The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2014, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the calendar year in which the number of new cases would reach 579.
Answers
The linear regression equation that represents this data set is equal to y = 120.8x + 2,114.
How to write the linear regression equation?First of all, we would determine the slope of the given data set by using this formula:
[tex]Slope = \frac{\sum (x-\bar x)(y-\bar y)}{\sum (x-\bar x)^2}[/tex]
For the sample mean (years), we have:
[tex]\bar x = \frac{0\;+\;1+\;2\;+\;3\;+4}{5} \\\\\bar x =\frac{15}{4} \\\\\bar x =3.75[/tex]
For the sample mean (cases), we have:
[tex]\bar y = \frac{904\;+\;900+\;833\;+\;837\;+754}{5} \\\\\bar y =\frac{4,228}{4} \\\\\bar y =1057[/tex]
The sums are given by:
∑(x - |x|) = (0 - 3.75) + (1 - 3.75) + (2 - 3.75) + (3 - 3.75) + (4 - 3.75)
∑(x - |x|) = - 3.75 - 2.75 - 1.75 - 0.75) + 0.25
∑(x - |x|) = -8.75.
∑(x - |x|)² = (-8.75)² = 76.5625.
∑(y - |y|) = (904 - 1057) + (900 - 1057) + (833 - 1057) + (837 - 1057) + (754 - 1057)
∑(y - |y|) = -153 - 157 - 224 - 220 - 303
∑(y - |y|) = -1,057.
∑(x - |x|)(y - |y|) = -8.75 × -1057
∑(x - |x|)(y - |y|) = 9,248.75.
Now, we can determine the slope:
Slope = 9,248.75/76.5625
Slope = 120.8.
Therefore, the equation is given by:
y = 120.8x + a
Next, we would find the value of a:
1057 = 120.8(-8.75) + a
a = 1057 + 1,057
a = 2,114.
Hence, the linear regression model is given by:
y = 120.8x + 2,114.
Since the new cases would reach 579, the calendar year would be calculated as follows:
579 = 120.8x + 2,114
120.8x = 579 - 2,114
120.8x = -1,535
x = -1,535/120.8
x = -12.71.
Year = 2014 + 12.71
Year = 2026.71 ≈ 2027.
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Related Questions
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
D. octagon
Step-by-step explanation:
How many sides does a regular n-gon have if the measure of one interior angle is 165?
Answers
The supplement of each interior angle has measure
180° - 165° = 15°
and so
n = 360°/15° = 24
since the exterior angles add up to 360° and are all congruent.
Which relations are functions?
Choose all answers that are correct:
Answers
Answer:
A. B and D are functions
Step-by-step explanation:
Functions are either one-to-one or many-to one (x-value --> y value)
C is not a function because -3 (x) maps to 1 and also to 0 (y).
CON
Enter a range of values for x.
a
a
3x-9⁰ 93°
27
26
[?]
Enter
Answers
Answer:
3° < x < 32.538°
Step-by-step explanation:
The possible values of the angle marked with an x-expression may not be as obvious as they first seem. There is a somewhat complicated interaction between the angle value and the length of the side(s) marked 'a'.
__
We can label the vertices of the figure A through D, clockwise from the bottom.
minimum xThe minimum value of angle ACB (marked 3x-9°) is 0°. That will be its measure when AB +BC = AC, or B lies on line AC. In this case, the value of x is ...
3x -9° = 0°
3x = 9° . . . . add 9°
x = 3° . . . . . divide by 3
maximum xvalue of 'a'
The maximum value of angle ACB will be found where both triangles are isosceles: AC ≅ BC ≅ DC. The length of 'a' can be found for that case using the Law of Sines:
27/sin(93°) = a/sin(43.5°) . . . where (180° -93°)/2 = 43.5° is the base angle
a = 27×sin(43.5°)/sin(93°) ≈ 18.611
value of 3x -9°
Angle ACB will obey the same Law of Sines requirement. If z represents the base angle in isosceles triangle ABC, then we have ...
sin(z)/18.611 = sin(180-2z)/26
Recognizing that sin(180-2z) = sin(2z) and using the double-angle formula, we find ...
sin(z)/18.611 = 2sin(z)cos(z)/26
sin(z)(1/18.611 -cos(z)/13) = 0 . . . . . subtract the right side, factor
This has solutions that make the factors zero:
sin(z) = 0 ⇒ z = 0 . . . . . . an extraneous solution in this case
cos(z) = 13/18.611 ≈ 45.6925°
Then the value of x can be found from ...
