Answer:
H0 : σ² = 10
H1 : σ² ≠ 10
X² = 20.124
Pvalue = 0.064776
there is significant evidence to conclude that the rebound lengtb of rockfall down a slope is not 10m²
Step-by-step explanation:
Given the data:
10.94 13.71 11.38 7.26 17.83 11.92 11.87 5.44 13.35 4.90 5.85 5.10 6.77
Using a calculator ;
The sample variance, s² = 16.77
α = 0.10
The null and alternative hypothesis :
H0 : σ² = 10
H1 : σ² ≠ 10
The test statistic :
X² = [(n - 1)*s² ÷ σ²]
s² = 16.77
n = sample size = 13 ; s²
X² = [(13 -1)*16.77 ÷ 10
X² = (12 * 16.77) / 10
X² = 201.24 / 10
X² = 20.124
The Pvalue using a Pvalue calculator ; degree of freedom (df) = 13 - 1 = 12
Pvalue = 0.064776
Pvalue < α ; Hence we reject the null
Hence, there is significant evidence to conclude that the rebound lengtb of rockfall down a slope is not 10m²
convert the given rectangular coordinates to polar coordinates
(-2, 5)
So in this question, we have to convert the rectangular coordinates to polar coordinates.
Polar coordinates are (r, Q).
To convert rectangular coordinates to polar coordinates we use that x is equal to rcosQ and y is equal to rsinQ
In this question x is equal to -2 and y is equal to 5.
Hence we have -2 is equal to rcosQ and 5 is equal to rsinQ .
From here, we have tanQ equal to -2.5 . Hence, Q = tan⁻¹ (-2.5)
We have x²+y² =r² and also x²+y² = 5²+2²=29 .
Hence, r=√29 and Q = tan⁻¹ (-2.5) .
Therefore the polar coordinates of (-2,5) are ( √29, tan⁻¹ (-2.5)).
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Chris completed a 100-meter breaststroke swimming race in 92.542 seconds.
Michael completed the 100-meter breaststroke swimming race in 95.6 seconds.
How much faster was Chris's time than Michael's? . I don’t need an explanation just tell me the answer it is not a… A B C D Type question just give me an answer
Chris's time 3.058 sec faster than Michael's.
What is meaning of faster?
Fast and fast refer to moving quickly. Fast can be used as an adverb or an adjective. Quick is an adjective, while rapidly is its adverbial counterpart.
Given that,
Chris completed a 100-meter breaststroke swimming race in 92.542 seconds.
Michael completed the 100-meter breaststroke swimming race in 95.6 seconds.
The difference of time between Chris and Michael to complete 100-meter breaststroke swimming is = (95.6 - 92.542) = 3.058 sec.
Since both are completed 100 meter breaststroke, thus the difference of time denotes the faster time.
Thus Michael's timing was 3.058 seconds slower than Chris'.
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Which fact represents the sum of (3 x 8) and (6 x 8)?
A. 9 x 8
B. 8 x8
C. 18 × 8
D 9x6
Answer:
Option A is the correct answer
Step-by-step explanation:
(3 × 8) + (6 × 8)
24 + 48 = 72
Thus, 9 x 8 = 72
Are the expressions 18+3.1 m+4.21 m-2 and 16+7.31 m equivalent
Answer:
Yes, they are equivalent.
Step-by-step explanation:
18 + 3.1m + 4.21m - 2
Combine like terms.
7.31m + 18 - 2
7.31m + 16 = 16 + 7.31m
Guests who appear on talk shows and interact with other guests for the benefit of an audience are participating in a
a. symposium. b. forum.
c. panel discussion.
d. governance group. e. service group.
Guests who appear on talk shows and converse with one another for the benefit of the audience make up a (C) panel discussion.
What is a panel discussion?Participants in a panel discussion are guests who appear on talk shows and engage in conversation with one another for the benefit of the audience.
A panel discussion, or simply a panel, is a gathering of people who talk about something in front of an audience, usually at fan conventions, conferences for business or academia, or on television.
Panels often have a moderator who leads the conversation and occasionally solicits questions from the audience with the intention of being both educational and entertaining.
