Answer:
75%
Step-by-step explanation:
Starting value: 12
Final Value: 21
Subtract final value minus starting value
Divide that amount by the absolute value of the starting value
Multiply by 100 to get percent increase
If the percentage is negative, it means there was a decrease and not an increase.
solve my homework and your smart and the brainiest person i know
Answer:
How are we supposted to do your homework if we dont have a picture or explanation of it??
Step-by-step explanation:
(1 point) A circular sector has radius r = 5.1 and central angle θ = 145º. Determine: Arclength = _____
Area = ______
The arclength of the circular sector with radius r = 5.1 and central angle θ = 145º is 13.06. The area of the circular sector is 32.54.
The arclength and area of a circular sector can be calculated using the following formulas:
Arclength = (θ/360) * 2πr
Area = (θ/360) * πr²
Where θ is the central angle in degrees, r is the radius, and π is the constant pi.
Plugging in the given values for r and θ, we get:
Arclength = (145/360) * 2π(5.1) ≈ 12.90
Area = (145/360) * π(5.1)² ≈ 32.91
So, the arclength of the circular sector is approximately 12.90 units and the area is approximately 32.91 square units.
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Lowest common factors and highest common factors
The Lowest Common Factor (LCF) and Highest Common Factor (HCF) are concepts used in mathematics to find the factors that are common to two or more numbers.
The LCF is the smallest factor that two or more numbers have in common, while the HCF is the largest factor that two or more numbers have in common.
For example, consider the numbers 12 and 18--
The factors of 12 are 1, 2, 3, 4, 6, and 12.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
The common factors of 12 and 18 are 1, 2, 3, and 6.
Therefore, the LCF of 12 and 18 is 6, and the HCF of 12 and 18 is 3.
Note that the LCF and HCF are also called the Lowest Common Denominator (LCD) and Highest Common Factor (HCF) respectively.
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giving brainly
Based on the concept of the global conveyor belt, what happens to ocean water as it moves from Antarctica to the equator?
It transfers thermal energy to deeper layers of the ocean.
It becomes less dense and rises to the surface.
It transfers thermal energy to the area, warming the equatorial waters.
It becomes more dense and sinks to the ocean bottom.
Answer:
The answer to your problem is, B: It becomes less dense and rises to the surface
Step-by-step explanation:
Remember a conveyor belt is a system of oceans which can transports water and propel deep currents of water bodies across the world based on the differences in water densities.
The ocean water moves from the Antarctica to the equator the cold ocean water mixes within the warm ocean water at the equator or the middle, which makes the water less dense and rises up to the surface
Thus the answer to our problem is, B It becomes less dense and rises to the surface.
CL 7-121. Kelly started the proof below to show that if TC ~=TM and AT bisects cTM, then CA~=MA. Copy and complete her proof.
Using the statements given for congruency the proof is -
TC ≅ TM Given
AT bisects ∠CTM Given
∠ATC ≅ ∠ATM Definition of bisect
AT ≅ AT Reflexive property
Δ ATC ≅ Δ ATM SAS theorem
CA ≅ MA ≅ Δs → ≅ parts
What is congruency?
If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.
A diagram of a diamond ACTM is given.
The line segment TC is equal and congruent to line segment TM.
This statement is already given in the question.
The line segment AT bisects angle CTM.
This statement is already given in the question.
The angle ATC is equal and congruent to angle ATM.
This statement is the definition of bisect.
The line segment AT is equal and congruent to line segment AT.
This statement is true by the reflexive property of the triangles.
Triangle ATC is equal and congruent to triangle ATM.
This statement is true by Side-Angle-Side (SAS) theorem of the triangles.
The line segment CA is equal and congruent to line segment MA.
This statement is true as the triangles are congruent to each other and congruent triangles have congruent parts.
Therefore, the proof is complete.
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RATIONAL EXPRESSIONS Restriction on a variable in a denominator: Quadra Find all excluded values for the expression. That is, find all values of u for which the expression is und (u-7)/(u^(2)-14u+49) If there is more than one value, separate them with comma
The excluded values of u in the expression (u-7)/(u^2-14u+49) are 7.
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2x-4=8
-2х+4у=-8
How do I change these two equations into y=mx+b then find out if they have no solution, infinite solution or one solution? Thank you!
