The expression that represents how much he will spend would be = y ( 5p + 1d)
How to derive the expression that shows how much he will spend?The amount of money that each pizza(p) is sold = $5 each.
The amount of money that each drink(d) is sold = $1.
The total money that Matthew may spend on the party is represented by = y.
Therefore the expression that will show how much he will spend would be = y ( 5p + 1d).
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Polygon ABCD is drawn with vertices A(−4, −4), B(−4, −6), C(−1, −6), D(−1, −4). Determine the image coordinates of C′ if the preimage is reflected across y = 4.
C′(−3, 6)
C′(−3, 14)
C′(−1, 6)
C′(−1, 14)
Answer:
(d) C'(-1, 14)
Step-by-step explanation:
You want the coordinates of C' after the point C(-1, -6) is reflected across the line y = 4.
ReflectionReflection across the horizontal line y=4 will not change the x-coordinate of the point, so C' has an x-coordinate of -1.
The point (-1, 4) on the line of reflection will be the midpoint of C and C', so we have ...
(C +C')/2 = (-1, 4)
C +C' = 2(-1, 4) = (-2, 8) . . . . .multiply by 2
C' = (-2, 8) -C
C' = (-2, 8) -(-1, -6) = (-1, 8+6)
C' = (-1, 14)
__
Additional comment
Effectively, the reflection across the line y=4 is the transformation ...
(x, y) ⇒ (x, 8 -y)
Answer:
C'(-1, -6).
Step-by-step explanation:
the reflection across y = 4 for point C(-1, -6).
When reflecting a point across a horizontal line like y = 4, the y-coordinate remains the same, and the x-coordinate is inverted with respect to the line of reflection.
For point C(-1, -6), the y-coordinate remains -6, and the x-coordinate is inverted across y = 4:
New x-coordinate = -1
So, the reflected image of point C across y = 4 is C'(-1, -6).
None of the provided options match this reflection, so it seems there might be an error in the given answer choices. The correct reflection of point C(-1, -6) across y = 4 is C'(-1, -6).
Calculate the slope based on the table below:
The slope of the points in this table is equal to 2.
How to calculate the slope based on the table?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following slope and data points on the line:
Points on x-axis = (-2, -1).Points on y-axis = (-3, -1).Substituting the given points into the slope formula, we have the following;
Slope, m = (-1 + 3)/(-1 + 2)
Slope, m = 2/1
Slope, m = 2.
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A textbook store sold a combined total of 251 biology and psychology textbooks in a week. The number of psychology textbooks sold was 61 less than the number of biology textbooks sold. How many textbooks of each type were sold? Number of biology textbooks sold Number of psychology textbooks sold:
The number of biology textbooks sold = 156
The number of psychology textbooks sold = 95
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Let x be the number of biology textbooks sold. Then, the number of psychology textbooks sold was x - 61.
The combined total of the two types of textbooks sold was 251, so we can write an equation:
x + (x - 61) = 251
Expanding the right side:
2x - 61 = 251
Adding 61 to both sides:
2x = 312
Dividing both sides by 2:
x = 156
the number of psychology textbooks sold = x - 61
= 156 - 61
= 95
So, 156 biology textbooks were sold and 95 psychology textbooks were sold.
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8. f(x) = -x^4 + 2x²-x-2
Domain:
Range:
Rel. Maximum(s):
Rel. Minimum(s):
End Behavior: As x→∞, f(x)→
As x→→→∞0. f(x)→
Inc. Intervals:
Dec. Intervals:
Domain is all real numbers and Range is all real numbers less than or equal to -2.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x) = -x⁴+ 2x²-x-2
Domain is all real numbers.
Range is all real numbers less than or equal to -2.
Relative Maximum is the function does not have any relative maximums.
Relative Minimum(s): The function does not have any relative minimums.
End Behavior as x approaches infinity, f(x) approaches negative infinity. This can be seen by observing that the leading term in f(x),
-x⁴ grows much faster than the other terms as x increases, so the overall value of f(x) becomes more and more negative as x approaches infinity.
Hence, Domain is all real numbers and Range is all real numbers less than or equal to -2.
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Sammie was babysitting and took the kids to McDonalds. She ordered 1 chicken sandwich for herself that cost $2.50 and 2 happy meals. If her total bill was $8.50, how much did each of the happy meals cost?
In investing $5,750 of a couple's money, a financial planner put some of it into a savings account paying 2% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 12% annual simple interest. The combined interest earned for the first year was $475. How much money was invested at each rate?
