The inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x
What is a function?A relation is a function if it has only One y-value for each x-value.
Let us consider the function f(x)=(x-3)²
Where x belongs to [1, 2]
f(x)=x²+9-6x
y=x²+9-6x
Interchange the variables.
x=y²+9-6y
y=3+√18+x
y=3-√18+x
Relace y with f⁻¹(x)
f⁻¹(x)=3+√18+x, 3-√18+x
Hence, the inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x
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If 4√5 = √n, the value of n is
A. 10
B. 20
C. 80
D. 100
we are given a classifier that performs classification on r 2 (the space of data points with 2 features (x1, x2)) with the following decision rule: h(x1, x2)
The decision rule given is x1 + x3 – 10 ≥ 0, which can be rearranged to x1 + x3 ≥ 10. This forms a line in the R2 space, and any point on or above this line will be classified as 1, while any point below this line will be classified as 0.
To draw the decision boundary, we can plot the line x1 + x3 = 10 on a graph with the x1 and x3 axes. The region above the line, where x1 + x3 ≥ 10, would be shaded to indicate that it is where the classifier predicts 1.
It is important to note that the classifier predicts 1 if x1 + x3 – 10 ≥ 0, but in the explanation above I have used x1 + x3 = 10 to draw the decision boundary, this is because x1 + x3 – 10 ≥ 0 is equivalent to x1 + x3 ≥ 10.
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solve: a + 1/10 = 5/10.
Answer:
5/10 - 1/10 = 4/10
a = 4/10
4/10 + 1/10 = 5/10
Step-by-step explanation:
Hope it helps! =D
problem 1. create two vectors named v and w with the following contents: v : 21,10,32,2,-3,4,5,6,7,4,-22 w : -18,72,11,-9,10,2,34,-5,18,9,2 a) print the length of the vectors b) print all elements of the vectors c) print elements at indices 3 through 7. d) print the sum of the elements in each vector. e) find the mean of each vector. (use r's mean() function) f) sort the vectors in descending order and then print. g) add vectors v and w. h) multiply vectors v and w. i) in vector v select all elements that are greater than zero. j) in vector w select all elements that are less than zero. k) multiply each element of vector v by 6. and then print. l) find maximum and minimum of each vector. m) in each vector, replace all negative values with the average of all numbers in the vector.
Vector v and w have lengths of 11 and contain elements of 21, 10, 32, 2, -3, 4, 5, 6, 7, 4, -22 and -18, 72, 11, -9, 10, 2, 34, -5, 18, 9, 2 respectively. The addition, multiplication, and sorting of both vectors were calculated, as well as the means, maximums, and minimums.
a) The lengths of the vectors v and w are both 11.
b) Vector v contains the elements 21, 10, 32, 2, -3, 4, 5, 6, 7, 4, -22 and vector w contains the elements -18, 72, 11, -9, 10, 2, 34, -5, 18, 9, 2.
c) Elements 3 through 7 of vector v are 2, -3, 4, 5, 6 and elements 3 through 7 of vector w are 10, 2, 34, -5, 18.
d) The sum of the elements in vector v is 60 and the sum of the elements in vector w is 91.
e) The mean of vector v is 5.454545454545455 and the mean of vector w is 8.272727272727273.
f) Vector v is sorted in descending order as 32, 21, 10, 7, 6, 5, 4, 4, 2, -3, -22 and vector w is sorted in descending order as 72, 34, 18, 11, 10, 9, 2, 2, -9, -5.
g) The addition of vectors v and w is 53, 82, 28, 2, 7, 13, 6, 8, -7, 4, -20.
h) The multiplication of vectors v and w is -378, 720, 352, -18.
i) Elements in vector v that are greater than zero are 21, 10, 32, 2, 4, 5, 6, 7, 4.
j) Elements in vector w that are less than zero are -18, -9, -5.
k) Vector v multiplied by 6 is 126, 60, 192, 12, -18, 24, 30, 36, 42, 24, -132.
l) The maximum of vector v is 32 and the minimum of vector v is -22. The maximum of vector w is 72 and the minimum of vector w is -9.
m) In vector v, all negative values are replaced with the average of all numbers in the vector, which is 5.454545454545455. In vector w, all negative values are replaced with the average of all numbers in the vector, which is 8.272727272727273.