The equation is now in the form y=mx+b, where m is 2 and b is -4. The second equation is now in the form y=mx+b, where m is -0.5 and b is -2.
What is an equation?An equation is an expression that shows the relationship between two or more variables. It is made up of mathematical symbols and operators and is used to solve problems. Equations can be used to express a variety of relationships, such as addition, subtraction, multiplication, division, and more complex equations. They also help to identify patterns or trends in data or to forecast future values.
To change these equations into y=mx+b form, we must first rearrange the equations.
For the first equation, 2x-4=8, we can move the 4 to the other side of the equation, giving us 2x = 12. We can then divide both sides by 2, giving us x = 6. So the equation is now in the form y=mx+b, where m is 2 and b is -4.
For the second equation, -2x+4y=-8, we can move the -2x to the other side of the equation, giving us 4y=-8-2x. We can divide both sides by 4, giving us y=-2-0.5x. So the equation is now in the form y=mx+b, where m is -0.5 and b is -2.
Now that both equations are in y=mx+b form, we need to compare their m and b values to determine if there is one solution, no solution or infinite solutions. We can see that m for both equations is different, so this means that the two equations are not the same, and there is no solution. This means that the two equations have no solution.
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Camilla and Kennedy received 27 combined likes on their social media posts. Kennedy has 5 more likes than Camilla.
Using single variable equation, we can conclude that Camilla received 11 likes and Kennedy received 16 likes.
Let x be the number of likes Camilla received and x+5 be the number of likes Kennedy received. We can set up an equation to solve for x:
x + (x+5) = 27
Simplifying the equation:
2x + 5 = 27
Subtracting 5 from both sides:
2x = 22
Dividing both sides by 2:
x = 11
So Camilla received 11 likes and Kennedy received 11+5=16 likes.
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Of the following parent functions, which one has D = (XER) and R = ([-1, 1], 2 points YER) (in interval form)? (Select all that apply) *
linear
quadratic
exponential
reciprocal
absolute value
square root
sine
cosine
The correct answer is sine and cosine.
The parent functions that have D = (XER) and R = ([-1, 1], YER) (in interval form) are sine and cosine.
Both sine and cosine are periodic functions that oscillate between -1 and 1 on the y-axis, meaning that their range is [-1, 1]. They also have a domain of all real numbers (XER), as they can take on any value for x and still produce a valid output.
The other parent functions listed, such as linear, quadratic, exponential, reciprocal, absolute value, and square root, do not have the same domain and range as sine and cosine. For example, the quadratic function has a domain of all real numbers, but its range is limited to values greater than or equal to the vertex. The reciprocal function has a range of all real numbers except for 0, and its domain is also all real numbers except for 0.
Therefore, the correct answer is sine and cosine.
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HELP HELP HELP
a student divided 3p^4-8x^2-11x+1 by x-2 using LONG DIVISION. Where did they go wrong?
The polynomial equation is solved and the value of A is given by the long division A = 3x³ + 6x² + 4x - 3 - 5/( x -2 )
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the polynomial equation be represented as A
Now , let the first equation be p
p = 3x⁴ - 8x² - 11x + 1
Let the second equation be q
q = ( x - 2 )
And , the value of A = p/q
On simplifying , we get
A = ( 3x⁴ - 8x² - 11x + 1 ) / ( x - 2 )
From the long division of polynomials , we get
Step 1 :
A = 3x³ + [ ( 6x³ - 8x² - 11x + 1 ) / ( x - 2 ) ]
The student went wrong while multiplying the quotient 3x³ with the divisor -2 , it should have been 6x³ instead of 6x²
Step 2 :
A = 3x³ + 6x² + [ ( 4x² - 11x + 1 ) / ( x - 2 ) ]
Step 3 :
A = 3x³ + 6x² + 4x + [ ( -3x + 1 ) / ( x - 2 ) ]
Step 4 :
A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]
Therefor , the long division is solved , A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]
Hence , the polynomial is A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]
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Question 5(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
Coins are placed into a treasure chest, and each coin has a radius of 1.4 inches and a height of 0.0625 inches. If there are 230 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
0.38 in3
126.39 in3
353.88 in3
88.47 in3
The coins take up approximately 35.259 cubic inches of space inside the treasure chest.
What is Volume?Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.
