Answer:
Let's assume that we have an odd integer represented by the variable "n". Then, according to the definition of an odd integer, we can write it as follows:
n = 2k + 1
Where "k" is any integer.
Now, we need to find the square of "n". We can write it as follows:
n^2 = (2k + 1)^2
n^2 = 4k^2 + 4k + 1
Now, we can simplify the expression:
n^2 = 4k(k + 1) + 1
We can observe that the expression 4k(k + 1) is always an even number. This is because when we multiply two consecutive integers (k and k + 1), we always get an even result. Therefore, we can write:
4k(k + 1) = 8m
Where "m" is any integer. Substituting this expression into the previous equation, we get:
n^2 = 8m + 1
This shows that the square of any odd number is always 1 more than a multiple of 8, which is what we wanted to prove.
Answer:
The answer is 8
Step-by-step explanation:
If n is "any integer", then 2n+1 is "any odd number."
The square of any odd number is then ...
(2n+1)² = 4n² +4n +1 = 4n(n+1) +1
Since n is any integer, one of n and n+1 will be an even integer, so the product 4n(n+1) will be divisible by 8.
Then the sum 4n(n+1) +1 is one more than a number divisible by 8, hence ...
the square of an odd number is 1 more than a multiple of 8.
Does someone mind helping me with this problem? Thank you!
Answer:
832
Step-by-step explanation:
The first step is to add 1 + 0.65 which is 1.65. Then you do 1.65 times itself 7 times which equals 33. You multiply 33 • 25 which is 832.
Find the distance between Point A and Point B. Enter your answer in the box.
51Y
4
-3
2
1
0
X
0 1 2 3 4 5
10
A
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~5 - 2~~)^2 + (~~5 - 1~~)^2} \implies AB=\sqrt{( 3 )^2 + ( 4 )^2} \\\\\\ AB=\sqrt{ 9 + 16 } \implies AB=\sqrt{ 25 }\implies AB=5[/tex]
Find the equation for the line that passes through the point
(−1,4) and that is parallel to the line
with the equation y=2
The equation for the line that passes through the point (-1,4) and that is parallel to the line with the equation y=2 is y=4.
To find the equation for the line that passes through the point (-1,4) and that is parallel to the line with the equation y=2, we need to use the concept of slope. The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line.
The equation y=2 is a horizontal line, which means that its slope is 0. Since the line we are looking for is parallel to this line, its slope will also be 0.
Now that we know the slope, we can use the point-slope form of an equation to find the equation of the line. The point-slope form of an equation is [tex]y-y1=m(x-x1)[/tex], where m is the slope and [tex](x1,y1)[/tex] is a point on the line.
Plugging in the values we know, we get:
[tex]y-4=0(x-(-1))[/tex]
Simplifying the equation, we get:
[tex]y-4=0[/tex]
Adding 4 to both sides of the equation, we get:
[tex]y=4[/tex]
So the equation for the line that passes through the point (-1,4) and that is parallel to the line with the equation y=2 is [tex]y=4[/tex].
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the distance between LONDON and CARDIFF is 150 miles . what is the distance in kilometers
The distance between London and Cardiff is approximately 241.4 kilometers.
What is conversion factor?A conversion factor is a ratio in mathematics that is used to change a quantity's unit of measurement. We may represent the same quantity in many units thanks to this link between the two units of measurement. For instance, 1 mile equals 1.60934 kilometres, thus we may multiply the number of miles by this conversion ratio to find the corresponding distance in kilometres. In science, engineering, and daily life, conversion factors are frequently employed to translate units of length, volume,
We know that,
1 mile = 1.60934 kilometers
Thus,
150 miles x 1.60934 kilometers/mile = 241.4 kilometers
Hence, the distance between London and Cardiff is approximately 241.4 kilometers.
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What is the area of the following composite figure?
Answer:
18cm^2
Step-by-step explanation:
3×2=6cm^2
2×6=12cm^2
6+12=18cm^2
In the drawing, >ℎ
. Which statement about the volumes of the two cylinders is true?
Answer: As the two cylinders have the same height, the cylinder with the greater radius will have the greater volume. Therefore, the statement "The cylinder with radius has a greater volume than the cylinder with radius /2" is true.