Fan convention film panels have been attributed with increasing box office revenues by creating anticipation.
Therefore, guests who appear on talk shows and converse with one another for the benefit of the audience make up a (C) panel discussion.
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REAL ANSWERS ONLY PLEASE! NEED THIS DONE ITS DUE SOON AND I DONT EVEN KNOW WHERE TO START! PLEASE SOMEONE!
Answer:
A.) Yes, because 0.064 is less than 0.4
Step-by-step explanation:
The equation [tex]0.4^3 = 0.064[/tex] is a counterexample to the given conjecture because 0.064 is less than 0.4. This shows that the cube of a number is not always greater than the number.
In general, the cube of a number is the result of multiplying the number by itself three times. For example, the cube of 2 is [tex]2 * 2 * 2 = 8[/tex], and the cube of 5 is [tex]5 * 5 * 5 = 125[/tex]. The cube of a number is always greater than the number when the number is positive, because a positive number multiplied by itself three times is always a larger number. However, when the number is negative or a decimal, this is not always the case.
In the given equation, 0.4 is a decimal number, and [tex]0.4^3[/tex] is the cube of 0.4. The result of this calculation is 0.064, which is less than 0.4. This means that the cube of 0.4 is not greater than 0.4, and therefore the given conjecture is false.
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 290 feet of If
antique picket fencing are to be used to enclose the garden, find the dimensions of the garden.
What is the length of the garden?
The length of the garden is
What is the width of the garden?
The width of the garden is
In order to enclose the garden's perimeter, vintage fence will be used. The perimeter of a rectangle-shaped garden is equal to the sum of the garden's two lengths and two widths.
Do the length and breadth calculations?In order to enclose the garden's perimeter, vintage fence will be used. The perimeter of a rectangle-shaped garden is equal to the sum of the garden's two lengths and two widths.
According to their estimates, our perimeter fence measures 220 feet, hence 220 = 2L + 2W.
We can make this more manageable if we divide everything by two: 110 = L + W
The width is now specified as being "exactly two-thirds of the length."
In math, the letter "=" equals the word "IS". Consequently, "the width is" becomes "W =," and "the two-thirds of the length" is precisely what it says, "(2/3) L."
W = (2/3)L is the result of adding these.
and we will add this W to the formula above (110 = L + W) to make 110 = L + (2/3)L.
If we substitute L with (3/3) L (that is, 1*L with 1 written 3/3) now we can add (3/3) as adding fractions requires a "common denominator."
L + (2/3)
L = (5/3)L
At this point, our equation is 110 = (5/3)L.
The right side (3/5) is now multiplied by the reciprocal on both sides, yielding (3/5)(110) = (3/5)(5/3)
L66 = L and W=2/3
L = (2/3)(66) = 44 = W
66 feet by 44 feet are the measurements of the square flower garden.
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Graph TU with endpoints T(1,2) and U(4,6) and its image after the composition.
Translation: (x, y) → (x-2, y-3)
Translation: (x, y) → (x-4, y + 5)
The graph of the line segment after the translation (x, y) → (x-2, y-3) and (x, y) → (x-4, y + 5) has been drawn.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
As per the given coordinate,T(1,2) and U(4,6)
Apply the translation (x, y) → (x-2, y-3)
T(1,2) → T'(1 - 2,2 - 3) = T'(-1,-1)
U(4,6) → U'(4 - 2,6 - 3) = U'(2,3).
Apply the translation (x, y) → (x-4, y + 5)
T(1,2) → T'(1 - 4,2 + 5) = T'(-3,7)
U(4,6) → U'(4 - 4,6 + 5) = U'(0,11)
All points have been plotted below.
Hence"After the translations (x, y) → (x-2, y-3) and (x, y) → (x-4, y + 5), the graph of the line segment has been drawn.".
