Answer:
y² - 4y - 77
Step-by-step explanation:
(y+7)(y-11)
y² - 11y + 7y - 77
y² - 4y - 77
With the help of scientists, farmers in the United Kingdom have been able to produce more and more grain per hectare each year. Here are the crop yields for several years:
Assuming that this trend continues, what crop yield is predicted for the year 2020 by the model? Round your answer to the nearest whole number. You must find the linear regression equation first.
A. 8,603 kg/ha
B. 8,232 kg/ha
C. 9,447 kg/ha
D. 7,382 kg/ha
Crop yield prediction in year 2020 is 9,447 kg/ha
What is linear regression ?Linear regression is an analytic statistical approach for predicting the relationships between an independent variable that determines the values of of or more dependent variables.
From the data given in the question
Equation of a straight line is y = a + bx
∑y = an + b∑x
∑xy = a∑x +b∑x²
The values are calculated in the table given below
X y x=X-1985 x² xy
1961 3090 -24 576 -74160
1968 4040 -17 289 -68680
1987 5830 2 4 11660
1992 5680 7 49 39760
2001 7630 16 256 122080
2004 8020 19 361 152380
_ _ _ _ _
∑x =11913 ∑y=34290 ∑x=3 ∑x²=1535 ∑xy=183040
Substituting the values
6a + 3b = 34290
3a + 1535b = 183040
solving the two by suitable elimination
6a + 3b = 34290
3(2a+b) = 3×11430
2a + b = 11430....(i)
and 3a + 1535b=183040....(ii)
a=173620/3067 = 5660.91
Putting a=5660.91 in (i)
2(5660.91) + b = 11430
b = 108.81
∴ a = 5660.91 and b = 108.81
Now substituting the values in the equation y=a+bx
y = 5660.91 + 108.81x
y = 5660.91 + 108.81(X-1985)
∴In 2020
y =5660.91 +108.81(2020 - 1985)
y = 9447.245
Learn more about Statistics here :
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Problem
Combine the like terms to create an equivalent expression:
y−(−3y)
please someone explain to me how to do this?
Suppose a + bi and c + di are complex numbers with b not equaling 0.
(a) Calculate (a + bi) + (c + di) and (a + bi)(c + di).
(b) Show that if both the sum and product are real numbers, then either the complex numbers are real numbers or conjugates.
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Answer:
(a) sum: (a+c) +(b+d)i
product: (ac -bd) +(bc +ad)i
(b) (b+d)=0 and (bc+ad)=0 ⇒ a=c, d=-b or b=d=0
Step-by-step explanation:
(a) Combining like terms the sum is ...
(a +bi) +(c +di) = (a+c) +(b+d)i . . . . sum
And the product is ...
(a+bi)(c+di) = ac +(ad+bc)i +bd·i²
Since i = √-1, i² = -1 and the product can be written as ...
(a+bi)(c+di) = (ac-bd) +(ad+bc)i . . . . product
__
(b) If both the sum and product are real numbers, then we have ...
b +d = 0
ad +bc = 0
The first equation tells us d = -b. Substituting that into the second equation, we get ...
a(-b) +b(c) = 0
b(c -a) = 0
The zero product rule tells us this will be true if and only if b = 0 or c = a.
if b = 0, then d = 0 and both numbers are real.
if c = a, then c+di = a-bi and the numbers are conjugates.
Hence, if both the sum and product are real, both are real numbers or they are conjugates.
A 42 gallon hot water tank hose 350 pounds of water what weight of water at 53 gallon tank hold
Answer:
441.66667 pounds
Step-by-step explanation:
divide 350/42 then multiply the quotient by 53
MFP15017010 2021 Question 2 2.1 Calculate the following 2- and 3-digit numbers using strategic doubling: 34 2.1.2 340 2.13 277 214 00 (10) 2.15 500
Answer:
plz check ur school solution down.