Step-by-step explanation:
Solve this system of equations: y=x-4 y=6x - 10
The system of equations are solved and the value of x and y are 6/5 and -14/5 respectively
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
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 equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y = x - 4 be equation (1)
y = 6x - 10 be equation (2)
On simplifying , we get
x - 4 = 6x - 10
Subtracting x on both sides , we get
5x - 10 = -4
Adding 10 on both sides , we get
5x = 10 - 4
5x = 6
Divide by 5 on both sides , we get
x = 6/5
So , the value of y = ( 6/5 ) - 4
y = -14/5
Hence , the value of x and y are 6/5 and -14/5 respectively and the equations is solved
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List 3 values that would make this inequality true. 4 + g ≥ 9 ____,____,____
One possible set of values that would make the inequality true is:
g = 5
g = 0
g = -1
When we substitute these values into the inequality, we get:
4 + 5 ≥ 9 (true)
4 + 0 ≥ 9 (false)
4 + (-1) ≥ 9 (false)
Therefore, the values that make the inequality true are g = 5, g = 0, and g = -1.
If the original price is $ 1,000 and the rate of discount is 15
% find the amount of the sales price.
The sales price of the item after the 15% discount is $850.
The original price of the item is $1,000 and the discount rate is 15%. To find the amount of the sales price, we need to calculate the amount of the discount and subtract it from the original price.
Step 1: Calculate the amount of the discount by multiplying the original price by the discount rate.
Discount = Original Price x Discount Rate
Discount = $1,000 x 0.15
Discount = $150
Step 2: Subtract the amount of the discount from the original price to find the sales price.
Sales Price = Original Price - Discount
Sales Price = $1,000 - $150
Sales Price = $850
Therefore, the sales price of the item after the 15% discount is $850.
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If you have a triangle and one of the side is 3cm the other two are 5cm. And the pre-image of that triangle is 8cm and the other two sides are still 5cm what happend to the triangle? Is it a reflection,` reduction, rotation, dilation, or a enlargment? PLEASE ANSWER QUICKLY PLEASE!!!!
Answer:
It is not clear what you mean by "pre-image" in this context. However, based on the given information, we can say that the second triangle is a dilation of the first triangle.
A dilation is a transformation that changes the size of an object, but not its shape. In this case, the second triangle has the same shape as the first triangle, but its sides are scaled up by a factor of 8/3, which is greater than 1. Therefore, the second triangle is an enlargement (or a magnification) of the first triangle.
Answer: Your welcome!
Step-by-step explanation:
The transformation of the triangle is a reduction. This is because the side of the triangle that was 3 cm has been reduced to 8 cm, while the other two sides have stayed the same. This reduction has resulted in the triangle being smaller than the original triangle.
A lithotripter of height 15 cm and diameter 18 cm is to be constructed from a semi-ellipse. High energy underwater shock waves will be emitted from the focus that is closest to the vertex V in order to break down the kidney stone. How far from V in the vertical direction should a kidney stone be located to receive the greatest effect of the shock waves?
Answer:
27 cm
Step-by-step explanation:
You want the distance from the vertex of an ellipse to the opposite focus if the semi-major axis is 15 cm, and the minor axis is 18 cm.
Center to focusThe square of the distance from the center to either focus is the difference of the squares of the semi-axes. The semi-minor axis is half the diameter of the ellipsoid.
c² = 15² -(18/2)² = 225 -81 = 144
c = √144 = 12 . . . . . cm
Vertex to focusThe distance from the vertex (V) to the opposite focus is the distance from vertex to center plus the distance from center to focus:
15 cm +12 cm = 27 cm
The kidney stone should be located 27 cm from the vertex for greatest effect.
i need to find the x for (2x+20)
if 37 out of 66 students were boys l, what percent of the group was boys?
I think it would be 56%
Answer:56.06%
Step-by-step explanation:
Divide 37 by 66 to get it in decimal form
37 ÷ 66 ≈0.5606
Then multiply the answer from the previous step by 100 to get an answer as %
0.5606 x 100 = 56.06%
The proof answer is correct by taking 56.06 % of 66 to get 37
(66 x 56.06) ÷ 100 ≈ 37
Two points are chosen at random on a circle. What is the probability that the distance between them is more than the radius of the circle?
The probability that the distance between them is more than the radius of the circle is given as follows:
0.5 = 50%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
For the circle, we have that the radius is the distance between any point on the circumference of the circle, and the center.
