Answer:
r² = 0.5652 < 0.7 therefore, the correlation between the variables does not imply causation
Step-by-step explanation:
The data points are;
X, Y
0.7, 1.11
21.9, 3.69
18, 4
16.7, 3.21
18, 3.7
13.8, 1.42
18, 4
13.8, 1.42
15.5, 3.92
16.7, 3.21
The correlation between the values is given by the relation
Y = b·X + a
[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]
Where;
N = 10
∑XY = 499.354
∑X = 153.1
∑Y = 29.68
∑Y² = 100.546
∑X² = 2631.01
(∑ X)² = 23439.6
(∑ Y)² = 880.902
From which we have;
[tex]b = \dfrac{10 \times 499.354 -153.1 \times 29.68}{10 \times 2631.01 - 23439.6} = 0.1566[/tex]
[tex]a = \dfrac{29.68 - 0.1566 \times 153.1}{10} = 0.5704[/tex]
[tex]r = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{\sqrt{\left [N\sum X^{2} - \left (\sum X \right )^{2} \right ]\times \left [N\sum Y^{2} - \left (\sum Y \right )^{2} \right ]}}[/tex]
[tex]r = \dfrac{10 \times 499.354 -153.1 \times 29.68}{\sqrt{\left (10 \times 2631.01 - 23439.6 \right )\times \left (10 \times 100.546- 880.902\right )} } = 0.7518[/tex]
r² = 0.5652 which is less than 0.7 therefore, there is a weak relationship between the variables, and it does not imply causation.
Find the product of 0.3×0.23
Answer:
0.069
Step-by-step explanation:
0.3*0.23=0.069
Triangle H N K is shown. Angle H N K is 90 degrees. The length of hypotenuse H K is n, the length of H N is 12, and the length of N K is 6. Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the value of n to the nearest whole number? 10 13 18 21
Answer:
13
Step-by-step explanation:
From the question, we are given a triangle HNK with an angle of 90°
The length of hypotenuse H K is n,
the length of HN is 12
the length of N K is 6.
From the above values, obtained in the question, we can see that this is a right angled triangle.
We are asked to find the length of the hypotenuse.
We can use Pythagoras Theorem of solve for this.
c² = a² + b²
where c = HK = n
a = NK = 6
b = HN = 12
c² = 6² + 12²
c² = 36 + 144
c² = 180
c = √180
c = 13.416407865
Approximately to the nearest whole number = 13
Therefore the value of HK = n = 13
We can also use Law of Cosines as given in the question to solve for this.
a² = b² + c² - 2ac × Cos A
where c = HK = n
a = NK = 6
b = HN = 12
Hence
c² = a² + b² - 2ab × Cos C
c = √ (a² + b² - 2ab × Cos C)
Where C = 90
c = √ 6² + 12² - 2 × 6 × 12 × Cos 90
c = 13.42
Approximately to the nearest whole number ≈ 13
Therefore the value of HK = n = 13
Answer:
B) 22 units
Step-by-step explanation:
edge 2020 :)
which phrase matches the algebraic expression bellow? 2(x+7)+10
Answer:
i think your answer is two times the sum of x and seven plus ten
if i am wrong than tell me
Step-by-step explanation:
hope this will help :)
G(x)= -\dfrac{x^2}{4} + 7g(x)=− 4 x 2 +7g, left parenthesis, x, right parenthesis, equals, minus, start fraction, x, squared, divided by, 4, end fraction, plus, 7 What is the average rate of change of ggg over the interval [-2,4][−2,4]open bracket, minus, 2, comma, 4, close bracket?
Answer:
-1/2Step-by-step explanation:
Given the function [tex]G(x)= -\dfrac{x^2}{4} + 7[/tex], the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;
Rate of change of the function is expressed as g(b)-g(a)/b-a
where a - -2 and b = 4
[tex]G(4)= -\dfrac{4^2}{4} + 7\\G(4)= -\dfrac{16}{4} + 7\\G(4)= -4 + 7\\G(4) = 3\\[/tex]
[tex]G(-2) = -\dfrac{(-2)^2}{4} + 7\\G(-2)= -\dfrac{4}{4} + 7\\G(-2)= -1 + 7\\G(-2)= 6[/tex]
average rate of change of g(x) over the interval [-2,4] will be;
[tex]g'(x) = \frac{g(4)-g(-2)}{4-(-2)}\\ g'(x) = \frac{3-6}{6}\\\\g'(x) = -3/6\\g'(x) = -1/2[/tex]
April typed a 5 page report in 50 mintues. Each page had 500 words at what rate is April typing
Answer:
Amy types at a rate of 50 words per minute
Step-by-step explanation:
In this question, we are interested in calculating the rate at which April is typing.
