The regression lines 3x+2y=26 and 6x+y=31 are linear regressions
The mean values are 4 and 7 and the correlation coefficient between x and y is 0.25The standard deviation of x is 2/13The mean value and the correlationWe have the equations to be:
3x+2y=26 and 6x+y=31
Make y the subject in the second equation
y = 31 - 6x
Substitute y = 31 - 6x in the first equation
3x+2[31 - 6x] = 26
Expand
3x+ 62 - 12x = 26
Collect like terms
3x - 12x = 26 - 62
Evaluate
-9x = -36
Divide by - 9
x = 4
Substitute x = 4 in y = 31 - 6x
y = 31 - 6 * 4
y = 7
This means that the mean values are 4 and 7
To determine the correlation coefficient, we make y the subject in 3x+2y=26 and x the subject in 6x+y=31.
So, we have:
y = 13 - 3x/2 and x = 31/6 - 1/6y
The above means that:
Bxy = -1/6 and Byx = -3/2
The correlation coefficient is then calculated as:
r^2 = Bxy * Byx
r = -1/6 * -3/2
r = 0.25
Hence, the correlation coefficient between x and y is 0.25
The standard deviation of xWe have:
Var(y) = 4
In (a), we have:
y = 13 - 3x/2
To solve further, we make use of:
Var(y) = Var(ax + b) = a^2Var(x)
This gives
Var(y) = Var(13 - 3x/2) = 13^2 * Var(x)
So, we have:
Var(y) = 13^2 * Var(x)
Substitute 4 for Var(y)
4 = 13^2 * Var(x)
Divide both sides by 13^2
4/13^2 = Var(x)
Express 4 as 2^2
(2/13)^2 = Var(x)
So, we have:
Var(x) = (2/13)^2
Take the square root of both sides
SD(x) = 2/13
Hence, the standard deviation of x is 2/13
Read more about regression lines at:
https://brainly.com/question/4341286
The following can be deposited in a savings account: (check all that apply)
1. Jewels
2. Cash
3. Paycheck
4. Coin
5. Checks
Answer: cash, paychecks, checks
Step-by-step explanation:
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Find the sum of 3.0478 and 4.92 using the correct number of significant digits.
A. 7.967
B. 7.97
C. 7.9
D. 8
Answer:
Since the least number of digits in the number is 2 decimal places
Round 3.0478 to 2 dp
3.05+4.92=7.97
B is the answer
Step-by-step explanation:
Give brainliest please
Answer:
B
Step-by-step explanation:
18/5 divided by 3/25
[tex] \frac{18}{5} \div \frac{3}{25} [/tex]
Answer:
30
Step-by-step explanation:
There are a few different ways we can approach this problem.
The easiest way is to flip the second fraction and multiply:
[tex]\dfrac{18}{5} \div \dfrac{3}{25}=\dfrac{18}{5} \times \dfrac{25}{3}=\dfrac{18 \times 25}{5 \times 3}[/tex]
To do this without a calculator, rewrite 18 as 6 x 3 and 25 as 5 x 5:
[tex]\dfrac{18 \times 25}{5 \times 3}=\dfrac{6 \times 3 \times 5 \times 5}{5 \times 3}[/tex]
Now we can cancel out the common factors of 5 and 3 from the numerator and denominator, and are left with:
[tex]\implies 6 \times 5 =30[/tex]
The quotient obtained from the division of given fractions is 30.
Given that, 18/5 divided by 3/25.
Dividing fractions is nothing but multiplying the fractions by reversing one of the two fraction numbers or by writing the reciprocal of one of the fractions. By reciprocal we mean, that if a fraction is given as a/b, then the reciprocal of it will b/a.
Here, 18/5 ÷ 3/25
= 18/5 × 25/3
= 6/1 × 5/1
= 30/1
Therefore, the quotient obtained from the division of given fractions is 30.
Learn more about the division of fractions here:
brainly.com/question/17205173.
#SPJ6
Find the exact value, without a
calculator.
