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.
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
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)
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
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]
Which of the following choices evaluates (-x)^2 when x=-1
Answers:
1)1
2)-2
3)-1
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]
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
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
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:
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!
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
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.
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 :)
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
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:
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).
To know more about Translation Vector visit:
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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
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
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 :)
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.
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.
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
-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]
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.
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
Find the product of 0.3×0.23
Answer:
0.069
Step-by-step explanation:
0.3*0.23=0.069
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!
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.
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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