From the question, we can deduce that she typed a 5 page report, with each page having a total of 500 words.
Now, if each page has 500 words, the total number of words in all of the pages will be 5 * 500 = 2,500 words
Now, from here, we can see that 2,500 words were typed in 50 minutes.
The number of words per minute will be ;
Total number of words/Time taken = 2500 words/50 minutes
That will give a value of 50 words per minute
Drag each tile to the correct box.
Answer:
The order is 4) → 5) → 6) → 7) → 2) → 1) → 3)
Please find diagram with the arrangements
Step-by-step explanation:
The horizontal width of an hyperbola
For
1) [tex]\dfrac{(y - 11)^2}{7^2} -\dfrac{(x - 2)^2}{6^2} = 1[/tex]
h = 2, k = 11
The widths are;
Horizontal (h - a, k) to (h + a, k) which is (2 - 7, 11) to (2 + 7, 11) = 14 units wide
(h, k - b) to (h, k + b) which is (2, 11 -6) to (2, 11 + 6) = 12 units wide
2)
[tex]\dfrac{(y - 1)^2}{5^2} -\dfrac{(x - 7)^2}{12^2} = 1[/tex]
h = 7, k = 1
(h - a, k) to (h + a, k) which is (7 - 5, 1) to (7 + 5, 1) = Horizontal width 10 units wide
(h, k - b) to (h, k + b) which is (7, 1 -12) to (7, 1 + 12) = 24 units wide
3) [tex]\dfrac{(x - 6)^2}{6^2} -\dfrac{(y + 1)^2}{3^2} = 1[/tex]
h = 6, k = -1
a = 8, b = 3
The widths are;
(6 - 8, -1) to (6 + 8, -1) Horizontal width = 16
(6, -1 - 3) to 6, -1 + 3) width = 6
4) [tex]\dfrac{(x - 4)^2}{2^2} -\dfrac{(y + 2)^2}{5^2} = 1[/tex]
h = 4, k = -2, a = 2, b = 5
(4 - 2, (-2)) to (4 + 2, (-2)) Horizontal width = 4
(4, -2 - 5) to (4, -2 + 5) width = 10
5) [tex]\dfrac{(y + 5)^2}{2^2} -\dfrac{(x + 4)^2}{3^2} = 1[/tex]
h = -4, k = -5, a = 2, b = 3
(-4 - 2, (-5)) to (-4 + 2, (-5)) Horizontal width = 4
(-4, -5 - 3) to (4, -5 + 3) width = 6
6) [tex]\dfrac{(y + 1)^2}{2^2} -\dfrac{(x - 1)^2}{9^2} = 1[/tex]
h = 1, k = -1, a = 2, b = 9
(1 - 2, (-1)) to (1 + 2, (-1)) Horizontal width = 4
(1, -1 - 9) to (1, -1 + 9) width = 18
7) [tex]\dfrac{(x + 7)^2}{4^2} -\dfrac{(y - 9)^2}{9^2} = 1[/tex]
h = -7, k = 9, a = 4, b = 9
(-7 - 4, 9) to (-7 + 4, 9) Horizontal width = 8
(-7, 9 -9) to (-7, 9 + 9) width = 18
Find an equation of the line: Through the point (2, −4) with a y-intercept of −2 Through the points (4,2) and (3,1) Through the point (3,2) with a slope of −2
Answer and Step-by-step explanation: Equations of line through points and slope can be determined by:
[tex]y-y_{0}=m(x-x_{0})[/tex]
m is slope
Point (2,-4) and y-intercept = -2Y-intercept is point (0,-2)
m = [tex]\frac{y_{a}-y_{b}}{x_{a}-x_{b}}[/tex]
m = [tex]\frac{-4-(-2)}{2-0}[/tex]
m = - 1
Equation:
[tex]y+2=-1(x-0)[/tex]
[tex]y=-x-2[/tex]
Points (4,2) and (3,1)m = [tex]\frac{2-1}{4-3}[/tex]
m = 1
Equation:
[tex]y-2=(x-4)[/tex]
[tex]y=x-2[/tex]
Point (3,2) and slope = -2m = -2
Equation:
[tex]y-2=-2(x-3)[/tex]
[tex]y=-2x+6+2[/tex]
[tex]y=-2x+8[/tex]
A toy box in the shape of a rectangular prism has a volume of 6,912 cubic inches. The base area of the toy box is 288 square inches. What is the height of the toy box?