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Every person has blood type O, A, B, or AB. A random group of people are blood-typed, and the results are shown in the table. A 2-column table with 4 rows is shown. The first column is labeled Blood Type with entries O, A, B, AB. The second column is labeled Number of People with entries 22, 20, 6, 2. Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .
The probabilities for each type of blood are given as follows:
Type B: 12%.Type AB: 4%.Type B or Type AB: 16%.How to obtain the probabilities?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
The total number of people is given as follows:
22 + 20 + 6 + 2 = 50.
6 people have type B, hence the probability is given as follows:
6/50 = 0.12 = 12%.
2 people have type AB, hence the probability is given as follows:
2/50 = 0.04 = 4%.
8 people have either type B or type AB, hence the probability is given as follows:
8/50 = 0.16 = 16%.
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What is the best name for this shape? Use the drop-down menus to explain your answer. 55° 125° 125° 55° Click the arrows to choose an answer from each menu. The shape has Choose... It has Choose.... It has Choose... The best name for this shape is Choose... angles that are acute and equal. angles that are obtuse and equal. angles that are right angles.
The best name for this shape is rectangle. There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle.
Four names for rectangles: what are they?Parallelograms, quadrilaterals, and polygons are some other names for rectangles that we use. This is so that it is clear that a rectangle meets the criteria for each of these other forms, as shown by its definition.There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle, hence the answer is that every rectangle is a parallelogram. Thus, it conforms to all of a parallelogram's characteristics.There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle, hence the answer is that every rectangle is a parallelogram.Parallelograms, quadrilaterals, and polygons are some other names for rectangles that we use.To learn more about rectangle refer to:
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How many pounds of chamomile tea that costs $18.10 per pound must be mixed with 12 lb of orange tea that costs
$ 12.22 per pound to make a mixture that costs $14.74 per pound?
lb
9 pounds of Chamomile tea needed to make a mixture that costs $14.74 per pound
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
let:
x pounds of Chamomile tea needed
Therefore,
18.10X + 12.22(12) = 14.74(12 + x)
18.10X + 146.64 = 176.88 + 14.74x
3.36X = 30.24
X = 9 pounds
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Complete the following table.
Population Growth Rate, k Doubling Time, T Country A 1.3% per year
Country B. 30 years
Population Growth Rate, k Doubling Time,
T
Country A
1.3% per year
years
Country B [% per year
30 years
(Round doubling time to the nearest whole number and round growth rate to the nearest tenth.)
The numbers that correctly complete this table are 53.83 years and 2.12%
How to calculate the doubling time using the population growth?The formula that can be used is:
Doubling time = 70 (constant)/ population growth
Doubling time =70 / 1.3
Doubling time = 53.84 years
How to calculate the population growth using the doubling time?The same formula can be applied:
33 = 70 (constant)/ population growth
population growth = 70 /33
population growth = 2.12 %
Based on this, the correct numbers to complete the table are 53.83 years and 2.12%.
Note: Here is the missing table:
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Write and solve a proportion for the following problem.
In a recent survey for the student council, Dominique found that 150 students
out of a total of 800 students on campus did not like soda. If half of the student
body was going to attend a dance, how many students could she expect would
want soda?
The students expected to like soda are 324
How to determine the number of studentsfrom the question, we have the following parameters that can be used in our computation:
150 students out of a total of 800 students on campus did not like soda.
This means that
650 students out of a total of 800 students on campus like soda.
i.e. 800 - 150 = 650
When half of the students are considered, we have
Soda = 650/2
Evaluate
Soda = 325
Hence, the number of students is 325
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What is the value of the expression
10/12 + 3/7
Answer:
= 53/42
Step-by-step explanation:
10/12 is equivalent to: 70/84
3/7 is equivalnt to: 36/84
Then:
10/12 + 3/7 = 70/84 + 36/84
= (70 + 36) / 84
= 106 / 84
= 53 / 42
Refer to the following distribution of commissions:Monthly Commissions Class Frequencies$600 up to $800 3800 up to 1,000 71,000 up to 1,200 111,200 up to 1,400 121,400 up to 1,600 401,600 up to 1,800 241,800 up to 2,000 92,000 up to 2,200 4For the preceding distribution, what is the midpoint of the class with the greatest frequency?O 1,500O 1,700O The midpoint cannot be determined.O 1,400
From the given table the greatest frequency is 40,
midpoint of greatest frequency =$2100.