$2,250 was invested at 2% and the remaining $3,500 was invested at 12%. The combined interest earned amount for the first year was $475.
The financial planner invested $5,750 of the couple's money. Let x be the amount of money invested in the savings account paying 2% annual simple interest and y be the amount of money invested in the riskier mini-mall development plan paying 12% annual simple interest. Since the combined interest earned for the first year was $475, we can write the equation 2x + 12y = 475. Since the total amount of money invested was $5,750, we can add the equation x + y = 5,750 to our system of equations. Solving the system of equations yields x = 2,250 and y = 3,500. Thus, $2,250 was invested at 2% and the remaining $3,500 was invested at 12%. The combined interest earned for the first year was $475.
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There are 70 students in a speech contest yesterday 1/5 of them gave their speeches today 2/7 of the remaining students gave their speeches how many students still haven't got their speeches
Step-by-step explanation:
You would need to start by finding how many students is 1/5 of them
So to find this out you would take 70 and divided it by 5
So 70/5 = 14
Take 70 and subtract 14 to get 56
Next find what 1/7 is
So 56/7 = 8
But because it’s 2 sevenths take the 1/7 and multiply by 2
8 x 2 = 16
So
Take the 56 and subtract 16 to get 40
To find the fraction form it would be
40/70 students
Just simplify now
4/7
Step-by-step explanation:
day 1
70*1/5= 14
70-14 = 56
day 2
2/7 * 56= 16
16+14 = 30.
Remaining students = 70 - 30 = 40
WILL GIVE BRAINLIEST!! Give an example of a system of two linear equations in two variables with 0, 1, or infinitely many solutions. Explain how you can determine whether this system has 0, 1, or infinitely many solutions without graphing. What does this reveal about the relationship between the lines on the graph?
Write at least 150–300 words please
The solution of a system of equations can be determined by dividing the coefficients of variables.
What are system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Solution of system of equations :-
Let the two system of equations be
a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0
1) Unique solution or one solution :-
The solution of the system of equations will be unique when,
a₁ / a₂ ≠ b₁ / b₂
2) Infinite solutions :-
The solution of the system of equations will have infinitely many solutions when,
a₁ / a₂ = b₁ / b₂ = c₁ / c₂
3) No solution :-
The solution of the system of equations will have no solutions when,
a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂
Hence, the solution of a system of equations can be determined by dividing the coefficients of variables.
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Hi can somebody please explain the second question and how you got it?
Thank you in advance!
Nice work on getting part (a) correct.
The 261% falls in the "250-300%" range, so they pay 8.5% of their yearly income toward health insurance.
8.5% of $65,500 = 0.085*65500 = 5567.50
That represents the yearly contribution. Divide that by 12 to find the monthly contribution.
5567.50/12 = 463.95833 = 463.96 approximately
Then round to the nearest dollar to get 464
Answer to part (b) is 464A (4,0).B (1.5), and C(-3,-5) are three vertices of a parallelogram ABCD. What is the ordered pair for D, the fourth vertex of the parallelogram?
Answer: In a parallelogram, opposite sides are equal in length and parallel, so if we subtract the vectors AB and BC from each other, we will get the vector for CD.
Given A = (4,0), B = (1.5,0), and C = (-3,-5), we can calculate the vectors AB and BC as follows:
AB = B - A = (1.5, 0) - (4, 0) = (-2.5, 0)
BC = C - B = (-3, -5) - (1.5, 0) = (-4.5, -5)
Next, we subtract these vectors to find the vector for CD:
CD = BC - AB = (-4.5, -5) - (-2.5, 0) = (-2, -5)
Finally, we add the vector CD to vertex C to find vertex D:
D = C + CD = (-3, -5) + (-2, -5) = (-5, -10)
So, the ordered pair for vertex D is (-5, -10).
Step-by-step explanation:
A boat starts at point A. It travels a distance of 7 km on a bearing of 135° to point B. From B it
travels 12 km on a bearing of 250° to point C. Using a scale of 1 cm: 1 km, draw a diagram to
show these bearings and journeys.
The diagram that represent the distance and the journeys is added as an attachment
How to make the diagramFrom the question, we have the following parameters that can be used in our computation:
Initial point = ADistance of 7 km on a bearing of 135° to point B. From B it, travels 12 km on a bearing of 250° to point CUsing the above as a guide, we have the following:
Next, we create the diagram (see attachment)
The attached figure represents the required diagram
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why when i calculate the uncertainty of a group of data does my uncetinty max is not greater than the actual math
The calculation of uncertainty depends on various factors, including the method used, the distribution of the data, and the number of data points. In some cases, the calculated uncertainty may be lower than the actual deviation of the data, especially if the data is not normally distributed or if the number of data points is small.