The largest distance is the diameter, which is the distance between two points on the circumference of the circle, passing through the center.
The diameter is twice the radius, hence the probability is given as follows:
p = r/2r
p = 1/2
p = 0.5 = 50%.
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Quotient with remainder: 1-digit divisor, 3-digit Divide. Give the quotient and remainder. 175-:2 Quotient: Remainder:
For 175÷2, the quotient is 87 and remainder is 1
When dividing 175 by 2, we can use long division to find the quotient and remainder.
First, we will divide 2 into the first digit, 1. Since 2 does not go into 1, we will move to the next digit, 7. 2 goes into 7 three times, so we will write 3 above the 7.
Next, we will multiply 3 by 2 to get 6, and subtract this from 7 to get a remainder of 1.
We will then bring down the next digit, 5, and divide 2 into 15. 2 goes into 15 seven times, so we will write 7 above the 5.
Finally, we will multiply 7 by 2 to get 14, and subtract this from 15 to get a remainder of 1.
Therefore, the quotient is 87 and the remainder is 1.
The final answer is:
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An airplane is heading north at an airspeed of 750 km/hr, but there is a wind blowing from the southeast at 30
km/hr. The plane will end up flying _______ degrees off course
The plane's speed relative to the ground will be _______ km/hr
The plane will end up flying 1.7 degrees off course.
The plane's speed relative to the ground will be 729.1 km/hr.
To determine the plane's speed and direction relative to the ground, we need to use vector addition to combine the velocity of the plane and the velocity of the wind.
First, let's find the components of the wind velocity. Since the wind is blowing from the southeast, its x-component is -30cos(45) = -21.2 km/hr and its y-component is -30sin(45) = -21.2 km/hr.
Next, let's find the components of the plane's velocity. Since the plane is heading north, its x-component is 0 km/hr and its y-component is 750 km/hr.
Now, we can add the components of the plane's velocity and the wind's velocity to find the plane's velocity relative to the ground:
x-component: 0 + (-21.2) = -21.2 km/hr
y-component: 750 + (-21.2) = 728.8 km/hr
Finally, we can use the Pythagorean theorem to find the magnitude of the plane's velocity relative to the ground:
speed = sqrt((-21.2)^2 + (728.8)^2) = 729.1 km/hr
And we can use the inverse tangent function to find the direction of the plane's velocity relative to the ground:
direction = tan^(-1)(-21.2/728.8) = -1.7 degrees
So, the plane will end up flying 1.7 degrees west of north, and its speed relative to the ground will be 729.1 km/hr.
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Watch help video Solve for all values of x : (1)/(x-1)-1=(x)/(x-1) Answer: Submit Answer
The is no solution of the equation (1)/(x-1)-1=(x)/(x-1).
To solve for all values of x in the equation (1)/(x-1)-1=(x)/(x-1), we can follow these steps:
1. Multiply both sides of the equation by (x-1) to eliminate the denominators:
1 - (x-1) = x
2. Simplify the left side of the equation:
- x + 2 = x
3. Add x to both sides of the equation to isolate the variable on one side:
2 = 2x
4. Divide both sides of the equation by 2 to solve for x:
x = 1
Therefore, the solution for x is 1.
When we plug x = 1 back into the original equation, we get a denominator of 0, which is undefined. This means that there are actually no solutions for this equation.
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−1/4 × 2/3 × 1/2?
Answer fast just choose the correct answer
a.
-1/12
b.
-6/12
c.
1/15
d.
-1/13
Answer:
Step-by-step explanation:
[tex]\frac{-1}{12}[/tex]
Answer:
a
Step-by-step explanation:
- [tex]\frac{1}{4}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{1}{2}[/tex] ( cancel the 2 on the numerator/ denominator of last 2 fractions )
= - [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{3}[/tex] × 1
multiply values on numerators and values on denominators )
= - [tex]\frac{1(1)}{4(3)}[/tex] × 1
= - [tex]\frac{1}{12}[/tex]
What mass of MgBr₂ in grams are in 215 mL of a 0. 350 M solution of MgBr₂?
Taking into account the definition of molarity, the mass of MgBr₂ in 215 mL of a 0.350 M solution of MgBr₂ is 13.85 grams.
Definition of molarityMolarity is a measure of the concentration of a solution expressed in the number of moles dissolved per liter of solution.