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Answer:
Translation (x, y) → (x - 2, y - 3):
T' (-1, -1)U' (2, 3)Translation (x, y) → (x - 4, y + 5):
T'' (-3, 7)U'' (0, 11)Step-by-step explanation:
Given endpoints of line segment TU:
T = (1, 2)U = (4, 6)Translation 1 (blue on attached diagram)
(x, y) → (x - 2, y - 3)This means to subtract 2 from the x-values of the endpoints, and subtract 3 from the y-values of the endpoints:
Therefore:
T' = (1 - 2, 2 - 3) = (-1, -1)U' = (4 - 2, 6 - 3) = (2, 3)Translation 2 (red on attached diagram)
(x, y) → (x - 4, y + 5)This means to subtract 4 from the x-values of the endpoints, and add 5 to the y-values of the endpoints:
Therefore:
T'' = (1 - 4, 2 + 5) = (-3, 7)U'' = (4 - 4, 6 + 5) = (0, 11)Mamadou leans a 18-foot ladder against a wall so that it forms an angle of 75° with
the ground. What's the horizontal distance between the base of the ladder and the
wall?
When class 11Y1 found that their favourite teacher, Mr Musson, was leaving they decided to organise a party for him.
Lewis, one of the class members, wants to buy 34 cartons of juice. He can buy a single carton of juice for 45p.
He can buy a pack of 4 cartons for £1.51.
Lewis buys all the cartons he needs for the least possible amount of money. How much did he spend?
The least total amount Lewis spends to buy 34 cartons of juice is £12.84 for Alternative B instead of £15.30 for Alternative A.
How is the total amount determined?We can determine the total amount for each alternative and compare the two using two mathematical operations of multiplication and division.
We can also compare the alternatives by determining their unit cost per carton using division.
Alternative A:The number of cartons of juice required = 34
The unit cost of a carton = £0.45 or 45p
The total cost of 4 cartons = £1.80 (£0.45 x 4)
The total amount Lewis would spend for Alternative A = £15.30 (£0.45 x 34)
Alternative B:Cost of a pack of 4 cartons = £1.51
Unit cost per carton of the 4-carton pack = £0.3775 (£1.51/4)
The total amount Lewis spends for Alternative B = £12.835 (34/4 x £1.51)
Thus, mathematically Alternative B presents a lower cost than Alternative A, Lewis would choose to spend £12.84.
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Great job , you’ve already earned 1300 points, it there are 5 more days in this month. How many points a day do you need to reach your goal of 1580 points?
Answer:
56 points
Step-by-step explanation:
Let's say that for the next 5 days, you earn x points each day. This means that you will earn 5x more points before the month ends.
Since you already earned 1300 points, you will have earned 1300 + 5x points, which through the question we know is equal to 1580 points. Using this knowledge, we can set up the equation below:
1300 + 5x = 1580
5x = 280
x = 56
Therefore, you will need 56 points each day to reach your goal.
if this helps you, it would help me a lot if you could mark this as brainliest :)
How can I turn a mixed fraction into a whole number?
Answer: Lets do 2 1/7
Step-by-step explanation: first you will start off by turning it to an improper fraction.
you multiply the denominator with the whole number (2x7) which you get 14 then add the numrinator with the number you got from multiplying (14+1= 15 then you get 15/7
Then after that divide the fraction 15/7 and you get 2 with a remander of 1
Here is a website you can use for fractions into whole numbers-https://www.cuemath.com
Select the two answers that describe the unit rate at which he walks.
1.5 seconds per meter
90 meters per second
30 meters every second
1.5 meters per second
1 meters every second
30 seconds per meter
The unit rate at which Darrell walks is 1.5 meters per second.
What is the unit rate?
A ratio that compares two amounts of DIFFERENT types of UNITS is called a rate. When a rate is expressed as a fraction, the denominator is 1 unit. Divide the numerator and denominator of the rate by the denominator to represent a rate as a unit rate.
Here, we have
Given
Darrell is walking for a distance of 90 meters in time 60 seconds.
We have to find the unit rate at which he walks.
To find out the unit rate we must divide the distance traveled by Darrell by the time taken to travel that distance.
The unit rate is given by :
Unit rate = Distance traveled in meters / Time taken in seconds
Unit rate = 90 meters / 60 seconds
Unit rate = 1.5 meters per second.
Hence, the unit rate at which Darrell walks is 1.5 meters per second.