Uncertainty Calculation ExplanationIt's also important to keep in mind that uncertainty is a measure of the spread of the data, not the absolute deviation from the mean. In other words, if the data is tightly clustered around the mean, the calculated uncertainty will be low, even if the maximum deviation from the mean is relatively high.
If you think your calculated uncertainty is not accurately representing the spread of your data, you may want to consider using a different method for calculating uncertainty, or checking the underlying assumptions of the method you are using to ensure that it is appropriate for your data set.
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The uncertainty of a group of data represents the range of possible values that the data could reasonably have and is not expected to exceed the actual mathematical value of the data.
The uncertainty of a group of data is determined by factors such as measurement error and natural variability in the data & represents the range of possible values that the data could reasonably have. It is not expected to exceed the actual mathematical value of the data because the mathematical value represents the best estimate of the true value based on the available data.
The uncertainty is a measure of the limitations and potential sources of error in the data and helps to quantify the level of confidence that can be placed in the mathematical value.
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(50 points) if anyone sees this can they help me out?
Classify each statement about the function f(x)=2x3+3 as true or false.
A) The domain of the function is all real numbers.
B) The range of the function is (−∞, 2).
C) The function has two x-intercepts.
D) The center of symmetry is (0, 3).
The function f(x)=(x−2)3 is transformed to g(x)=(x+1)3−2.
What transformations are performed from function f to function g?
A) Function f is translated to the left 2 units.
B) Function f is translated to the left 3 units.
C) Function f is translated up 1 units.
D) Function f is translated down 2 units.
The function f(x)=x+4−−−−√3 is transformed to f(x)=x−1−−−−√3+3.
What transformations are performed from function f to function g?
A) Function f is translated to the right 3 units.
B) Function f is translated down 1 unit.
C) Function f is translated to the right 5 units.
D) Function f is translated up 3 units
Graph this polynomial function by using its intercepts.
f(x)=x3+3x2−4x−12
Plot the points that represent the x- intercepts and y-intercept on the graph
For the first part of the question, here is my classification of each statement:
A) True. The domain of the function is all real numbers.
B) False. The range of the function is all real numbers.
C) False. The function has no x-intercepts.
D) False. The center of symmetry is (0, 0).
For the second part, the transformations performed from function f to function g are:
A) Function f is translated to the left 3 units.
For the third part, the transformations performed from function f to function g are:
A) Function f is translated to the right 3 units.
B) Function f is translated up 3 units.
For the last part, you would need to find the x and y-intercepts of the polynomial function, and plot them on the graph. The x-intercepts can be found by setting x=0 in the equation and solving for y. The y-intercept can be found by setting y=0 and solving for x. Once the intercepts are found, you can plot them on the graph and connect them to form the graph of the polynomial function.
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
A is true because any real value of x will always produce a real value of yB is not true because it would contradict option A as explained previouslyC is not true because there is only one positive real root by Descartes' Rules of Signs, so there is only one real root and two imaginary rootsD is true because the function is odd, so it is held that f(-x) = -f(x) which is true for the given functionProblem 2
A is falseB is trueC is falseD is trueProblem 3
I cannot read your problem
Problem 4
[tex]f(x)=x^3+3x^2-4x-12\\0=x^3+3x^2-4x-12\\0=x^2(x+3)-4(x+3)\\0=(x^2-4)(x+3)\\0=(x-2)(x+2)(x+3)\\x_1=-3,\,x_2=-2,\,x_3=2[/tex]
Hence, the graph of the function would have points at (-3,0) (-2,0) and (2,0).
solve for x please and thank you
Step-by-step explanation:
this is the process and figure is cointerior
Aled and Gareth went on holiday to France.
The total cost of the holiday was £660.
• Aled’s mother paid 1/3 of the total cost.
• Aled and Gareth shared the remaining cost in the ratio 1:9 .
Calculate how much each person paid towards the cost of the holiday.
Answer:
Aled's mother paid £220.
Aled paid £44.
Gareth paid £396.