3x -9° = 180° -2z ≈ 88.615°
x ≈ 3° +(88.615°/3) = 32.538°
_____
Additional comment
In the above, we have shown numerical values for the side lengths and angles in the maximum-x case. The various expressions can be combined to give ...
3(x -3°) = 180° -2(arccos(13/27×sin(93°)/sin(43.5°)))
x = 63° -2/3·arccos(13/27·sin(93°)/sin(43.5°))
A student gives the answer to a probability problem as 6/5. tell why this answer must be incorrect.
Answers
Answer:
Probability of an event must be from 0 to 1.
Here,6/5 is more than 1 i.e. 1.2.
Hence,the answer is incorrect.
An ice-cream from a restaurant costs $3 originally. The price is reduced to $2 one weekend. What is the percent change?
Answers
please please please help help help !!
Answers
Answer:
The axis of Symmetry divides a line into two equal halves.
Step-by-step explanation
An easy relation to get this value without plotting a graph is x = –b/2a
Where
a = coefficient of x²
b = coefficient of x
From the Question, We need a symmetry of value –½
The only Option that'll give this value is OPTION D
2x – y = 5 – 2x²
Since its a line, Don't forget to make "y" subject before doing any operation.
y = 2x² + 2x – 5
a = 2
b= 2
x = –(2)/2(2)
= –2/4
= –½
Which graph represents the polynomial function f(x)=x^3+x^2−2x
Answers
By finding the roots of the polynomial, we conclude that the correct graph is the second one.
Which is the graph of the polynomial?
Here we have the polynomial:
[tex]f(x) = x^3 + x^2 - 2x[/tex]
To identify it, we need to find the roots, we can rewrite the equation as:
[tex]f(x) = x*(x^2 + x - 2)[/tex]
And we can rewrite the last part by using the Bhaskara's formula:
[tex]x = \frac{-1 \pm \sqrt{1^2 + 4*2} }{2} \\\\x = (-1 \pm 3)/2[/tex]
Then the roots are:
x = -2
x = 1
Then we rewrite:
[tex]f(x) = x*(x + 2)*(x - 1)[/tex]
So the roots are at x = 0, x = -2, and x = 1.
The graph with these roots is the second graph (top right).
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Write an equation in slope-intercept form for the line with slope 8 and y-intercept 9.
Answers
Answer:
y = 8x + 9
Step-by-step explanation:
Slope-intercept form of an equation is a fill-in-the-blank formula for writing an equation of a line. It is in the form:
y = mx + b
where m is the slope and b is the y-intercept (hence the name) In the problem slope is given, fill it in for m, next to the x. Y-intercept is given in the question also, fill it in in place of b.
y = 8x + 9
A triangle has sides of lengths 16,14 and 50 .is the triangle right angle triangle?
Answers
Answer:
no
Step-by-step explanation:
using the converse of Pythagoras' identity
If the square on the longest side is equal to the sum of the squares of the other 2 sides, then the triangle is right.
longest side = 50 ⇒ 50² = 2500
16² + 14² = 256 + 196 = 452
since 452 ≠ 2500 then the triangle is not right
A triangle has sides of lengths 16,14 and 50. Is the triangle right angle triangle?
❒ Explanation -:We will solve this question using Pythagoras theorem.
We know,
[tex] \small \boxed{\rm{ c² = a² + b²}}[/tex]
[tex] \small\rm{Where,} [/tex] [tex]\small\sf{ c > a \: and \: c > b}[/tex]
[tex] \small\sf{ 50² = 16² + 14²}[/tex]
[tex]2500 = 256+ 196[/tex]
[tex]2500≠452[/tex]
[tex] \small\bf{ c² ≠ a² + b²}[/tex]
Hence, the triangle is not a right-angled triangle.