Step-by-step explanation:
Graph the line. y = -5x + 1
an experiment consists of tossing a coin five times and observing and the sequence of heads and tails. find pr
Answer:
[tex]P(TTTTT) = \frac{1}{32}[/tex]
Step-by-step explanation:
Given
[tex]n = 5[/tex] --- toss
See comment for complete question
Required
[tex]P(TTTTT)[/tex]
First, we calculate the number of possible outcomes
A coin has 2 faces; Since the coin is to be tossed 5 times;
[tex]Outcome = 2^5[/tex]
[tex]Outcome = 32[/tex]
There is only one outcome of TTTTT;
So:
[tex]P(TTTTT) = \frac{1}{32}[/tex]
If POR ~ ASTU, what is the scale factor of APQR to ASTU?
A. 1/5
B. 1/4
C. 5
D. 4
Answer:
[tex]k = \frac{1}{5}[/tex]
Step-by-step explanation:
Given
The attached triangles
Required
The scale factor
From the attachment, we have:
[tex]TU = 4[/tex]
[tex]QR = 20[/tex]
So, the scale factor from PQR to STU is:
[tex]k = \frac{TU}{QR}[/tex]
[tex]k = \frac{4}{20}[/tex]
[tex]k = \frac{1}{5}[/tex]
What is the length of PO
These are similar triangles, therefore their sides are proportional.
36 / 24 = PO / 36
24PO = 1296
PO = 54
Hope this helps!
Which one correct answer??
What is the question of it ?
2 2/3 +2 2/3 + 2 2/3 +2 2/3
Answer:
10.6666666667 is your answer
just round this to the nearest tenth
9514 1404 393
Answer:
10 2/3
Step-by-step explanation:
Multiplication works nicely on problems involving repeated addition:
2 2/3 +2 2/3 + 2 2/3 +2 2/3 = 4 × (2 2/3) = 4×2 +4×2/3 = 8 +8/3
= 8 + 2 2/3 = 10 2/3
Si una vara 2,15 mts de longitud da una sombra de 6,45 mts
Answer:
he casted 4.3. away
Step-by-step explanation:
A man invested N80 at a certain rate of simple interest. If at the end of 5 years the money amounted to N88, what was the rate of simple interest paid?
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Answer:
2%
Step-by-step explanation:
The amount of interest is the difference between the total amount and the principal amount:
N88 -N80 = N8 . . . . the amount of interest
The interest amount is given by the formula ...
I = Prt
Solving for r, we find ...
r = I/(Pt) = 8/(80×5) = 1/50 = 2%
The rate of simple interest paid was 2%.
in order to apply the law of cosines to find the length of the side of a triangle, is it enough to know which of the following?
A. The area of a triangle
B. The lengths of two of the triangle's sides and the measure of the angle between them
C. At least two of the angles of the triangle and the length of one of its sides
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Answer:
B. The lengths of two of the triangle's sides and the measure of the angle between them
Step-by-step explanation:
The usual formulation of the law of cosines is something like this:
c² = a² +b² -2ab·cos(C)
where 'c' is the side opposite angle C, and 'a' and 'b' are the other two sides. That is, to use this formula directly, one needs two side lengths and the measure of the included angle.
_____
Additional comment
One can use the law of cosines to solve a triangle when any two sides and one angle are known. The use of the formula will give a quadratic in the unknown side length, if it is not the side opposite the known angle. As with the law of sines, if the angle is opposite the shorter of the two given sides, there may be two solutions for the length of the third side.
Answer:
The answer is B.)
Step-by-step explanation:
Find the measure of the missing angles.
WILL GIVE BRAINLIEST
Answer:
h= 60
g= 120
m= 147
k= 33
Step-by-step explanation:
We know that all three lines are straight an continuous, so, at any given point the angles should add up to 180 degrees.
This immediately helps with angle h:
120 + h = 180
h = 60
As well as m:
33 + m = 180
m = 147
There are two ways to solve the next part:
First and most familiar way:
h + g = 180
60 + g = 180
g = 120
and:
m + k = 180
147 + k = 180
k = 33
The other way that I prefer is that the angles opposite of each other when two lines intersect are equal. I don't know if that makes sense, it's hard to explain in this format.