Step-by-step explanation:
1-(1/3)= 2/3 [fraction of amt. Aled and Gareth paid]
£660×(2/3)= £440 [amt. Aled and Gareth paid]
total units= 1+9
= 10
10 units= £440
1 unit= £440÷10
= £44
9 units= £44×9
= £396
£660×(1/3)= £220
Convert each rate to a unit rate. $4.25 for 64 fluid ounces 297 miles on 11 gallons of gas 124 feet in ten seconds
Answer:
$4.25 for 64 fluid ounces = $0.06640625 per fluid ounce
297 miles on 11 gallons of gas = 27 miles per gallon
124 feet in 10 seconds = 12.4 feet per second
Step-by-step explanation:
In the house, m∠ 1 = 45⁰. Find the measure of ∠ 2.
The value of measure ∠2 is, 135°.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In the house,
⇒ m ∠1 = 45°
We know that;
An exterior angle of a triangle is the sum of two opposite angle of a triangle.
Hence, We can formulate;
⇒ m ∠2 = m ∠1 + 90°
⇒ m ∠2 = 45° + 90°
⇒ m ∠2 = 135°
Thus, We get;
⇒ m ∠2 = 135°
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If you are on an island and there are already 375 inhabitants, and
for every footprint there is one eyeball, for every 32 pineapples there
are 40 ducks, for every 2 hands there is one inhabitant, for every
palm tree there are 12 pineapples, for every hand there is one
eyeball, for every lizard there are 4 footprints, for every 30 palm
trees there is one wave, for every 2 turtles there is 1 anchor, for
every palm tree there are 8 cacti, for every 120 anchors there is one
wave, for every 0.5 lizards there are 20 ducks, for every 20 turtles
there are 30 pineapples, for every 5 waves there are 3 canoes. How
many cacti are there on the island? Show your work!
Answer:
3000
Step-by-step explanation:
8 x 375 = 3000
Find the value of x.
5
4
3
12
X
a. 24
b. 36
c. 40
d. 45
By the 1/3 ratio, the value of x for the given figure is 33 units.
What is ratio?A ratio is an ordered pair of integers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio may be written as: 1: 3 (for every one boy, there are three girls). A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
Here,
4/12=3/x1=5/x2
1/3=3/x1
x1=9 units
1/3=5/x2
x2=15 units
12+15+9=33 units
The value of x for the given figure is 33 units by the ratio of 1/3.
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a) A wall has a length of 15m and breadth 7cm. The wall also has a square shaped window of length 4m. What is the cost of coloring the wall at Rs. 15 per meter square? 11
Using the formula of area of rectangle and square, the cost of painting is Rs. 1335
What is Area of RectangleThe area of a rectangle is equal to the product of its length and width. Mathematically, it can be represented as:
Area = Length × Width
In this problem, we need to substitute the values and calculate the area of the rectangular wall and then subtract the area of the window from it.
Area of rectangle = 15 * 7 = 105m²
The area of the window is calculate by using the formula of area of square.
Area of square = 4 * 4 = 16m²
Area of wall painted = 105 - 16 = 89m²
The cost of painting one square meter = Rs. 15
1m² = Rs. 15
89m² = x
x = 15 * 89
x = Rs. 1335
The cost is Rs. 1335
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Read the problem.
There are 60 students in the Geneva Middle School marching band. 20% of those
students play the trombone.
Shade the grid to show the percent of students in the marching band who play the trombone.
How many students in the marching band play the trombone? You can use your model to
help.
Answer: If 20% of the 60 students in the Geneva Middle School marching band play the trombone, then 60 * 20% = 12 students play the trombone. To shade the grid to show the percent, you can shade 20 out of 100 squares on the grid, or 1/5 of the total number of squares.
Step-by-step explanation:
A car is purchased under the following conditions. There is a 12% discount because of the Happy Easter Sale and another 5% discount because the purchaser is a valued customer. After these discounts the GST increases the price by 10%.
If the customer paid $14 000, what was the original purchase price of the car before any of the discounts and taxes?
Please explain. p.s I know that the answer is $15 224, but I still need an explanation
thanks. :)
The original purchase price of the car before any of the discounts and taxes is,
⇒ $15,024
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
There is a 12% discount because of the Happy Easter Sale and another 5% discount because the purchaser is a valued customer. After these discounts the GST increases the price by 10%.
Here, the customer paid $14 000.
