The regression sum of squares (RSS) represents: a. The amount of variation in Y around its mean that the regression function can account for.
What is regression sum of squares?
The regression sum of squares serves as the sum of the differences that exist between the predicted value and the mean of the variable.
The Sum of Squared Error however states the difference between the observed and the predictive value.
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Find the nth taylor polynomial for the function, centered at c. f(x) = ln(x), n = 4, c = 5
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Given:
f(x) = ln(x)
n = 4
c = 3
nth Taylor polynomial for the function, centered at c
The Taylor series for f(x) = ln x centered at 5 is:
[tex]P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+ \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]
Since, c = 5 so,
[tex]P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+ \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}[/tex]
Now
f(5) = ln 5
f'(x) = 1/x ⇒ f'(5) = 1/5
f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25
f'''(x) = 2/x³ ⇒ f'''(5) = 2/5³ = 2/125
f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625
So Taylor polynomial for n = 4 is:
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Hence,
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
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Please please please help
Answer:r=14°
Step-by-step explanation:
(5r-5)°+ (8r+3)°=180
(Sum of angles on a straight line =180°)
Collect like terms
5r+8r-5+3=180
13r-2=180
13r=180+2
13r=182
r=182/13
r=14°
sketch graphs of the following on the same plane using different colours y=2x-3;y=-3;x=-3;2x+3y-6=0
The graph of the four linear equations is the one we can see below, such that:
Blue line is y = -3Green line is x = -3Orange line is y = 2x - 3Purple line is 2x + 3y - 6 = 0.How to graph the linear equations?
Here we have the set of linear equations:
y = 2x - 3y = -3x = -32x + 2y - 6 = 0We want to graph these 4 lines on the same coordinate axis.
The line:
y = -3
Is an horizontal line at y = -3
The line:
x = -3
Is a vertical line at x = -3.
And the other two are common linear equations that are graphed in the usual way, then the graph of all the linear equations is the one you can see below.
Where:
Blue line is y = -3Green line is x = -3Orange line is y = 2x - 3Purple line is 2x + 3y - 6 = 0.If you want to learn more about linear equations:
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area of an isosceles triangle is 60 square cm. If the measure of its equal sides is 13 square cm then find the base sides.
The base side of the isosceles triangle in discuss as described in the task content is; 10cm.
What is the length of the base side of the isosceles triangle?According to the task content, the area of the isosceles triangle is 60 square cm.
Since, the length of its longest sides is 13 cm and since it follows from convention that the bisection of an isosceles triangle results in the formation of two right-triangles.
Consequently, it follows from Pythagoras triples that the height of each right triangle is 12 and its base is; 5.
Consequently, the base of the whole isosceles triangle is; 2 × 5 = 10cm.
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Use completing the square to solve for x in the equation (x 7) (x minus 9) = 25.
The values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].
To find the values of x:
Given equation: [tex](x+7)(x-9)=25[/tex]
Then: [tex]x(x-9)+7(x-9)=25[/tex]
Using the distributive property: [tex]a.(b+c)=a.b+a.c[/tex]
[tex]x^{2} -9x+7x-63=25[/tex]
Combine like terms:
[tex]x^{2} -2x-63=25[/tex]
Subtract 25 from both sides and obtain:
[tex]x^{2} -2x-88=0[/tex]
Using completing square form:
Add and subtract [tex](\frac{2}{2} )^{2} =1[/tex] we have:
[tex]x^{2} -2x-88+1-1=0\\(x-1)^{2} -89=0[/tex]
Add 89 to both sides we have:
[tex](x-1)^{2} =89[/tex]
Taking square roots on both sides, obtain:
[tex]x-1=[/tex] ± [tex]\sqrt{89}[/tex]
Add 1 to both sides we have:
[tex]x=1[/tex]±[tex]\sqrt{89}[/tex]
Therefore, the values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].