Solution:
The volume of each coin is a cylinder with radius 1.4 inches and height 0.0625 inches. The volume V of one coin is given by:
V = πr²h
= 3.14 x 1.4² x 0.0625
= 0.1533 cubic inches (rounded to four decimal places)
Since there are 230 coins in the treasure chest, the total volume of the coins is:
Total volume = 230 x V = 230 x 0.1533 = 35.259 cubic inches (rounded to three decimal places)
Therefore, the coins take up approximately 35.259 cubic inches of space inside the treasure chest.
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Isaiahs weekly allowance was $70.00 . He received for each chore that he that he completed 1/8 pf his weekly allowance. Calculate isaiah's allowance for the week
Isaiah's allοwance fοr the week wοuld be $43.75.
What are fractiοns?In mathematics, a fractiοn represents a part οf a whοle οr a ratiο between twο quantities. It is written as a number οr expressiοn (the numeratοr) abοve a line and anοther number οr expressiοn (the denοminatοr) belοw the line, and is typically expressed as a/b.
The numeratοr represents the number οf equal parts being cοnsidered, while the denοminatοr represents the tοtal number οf equal parts that make up the whοle. Fοr example, the fractiοn 3/4 represents three οut οf fοur equal parts, οr three-quarters οf the whοle.
Fractiοns can be used tο express values between whοle numbers, and they can be used in οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. Fractiοns can alsο be cοnverted tο decimals οr percentages fοr ease οf cοmparisοn οr calculatiοn.
Cοmmοn types οf fractiοns include prοper fractiοns (where the numeratοr is less than the denοminatοr, such as 1/2), imprοper fractiοns (where the numeratοr is greater than οr equal tο the denοminatοr, such as 5/3), and mixed numbers (where the fractiοn is represented as a whοle number and a prοper fractiοn, such as 3 1/2).
Isaiah's allοwance fοr the week can be calculated by adding up the amοunt he earned fοr each chοre he cοmpleted. Since he earned 1/8 οf his weekly allοwance fοr each chοre, the amοunt he earned fοr a single chοre can be calculated as:
1/8 * $70.00 = $8.75
Therefοre, if Isaiah cοmpleted n chοres in a week, his tοtal earnings fοr the week wοuld be:
Tοtal earnings = n * $8.75
Fοr example, if he cοmpleted 5 chοres in a week, his tοtal earnings wοuld be:
Tοtal earnings = 5 * $8.75 = $43.75
Sο Isaiah's allοwance fοr the week wοuld be $43.75 if he cοmpleted 5 chοres. The amοunt οf his allοwance wοuld depend οn the number οf chοres he cοmpleted during the week.
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The angle of elevation from your hand to a kite is 65∘ and the distance from your hand to the kite is 287 feet. How high is the kite when your hand is 5 feet from the ground?
The height of the kite from the ground is 620.5 feet.
How to find the height of the kite?The angle of elevation from your hand to a kite is 65∘ and the distance from your hand to the kite is 287 feet.
Therefore, the height of the kite when your hand is 5 feet from the ground can be found as follows:
The situation forms a right angle triangle. Therefore, the height of the kite can be found using Pythagoras's theorem.
Hence,
tan 65 = opposite / adjacent
tan 65 = h / 287
cross multiply
h = 287 × tan 65
h = 615.473486186
Therefore,
height of the kite = 615.473486186 + 5
height of the kite = 620.5 feet
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if l || m, find the value of x
Answer:
I need a graph to answer this question
Step-by-step explanation:
find the values x and y given : m is parallel to n, angle 4= 6x-5, angle 10 = 5x + 8, angle 9 = 3y - 10
Answer:
Without a diagram or additional context, it's difficult to determine the values of x and y precisely. However, we can use the given information to set up some equations and solve for x and y in terms of each other.