If each of the numbers in the following data set were multiplied by 12, what
would be the median of the data set?
28, 58, 20, 14, 18, 71, 36
Answers
Answer:
answer: 336!!
Step-by-step explanation:
have a good day!
Connor got to the beach at 9:58 A.M. He hunted for seashells, played in the waves, ate lunch, watched the birds dive in the water, and built a sand castle. He left the beach at 5:26 P.M. How long was he at the beach?
Answers
7hours 28 minutes
Step-by-step explanation:
I WILL GIVE BRAINLIEST FOR CORRECT ANSWER
The graph of the system of equations y= 2x+3 and y= x+5 is shown on the coordinate plane (image included). What is the solution to the system of equations?
Answers
Answer:
A
Step-by-step explanation:
The answer is A because the point intercepts at (2,7), and answer A has the points (2,7) in it's answer.
You roll a 6-sided die.
what is p(even or factor of 45)?
write your answer as a percentage.
Answers
Answer:
p(even or factor of 45) = 100%Step-by-step explanation:
let S₁ be the set of factors of 45 that are less or equal to 6:
S₁ : {1 , 3 , 5}
let S₂ be the set of the even numbers that are less or equal to 6:
S₂ : {2 , 4 , 6}
S₁ ∪ S₂ = {1 ,2 , 3 , 4 , 5 , 6}
⇒ card(S₁ ∪ S₂) = 6
Then
p(even or factor of 45) = p(S₁ ∪ S₂) = 6/6 = 1
Therefore
p(even or factor of 45) = 100%
When a figure appears to have depth as you look at it, it is called _____________.
A. perspective
B. solid
C. length
D. net
Answers
Answer:
the answer would b B solid
Step-by-step explanation:
because the figure appears to have depth as you look at it so it is solid.
What is 3-eighths times 4 and 3-sixths times 4?
You will be marked Brainliest if you answer this question correctly!
Please help ASAP
Answers
Answer:
As a fraction it would be 4.5
Step-by-step explanation:
3/4 × 6 = 92 = 4 12 = 4.5
does anyone know what 3 x (8+2) x 5 is? i really need it for homework due tomorrow thank you!
Answers
3 x 10 x 5
30 x 5
= 150
Someone please help me before I frl cry
Answers
Answer:
Equation: 4x = 128
[tex]m\angle 1 = 84\degree[/tex]
[tex]m\angle 2 = 96\degree[/tex]
Step-by-step explanation:
[tex]m\angle 1+ m\angle 2 =180\degree[/tex] (Linear pair angles)-> (x + 52)° + (3x)° = 180°-> (4x + 52)° = 180° -> 4x + 52 = 180-> 4x = 180 - 52-> 4x = 128 ( This is the required equation)-> x = 128/4-> x = 32[tex]m\angle 1 = (32+52)\degree = 84\degree[/tex][tex]m\angle 2 = (3*32)\degree = 96\degree[/tex]The distance from the base of the tree to the tip of the shadow is 24 feet.
Sin 20 degrees = 0.3420
Cos 20 degrees = 0.9396
Tan 20 degrees = 0.3639
————————————————————————
Which measurement is closest to the heigh of the tree?
A. 8.2
B. 8.7
C. 22.6
D. 25.54
E. 65.95
Answers
The measurement is closest to height of tree is 8.7
The correct option is (B).
What is trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
As the distance between base and tip of tree's shadow is 24 feet
Angle of Elevation is 20 degrees
[tex]tan \theta \; = \frac{P}{B}[/tex]
tan 20 = [tex]\frac{P}{24}[/tex]
0.3639 = [tex]\frac{P}{24}[/tex]
P= 0.3639 *24
P = 8.7336
The measurement is closest to height of tree is 8.7
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if x = 5, then 3x + 4x - 15 equals = ?
Answers
Answer:
If x = 5, then 3x + 4x - 15 equals 20
Step-by-step explanation:
Here, we are given the value of x, which is 5.