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The complete question is given below:
Use completing the square to solve (x + 7)(x – 9) = 25 for x.
A herd of 21 horses has 6 white and some black horses. What is the ratio of white to black horses
The ratio of white to black horses is 2:5.
What is the ratio of white to black horses?Ratio expresses the relationship between two or more numbers. Ratio is used to compare two or more numbers with each other. It shows the frequency that one value is contained within other value(s).
The ratio of white to black horses = number of white horses : number of black horses
number of white horses = 6 number of black horses : total number of horses - number of white horses: 21 - 6 = 15The ratio of white to black horses = 6 : 15
6 : 15 is not expressed in its simplest form yet. To convert the ratio to its simplest form, divide the numbers by a common factor of 6 and 15. A common factor is a number that divides two or more numbers perfectly with leaving any remainder. A common factor of both numbers is 3
(6/3) : (15/3) = 2 : 5
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MULTIPLY (x^2-5x)(2x^2+x-3)
[tex]\bf{ (x^2-5x)(2x^2+x-3)}[/tex]
[tex]\bf{Distribute \ the \ sum \ group. }[/tex]
[tex]\boldsymbol{\sf{x^{2} (2x^{2} +x-3)-5x(2x^{2} +x-3) }}[/tex][tex]\bf{Expand \ the \ distribution \ of \ terms. }[/tex]
[tex]\boldsymbol{\sf{2x^{4}+x^{3}-3x^{2} -5x(2x^{2} +x-3) }}[/tex][tex]\boldsymbol{\sf{2x^{4}+x^{3}-3x^{2} -(10x^{3}+5x^{2} -15x) }}[/tex][tex]\bf{Remove \ parentheses. }[/tex]
[tex]\boldsymbol{\sf{2x^{4}+x^{3}-3x^{2} -10x^{3}+5x^{2} -15x }}[/tex][tex]\bf{Collect \ like \ terms. }[/tex]
[tex]\boldsymbol{\sf{2x^{4}+(x^{3}-10x^{3})+(-3x^{2} -5x^{2} )+15x }}[/tex][tex]\bf{Simplify}[/tex]
[tex]\boxed{\boldsymbol{\sf{2x^{4}-9x^{3}-8x^{2} +15x }}}[/tex]Two parallel lines are cut by a transversal. Complete the following statements.
The consecutive interior angles is...
supplementary, complementary, congruent
The alternate interior angles is...
supplementary, complementary,congruent
To complete the statements;
The consecutive interior angles is supplementary
The alternate interior angles is congruent
Properties of parallel lines cut by a transversal
The properties are;
Corresponding Angles are congruentAlternate Exterior Angles are congruentAlternate Interior Angles are congruentConsecutive Interior Angles sum to 180 degrees, that is, they are supplementaryConsecutive interior angles are supplementary
Alternate interior angles are congruent
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10 points!!!!!!!!!!!!!!!!!!!!!
Answer:
23
Step-by-step explanation:
What must be added to: (a) x-y + 4z to get 5x - 4y + 8z?
Answer:
4x-3y+4z
Step-by-step explanation:
There are lot's of process to answer it but i will show one easy way to find the answer.
To find the required answer we need to subtract 5x - 4y + 8z by x-y + 4z, we get
5x - 4y + 8z
-x + y - 4z [Note: while subtracting we must change the sigh that one ___________who we are subtracting]
4x-3y+4z which is a required answer
Answer:
4x - 3y + 4z
Step-by-step explanation:
Let the unknown value that we have to add be 'a'.
Let us make an expression like this.
x -y + 4z + a = 5x - 4y + 8z
Now make 'a' the subject of the equation.
a = 5x - 4y + 8z - x + y - 4z
Now combine like terms.
a = 5x - x - 4y + y + 8z - 4z
a = 4x - 3y + 4z
Now let us check whether the answer is correct or wrong.
We can replace 'a' with ( 4x - 3y + 4z ).