In 60 seconds, Darrell walks 90 meters. Select the two answers that describe the unit rate at which he walks.
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Sarah is setting up a garden plot in the shape of a right triangle. One leg off the triangle will be 7 feet longer than the other and the hypotenuse will be 1 foot longer than the longest leg. Find the length of each side of the garden plot. As a part of your work, include a sketch with the sides labeled. Show work algebraically.
The smallest leg of the triangular garden is 5 feet while the biggest leg is 12 feet.
What is a triangle?The three-sided shape known as a triangle is sometimes used to allude to it.
The area of a triangle is defined as (1/2) base height, and the sum of all three angles within a triangle will be 180°.
As the given triangular garden has been drawn below,
By Pythagoras' theorem,
x² + (x + 7)² = (x + 8)²
x² + x² + 49 + 14x = x² + 64 + 16x
x² - 2x - 15 = 0
x² - 5x + 3x - 15 = 0
x(x - 5) + 3(x - 5) = 0
(x + 3)(x - 5) = 0
x = -3,5
Since length can never be negative thus x = 5.
The smallest leg = 5 feet
Biggest leg = 5 + 7 = 12 feet
Hence "The triangular garden's smallest leg is 5 feet long, while its longest leg is 12 feet".
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solve the inequality 3|2x - 4| > 6 graphically. Write the solution in interval notation
Answer:
Step-by-step explanation:
To solve this inequality graphically, we need to find the values of x that make the inequality true. We can start by looking at the absolute value expression on its own.
The absolute value of a number is always non-negative, so we can split the inequality into two cases: when the expression inside the absolute value is positive, and when it is negative.
For the first case, we have:
3|2x - 4| > 6
2x - 4 > 0
x > 2
For the second case, we have:
3|2x - 4| > 6
2x - 4 < 0
x < 2
So, the solution to the inequality is the union of these two cases: x > 2 or x < 2. In interval notation, this is written as (-infinity, 2) U (2, infinity).
Answer:
(-∞, 1) ∪ (3, ∞)
Step-by-step explanation:
You want a graphical solution to 3|2x -4| > 6.
GraphThe attached graph is of the expression ...
3|2x -4| -6
This is greater than 0 where x is a solution to the given inequality. It is greater than 0 for x < 1 or for 3 < x. In interval notation, the solution is ...
(-∞, 1) ∪ (3, ∞)
What rigid motion maps the solid-line figure onto the dotted-line figure?
A reflection
B. rotation
C. translation
Answer:
A. Reflection
feet is given by h
Layla launches a toy rocket from a platform. The height of the rocket in
-16t² + 136t + 72 where t represents the time
in seconds after launch. How many seconds have gone by when the
rocket is at its highest point?
Answer:
=
seconds
Submit Answer
Answer:
The time when the rocket is at its highest point is 8.5 seconds.
Which answer choice best represents 3/15?
Select the Hint button to view a hint. You will get 14 points.
A: 5/6 5
B: 5/1 5
C: 6/1 5
D: 6/6 5
The equivalent fraction for the given fraction is 1/5.
What is an equivalent fraction?Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.
The given fraction is 3/15.
The equivalent fraction is 3/15 =1/5
Therefore, the equivalent fraction for the given fraction is 1/5.
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Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
1
x + 7 = 8
X=
Answer:
x = 1
Step-by-step explanation:
x + 7 = 8 ( isolate x by subtracting 7 from both sides )
x = 8 - 7 = 1
A bag contains 1 gold marbles, 6 silver marbles, and
28 black marbles. Someone offers to play this game:
You randomly select one marble from the bag. If it
is gold, you win $3. If it is silver, you win $2. If it is
black, you lose $1.
To calculate the expected value of playing this game, we need to multiply the value of each possible outcome by its probability of occurring and then add these values together. In this case, there is 1 gold marble, 6 silver marbles, and 28 black marbles in the bag, for a total of 35 marbles. So, the probability of selecting a gold marble is 1/35, the probability of selecting a silver marble is 6/35, and the probability of selecting a black marble is 28/35. The value of winning $3 if a gold marble is selected is $3 * (1/35) = $0.09. The value of winning $2 if a silver marble is selected is $2 * (6/35) = $0.34. And the value of losing $1 if a black marble is selected is -$1 * (28/35) = -$0.80. Adding these values together, we get $0.09 + $0.34 - $0.80 = -$0.37. Therefore, the expected value of playing this game is approximately -$0.37.