Simplify[tex]\frac{9x^{16} }{6(x^{2} )^{3}x^{2} } }[/tex]
Answer:
[tex]\displaystyle \frac{3x^8}{2}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex] Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex] Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{9x^{16}}{6(x^2)^3x^2}[/tex]
Step 2: Simplify
Exponential Rule [Powering]: [tex]\displaystyle \frac{9x^{16}}{6x^6x^2}[/tex]Exponential Rule [Multiplying]: [tex]\displaystyle \frac{9x^{16}}{6x^8}[/tex]Exponential Rule [Dividing]: [tex]\displaystyle \frac{9x^8}{6}[/tex]Simplify: [tex]\displaystyle \frac{3x^8}{2}[/tex]Part C of Jim and his dad are building a rectangular flower bed.
If Jim and his dad decide to decrease the width of the flower bed from 15 feet, what happens to its length?
Convert the following fraction to a decimal.
1/3
A. 0.3
B. 0.03
C. 0.303
D. 3.9
Answer:
Option A, 0.3
Step-by-step explanation:
Step 1: Convert the fraction into a decimal
Technically, 1/3 is an irrational number meaning that it never ends. However, if we round it, it would round to 0.3 since 1/3 = 0.3333333.....
Answer: Option A, 0.3
Use all the six numerals 4, 5, 6, 7, 8 and 9 to form two 3-digit even numbers whose sum is smallest, and what is the sum?
Step-by-step explanation:
this Is hard to find.............
Answer:
The numbers should be even, it means the unit digits are 4, 6 or 8.
The numbers should be minimal, it means the hundred's digits are 4 and 5.
With this we have possible numbers:
4x6 and 5y8, here 6 and 8 could be exchanged.The options are:
496 and 578 or476 and 598 or498 and 576 or478 and 596The sum of the two numbers is:
1074Surface roughness of pipe. Refer to the Anti-corrosion Methods and Materials (Vol. 50, 2003) study of the sur- face roughness of coated interior pipe used in oil fields, Exercise 7.26 (p. 311). The data (in micrometers) for 20 sampled pipe sections are reproduced in the table on p. 391.
a. Give the null and alternative hypotheses for testing whether the mean surface roughness of coated interior pipe, H, differs from 2 micrometers.
b. The results of the test, part a, are shown in the MINITAB printout at the bottom of the page. Locate the test statistic and p-value on the printout.
The minitab report isn't given.
Answer:
H0 : μ = 2 um
H1 : μ ≠ 2 um
Step-by-step explanation:
The mean surface roughness of coated interior pipe is given as 2um.
This refers to the population mean, μ = 2 um
Therefore, the null hypothesis which usually aligns with the population mean value will be stated as :
H0 : μ = 2 um
The alternative hypothesis is used to test the claim that the mean surface roughness is different from 2 ; hence no direction is given, this is thus a 2 - tailed test
H1 : μ ≠ 2 um
Area: Change in Dimensions
A rectangle FGHJ has a width of 3 inches and a length of 7 inches.
Step-by-step explanation:
this is not complicated at all. first and second graders can do a-c (come on, you know how to calculate the area of a rectangle) and with some imagination also d and e.
this is meant for you to actually do it so that you get a feeling for these things.
I will therefore leave the pure calculation to you.
and I will give you some help for the conceptual/ theoretical part.
the area of a rectangle is, of course, length × width (or height some on the view you have on an object).
let's just call them l and w.
so the regular area is
Ar = l×w
now one dimension (or example and for the width, but it does not matter, it is the same for the length) is doubled.
it simply means the new width is twice the old width.
so the area with a double width is
A2w = l×(2×w) = 2×(l×w)
so, that means also the area is doubled compared to the regular area.
now, both dimensions are doubled.
A2w2l = (2×l)×(2×w) = 4×(l×w)
so, the area grew 4 times a large as the regular area.
what is the rule here ?
let's triple the dimensions.
A3w3l = (3×l)×(3×w) = 9×(l×w)
as you can easily see : the new area grows with the square of the scaling factor, when we change both dimensions equally.
the reason is simple - as our little equations show, we have to multiply in the scaling factor of every dimension in play.
therefore, the new area grows with the product of the scaling factors of the involved dimensions. if both scaling factors are the same, then the area grows therefore by the square of the common factor.
and this principle applies to every shape, where the area is constructed out of 2 dimensions. any other additional multiplication factors don't matter for this, because this is all one big multiplication of several factors, and if you multiply one of these factors by an additional factor, the whole result changes by that factor.
y=5/3x + 3 in ordered pairs
Answer:
(3,8) ; (-3,-2) ; (6,13)
Step-by-step explanation:
A linear equation in Slope Intercept Form is given to us and we need to write the ordered pairs for x and y . The given equation is ,
[tex]\rm\implies y =\dfrac{5}{3}x + 3 [/tex]
For finding the ordered pairs , substitute different values of x to get different values of y.