First, since m is parallel to n, we know that angles 4 and 9 are alternate interior angles and angles 10 and 9 are corresponding angles. Therefore:
angle 4 = angle 9 (alternate interior angles)
angle 9 + angle 10 = 180 degrees (interior angles on the same side of the transversal)
angle 4 + angle 10 = 180 degrees (corresponding angles)
Substituting the given expressions for each angle, we have:
6x - 5 = 3y - 10
5x + 8 + 3y - 10 = 180
6x - 5 + 5x + 8 = 180
Simplifying the second equation by combining like terms, we get:
8x + 3y - 2 = 0
We can now solve for one variable in terms of the other. From the first equation, we have:
6x = 3y + 5
x = (3/2)y + (5/6)
Substituting this expression for x into the third equation, we get:
6((3/2)y + (5/6)) - 5 + 5((3/2)y + (5/6)) + 8 = 180
Simplifying and solving for y, we get:
y = 29/9
Substituting this value for y back into the expression we found for x, we get:
x = (3/2)(29/9) + (5/6) = 59/6
Therefore, the values of x and y that satisfy the given conditions are x = 59/6 and y = 29/9.
how do you solve 83 = y/5?
Answer: 415
83 = [tex]\frac{y}{5}[/tex]
83(5) = y
415 = y
Answer:
y = 415
Step-by-step explanation:
83 = y/5
83 x 5 = y
415 = y
Mika can eat 21 hot dogs in 6 minutes. She wants to know how many minutes it would tske her to eat 35 hot dogs if she can keep up the same pace. How many minutes would Mika need to eat 35 hot dogs?
We can use a proportion to solve the problem:
Let x be the number of minutes it would take Mika to eat 35 hot dogs
Then we can set up the proportion:
21 hot dogs / 6 minutes = 35 hot dogs / x minutes
To solve for x, we can cross-multiply:
21 hot dogs * x minutes = 6 minutes * 35 hot dogs
21x = 210
x = 10
Therefore, it would take Mika 10 minutes to eat 35 hot dogs if she can keep up the same pace.
Hi Please help due today ty!
Answer:
24 antelopes, 36 monkeys
Step-by-step explanation:
6 : 7 means that for every 6 antelopes, there are 7 monkeys, so
a/6 = m/7 (1)
where a is the number of antelopes, m is the number of monkeys (before the 8 were born).
After 8 monkeys are born, the new ratio becomes:
a/2 = (m+8)/3 (2)
You can solve a and m for these two equations:
Rewrite (1) as 7a = 6m (cross product)
Rewrite (2) as 3a = 2m+16 (cross product)
=> 2m = 3a-16 (isolate 2m)
=> 6m = 9a-48 (multiply by 3)
Plug in (2) into (1):
7a = 9a-48 =>
-2a = -48
a = 24 antelopes
m = (a/6)*7 = 28 monkeys BEFORE the 8 newborns, so now there are
24 antelopes and 28+8=36 monkeys
polygon use the angles to find h
The value of h is 18.
What is Polygons?Polygons are closed figures which has at least three set of line segments joined together.
The polygon with least number of sides is triangle.
Given a polygon and all its interior angles are given.
Sum of the interior angles of a polygon is given by,
Sum = (n - 2) 180°, where n is the number of sides of the polygon.
Here, n = 7
6h + 132 + 146 + (6h + 10) + (6h + 10) + 146 + 132 = (7 - 2) 180
18h + 576 = 5 × 180
18h = 900 - 576
18h = 324
h = 18
Hence the value of h is 18.
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Write the decimal number that has the specified place values. 4 ones, 0 hundredths, 6 tens, 9 hundreds, 8 tenths
The answer of decimal number that has the specified place values is 964.8.
To write the decimal number, we need to understand the place value of each digit.
The place values are as follows:
- 9 hundreds = 900
- 6 tens = 60
- 4 ones = 4
- 8 tenths = 0.8
- 0 hundredths = 0.00
To write the decimal number, we add the place values together:
900 + 60 + 4 + 0.8 + 0.00 = 964.8
Therefore, the decimal number that has the specified place values is 964.8.
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Nadia has log that are 3 m long how many logs does she need when the river is 12 m
Answer:
Step-by-step explanation:4. 12 divided by 3 is 4 so 4
1. Which of the following are the possible
lengths to complete a triangle with
side lengths of 14 in. and 8 in.?
A greater than 6 in., less than 20 in.
B greater than 6 in., less than 22 in.
Ogreater than 4 in., less than 20 in.
D greater than 4 in., less than 22 in
Answer: A
Step-by-step explanation:
To form a triangle, the two smaller lengths must be bigger than the largest side(Hopotonuse or sum, cant spell)
8 + 7 = 15
15>14
The possible lengths to complete a triangle with side lengths of 14 in. and 8 in. are 6 < x < 22.
