inches³
Step-by-step explanation:
Volume of Cylinder = height × base, where base = [tex]\pi[/tex]r².
The radius (r) is given, 5 inches, and so is the height, 7 inches.
We simply substitute these values into the equation.
V(volume) = 7 × [tex]\pi[/tex] × 5²
= 175[tex]\pi[/tex]
= 549.77871437821...
when we round that to the nearest tenth,
≈ 549. 8
Koalas weigh 6 kilograms on average. how many cells are in the average koala.
HELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLO
Answer:
hi
Step-by-step explanation:
WILL GIVE BRAINLIEST TO BEST ANSWER, THANKS, 5 STARS!
PLEASE HELP!!
What are the zero(s) from the function f(x)=-4x^2-16x-12
(Select all that apply)
(4,0)
(-12,0)
(-4,0)
(1,0)
(-3,0)
(-1,0)
(3,0)
Answer: (-3, 0) and (-1, 0)
Step-by-step explanation:
[tex]-4x^2-16x-12[/tex]
[tex]\mathrm{Rewrite\:}-16\mathrm{\:as\:}-4\cdot \:4[/tex]
[tex]\mathrm{Rewrite\:}-12\mathrm{\:as\:}-4\cdot \:3[/tex]
[tex]=-4x^2-4\cdot \:4x-4\cdot \:3[/tex]
[tex]\text{Factor out common term -4}[/tex]
[tex]=-4\left(x^2+4x+3\right)[/tex]
[tex]x^2+4x+3[/tex]
[tex]=\left(x^2+x\right)+\left(3x+3\right)[/tex]
[tex]=x\left(x+1\right)+3\left(x+1\right)[/tex]
[tex]\mathrm{Factor \ out \ common \ term \ x+1}[/tex]
[tex]=\left(x+1\right)\left(x+3\right)[/tex]
[tex]=-4\left(x+1\right)\left(x+3\right)[/tex]
Roots:
x + 3 = 0 and x + 1 = 0
x = 0 - 3 x = 0 - 1
x = -3 x = -1
Therefore, the zeroes of the function are (-3, 0) and (-1, 0)
please help i am confused.
Answer:
12.16 inches.
Step-by-step explanation:
Use pythagoras thereom since they are right angle triangles. A² = c² - b².
For NP triangle:
10² - 4² = 84. square root of 84 is 9.165.
For MN triangle:
5² - 4² = 9. square root of 9 is 3.
finally, add them up:
3 + 9.165 = 12.165, to 2 d.p., it is 12.16 inches.
Eliminate the parameter to complete the statements describing the equations
x = 3cos(t) - 2 and y = 2sin(t) + 1.
The rectangular form of this equation is
A. 4(x + 2)2 + 9(y – 1)2 = 36
B. 9(x + 2)2 + 4(y - 1)2 = 36
C. 4(x - 2)2 + 9(y + 1)2 = 36
D. 9(x - 2)2 + 4(y + 1)2 = 36
The equations represent a/an
Answer:
A
ellipse
Step-by-step explanation:
Answer:
1.) The rectangular form of this equation is (A)
.2.) The equations represent a/an (ellipse)
.
Step-by-step explanation:
Edge 2022
10 A grocery store bought 1,600 cans of
vegetables in different sizes. Of the cans,
25% contained less than 400 grams of
vegetables, 15% contained between 400
and 500 grams of vegetables, and the
rest contained more than 500 grams of
vegetables.
How many cans contained more than 500
grams of vegetables?
F 1,120
H 640
G 800
J 960
Answer:
1020 cans
Step-by-step explanation:
100-25
=75%
0.75x1600
1200cans
100-15
=85%
0.85x1200
=1020 cans
Help me understand how to do this please. (?)
Step-by-step explanation:
part 1: the exponent is the power or the number you see ontop of n. it indicates how many times n is multiplied by itself. so for the first question n is multiplied by itself 6 times. so the answer should be n×n×n×n×n×n.
part 2 is similar to part 1.
since there is a total of 6 ns we can say that it is n^6.
feel free to ask if you need any further guidance.
How many different triangles can you make if you are given the measurments or two sides an angle that is not between those two sides
Answer:
2.
Step-by-step explanation:
This is called the ambibuous case where 2 sides are given and angle opposite one of these sides.
2 traingles are possible.
What is the sum of 5 times a number and 7 is 2
Answer:-1
Step-by-step explanation:
5x+7=2
5x=5
X=1
Would a compound event involving a standard number cube and a spinner be dependent or independent?
Since the result of the number cube and the result of the spinner do not effect each other, the events are independent.