30°
sin 15° sin
tan 15º =
2
cos 15° 30°
2
COS
II
[ ? ] - [
] + [
Enter
[tex]sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \qquad cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin\left( \cfrac{30^o}{2} \right)\implies \sqrt{\cfrac{1-cos(30^o)}{2}}\implies \sqrt{\cfrac{1-\frac{\sqrt{3}}{2}}{2}}\implies \sqrt{\cfrac{~~\frac{2-\sqrt{3}}{2}~~}{2}}[/tex]
[tex]\sqrt{\cfrac{2-\sqrt{3}}{2}\cdot \cfrac{1}{2}}\implies \sqrt{\cfrac{2-\sqrt{3}}{4}}\implies \boxed{\cfrac{\sqrt{2-\sqrt{3}}}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos\left( \cfrac{30^o}{2} \right)\implies \sqrt{\cfrac{1+cos(30^o)}{2}}\implies \sqrt{\cfrac{1+\frac{\sqrt{3}}{2}}{2}}\implies \sqrt{\cfrac{~~\frac{2+\sqrt{3}}{2}~~}{2}} \\\\\\ \sqrt{\cfrac{2+\sqrt{3}}{2}\cdot \cfrac{1}{2}}\implies \sqrt{\cfrac{2+\sqrt{3}}{4}}\implies \boxed{\cfrac{\sqrt{2+\sqrt{3}}}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{~~ sin\left( \frac{30^o}{2} \right)~~}{cos\left( \frac{30^o}{2} \right)}\implies \cfrac{~~\frac{\sqrt{2-\sqrt{3}}}{2} ~~}{\frac{\sqrt{2+\sqrt{3}}}{2}}\implies \cfrac{\sqrt{2-\sqrt{3}}}{2}\cdot \cfrac{2}{\sqrt{2+\sqrt{3}}} \\\\\\ \cfrac{\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\implies \blacktriangleright \sqrt{\cfrac{2-\sqrt{3}}{2+\sqrt{3}}} \blacktriangleleft[/tex]
If a chain is on 24 tooth front gear and 8 tooth rear gear determine whether this combination will result in high speed than a 2 to 1 gear ratio, assuming the speed you are pedalling is the same
24/8 = 3
the 24 to 8 gear = 3:1 ratio which is greater than 2:1
Question 1 of 10
How many solutions are there to the equation below?
x² =-64
A. 0
B. 2
C. 16
D. 8
E. -8
someone help me with my homework
Answer:
Cite evidence from the text to explain Her as role in Greek mythology
Let
[tex]Let \\ \displaystyle\sf S = \sum_{k=1}^n \dfrac{n}{n^2+kn + k^2} [/tex] and ,
[tex]\displaystyle \sf T_n =\sum_{k=0}^{n-1}\dfrac{n}{n^2+kn+k^2}[/tex] ,
[/tex]
where n = 1,2,3,4..... Then ,
[tex]A)\quad S_n < \dfrac{\pi}{3\sqrt3} \qquad \qquad B)\quad S_n >\dfrac{\pi}{3\sqrt3}\\\\ C)\quad T_n >\dfrac{\pi}{3\sqrt3}\qquad\qquad D)\quad T_n < \dfrac{\pi}{3\sqrt3}[/tex]
Answer:
A, D
Step-by-step explanation:
You want to know the bound for the values of Sn and Tn, given their definitions as ...
[tex]\displaystyle S_n=\sum_{k=1}^n{\dfrac{n}{n^2+kn+k^2}}\\\\T_n=\sum_{k=1}^{n-1}{\dfrac{n}{n^2+kn+k^2}}[/tex]
ValuesAll we need to do to determine the correct answer choices is evaluate the sums for some value of n.
For n=2, the value of S2 is ...
S2 = 2/(4+2+1) +2/(4+4+4) = 2/7 +2/12 = 19/42 ≈ 0.4524
For n=2, the value of T2 is ...
T2 = 2/(4+2+1) = 2/7 ≈ 0.2857 . . . . . 1/(3n) less than the value of Sn
Both of these values are less than π/(3√3) ≈ 0.6046.
The correct answer choices are ...
A) Sn < π/(3√3)
D) Tn < π/(3√3)
__
Additional comment
For the purpose here, it is not necessary to determine the limiting value of either Sn or Tn. It is only necessary to demonstrate which side of the given value the terms of either sequence lie.