2. Which system has an infinite number of solutions?
a. x ÷ 2=y
4=2y - x
b. 2y ÷ 6 = 4x
-3 = y - 2x
c. y ÷ 3 = 2x
4x = 2y - 3
d. y = 2x - 5
-2 = y - 2x
A set of two or more linear equations involving the same set of variables make up a linear system of equations, which is the type of system of equations in question.
Substitution methodAnswer: d. y = 2x - 5; -2 = y - 2xy = 2x - 5 and -2 = y - 2x has an infinite number of solutions.This system can be written as y = 2x - 5 and -2 = y - 2x.Since they have the same equation, they have an infinite number of solutions.The equation y = 2x - 5 can be rearranged to x = (y + 5)/2, and when this is substituted into -2 = y - 2x, the equation becomes -2 = y - 2(y +5)/2, simplifying to 0 = 5y + 10.This equation has an infinite number of solutions, since any value of y will satisfy the equation.For example, if y = -2, then x = 0; and if y = 6, then x = 4. All real numbers satisfy the equation, so the system has an infinite number of solutions.To learn more about infinite number of solutions refer to:
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4. Suppose a firm’s short-run total cost curve is given by TC = 6Q2 + 5Q + 10
a) Derive the ATC, AVC, AFC, and MC functions (8 pts)
b) How many units will the firm supply if market price is 29 ? (2 pts)
c) How much is TR? How much is the profit? (4 pts)
The value of ATC, AFC, TVC if TC = 6Q² + 5Q + 10, are 6Q + 5 + 10/Q, 5 + 6Q, 5Q + 6Q² respectively.
What is ATC?Average total cost (ATC) is calculated by dividing the entire cost by the total amount of output produced. The additional cost incurred by creating one more unit of output is known as marginal cost (MC).
Given:
TC = 6Q² + 5Q + 10,
Calculate the value of AFC as shown below,
AFC = 10 / Q
Calculate the value of TVC as shown below,
TVC = TC - TFC
TVC = 5Q + 6Q²
Calculate the value of AFC as shown below,
AFC = TVC / Q
AFC = 5Q + 6Q² / Q
AFC = 5 + 6Q
Calculate the value of ATC as shown below,
ATC = TC / Q
ATC = 6Q² + 5Q + 10 / Q
ATC = 6Q + 5 + 10/Q
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how many solutions are there for linear equations? what are they and how can you tell?
Answer:
Step-by-step explanation: There are three possible solutions for a linear equation: no solution, one unique solution, and infinitely many solutions.
A linear equation is an algebraic equation in which the highest exponent of the variables is 1. For example, 2x + 3 = 5 is a linear equation because the highest exponent of the variable x is 1.
If a linear equation has no solutions, this means that the equation is contradictory and there is no possible value of the variable that can make the equation true. For example, the equation 2x + 3 = 5 has no solutions because it is already true for all possible values of x.
If a linear equation has a unique solution, this means that there is only one possible value of the variable that can make the equation true. For example, the equation 2x + 3 = 5 has a unique solution because there is only one value of x that can make the equation true (in this case, x = 1).
If a linear equation has infinitely many solutions, this means that there are an infinite number of possible values of the variable that can make the equation true. This typically happens when the equation has the form of 0 = 0, which is always true for any value of the variable. For example, the equation 0 = 0 has infinitely many solutions because it is true for all possible values of x.
In general, you can tell whether a linear equation has no solutions, a unique solution, or infinitely many solutions by solving the equation. Solving a linear equation involves isolating the variable on one side of the equation and then using algebraic techniques to find its value. If you are able to find a unique value for the variable, then the equation has a unique solution. If you are unable to find a unique value for the variable, then the equation either has no solutions or infinitely many solutions.