1. Substitute 5 as the value of x in the equation:
3x + 4x - 15 = ?
3(5) + 4(5) - 15 = ?
15 + 20 - 15 = ?
2. Simplify:
15 + 20 - 15 = ?
35 - 15 = ?
20 = ?
3. Check your work:
3x + 4x - 15 = 20
3(5) + 4(5) - 15 = 20
15 + 20 - 15 = 20
20 = 20 ✅
Therefore, if x = 5, then 3x + 4x - 15 equals 20
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Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. what value of x satisfies this equation? round your answer to the nearest hundredth. the value of x is .
Answers
The values of x in f(x) = 3|x - 2| + 6 when f(x) = 18 are 6 and -2
How to determine the value of x?The function is given as:
f(x) = 3|x - 2| + 6
The value of f(x) is
f(x) = 18
So, we have:
3|x - 2| + 6 = 18
Subtract 6 from both sides
3|x - 2| = 12
Divide both sides by 3
|x - 2| = 4
Remove the absolute bracket
x - 2 = 4 or x - 2 = -4
Add 2 to both sides
x = 6 or x = -2
Hence, the values of x are 6 and -2
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a lawn sprinkler waters a lawn in a circle as shown
Answers
Part A
I'm assuming you want the area of a circle with radius 17 yards.
We'll use the formula below
A = pi*r^2
A = (22/7)*17^2
A = (22*17^2)/7
A = 6358/7
A = 908 2/7
The sprinkler covers an area of about 908 2/7 square yards.
You'll type 908 in the left-most box
Then for the other two boxes, you'll have 2 up top and 7 down below to represent the fraction 2/7
The number 908 2/7 is a mixed number.
=======================================================
Part B
You mentioned that the radius reduces to 11 yards here. We'll use the same formula as above and pi = 22/7 approximately
A = pi*r^2
A = (22/7)*11^2
A = (22*11^2)/7
A = 2662/7
A = 380 2/7
The sprinklers can water an area of about 380 2/7 square yards.
This value is also a mixed number
380 is the value in the left most box (it's the whole part)
The other two boxes are filled out the same exact way as the previous part above.
A person can read 24 pages of a book in 1/3 of an hour. What is this person's reading rate in pages per hour?
48
12
72
8
Answers
Answer:
72
Step-by-step explanation:
If he reads 24 pages in 1/3 of an hour, he reads 3 times as many pages in 1 hour.
3 × 24 pages = 72 pages
Answer: 72
What will be the new function g(c) if f(x) = 2^x is translated 2 units down and
3 units left?
Answers
Answer:
The new function is
[tex]g(x) = {2}^{x + 3} - 2[/tex]
I need help with this question asap please
Answers
Use the stem-and-leaf plot below to match each term with the correct value. (Round to the nearest whole number.)
Answers
Answer:
Step-by-step explanation:
16, 18, 23, 25, 26, 34, 37, 37, 40, 41, 46
( 16 + 18 + 23 + 25 + 26 + 34 + 37 + 37 + 40 + 41 + 46 ) ÷ 11 = 31.181818...
mean ≈ 31
median = 34
mode = 37
What is the Parent Function?
What Are The Transformations?
Answers
Answer:
Parent function:
[tex]x^2+y^2=r^2[/tex]
General equation:
[tex](x-h)^2+(x-k)^2=r^2[/tex]
Transformations:
Its a circle with a center of (100,60) and a radius of 15
PLEASE HELP!!!
Which of the following is the Best Buy?
1 L for $1.68
0.5 L for $1.29
2 L for $3.40
3 L for $5.07
Answers
Answer:
it's 1 L
Step-by-step explanation:
it's pretty easy just do some multiplication
Martin takes a test that has five multiple choice questions. Each question has three possible
answers. If Martin guesses on each question, in how many different ways can he answer the
questions on the test?
Answers
Answer:
about 2/5 of the question probability lol
The city library has 763,045 books. What is the value of the digit 6 in this
number?
I tried to do this problem but I have to do something like this
Answers
Answer:
The 6 is in the ten-thousands place
Step-by-step explanation:
6 written as a ten-thousand is 60,000