Answer:
h= 24 inches
Step-by-step explanation:
(Volume)= (Base Area) * (Height)
6,912= 288h
h=
Hi how to solve this pythagoras theorem
Answer:
The perimeter of the triangle is 40.
Step-by-step explanation:
Pythagorean Theorem: If x and y are the leg lengths of a right triangle, then r = √(x^2 + y^2) is the length of the hypotenuse. Alternatively, x^2 + y^2 = r^2.
The side lengths 2x, 4x - 1 and 4x + 1 are already arranged in ascending order. Thus, (2x^)2 + (4x - 1)^2 = (4x + 1).
Performing the indicated operations, we get:
4x^2 + 16x^2 - 8x + 1 = 16x^2 + 8x + 1. Simplify this first by combining like terms:
20x^2 - 16x = 16x^2, or
4x^2 - 16x = 0, or
4x(x - 4) = 0. Thus, x = 0 (which makes no sense here) or x = 4.
The perimeter of the rectangle is the sum of the three sides 2x, 4x - 1 and 4x + 1. Substituting 4 for x, we get
P = 8 + 16 - 1 + 16 + 1, or 40.
The perimeter of the triangle is 40.
If a 100-pound block of ice is placed on an inclined plane that makes an angle of 35° with the horizontal, how much friction force will be required to keep it from sliding down the plane? Choose the equation that could be used to solve the problem if x represents the force required to keep the block from sliding down the plane.
Answer:
F = 100(.5736)
= 57.36 lbs. (rounded off to 2 decimal places)
2) sin60 = .866
F = 18(.866)
= 15.59 lbs. (rounded off to 2 decimal places)
Step-by-step explanation:
F = friction
Answer:
100sin35° = x
Step-by-step explanation:
I did the assignment, this was the correct answer for me.
Find the total surface area.
Answer:
143.4 mi²
Step-by-step explanation:
Top: 8x6=48
Bottom: 3x8=24
Sides: 3x8=24 and 24
Trapezoids sides: (6+3)/2*2.6=4.5*2.6=11.7 and 11.7
TOTAL: 48+24+24+24+11.7+11.7= 143.4 mi²
Triangle ABC is translated to image A′B′C′. In this translation, A(5, 1) maps to A′(6, –2). The coordinates of B′ are (–1, 0). What are the coordinates of B? B( , )
Answer:
-2, 3
Step-by-step explanation:
To find the coordinates of B, we need to understand the translation that has taken place. In a translation, each point of a figure is moved the same distance and in the same direction.
In this case, point A(5, 1) has been translated to point A'(6, -2). To find the distance and direction of the translation, we subtract the coordinates of A from the coordinates of A': Translation Vector [tex]= (6 - 5, -2 - 1) = (1, -3)[/tex] The translation vector represents the change in x and y coordinates between the original figure and its translated image.
Since B' has coordinates (-1, 0), we can apply the translation vector to find the coordinates of B as follows: B = B' - Translation Vector B [tex]= (-1, 0) - (1, -3)[/tex] B [tex]= (-1 - 1, 0 - (-3)) B = (-2, 3)[/tex] So, the coordinates of B are (-2, 3).
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show that (2x+3)^3 = 8x^3+36x^2+54x+27 for all values of x
Answer:
see explanation
Step-by-step explanation:
Given
(2x + 3)³
= (2x + 3)(2x + 3)(2x + 3) ← expand the last 2 factors using FOIL
= (2x + 3)( 4x² + 12x + 9)
= 2x(4x² + 12x + 9) + 3(4x² + 12x + 9) ← distribute parenthesis
= 8x³ + 24x² + 18x + 12x² + 36x + 27 ← collect like terms
= 8x³ + 36x² + 54x + 27
write 39/5 as a mixed numer
Answer:
6 9/5Step-by-step explanation:
39/5 as a mixed number;
39/5 as a mixed number;39 ÷ 5 = 6 remaining 9
Therefore:
6 9/5
8) There are 2116 students in a school .In how many equal rows and columns can they be arranged for a drill display?