Write a rule that would dilate a figure from the origin by a scale factor of 4.* 1 point
Your answer
Write the coordinates of (-2, 8) after it is dilated from the origin by a scale
factor of 1/2.
(-2,8)
(2,8)
O (1.4)
O (4,-1)
Write the coordinates of the point (2, 3) after is has been reflected across
the y-axis.
O (2,3)
O (-2,3)
O (3,2)
(3, 3)
*1 point
Your answer
* 1 point
State the scale factor to dilation from the origin point A (4, 3) to point A' (12, * 1 point
9).
The rule of dilation is (4x, 4y)
The coordinates of the image is (-1, 4) The coordinates of the image is (-2, 3) The scale factor is 3The rule of dilationFrom the question, we have the following parameters that can be used in our computation:
Scale factor = 4
This means that
Image = point * scale factor
So, we have
Image = (x, y) * 4
Evaluate
Image = (4x, 4y)
The coordinates of the imageHere, we have
Point = (-2, 8)
Scale factor = 1/2
So, we have
Image = (-2, 8) * 1/2
Image = (-1, 4)
The coordinates of the imageHere, we have
Point = (2, 3)
Transformation = reflected across the y-axis.
So, we have
Image = (-x, y)
Image = (-2, 3)
The scale factorHere, we have
A (4, 3) to point A' (12, 9)
The scale factor is
Scale factor = A'/A
So, we have
Scale factor = (12, 9)/(4, 3)
Evaluate
Scale factor = 3
Hence, the scale factor is 3
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If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle, then are the triangles congruent?
The triangles are considered to be congruent if one right triangle's hypotenuse and another right triangle's hypotenuse are equal.
Given, assuming that the hypotenuse of one right triangle is equivalent to the hypotenuse of another right triangle, then the triangles are harmonious.
The given statement must be verified as true or false by us.
According to the RHS congruence theorem, two right-angled triangles are congruent if the hypotenuse and side of one triangle are equal to the hypotenuse and side of another.
The hypotenuse and the side of the triangle that corresponds to it must be equal according to the RHS rule.
The hypotenuses of the two triangles are equal, per the question.
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One tablecloth 48 inches wide & 72 inches long. Want 2nd tablecloth 30 inches wide how long should it be
The length (in inches) of the second tablecloth is 43.75 inches
How to determine the length of the second tablecloth?From the question, we have the following parameters that can be used in our computation:
Width = 48 inches. and Length = 72 inches ⇒ Small tablecloth
Width = 30 inches. and Length = ?? inches ⇒ Large tablecloth
Represent the unknown length with x
So, we have
Width = 48 inches. and Length = 72 inches ⇒ Small tablecloth
Width = 30 inches. and Length = x inches ⇒ Large tablecloth
This shows a direct variation
So, we cross multiply the equation
x * 48 = 70 * 30
So, we have
x = 70 * 30/48
Evaluate
x = 43.75
Hence, the length is 43.75 inches
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Could I get some help with this? Thanks! Here’s the question to go along with it.
For each diagram, calculate the value of x. Show your work and include an explanation of what you used (definitions and theorems) to solve the problem. If not possible, state why.
Based on the two (2) parallel lines m||n, the value of x is equal to 4.
What is the vertical angles theorem?The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
In Geometry, when two (2) parallel lines are cut by a transversal, the pair of vertically opposite angles that are formed would always be equal to each other. In this context, we have the following;
m∠2 = m∠3
7x - 3 = x + 21
7x - x = 21 + 3
6x = 24
x = 24/6
x = 4.
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i will compare the calculated r-value against a critical value to deduce whether or not the value is statistically significant enough to act as a model for the entire world population.?
There is insufficient evidence to conclude that there is a significant linear relationship between
x and y because the correlation coefficient is not significantly different from zero.
The correlation coefficient, r, tells us about the strength and direction of the linear relationship between x and y.
However, the reliability of the linear model also depends on how many observed data points are in the sample.
We need to look at both the value of the correlation coefficient r and the sample size n, together.
We perform a hypothesis test of the “significance of the correlation coefficient” to decide whether the linear relationship in the sample data is strong enough to use to model the relationship in the population.