What is Triangle Inequality?The triangle inequality theorem states that for any given triangle, the total of the two sides is always greater than the sum of the three sides. The Triangle is a polygon with three line segments as its boundaries. That is the tiniest polygon imaginable.
We have side lengths of 14 in. and 8 in.
Using Triangle inequality we know that the sum of two is greater than the third side.
Also, the range for third side is
14 + 8 = 22 inch
14 - 8 = 6 inch
So, the third side lies between as 6 < x < 22.
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If i is the imaginary unit, the expression i^(8)+i^(9)+i^(10)+i^(11) is equivalent to
The expression [tex]i^{8}+i^{9}+i^{10}+i^{11}[/tex] is equivalent to 0 + i - 1 - i, which simplifies to -1.
Using the property of imaginary unit i, we know that [tex]i^2=-1[/tex]. Therefore, i^8 can be written as [tex](i^2)^4[/tex] which is equal to[tex]1^4 = 1[/tex]. Similarly, i^9 can be written as i^8i which is equivalent to i, i^10 can be written as [tex]i^8i^2[/tex] which simplifies to -1, and i^11 can be written as i^8*i^3 which simplifies to -i. Thus, [tex]i^{8}+i^{9}+i^{10}+i^{11}[/tex] can be simplified to 1 + i - 1 - i, which equals 0 - 0i. Finally, 0 - 0i can be expressed as -1 + 0i, which means that the expression is equivalent to -1.
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Find the following for the function f(x)=3x^2+3x−3 (a) f(0) (b) f(3) (c) f(−3) (d) f(−x) (e) −f(x) (f) f(x+2) (g) f(3x) (h) f(x+h)
a) f(0) = 3(0)^2 + 3(0) - 3 = -3
b) f(3) = 3(3)^2 + 3(3) - 3 = 33
c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
e)−f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3
We are asked to find the following for the function f(x)=3x^2+3x−3: (a) f(0) (b) f(3) (c) f(−3) (d) f(−x) (e) −f(x) (f) f(x+2) (g) f(3x) (h) f(x+h)
(a) f(0) = 3(0)^2 + 3(0) - 3 = -3
(b) f(3) = 3(3)^2 + 3(3) - 3 = 33
(c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
(d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
(e) −f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
(f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
(g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
(h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3
I hope this helps! Let me know if you have any further questions.
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Find the inverse function of f(x) = - Vx+1+6. Specify the domain for f^-1(x) f^-1(x)__________ Domain of f-1(x) using interval notation:________
The inverse function of f(x) = - Vx+1+6 is f^-1(x) = - Vx-7. The domain of f^-1(x) is [-1, ∞), or in interval notation, [-1, ∞).
The inverse function of f(x) = -√x+1 + 6 can be found by following the steps below:
1. Swap the x and y values, so y = -√x+1 + 6 becomes x = -√y+1 + 6
2. Solve for y by isolating it on one side of the equation:
x - 6 = -√y+1
(x - 6)² = y+1
y = (x - 6)² - 1
3. The inverse function is therefore f^-1(x) = (x - 6)² - 1
The domain of f^-1(x) can be found by considering the restrictions on the original function. Since the original function has a square root, the value inside the square root must be greater than or equal to zero. This means that:
x+1 ≥ 0
x ≥ -1
So, the inverse function of f(x) = -√x+1 + 6 is f^-1(x) = (x - 6)² - 1, and the domain of f^-1(x) is [-1, ∞).
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p(x)=7x^(3)-10x^(2)+8x-5 According to the rational zero theorem, the possible zeros for p(x) are +-((1,5)/(1,7))
Yes, according to the Rational Zero Theorem, the possible zeros of the polynomial p(x) are +-(1,5/1,7). The only factorization that works in this case is p/q = 1.5/1.7, which yields the zeros +-(1,5/1,7).
The Rational Zero Theorem states that any rational zero of a polynomial can be expressed in the form p/q, where p and q are factors of the constant term (an) of the polynomial and q does not divide a0.
In our case, the constant term of p(x) is a3=5, so the possible rational zeros are of the form p/q, where p is a factor of 5, and q is a factor of 8.
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Mrs.. Tomas says that the number of the students in her class this week has no variability. Her student, Peirce, says that it does not have a variability because someone could be absent. Do you agree or disagree? Why or why not?
Agree with the statement " it does have a variability because someone could be absent".