Let us see.
x - y + 4z + 4x - 3y + 4z
Combine like terms.
5x - 4y + 8z
Yes, we are getting the same answer!
Therefore,
we need to add 4x - 3y + 4z to get 5x - 4y + 8z to x - y + 4z.
Fractions equivalent to 2/100
Answer:
1/50
Steps:
Recall 2 can divide 100
therefore
2/100 = 1/50
This question is down below.
Answer:
Step-by-step explanation:
15 hope it help
the perimeter of a rectangular plot of land whose length is (2x+5) and width (x-10)m is 80m Find;
i. the value of x
ii. the area of the plot
iii the cost of weeding the plot at $ 0.24 per m square
Answer:
x = 15
The area is 175 [tex]meters^{2}[/tex]
Cost of weeding is $42
Step-by-step explanation:
The perimeter includes two lengths and two widths, so the equation for x would be
2(2x +5) + 2(x -10) = 80 Distribute the 2's
4x + 10 + 2x -20 = 80 Combine the like terms
6x -10 = 80 Add 10 to both sides
6x = 90 Divide both sides by 6
x = 15
Area is length times width. We need to find the length and width.
2x + 5
2(15) + 5
30 + 5
35 is the width
x -10
15-10
5 is the length
A = (l)(w)
A = (35)(5)
A = 175 The area is 175
The cost of weeding is 175 x .24 = 42
Use the equation to complete an algebraic proof that proves the answer is x = 7/6. Write your proof in your journal and upload your answer. You will be awarded 5 points for the statements and 5 points for the reasons.
I need the algebraic proofs please!!!
Using the algebraic equation, (2x + 6)/5 = 4x - 3, it has been proved that x = 7/6
Algebraic Proof for the Given Algebraic Equation
The given algebraic equation is,
(2x + 6)/5 = 4x - 3
2x + 6 = 5(4x - 3)
2x + 6 = 20x - 15
20x - 15 = 2x + 6
This algebraic equation can be written as,
20x - 2x - 15 = 6
18x = 15 + 6
18x = 21
x = 21/18
x = 7/6
Hence, using the given algebraic equation, it has been proved that the value of x is 7/6.
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6 Find the value of x from the following figures.
1)
Find the area of a circle if i) radius is 21cm ") diameter is 28cm
Answer:
i) 441π cm² ≈ 1385.4 cm²
ii) 196π cm² ≈ 615.8 cm²
Step-by-step explanation:
The areas of circles with radius 21 cm or diameter 28 cm can be found using the appropriate area formula.
i)The formula for the area of a circle based on its radius is ...
A = πr²
When the radius is 21 cm, the area is ...
A = π(21 cm)² = 441π cm² ≈ 1385.4 cm²
ii)The formula for the area of a circle based on its diameter is ...
A = (π/4)d²
When the diameter is 28 cm, the area is ...
A = (π/4)(28 cm)² = 196π cm² ≈ 615.8 cm²
Answer:
Before multiplying by pi. 441π cm²
After multiplying by pi. 1384.74 cm²
Step-by-step explanation:
The formula for area of a circle is πr².
r=radius
Square the radius.
21²=441
If they want the answer in this form: 441π cm². If not, then use 3.14 for π.
441*3.14=1384.74
The answer is 1384.74 cm².
Hope this helps!
A monkey has a strict banana eating
schedule. On a sunny day it eats 20
bananas and on a rainy day it eats 12
bananas. In 8 consecutive days it eats
112 bananas. Question: how many
sunny days are there in these 8 days?
Larry took 21 minutes to do 7 math problems. Mary took 19 minutes to do 8 math problems. Which student
did more problems per minute
a=3. b=2
5ab+4b+10a
help please?