The sample data are used to compute r, the correlation coefficient for the sample. If we had data for the entire population, we could find the population correlation coefficient. But because we have only have sample data, we cannot calculate the population correlation coefficient. The sample correlation coefficient, r, is our estimate of the unknown population correlation coefficient.
The symbol for the population correlation coefficient is ρ, the Greek letter “rho.”
The hypothesis test lets us decide whether the value of the population correlation coefficient
ρ is “close to zero” or “significantly different from zero”. We decide this based on the sample correlation coefficient r and the sample size n.
If the test concludes that the correlation coefficient is significantly different from zero, we say that the correlation coefficient is “significant.”
There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero. What the conclusion means: There is a significant linear relationship between x and y. We can use the regression line to model the linear relationship between x and y in the population.
If the test concludes that the correlation coefficient is not significantly different from zero (it is close to zero), we say that correlation coefficient is “not significant.”
“There is insufficient evidence to conclude that there is a significant linear relationship between
x and y because the correlation coefficient is not significantly different from zero.” What the conclusion means: There is not a significant linear relationship between x and y. Therefore, we CANNOT use the regression line to model a linear relationship between x and y in the population.
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We must consider the sample size n together with the correlation coefficient r's value.
To determine whether the linear relationship in the sample data is strong enough to utilize to model the relationship in the population, we conduct a hypothesis test of the "significance of the correlation coefficient."
The correlation coefficient for the sample, r, is calculated using the sample data. The population correlation coefficient could be discovered if we had data for the entire population. However, we are unable to determine the population correlation coefficient because we only have sample data. Our best guess for the unknown population correlation coefficient is the sample correlation coefficient, or r.
The Greek letter "rho" serves as the sign for the population correlation coefficient.
is "near zero" or "quite different from zero." Based on the sample correlation coefficient r and the sample size n, we make this determination.
We refer to the correlation coefficient as "significant" if the test results show that it differs considerably from zero.
The fact that the correlation coefficient differs sufficiently from zero is sufficient evidence that x and y are meaningfully related linearly. The result indicates that there is a significant linear relationship between x and y. The regression line can be used to model the population's linear relationship between x and y.
Because the correlation coefficient does not deviate considerably from zero, x and y. What the conclusion says is that x and y do not have a meaningful linear connection.
Ability Test-C
The length and wide of rectangular box is 16cm and 12cm respectively. How many cubical packets is each of 64cm³ can be placed on the floor? If 3 layers of such boxes are placed on the top what is the volume of the rectangular box?
Note that to achieve a volume of 64cm³, the height of the cuboidal packet will equal 0.33cm²; If three layers of such are stacked on each other the total volume gained is: 192cm³.
What is the volume of a cuboid?The volume of a cuboid is given as L x B x H.
Where L = Lenght
B = Breath (or Width); and
H = Height.
To solve this problem, we need to first find the height of the box.
Since the volume of a Cuboid is given as L x B X H,
and we have
L = 16 and
B = 12, and
V= 64cm³
Then the expression for getting H will evolve from:
64 = 16 x 12 x H
64 = 192 x H
H = 64/192
H = 0.33cm
If three layers are placed on top of the volume amounts to:
64 x 3 = 192cm³
As a result, it is reasonable to declare that the height of the cuboidal packet will equal 0.33cm² to derive a volume of 64cm³; if three layers of such are piled on top of each other, the total volume acquired is: 192cm³.
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Damian works after school. Each day he earns a set amount, plus an hourly wage. The function f(x)=12 x+10 models the amount he earns each day for working x hours. How much does Damian earn on Friday if he works for 2.75 hours?
$=________
The amount Damian earns on Friday if he works for 2.75 hours is $43
How to determine the amount Damian earns on Friday if he works for 2.75 hours?From the question, we have the following parameters that can be used in our computation:
f(x) = 12x + 10
For working for 2.75 hours, the value of x is
x = 2.75
Substitute x = 2.75 in the equation f(x) = 12x + 10
So, we have the following representation
f(2.75) = 12 x (2.75) + 10
Evaluate the sum of products
f(2.75) = 43
hence, the earnings is $43
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