<95141404393>
if h=5 what is 2 x (6-h
Answer:
Step-by-step explanation:
Equation : 2 × (6 - h)
Because h = 5, replace the variable h with 5.
2 × (6 - 5)
Solve the equation in the parentheses.
6 - 5 = 1
The equation is now 2 × 1, which is equal to 2.
So, 2 × (6 - h) is 2.
Hope this helped !
Find the measures of angles 1 through 6.
Answer:
<1 = 88° , <2 = 129°, <3 = 82°, <4 = 147°, <5 = 94°, <6 = 86°
Step-by-step explanation:
<1 + 92° = 180°
<1 = 88°
<2 + 51° = 180°
<2 = 129°
<3 + 98° = 180°
<3 = 82°
<4 + 33° = 180°
<4 = 147°
<1 + <2 + <3 + <4 + <5 = 540°
88° + 129° + 82° + 147 + <5 = 540°
<5 = 94°
<5 + <6 = 180°
94° + <6 =180°
<6 = 86°
Please help again,am very slow of mathematics,
please po!
Step-by-step explanation:
a) 7/10
b) 9/10
c) 4/10 = 2/5
d) 9/10
e) 2/10 = 1/5
I hope it helped you
which statement about the transformation is true? A. the unshaded octagon is a reflection because it is a flip over a diagonal line B. the unshaded octagon is a dilation because it is smaller than the shaded octagon C. the unshaded octagon is a horizontal translation because it is directly to the left of the shaded octagon D. the unshaded octagon is a vertical translation because it is directly under the shaded octagon
-
The expression (3 - 7i)^2 equivalent to
Answer:
-40-42i
Step-by-step explanation:
9-42i+49i^2=9-42i-49=-40-42i
Help, this is my math hw and I don't get it!
Pictures are attached below...
I need to show my work too, so i need a file to your work!
I'll mark brainliest if you can answer it.
please help I will give brainiest pls
can somebody help me please
Answer:
35, 13, 1, -1, 7
Step-by-step explanation:
Repeated evaluation of the same function is accomplished easily by a calculator or spreadsheet. It is a good idea to become familiar with this technology.
__
If you're doing this by hand, writing the equation in Horner form can make it easier to evaluate.
f(x) = (5x -7)x +1
Then ...
f(-2) = (5(-2) -7)(-2) +1 = (-17)(-2) +1 = 34 +1 = 35
f(-1) = (5(-1) -7)(-1) +1 = (-12)(-1) +1 = 12 +1 = 13
f(0) = 1 . . . . the constant term
f(1) = (5(1) -7)(1) +1 = (-2)(1) +1 = -2 +1 = -1
f(2) = (5(2) -7)(2) +1 = (3)(2) +1 = 6 +1 = 7
In order, the f(x) values are 35, 13, 1, -1, 7.
This recipe makes 10 flapjacks.
How much of each ingredient is needed to make 35 flapjacks by following this recipe?
Recipe: Makes 10 flapjacks
140 g margarine
120 g sugar
100 ml syrup
240 g oats
50 g raisins
Answer:
Multiply each measure of ingredients by 3.5
Step-by-step explanation:
This recipe makes 10 flapjacks. We want to be able to make 35 flapjacks.
Divide 35 by 10 to find the ratio of these 2 numbers.
35 / 10 = 3.5
Now we can multiply the measures by this number to find out how much of each ingredient we need.
140 * 3.5 = 490
120 * 3.5 = 420
100 * 3.5 = 350
240 * 3.5 = 840
50 * 3.5 = 175
Answer:
Recipe: Makes 35 flapjacks
490 g Margarine
420 g sugar
350 ml syrup
840 g oats
200 g raisins
The expression (3 - 7i)2 is equivalent to
Answer:
Step-by-step explanation:
I will give Brainliest! :<
This meal costs $75.00.
Fatima used a 20% off coupon and then tax was added.
The total after the coupon and tax was $75.00.
What was the tax rate?
Submit and EXPLAIN, please!