What is meant by variability?
The degree to which the data points in a statistical distribution or data collection deviate from the average value and from one another is virtually by definition the measure of variability. A mean is a common tool used by analysts to describe the centre of a population or a process. Although the mean is important, variability elicits stronger reactions in people. Values in a dataset are more consistently distributed when a distribution has less variability. The data points are more diverse and extreme values are more probable when the variability is bigger. As a result, comprehension of variability aids in understanding the possibility of uncommon events.
Peirce says that there is variability because someone could be absent.
I agree with Peirce's statement.
Because when someone is absent, the number of students changes and there is variability.
Now the range of variability changes with how many students are absent.
If there are only a few students absent, then the variability can be low.' But if there are many students absent in the class, then will be a higher variability.
Therefore there can be variability when someone could be absent.
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4 Let f(x)= with f(0) = 2 and f(1) = 9. Find a and k and then evaluate the function f(2). a +5ekx a = (Type an exact answer in simplified form. Use integers or fractions for any numbers in the express
The value of the function at x = 2 is 11.8.
We can start by using the given values for f(0) and f(1) to create a system of equations and solve for a and k.
f(0) = 2 = a + 5ek(0)
f(1) = 9 = a + 5ek(1)
Simplifying the first equation gives us a = 2 - 5ek(0) = 2. Substituting this value of a into the second equation gives us:
9 = 2 + 5ek
7 = 5ek
k = ln(7/5)/e
Now we can substitute this value of k back into the first equation to find a:
2 = a + 5e^(ln(7/5)/e)(0)
2 = a
So, our function is f(x) = 2 + 5e^(ln(7/5)/e)x.
To evaluate f(2), we simply plug in x = 2:
f(2) = 2 + 5e^(ln(7/5)/e)(2)
f(2) = 2 + 5(7/5)^2
f(2) = 2 + 5(49/25)
f(2) = 2 + 9.8
f(2) = 11.8
Therefore, the value of the function at x = 2 is 11.8.
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Which variable makes most sense to use as the explanatory variable and which should be used as the response variable and which is not a variable?
1. Cold 2. Health Condition 3. Placebo 4.Vitamin C 5. Treatment
The explanatory variable is the one that is thought to influence or cause changes in the response variable. In this case, the most logical explanatory variable would be the treatment (5).
Since it is the factor that is being manipulated to potentially affect the other variables. The response variable would be the health condition (2), An explanatory variable, is also known as an independent variable or predictor variable since it is the outcome that is being measured in response to the treatment. The other variables, cold (1), placebo (3), and vitamin C (4), are not considered variables in this case because they are not being manipulated or measured.
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Karabo and John are at the same stop alongside a highway.Karabo started driving along highway at a constant speed of 80km/h.An hour later, John started driving along the same highway in the same direction as Karabo at a constant speed of 100km/h.How long will it take for John to catch up with Karabo?
Therefore, it will take John 4 hours to catch up with Karabo.
What is equation?In mathematics, an equation is a statement that shows the equality of two expressions. An equation usually contains one or more variables (represented by letters) and a mathematical expression on each side of an equals sign (=). The value of the variable(s) that make the equation true are called the solutions or roots of the equation. Equations are used in many areas of mathematics and science to describe relationships between variables or to solve problems. They are an important tool for modeling real-world phenomena and making predictions about how systems will behave under different conditions.
Here,
Let's call the time it takes for John to catch up with Karabo "t" (measured in hours).
In the hour that Karabo has been driving, she has covered a distance of:
distance = speed x time = 80 km/h x 1 h = 80 km
When John starts driving, he is behind Karabo by this distance. However, he is driving faster, so he will catch up to her eventually.
We can set up an equation to represent this situation:
distance covered by John = distance covered by Karabo
We know that John's distance is equal to his speed multiplied by the time he drives:
distance covered by John = 100 km/h x t
We also know that Karabo's distance is equal to the distance she covered in the hour before John started driving, plus the distance she covers during the time it takes John to catch up with her:
distance covered by Karabo = 80 km + 80 km/h x t
Now we can set these two expressions equal to each other and solve for t:
100 km/h x t = 80 km + 80 km/h x t
100 km/h x t - 80 km/h x t = 80 km
20 km/h x t = 80 km
t = 80 km / 20 km/h
t = 4 hours
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