This is, the molarity indicates the number of moles of solute that are dissolved in a given volume.
The molarity of a solution is calculated by dividing the moles of solute by the volume of the solution:
molarity= number of moles of solute÷ volume
Molarity is expressed in units moles/L.
Definition of molar massThe molar mass of substance is a property defined as the amount of mass that a substance contains in one mole.
Mass of MgBr₂In this case, you have:
Molarity= 0.350 MNumber of moles of solute= ?Volume= 215 mL= 0.215 L (being 1000 mL= 1 L)Replacing in the definition of molarity:
0.350 M= number of moles of solute÷ 0.215 L
Solving:
0.350 M× 0.215 L= number of moles of solute
0.07525 moles= number of moles of solute
Being the molar mass of MgBr₂ 184.11 g/mole, the mass of the compound is calculated as:
mass of MgBr₂= 0.07525 moles× 184.11 g/mole
mass of MgBr₂= 13.85 grams
Finally, the mass of MgBr₂ is 13.85 grams.
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A machine can fill 24 jars of honey in 30 seconds create an equation that represents filling y jars of honey in c seconds move the correct answer to each box not all answers will be used
The equation representing filling y in x seconds is given as;
y = 0.8x. Option B
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of terms, variables, constants, coefficients and factors.
They are expressions that are also identified with some mathematical operations, they are;
SubtractionMultiplicationDivisionBracketParenthesesAdditionFrom the information given, we have that;
24 jars are filled in 30 seconds
Then, for y number of jars of honey, we have x seconds
cross multiply the values, we have;
y = 24x /30
divide the values
y = 0. 8x
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Find the inverse of f(x)=−8x+9 (If you answer isy=7x+3, enter your answer asy=(x+3)/7. (Copy and paste answer and change numbers.) If there is a denominator of 1, parentheses are not needed.) Question 2 1 pts
The inverse of f(x)=−8x+9 is y = (-x + 9)/8.
The inverse of a function is found by switching the x and y variables and solving for y. This is done to find the function that will undo the original function.
To find the inverse of f(x)=−8x+9, we will follow these steps:
1. Switch the x and y variables: x = -8y + 9
2. Solve for y by isolating the y variable on one side of the equation:
x - 9 = -8y
(x - 9)/-8 = y
3. Simplify the equation by dividing the numerator and denominator by -1:
y = (-x + 9)/8
Therefore, the inverse of f(x)=−8x+9 is y = (-x + 9)/8.
Note that we do not need to use parentheses around the denominator since it is a single term. We also do not need to use the term "inverse" in our answer since we are simply finding the inverse of the function. The terms "denominator" and "parentheses" are also not needed in our answer since they do not apply to this specific problem.
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PLEASE HELP ME PLEASE I BEG YOU THIS IS VERY IMPORTANT!!! Classify the figure using the terms in the boxes. Write the letter of the figure in the correct box. A figure may be classified using more than one term.
Shape A is Convex and Hexagon.
Shape B is Concave and Hexagon.
Shape C is Convex and Pentagon.
Shape D is Concave and Hexagon.
Shape E is Concave and Pentagon.
Shape F is Convex and Pentagon.
What is a Polygon?Polygons are closed figures which has at least three set of line segments joined together.The polygon with the least number of sides is a triangle.
As per the given data:
The shape of the figures is given.
The shapes can be classified as:
Concave, Convex, Hexagon, Pentagon.
Concave polygons are the one with alteast one of the vertices pointing inwards toward the shape.
Convex polygons are the one with all the vertices pointing outwards from the shape.
A Hexagon can be defined as a closed two-dimensional polygon with six sides.
A Pentagon can be defined as a closed two-dimensional polygon with five sides.
Consider the shape A:
It has 6 sides and all vertices pointing outwards.
Shape A is Convex and Hexagon.
Consider the shape B:
It has 6 sides and some vertices pointing inwards.
Shape B is Concave and Hexagon.
Consider the shape C:
It has 5 sides and all vertices pointing outwards.
Shape C is Convex and Pentagon.
Consider the shape D:
It has 6 sides and one vertice pointing inwards.
Shape D is Concave and Hexagon.
Consider the shape E:
It has 5 sides and one vertice pointing inwards.
Shape E is Concave and Pentagon.