Answer:
68
Step By Step Explanation:
Evaluate for a=3,b=2
(5)(3)(2)+(4)(2)+(10)(3)
(5)(3)(2)+(4)(2)+(10)(3)
=68
Answer:
The solution is 68
Step-by-step explanation:
a = 3 and b = 2
5ab+4b+10a
= 5(3)(2)+4(2)+10(3)
= 5(6)+8+30
= 30+8+30
= 38+30
= 68
The function D(t)=18t2−130t gives the distance a car going a certain speed will skid in t seconds. Find the time it would take for the car to skid 150 feet.
The time it will take for the car to skid for 150 feet is 8.23 seconds.
How to find the time the car will skid?The function D(t) = 18t² − 130t gives the distance a car going a certain speed will skid in t seconds.
The time the it would take for the car to skid for 150 feet can be calculated as follows:
Therefore,
D(t) = 18t² - 130t
150 = 18t² - 130t
18t² - 130t - 150 = 0
divide by 3
9t² - 65t - 75 = 0
Hence,
t = 65 ± 5√277 / 18
t = 8.23425471586 or -1.01166666667
Hence,
t = 8.23 seconds.
Therefore, the time it will take for the car to skid for 150 feet is 8.23 seconds.
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if the perimeter of an equilateral triangle is 24cm, find the length of it's side
Answer:
it's side length equals to 8.
Step-by-step explanation:
Hello!An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle.
Perimeter: 3 x side of equilateral triangle
[tex]24 = 3 \times each \: sides[/tex]
divide both sides by 3
[tex]one \: of \: its \: side = 8[/tex]
Thus, as all the three sides equals to 8.
Hope it helps!
Which of the following values would complete the ordered pair if the point is on the graph of f(x) = -3x + 2?
(-1, )
0-1
05
01
0-5
The y-coordinate that completes the point exists 5.
What is an ordered pair?An ordered pair (x, y) denotes the x-and-y coordinates of a general point, where x exists the input value of a function and y exists the output value of a function.
The output value exists y = f(x) and must be found using the rule (function) to the given input value.
In this case the rule exists f(x) = - 3x + 2, and the input value, x, exists - 1 (the first value of the ordered pair).
This exists the mathematical procedure:
x = - 1
f(x) = f (-1)
Then substitute the value x = -1 then
f(-1) = -3 (-1) + 2 = 3 + 2 = 5.
Therefore, the correct answer is option b) 5.
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A coach shows the following ratio table to a team. The table shows the average amount of calories burned for a certain number of minutes of running.
Practice
Minutes of running
Calories burned
4
20
8
40
?
100
Based on the table, how many minutes does a person need to run to burn 100 calories?
12
20
28
68
Based on the table, the minutes a person has to run to burn 100 calories is 20 minutes
How many minutes does a person have to run?Ratio shows the equivalent relationship that exists between two or more numbers. A ratio table can be described as table that shows equivalent relationship between two numbers.
The first step is to determine the ratio between the minutes run and the calories burned. To do this, divide any of the minutes run on the table by the corresponding calories burned.
Ratio = minutes run / calories burned
8 / 40 = 1/5
Now, multiply this ratio by 100
1/5 x 100 = 20 minutes
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which of the following tools is used to construct an angle bisector
Answer:
Tools used to construct a bisector are 1》pencil ,2》Eraser ,3》protector ,4》Compass ,5》Sharpner etc ....
Convert a normally distributed score of 80 with a mean of 70 and a standard deviation of 6 into a z score.
Answer:
5/3
Step-by-step explanation:
z = (Distributed score - Mean)/Standard deviation= (80-70)/6 = 5/3
Step-by-step explanation:
z = (specific score - mean) / standard deviation
in our case
z = (80 - 70)/6 = 10/6 = 5/3 = 1.666666... ≈ 1.67
as most z-tables round the z-scores to hundredths.
not to forget : the sign matters. so, don't worry, if you have e.g. a specific score of 60 :
(60 - 70)/6 = -10/6 = -5/3 = -1.666666... ≈ -1.67
you did not do anything wrong. that is all ok and valid.