Answer:
46
Explanation:
root of 2116
=46×46
Therefore 46 columns and 46 rows
Answer:
46 rows, 46 columns.
Step-by-step explanation:
First factor 2116:
2) 2116
2 } 2058
23 ) 529
23
2116 = 2*2*23*23
= 46 * 46
Which of the following choices evaluates (-x)^2 when x=-1
Answers:
1)1
2)-2
3)-1
plz help thanks, will give brainliest!
Answer:
D.
Step-by-step explanation:
[tex]\frac{x^{2/3}}{y^{-3/4}}[/tex]
= [tex]x^{2/3}y^{3/4}[/tex]
= [tex]\sqrt[3]{x^2} * \sqrt[4]{y^3}[/tex]
So, D is your answer.
Hope this helps!
If x-a is a factor of polynomial x3-mn2-2nax+na2 prove that a=m+n and a is not = 0
Step-by-step explanation:
hope this helps
pls mark me brainliest
Solve the equation 1) 4.3^x+1 = 27+9^x
2) 3^x+5= 3^x+3+8/3
Answer:
Step-by-step explanation:
4*3^x+1=27+(3^2)^x
(3^2)^x=(3^x)^2
3^x=t
4t+1=27+t^2
t^2-4t+27-1=0
t^2-4t+26=0
delta=4^2-4*1*26=16-84=-68<0
the equation has not real solutions
A shell of mass 8.0-kg leaves the muzzle of a cannon with a horizontal velocity of 600 m/s. Find the recoil velocity of the cannon, if its mass is 500kg.
Answer:
velocity of recoil velocity of cannon is -9.6 m/sec
Step-by-step explanation:
according to law of conservation of momentum
total momentum of isolated system of body remains constant.
momentum = mass of body* velocity of body.
__________________________________
in the problem the system is
shell + cannon
momentum of shell = 8*600 = 4800 Kg-m/sec
let the velocity of cannon be x m/sec
momentum of cannon = 500*x = 500x Kg-m/sec
initially the system of body is in rest (before the shell is fired) hence, total momentum of the system i is 0
applying conservation of momentum
total momentum before shell fired = total momentum after the shell is fired
0 = momentum of shell + momentum of cannon
4800 + 500x = 0
x = -4800/500 = -9.6
Thus, velocity of recoil velocity of cannon is -9.6 m/sec
here negative sign implies that direction of velocity of cannon is opposite to that of velocity of shell.
PLEASE help me with this question! This is really urgent! No nonsense answers please.
Answer:
The correct answer is b.
Step-by-step explanation:
if you arrange the data set in ascending order you will have:
x y
-2 [tex]\frac{1}{100}[/tex]
-1 [tex]\frac{1}{10}[/tex]
0 1
1 10
3 1000
Exponential growth is an increase in a specific way of a data set over time. here, as x increases by a +1, y increases with ×10
Need help ASAP!!!! THX
Answer:
C
Step-by-step explanation:
f(x) = x - 2
f(2) = (2) - 2
f(2) = 0
A + B are wrong cuz..
f(-2) = -2 - 2
f(-2) = -4
A survey asked students at Wilson Academy which status they would prefer—to be happy, healthy, or rich—and how much pressure they felt from their homework. The two-way table of row relative frequencies below shows the data.
Answer:
A. A student who prefers to be healthy is more likely to feel very little pressure from homework than a student who prefers to be rich.
Step-by-step explanation:
Answer:
A THE RIGHT ANSWER
Step-by-step explanation:
-3 = 7 - BLANK pls tell me what blank is
Answer:
10
Step-by-step explanation:
-3 = 7 - x
Add x to both sides
x -3 = 7 - x +x
x - 3 = 7
Now, add 3 to both sides
x - 3 + 3 = 7 + 3
x = 10
Answer:
[tex]\boxed{10}[/tex]
Step-by-step explanation:
[tex]-3=7- \sf BLANK[/tex]
[tex]\sf Subtract \ 7 \ from \ sides.[/tex]
[tex]-3-7=-7+7- \sf BLANK[/tex]
[tex]-10=- \sf BLANK[/tex]
[tex]\sf Multiply \ both \ sides \ by \ -1.[/tex]
[tex]-10(-1)=(-1)- \sf BLANK[/tex]
[tex]10= \sf BLANK[/tex]
Find the area. Round to the nearest tenth.