Answer:
The discount given on the cost of the meal is $15
Step-by-step explanation:
How to calculate tax on a given price
According to the question, we are given the following information
The original cost of the meal = $75
Off coupon = 20%
Required
The number of coupons given
coupon amount = 0.2 * 75
coupon amount = $15
Hence the discount given on the cost of the meal is $15
what is the solution to the system of equations graph below
[tex]\large\pink{\mid{\underline{\overline{\tt { →\: (-5,1)}\mid}}}}[/tex]
Option ( A ) → (-5,1)Intersecting lines→ When two lines share exactly one common pointcuz here,the pôint where two lines meet is (-5,1) hence this is the solution of above graph.x = -5 , y = 1_______________☃️[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]
Please help :) (its for my friend, cause she wont belive me!)
If your friend has 7 apples, you take 3. How much do you have?
Answer:
the answer its 3 :)
Step-by-step explanation:
matematicas amigo
Find any in the sequence -3, 6, -12, 24
Answer: 3
Step-by-step explanation:
go in evenly
meter and Area
1
Casey wants to put new carpet in her bedroom. A drawing of Casey's room is below. It consists of two sections: a square and a
rectangle
The rectangular section has the same width as the square section, but wice the length. If one side of the square section measures 3
yards, how many square yards of carpet should Casey buy for her room?
A 36 square yards
OB 24 square yards
OC 18 square yards
D. 27 square yards
Answer:
18 square yards
Step-by-step explanation:
because if you do 3x3 twice then add the two numbers you get you will get 18.
Please can anyone solve this question I need it...
I'll mark as BRAINLIEST ANSWER...
Answer:
x = 4/3
y = 0
z = 5/4
Step-by-step explanation:
PQ means multiplied matrices.
P+Q means added matrices.
PQ = =
4x+0 4y+0z 4x 4y
0x+5×0 0y+5z 0 5z
P+Q = =
4+x 0+y 4+x y
0+0 5+z 0 5+z
so, for PQ = P+Q we have
4x = 4+x
4y = y
5z = 5+z
4x = 4 + x
3x = 4
x = 4/3
4y = y
3y = 0
y = 0/3 = 0
5z = 5 + z
4z = 5
z = 5/4
3/2 times 6/2 times 2
Answer:
9
Step-by-step explanation:
3/2x6/2=18/2 Simply that and it turns to 9.
Answer:
9
Step-by-step explanation:
3*6*2 = 36
2*2 = 4
36/4 = 9
I multiplied the numerators together and the denominators together.
PLEASE RATE!! I hope this helps!!
please help me thank u :)
Answer:
The answer would be 17
Step-by-step explanation:
Answer:
x = 17
Step-by-step explanation:
Pythagorean Theorem: a^2 + b^2 = c^2
15^2 + 8^2 = c^2 (15^2 = 225 and 8^2 = 64)
225 + 64 = 289
[tex]\sqrt{289}[/tex] = 17
What are the coordinates of a point on the unit circle if the angle formed by the positive x-axis and the radius is 45? (WHO WANTS BRAINLIEST?!)
Answer:
the 45 degree angle is in the first quadrant, the coordinates are (√2/2, √2/2) (square root of 2 on the top, 2 on the bottom)
what is the probability scale that you will buy a new pair of shoes soon
Answer:
The probability scale for this question is not 100% sure to buy shoes so the scale is given to be even chance(1/2).
Step-by-step explanation:
Pattern A follows the rule "add 5" and Pattern B follows the rule "subtract 2." Pattern A 5 10 15 20 25 Pattern B 20 18 16 14 12 Which ordered pairs are formed from combining a term in Pattern A with its corresponding term in Pattern B? Select all correct answers.
Answer:
(10, 20)
(25, 12)
(15, 20)
Step-by-step explanation:
Hopes this helps! :)
Answer:
the correct answers are,
(15, 16)
(25, 12)
(5, 20)
Write 0.00205 in scientific notation.
Answer:
Therefore, 0.00205 in scientific notation is 2.05 × 10-3 and It has 3 significant figures. In scientific e-notation it is written as 2.05e-3.
Step-by-step explanation:
Answer:
[tex]2.05 \times 10 ^{ - 3} [/tex]