Now, Let the original price = x
Hence, We can formulate;
⇒ x - (12% of x) - 5% of x + 10% of x = 14,000
⇒ x - 12x/100 - 5x/100 + 10x/100 = 14,000
⇒ (100x - 12x - 5x + 10x) / 100 = 14,000
⇒ 93x/100 = 14,000
⇒ 93x = 1400000
⇒ x = $15,024
Thus, The original purchase price of the car before any of the discounts and taxes is,
⇒ $15,024
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Simplify the expression 12p-8p,4p(3-2)
The value of the expression is A = 4p ( 3 - 2 ) = 4p
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
A = 12p - 8p be equation (1)
On simplifying the equation , we get
Taking the common factor as 4p in the expression , we get
A = 4p ( 3 - 2 )
On further simplification , we get
A = 4p
Therefore , the value of A is 4p
Hence , the expression simplified is 4p
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Find the perimeter and area of
The perimeter and area of the figure are 40.8 units and 110 square units respectively.
How to determine for the perimeter and area of the figure.From the question, we have the following parameters that can be used in our computation:
The figure
Using the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²],
where d is the distance between the points (x₁, y₁) and (x₂, y₂).
So, we have
AB = √[(8-8)² + (9-2)²] = 7
BC = √[(3-8)² + (13-9)²] = 6.4
CD = √[(-3-3)² + (9-13)²] = 7.2
DE = √[(-3+3)² + (9-13)²] = 9
EA = √[(8+3)² + (2-0)²] = 11.2
DB = √[(8+3)² + (9-9)²] = 11
Perimeter = AB + BC + CD + DE + EA.
Perimeter = 7 + 6.4 + 7.2 + 9 + 11.2
Perimeter = 40.8 units.
The figure is observed to be a trapezium ABDE and a triangle BCD.
Triangle BCD have base length DB = 11 with height from C to DB equal to 4.
Trapezium ABDE have sides AB and DE parallel to each other, and height DB = 11.
area of triangle BCD = 1/2 × 11 × 4 = 22 square units
area of trapezium ABDE = 1/2 × (7 + 9) × 11 = 88 square units
Total area ABCDE = 22 + 88
Total area = 110 square units
Hence, the perimeter and area of the figure are 40.8 units and 54 square units respectively.
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For Cynthia's fourth lab report, she calculated the ratio of velocities before and after the impact of a basketball bouncing on a court. This measurement is called the coefficient of restitution. She got the following four values.
0. 72
0. 75
0. 73
0. 76
The accepted value is 0. 77.
Cynthia's percent error was [blank]−−−−−−%.
Enter your answer as the number that correctly fills in the blank, rounded to two decimal places, like this: 42. 53
Cynthia's percent error in her fourth lab report was 4.38%.
Percent error is a measure of the accuracy of a numerical result, expressed as a percentage of the difference between the actual value and the calculated or measured value. It is calculated using the formula -
Percent Error = (|Actual value - Calculated value| / Actual value) * 100
In order to calculate Cynthia's percent error, we will use the formula:
Percent Error = (|Accepted Value - Measured Value| / Accepted Value) * 100%
For the mean of her four measured values (0.7325), the percent error would be:
Percent Error = (|0.77 - 0.7325| / 0.77) * 100% = 4.38%
So, the answer to be entered rounded to two decimal places is 4.38.
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Boden's account has a principal of $600 and a simple interest rate of 3.9%. Complete the number line. How much money will be in the
Answer:
Step-by-step explanation:
If Boden's account has a principal of $600 and a simple interest rate of 3.9%, then the interest he earns each year can be calculated as follows:
Simple Interest = Principal * Rate * Time = $600 * 3.9% * 1 = $23.40
So, after one year, the amount of money in the account will be $600 + $23.40 = $623.40
This process can be repeated for multiple years to find the amount of money in the account for a specific time period.
Given f(x)=4(x−2)^3+2, classify each statement about f^−1(x) as true or false.
Choose the answers which are correct or false.
1. The point of symmetry on f^−1(x) is (2,2).
2. The domain of f^−1(x) is (−∞,4).
3. The graphs of f^−1(x) and f(x) are reflections across the line y = x
4. f^−1(x) is not a function.
Answer:
1. True
2. False
3. True
4. False
Step-by-step explanation:
Given function:
[tex]f(x)=4(x-2)^3+2[/tex]
1. Point of SymmetryThe point-of-symmetry of a cubic graph is its point of inflection.
To find the x-value of the point of inflection of a cubic function, differentiate the function twice:
[tex]f'(x)=12(x-2)^2[/tex]
[tex]f''(x)=24(x-2)[/tex]
Set the second differentiated function to zero and solve for x:
[tex]\implies 24(x-2)=0[/tex]
[tex]\implies x-2=0[/tex]
[tex]\implies x=2[/tex]
Substitute the found value of x into the original function to find the y-value of the point of inflection:
[tex]\implies y=4(2-2)^3+2[/tex]
[tex]\implies y=4(0)^3+2[/tex]
[tex]\implies y=0+2[/tex]
[tex]\implies y=2[/tex]
Therefore, the point of symmetry of the cubic function is (2, 2).