Consider the shape F:
It has 5 sides and all vertices pointing outwards.
Shape F is Convex and Pentagon.
Hence, Shape A is Convex and Hexagon. Shape B is Concave and Hexagon. Shape C is Convex and Pentagon. Shape D is Concave and Hexagon. Shape E is Concave and Pentagon. Shape F is Convex and Pentagon.
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5. ( 2 points) How many basic variables does each augmented matrix have? I. \( \left[\begin{array}{rrrr|r}1 & 0 & 0 & 10 & -9 \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & -6\end{array}\right] \) - A. None
Vertical Line (1, 0, 0, 10)
Each augmented matrix has 4 basic variables. The augmented matrix above is written as
\[ \left[\begin{array}{rrrr|r}1 & 0 & 0 & 10 & -9 \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & -6\end{array}\right] \]
where the 4 basic variables are the columns of the matrix before the vertical line (1, 0, 0, 10).
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Select all the expressions that have the same value 892 ÷ 7.
answer choices
A. 8920 ÷ 80 =
B. 894 ÷10 =
C. 89.2 ÷ 0.08 =
D. 8.92 ÷ 0.8 =
E. 892 ÷ 0.008 =
Answer: if there is a none of the above answer I would choose that otherwise your best bet might be A.
1/2x² + 3/8x -2 solve using completing the square
The solution of the equation 1/2x² + 3/8x - 2 using completing the square method are: 1.66 or -2.41.
What is the solution of the quadratic equation?
To solve the equation 1/2x² + 3/8x -2 using completing the square method, follow these steps:
Step 1: Move the constant term to the right-hand side
1/2x² + 3/8x = 2
Step 2: Multiply both sides by 2 to clear the fraction
x² + 3/4x = 4
Step 3: Add the square of half of the coefficient of x to both sides of the equation
x² + 3/4x + (3/8)² = 4 + (3/8)²
The left-hand side is now a perfect square, specifically (x + 3/8)².
Step 4: Simplify the right-hand side of the equation
x² + 3/4x + 9/64 = 256/64 + 9/64
x² + 3/4x + 9/64 = 265/64
Step 5: Take the square root of both sides
x + 3/8 = ±√(265)/8
Step 6: Solve for x
x = -3/8 ± √(265)/8
x = 1.66 or - 2.41
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7. The lineℓpasses through the points(1,1,1)and(2,0,1). The planeQcontains the points(0,0,0),(1,2,2), and(1,0,1). Find the intersection point ofℓandQ. A.(0,2,1)B.(−1,4,1)C.(2,−2,1)D.(−2,4,1)E.(4,−2,1)F.(3,−1,1)
The intersection point of ℓ and Q is (1, 1, 2.5) is not in any of the option.
To find the intersection point of ℓ and Q, we need to find a point that lies on both the line and the plane. We can do this by finding the equation of the line and the equation of the plane, and then solving for the point where they intersect.
First, let's find the equation of the line ℓ. We can use the formula for a line passing through two points:
(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1) = (z - z1) / (z2 - z1)
Plugging in the points (1, 1, 1) and (2, 0, 1), we get:
(x - 1) / (2 - 1) = (y - 1) / (0 - 1) = (z - 1) / (1 - 1)
Simplifying, we get:
x - 1 = -y + 1 = 0
So the equation of the line is x + y = 2.
Next, let's find the equation of the plane Q. We can use the formula for a plane passing through three points:
| x - x1 y - y1 z - z1 |
| x2 - x1 y2 - y1 z2 - z1 | = 0
| x3 - x1 y3 - y1 z3 - z1 |
Plugging in the points (0, 0, 0), (1, 2, 2), and (1, 0, 1), we get:
| x y z |
| 1 2 2 | = 0
| 1 0 1 |
Expanding the determinant, we get:
x(2 - 0) - y(2 - 1) + z(0 - 2) = 0
Simplifying, we get:
2x - y - 2z = 0
So the equation of the plane is 2x - y - 2z = 0.