Put x = 3 :-
[tex]\rm\implies y =\dfrac{5}{3}\times 3 + 3 [/tex]
[tex]\rm\implies y = 5+ 3 [/tex]
[tex]\rm\implies y =8[/tex]
Put x = -3 :-
[tex]\rm\implies y =\dfrac{5}{3}\times -3 + 3 [/tex]
[tex]\rm\implies y = -5+ 3 [/tex]
[tex]\rm\implies y =-2[/tex]
Put x =6 :-
[tex]\rm\implies y =\dfrac{5}{3}\times 6 + 3 [/tex]
[tex]\rm\implies y = 10+ 3 [/tex]
[tex]\rm\implies y =13[/tex]
Therefore ,
[tex]\small\implies\boxed{\rm\blue{ Odered \ Pairs \ = (3,8) ; (-3,-2) ; (6,13) }}[/tex]
FIND THE LENGTH OF MP
Answer:
D.21
Step-by-step explanation:
MP=MV - PV= 67 -46 = 21
Figure out the pattern, and write the next number.
2,6,21,88
A sales firm receives an average of three calls per hour on its toll-free number. For any given hour, find the probability that it will receive at least three calls. Use the Poisson distribution.
Answer:
At most 3 calls: 64.7%
At least 3 calls: 57.7%
5 or more calls: 18.5%
Step-by-step explanation:
I am need help and an explanation on how to read these graphs.
Answer:
A is the answer
Step-by-step explanation:
A
plz mark it brainlist
HELP HELP HELP HELP PLEASE
Answer:
It is indeed 63
Step-by-step explanation:
The easy way to go about this is to recognize that if the triangles are similar, the ratio between the similar sides will be the same.
Notice:
4/5 = 36/45
So:
4/7 should = 36/x
If:
4/7 = 36/x
4x/7 = 36
4x = 36*7
x=36*7/4
x=63
Convert 0.181818 … to a fraction by writing the repeating decimal as an infinite geometric series. Show all of your work (please)
0.181818… = 18 (0.010101…)
… = 18 (0.01 + 0.0001 + 0.000001 + …)
… = 18 (1/100 + 1/100² + 1/100³ + …)
… = 18 (1 + 1/100 + 1/100² + 1/100³ + …) - 18
Then you have
[tex]0.181818\ldots = \displaystyle18\sum_{k=0}^\infty\frac1{100^k} - 18 = \frac{18}{1-\frac1{100}} - 18 = \boxed{\frac2{11}}[/tex]
Catriona spotted a major problem having to do with patient billing. A number of people may have received the wrong bills. When should she have told her boss? O a) When she was evaluating how to alert the patients O b) After she sent patient notices out c) When she first noticed the problem O d) After she decided on a communication plan
Answer:
C
Step-by-step explanation:
When she first noticed the problem
the table shows linear relashonsips between x and y write an equation in slope intercept form for this relashonsip!!!!!!!!!!!!!!!!!!!!!!!
QUICK PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]y=-2x+6[/tex]
Step-by-step explanation:
Slope-intercept form is given as [tex]y=mx+b[/tex], where [tex]m[/tex] is slope and [tex]b[/tex] is the y-intercept.
To find the slope of a line that passes through two points [tex](x_1, x_2)[/tex] and [tex](y_1, y_2)[/tex], use the slope formula:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let:
[tex](x_1, y_1)\implies (1, 4)\\(x_2, y_2)\implies (0, 6)[/tex]
The slope of the line that passes through these two points is:
[tex]m=\frac{6-4}{0-1}=\frac{2}{-1}=-2[/tex]
Now substitute [tex]m=-2[/tex] and any point to solve for [tex]b[/tex]:
[tex]y=mx+b,\\6=-2(0)+b,\\6=0+b,\\b=6[/tex]
Therefore, the slope-intercept form of a line that is represented by the table is [tex]\boxed{y=-2x+6}[/tex]