A company found that an experienced surveyor can survey a roadbed in 7 hours. An apprentice surveyor needs 8 hours
to survey the same stretch of road. If the two work together, find how long it takes them to complete the job.
***
The number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.
Rate of workHours it takes the experienced surveyor = 7 hoursSurveyors rate of work = 1/7Hours it takes the apprentice = 8 hoursApprentice rate of work = 1/8If the two work together;
Time taken for both to complete the task = Surveyors rate of work + Apprentice rate of work
= 1/8 + 1/7
= (7+8) / 56
= 15/56 hours
Therefore, the number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.
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HELP ‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️WILL MARK BRAINLYEST‼️‼️‼️
In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is
$43. I have four times as many one-dollar bills as ten-dollar bills. Altogether, there are 13 bills in my wallet.
How many of each bill do I have?
Answer:
8 one-dollar bills
3 five-dollar bills
2 ten-dollar bills
Step-by-step explanation:
Let x = # of one-dollar bills, y = # of five-dollar bills, and z = # of ten-dollar bills. Total amount in the wallet is $43, so the first equation would be 1x + 5y + 10z = 43. Next, there are 4 times as many one-dollar bills as ten-dollar bills, so x = 4z. There are 13 bills in total, so x + y + z = 13
x + 5y + 10z = 43
x = 4z
x + y + z = 13
x + 5y + 10z = 43
x + 0y - 4z = 0
x + y + z = 13
5y + 14z = 43
-y - 5z = -13
5y + 14z = 43
-5y - 25z = -65
-11z = -22
z = 2
x = 4z
x = 4*2 = 8
x + y + z = 13
8 + y + 2 = 13
10 + y = 13
y = 3
how 4-digit positive integers have four differennt digits, where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largets digt
Answer:
There are 9 possible thousands digits, because 0 cannot be the leading digit.
There are 2 possible ones digits, 0 and 5.
If the ones digit is 5:
There are 5 possible thousands digits: 1, 2, 3, and 4.For each possible thousands digit, there are 5 possible hundreds digits. (We used one of the digits above to be the thousands digit, but 0 is a possible hundreds digit.)For each possible pair of thousands-and-hundreds digits, there are 4 possible tens digits.
So there are 5 x 5 x 4 = 100 possible 4-digit numbers that end in 5 with no repeated digit and no digit larger than 5.
If the ones digit is 0:
There are 5 possible thousands digits.For each possible thousands digit, there are 4 possible hundreds digits.For each possible pair of thousands-and-hundreds digits, there are 6 possible tens digits.
So there are 5 x 4 x 6 = 120 possible 4-digit numbers that end in 0 with no repeated digit and no digit larger than 5.
100+120=220
Answer: 220 possible numbers.
4/7+3/7 1/5.3/2-4/10
Answer:
3/10
Step-by-step explanation:
=4/7 + 9/70 - 4/10
=l.C.M of 7 , 70 and 10 =70
=4/7 .10/10 +9/70 -4/10 .7/7
=40/70 +9/70 -28/70
=40+9-28/70
=49-28/70
=21/70
=3/10
The university theatre department is selling tickets to their
upcoming performance. Three senior citizen tickets and one
student ticket were sold for $38. Three senior citizen ad two
student tickets were sold for $52. Determine the cost of a
senior citizen ticket, x and the price of a student ticket, y. Write
your answer as an ordered pair (x,y).
Answer:
(8,14)
Step-by-step explanation:
3x+2y=52
3x+1y=38 Subtract these equations using elimination method to get y=14
Then substitute y=14 to either equation
the bottom one is easier so
3x+1(14)=38 distribute 1 to 14 and any number times one is 1
3x+14=38 Subtract 14 from both sides
3x=24 Divide by 3
x=8 so check now
3(8)+1(14)=38
24+14=38?
38=38? yes