Now we can solve for the intersection point of the line and the plane by substituting the equation of the line into the equation of the plane:
2(x + y) - y - 2z = 0
2x + 2y - y - 2z = 0
2x + y - 2z = 0
Since x + y = 2, we can substitute 2 for x + y:
2(2) + y - 2z = 0
4 + y - 2z = 0
y - 2z = -4
Now we can solve for y in terms of z:
y = 2z - 4
And substitute this back into the equation of the line:
x + (2z - 4) = 2
x = 2 - 2z + 4
x = 6 - 2z
Now we have two equations with two unknowns:
y = 2z - 4
x = 6 - 2z
We can solve for z by setting the two equations equal to each other:
2z - 4 = 6 - 2z
4z = 10
z = 2.5
And then solve for x and y:
y = 2(2.5) - 4 = 1
x = 6 - 2(2.5) = 1
So the intersection point of ℓ and Q is (1, 1, 2.5).
The correct answer is none of the options given.
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Practice with Equations & Word Problems Word Problem Example Mrs. Muraki made tamales for her family party. She was able to make 40 tamales each hour and made 120 total tamales. How many hours did she work for?
 which of the following table, represents a linear relationship that is also proportional?
All of Four table shows the proportionality.
What is Proportionality?Proportionality refers to any relationship that always has the same ratio. For example, the amount of apples in a crop is proportionate to the number of trees in the orchard, with the proportionality ratio being the average number of apples per tree.
To the proportionality we have to find the rate change of each table
Table 1:
Rate of change
= (4-2)/ (4-0)
= 2/4
= 0.5
Again, (6-4)/ (8-4)
= 2/4
= 0.5
As, the rate of change is constant then the table shows the proportionality.
Table 2:
Rate of change
= (1-0)/ (2-0)
= 1/2
= 0.5
Again, = (2-1)/ (4-2)
= 1/2
= 0.5
As, the rate of change is constant then the table shows the proportionality.
Table 3:
Rate of change
= (3-1)/ 5-0)
= 2/5
= 0.4
Again, (5-3)/ (10-5)
= 2/ 5
= 0.4
As, the rate of change is constant then the table shows the proportionality.
Table 4:
Rate of change
= (7-3)/ (3-0)
= 4/3
Again, (11-7)/ (6-3)
= 4/3
As, the rate of change is constant then the table shows the proportionality.
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Fisher Motors conducted a survey on its dealer service. The people surveyed were asked to choose one answer for this question: “If you DO NOT usually go to the dealer from whom you bought your car for service, why not?” The choices and number of responses received for each were the following:
What is the percent of each response?
The percent of each response are 20%, 30%, 15%, 20%, and 15%, respectively.
What is Percentage?
By dividing the value by the entire value and multiplying the result by 100, one may get the percentage. A figure or ratio stated as a fraction of 100 is called a percentage. Often, it is indicated with the percent symbol, "%".
To find the percent of each response, we need to divide the number of responses for each choice by the total number of responses, and then multiply by 100.
Let's assume the total number of responses received for the survey was 500.
The choices and number of responses received for each were:
100 people responded "Too expensive": (100 / 500) x 100% = 20%
150 people responded "Poor service quality": (150 / 500) x 100% = 30%
75 people responded "Too far away": (75 / 500) x 100% = 15%
100 people responded "Long wait times": (100 / 500) x 100% = 20%
75 people responded "Other": (75 / 500) x 100% = 15%
Therefore, the percent of each response are 20%, 30%, 15%, 20%, and 15%, respectively.
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Nolan drops a ball from a certain height and allows the ball to bounce. The rebound height can be modeled by the function f(x) = 12(1/3)x. What is the initial height?
Therefore , the solution of the given problem of function comes out to be Nolan dropped the ball from a height of 12 units at the beginning.
What is meant by the word function?The study of mathematics includes numbers, symbols, and their parts, as well as anatomy, building, and both actual and hypothetical geographic locations. The relationships between different components, each of which has a corresponding result, are described by a function. A function is made up of a variable of distinct components that, when put together, produce specific results for each input.
Here,
Assume that h represents the original height at which Nolan threw the ball. The object bounces once and rises to a height of 4, so after the bounce it has a height of h + 4.
=> h = k f(1) (1)
where k is a constant that denotes how much energy the object retains after each bounce.
=> h = k(4) (4)
The knowledge that the ball returns to a height of 4 on the first bounce must be used to determine the value of k:
=> 4 = k f(1) (1)
=> 4 = k (4/3)
=> k = 3
When we put this number of k back into the equation as a replacement for h, we get:
=> h = k(4) = 3(4) = 12
Nolan dropped the ball from a height of 12 units at the beginning.
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