6 ft
3 ft
12.16 ft
9.16 ft
Answer:
100.5 ft^2
Step-by-step explanation:
First find the area of the rectangle
A = l*w
A = 12.16 * 6
A =72.96 ft^2
Then find the area of the triangle
A = 1/2 bh
The base is 12 ft - 6ft = 6ft
The height is 9.16 ft
A = 1/2 ( 9.16) * 6
A = 27.48 ft^2
Add them together
27.48+72.96
100.44 ft^2
Round to the nearest tenth
100.5 ft^2
Answer:
[tex]\huge \boxed{\mathrm{100.4 \ ft^2 }}[/tex]
Step-by-step explanation:
To find the area of the shape, we can add the area of the rectangle with the area of the triangle.
Area of rectangle :
base × height
6 ft × 12.16 ft
72.96 ft²
Area of triangle :
base × height × 1/2
(12 ft - 6 ft) × 9.16 ft × 1/2
6ft × 9.16 ft × 1/2
27.48 ft²
Adding the areas.
72.96 ft² + 27.48 ft²
100.44 ft²
≈ 100.4 ft² (rounded to nearest tenth)
How to do this question plz.
plz work out for me in your notebook or sheet if you can plz the question so I can understand more plzz
Answer:
[tex]3\pi[/tex]
Step-by-step explanation:
The circumference of a circle is [tex]2\pi r[/tex].
If we want to find the circumference of this semi-circle, we can find the circumference if it was a whole circle then divide by 2.
[tex]2 \cdot \pi \cdot r\\2 \cdot \pi \cdot 3\\6 \cdot \pi\\ 6\pi[/tex]
Now we know the circumference of the whole circle.
To find the circumference of half the circle we divide by 2.
[tex]6\pi \div 2 = 3\pi[/tex]
Hope this helped!
In a given set of items, the mode is items which ?
a. appears first
b. appears fewest
c. appears farthest
d. appears most
Answer:
d. appears most
Step-by-step explanation:
Mode is the number that appears the most often in a set of data
A mother who is 35 years old has two sons, one of whom is twice as old as the other. In 3 years the sum of all their ages will be 59 years. How old are the boys at present ?
Answer:
son2: 5
son1: 10
Step-by-step explanation:
2x (son1) + x (son2) + 35 (mother) + 3 (years)*3 (people) = 59
3x = 15
x = 5
The age of each boy at present will be 2 years and 3 years.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Let the age of the sons will be x and y.
A mother who is 35 years old has two sons, one of whom is twice as old as the other. Then the equation will be
x = 2y
In 3 years, the sum of all their ages will be 59 years. Then the equation will be
x + y + x + 1 + y + 1 + x + 2 + y + 2 + 35 = 59
Simplify the equation, we have
3x + 3y + 41 = 59
6y + 3y = 59 – 41
9y = 18
y = 2
Then the value of x will be
x = 2y
x = 2(2)
x = 4
Thus, the age of each boy at present will be 2 years and 3 years.
More about the linear system link is given below.
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FOLLOW THE STEP: reduce to simplest form
-7/12 + 3/8 = ______
Answer:
-5/24
Step-by-step explanation:
get a common denominator = 24
-14/24 + 9/24 = -5/24
Answer:-5 /24 ez
Step-by-step explanation:
Is △FHK similar to △GHJ? If so, which postulate or theorem proves these two triangles are similar? △FHK is similar to △GHJ by the SSS Similarity Theorem. △FHK is similar to △GHJ by the SSA Similarity Theorem. △FHK is similar to △GHJ by the SAS Similarity Theorem. △FHK is not similar to △GHJ.
Answer:
ΔFHK and ΔGHJ are the similar triangles by SAS similarity theorem.
Step-by-step explanation:
Picture for the given question is missing; find the picture attached.
If [tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex] and ∠H ≅ ∠H
Then ΔFHK ~ ΔGHJ
[tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex]
[tex]\frac{(12+10)}{10}=\frac{(15+18)}{15}[/tex]
[tex]\frac{22}{10}=\frac{33}{15}[/tex]
[tex]\frac{11}{5}=\frac{11}{5}[/tex]
Since, [tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex] and ∠H ≅ ∠H [By reflexive property]
Therefore, ΔFHK and ΔGHJ are the similar triangles by SAS similarity theorem.
Option (3) will be the answer.
Answer:
ΔFHK and ΔGHJ are similar triangles by the SAS similarity theorem.
Step-by-step explanation:
Verified correct with test results.