What are dependent and independent events?When one trial affects the next trial, the events are called dependent. One example is taken a card without replacement from a standard deck, as in each trial, the number of cards remaining decreases, hence the probabilities are affected.When there is no effect of one trial on another, the events are called independent.In this problem, the result of the number cube does not affect the result of the spinner, as they are rolled separately, hence the events are independent.
More can be learned about independent events at https://brainly.com/question/14478923
reflect the shape A in the line
x=1
What are the coordinates of the vertices of the image?
its for a maths test!!!!!!!!!!!!!!!!!!!!!!!!!!
correct answers to be awarded brainley
.
i dont knowkkkkkkkkkkkkk
What is 6
4
-237
-
?
10
A. 3.
C. 3
19
20
5
B. 3
D. 4
10
10
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6\dfrac{1}{4} - 2\dfrac{3}{10}}\\\\\mathsf{\rightarrow \dfrac{6\times4+1}{4} - \dfrac{2\times10+3}{10}}\\\\\mathsf{\rightarrow \dfrac{24 + 1}{4} - \dfrac{20 + 3}{10}}\\\\\mathsf{\rightarrow \dfrac{25}{4} - \dfrac{23}{10}}\\\\\mathsf{\rightarrow \dfrac{79}{20}}\\\\\mathsf{\approx 3\dfrac{19}{20}}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{Option\ C. \ 3 \dfrac{19}{20}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Stella's monthly bank statement showed the following deposits and withdrawals: − −$34.71, − −$100.08, $111.62, $92.93, − −$27.27 If Stella's balance in the account was $20.1 at the beginning of the month, what was the account balance at the end of the month?
Answer: $ 27.27
Step-by-step explanation:
Answer:
62.59
Step-by-step explanation:
how to tell if something is cubed or squared being ft^3 or ft^2
Answer:
Check the power
Step-by-step explanation:
You can tell if a quantity has been cubed or squared by looking at its power.
For example, ft^3 has a power of 3 (meaning feet is raised to 3) which means whichever number ft^3 is used with, has been cubed, generally volume of any shape
Similarly, ft^2 has a power of 2 (meaning feet is raised to 2) which means whichever number ft^2 is used with, has been squared, generally area of any shape
===========================================================
If something is squared, it's multiplied times itself 2 times.
Example:-
[tex]\bigstar\boxed{\pmb{4*4=4^2}}\longleftarrow\sf{4~squared~}[/tex]
You should also notice that the exponent of 4 is 2.
So if something is squared, its exponent is 2.
If something is cubed, it's multiplied times itself 3 times.
Example:-
[tex]\bigstar{\boxed{\pmb{4*4*4=4^3}}\longleftarrow\sf{4~cubed}[/tex]
You should also notice that the exponent of 4 is 3.
So if something is cubed, its exponent is 3.
=======================================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
Damian needs to buy 5 pints of juice but the store doesn't sell juice in pints, so damian buys 3 quarts of juice. does damian buy enough juice if not how much more does he have left or need to have enough?
Answer:
Damain has bought enough juice.
Step-by-step explanation:
1 qt(quart) = 2 pints.
3 qt = 6 pints.
6 pints > 5 pints (6 pints is bigger than 5 pints)
Therefore, Damain has bought enough juice.
Please mark as brainliest!
Help! How do I fill out the box at the top of the page? This isn't making sense (I'm in 7th)
Answer:
x= 4
y= 9
so in that case (x,y) would be (4,9)
then you go down to the x axis and go to 4.
then you go up 9 and that is your first point
same thing for the rest of them so it would be (6,3)
(1,3)
(8,7)
(8,9)
help!!
For what value of x is the value of the square of the binomial 2x +3
is 9 greater than the value of the square of the binomial 2x -3?
Answer:
x = 3/8
Step-by-step explanation:
The difference of the two squares can be found several ways. One way uses the "difference of squares" special form.
a² -b² = (a -b)(a +b)
For the given squares, this is ...
(2x +3)² -(2x -3)² = ((2x +3)-(2x -3))((2x +3) +(2x -3)) = 6(4x) = 24x
We want to find x that makes this difference be 9:
24x = 9
x = 9/24 = 3/8
For the value x = 3/8, the difference between the squares of the binomials will be 9.
Use: nCk = n!/k! (n-k)!
At a local cafeteria there are ten vegetable selections available. How many three-vegetable plates may be made
Answer:
120
Step-by-step explanation:
The formula [tex]nCk=\frac{n!}{k!(n-k)!}[/tex] describes how many ways [tex]k[/tex] items can be chosen given [tex]n[/tex] total items. In this scenario, [tex]n=10[/tex], and [tex]k=3[/tex], thus:
[tex]\frac{10!}{3!(10-3)!}=120[/tex]
This means that you can make 120 three-vegetable plates