The inverse of a cubic function its reflection in the line y = x.
As the point of symmetry is (2, 2), then its reflection in the line y = x is also (2, 2).
So the point of symmetry on f⁻¹(x) is (2, 2).
2. DomainThe given function has an unrestricted domain and range.
Domain of f(x): (-∞, ∞) → all real numbersRange of f(x): (-∞, ∞) → all real numbersThe domain of the inverse function is the range of the function.
The range of the inverse function is the domain of the function.
Therefore, as the domain and the range of the original function are unrestricted, so are the domain and range of the inverse function.
Domain of f⁻¹(x): (-∞, ∞) → all real numbersRange of f⁻¹(x): (-∞, ∞) → all real numbers3. Reflection across the line y = xThe inverse of a cubic function with an unrestricted domain is its reflection across the line y = x.
Therefore, the graphs of f⁻¹(x) and f(x) are reflections across the line y = x.
4. Inverse functionTo find the inverse of the given function, swap x and y:
[tex]\implies x=4(y-2)^3+2[/tex]
Rearrange to make y the subject:
[tex]\implies x-2=4(y-2)^3[/tex]
[tex]\implies \dfrac{x-2}{4}=(y-2)^3[/tex]
[tex]\implies \sqrt[3]{\dfrac{x-2}{4}}=y-2[/tex]
[tex]\implies y=\sqrt[3]{\dfrac{x-2}{4}}+2[/tex]
Replace y with f⁻¹(x):
[tex]\implies f^{-1}(x)=\sqrt[3]{\dfrac{x-2}{4}}+2[/tex]
As we have already established, the domain and range of the inverse function are unrestricted. As each x-value has only one y-value associated with it, f⁻¹(x) is a function.
The __ of the __ between the mean of the data set and the individual numbers in the data set
(mean absolute deviation)
The missing words in the statement are mean and absolute deviation respectively.
What is mean absolute deviation (MAD)The mean absolute deviation (MAD) is a measure of the average magnitude of the differences between individual values in a data set and the mean of the data set. It is calculated by first finding the absolute value of the difference between each data point and the mean, summing these absolute values, and then dividing by the number of data points. The resulting value provides a measure of the "typical" or average deviation of individual data points from the mean, without considering the direction of the deviation (positive or negative). The mean absolute deviation is often used as a summary statistic for data that is not normally distributed or when the variance or standard deviation are not meaningful.
The mean of the absolute deviation between the mean of the data set and the individual numbers in the data set is referred to as the mean absolute deviation (MAD).
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The difference of the data between the mean of the data set and individual numbers in the data set is called the deviation.
What is mean absolute deviation?Mean Absolute Deviation (MAD) is a measure of the average distance between the values in a dataset and the mean of that data set. It is calculated by finding the absolute difference between each value and the mean, summing them, and dividing by the total number of values. MAD is commonly used as a way to describe the variability or dispersion of a set of data.
In other words, the mean absolute deviation (MAD) is the average distance between each data value and the mean of the data set.
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There are 13
books on a shelf. 6 of these books are new.
(a) What is the ratio of used books to all books?
(b) What is the ratio of new books to used books?
The ratio of used books to all books is 7 : 13 and the ratio of new books to used books is 6 : 7
If there are 13 books on a shelf. 6 of these books are new.
(a) The ratio of used books to all books
Number of all books = 13
Number of used books = total no. of books - no. of new books
= 13 - 6
= 7
So, ratio of used books to all books
= no. of all books : no. of total books
= 7 : 13
Thus, the ratio of used books to all books = 7 : 13
(b) The ratio of new books to used books
Number of new books = 6
Number of used books = 7
So, the ratio of new books to used books
= no. of new books : no. of used books
= 6 : 7
Thus, the ratio of new books to used books = 6 : 7
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Express sin T as a fraction in simplest terms
Solving the provided question, we can say that by Pythagoras theorem VT² = 18² + 24² = 900 => VT = [tex]\sqrt{1900} = 30[/tex]
what is Pythagorean theorem?The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.
Pythagoras theorem
VT² = 18² + 24² = 900
VT = [tex]\sqrt{1900} = 30[/tex]
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