Relative frequency is also referred to as the empirical probability, which is calculated by the division of each frequency by the total number of frequency in the sample.
We can answer the question creating the following table:
Class Frequency Rel. Frequency
$600-$800 3 3/120=0.025
$800-$1000 7 7/120=0.059
$1000-$1200 11 11/120=0.092
$1200-$1400 22 22/120=0.183
$1400-$1600 40 40/120=0.333
$1600-$1800 24 24/120=0.2
$1800-$2000 9 9/120=0.075
$2000-$2200 4 4/120=0.033
Total 120 1
From the above table the greatest frequency is 40,
midpoint of greatest frequency =$2100.
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What are the coordinates of the point on the directed line segment from (−10,−10) to ( − 4 , 2 ) that partitions the segment into a ratio of 5 to 1?
The required point that divides the line into 5:1 is given by (-5,0)
What is the section formula?Let M(x, y) be the point which divides line segment PQ internally in the ratio m : n. PA, MN and QR are drawn perpendicular to x- axis. PS and MB are drawn parallel to x – axis. This is known as section formula.
Given here: A line segment with end points (−10,−10) to ( − 4 , 2 )
Now the coordinates of the point that divides a line in the ratio m:n is given by
x= mx₂+nx₁ /m+n
y=my₂+ny₁/m+n
Thus the co-ordinates are x=5×-4+1×-10 / 5+1
=-30/6
= -5
And y= 5×2+1×-10 / 6
=0
Hence, The required point that divides the line into 5:1 is given by (-5,0)
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Determine whether the statement below is true or false. Justify the answer. Elementary row operations on an augmented matrix never change the solution set of the associated linear system. A. The statement is true. Each elementary row operation replaces a system with an equivalent system B. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, replacing one row by the sum of itself and a multiple of another row can change the solution set of that system. C. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, scaling a row by a nonzero constant can change the solution set of that system. D. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found.
Elementary row operations are always applied to an augmented matrix after the solution has been found. So the option D is correct.
Elementary row operations:
1. It is possible to convert a system of linear equations into an equivalent system, or into a new system of equations that has the same solutions as the original system, using these straightforward techniques.
2. In order to convert a matrix to row echelon form, Gaussian elimination is used.
3. Simple row operations on an augmented matrix never alter the underlying linear system's solution set.
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Help with this equation
Translations between points B and B' and points S and S' are result of using translation vector T(x, y) = (- 3, - 1).
How to determine the translation formula behind two-point transformation
In this problem we find the case of two points being translated by rigid transformation formula. Translations are defined by following equations:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original point.P'(x, y) - Resulting point.T(x, y) - Translation vector.First, derive translation vector from translation formula:
T(x, y) = B'(x, y) - B(x, y)
T(x, y) = (- 9, - 2) - (- 6, - 1)
T(x, y) = (- 3, - 1)
Second, check that point S' is the image of point S:
S'(x, y) = S(x, y) + T(x, y)
S'(x, y) = (5, 1) + (- 3, - 1)
S'(x, y) = (2, 0)
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When an economy produces a good where the marginal benefit equals the marginal cost it is
At that level of output and price, profit is maximized when marginal revenue and the marginal cost of production are equal:
MR = *TR/*Q
MC = *C/*Q
Eq. = MR = MC
where, MR = Marginal Revenue
MC = Marginal Cost
* = Change in
TR = Total Revenue
Q = Quantity
C = Cost
The marginal revenue rule states that by selecting the amount at which marginal revenue equals marginal cost, we can maximize the net benefit of any action. The activity's net benefit is maximum at this amount.
The corporation eventually reaches the point at which manufacturing any more units will raise the cost of production per unit, which is known as its optimum production level.
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X
%
60°
4
Z
30%
Y
Given right triangle XYZ, what is the value of tan(Y)?
02/0
O
O
O
3
√3
2
O2√3
3
The value of tan(Y) = 0.75.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and with the trigonometric functions that describe those relationships.
Since triangle XYZ is a right triangle, we can use the trigonometric ratios of sine, cosine, and tangent to find the value of tan(Y). We can use the Pythagorean theorem to find the lengths of the sides XZ and YZ.
XZ = √(X^2 + Z^2) = √(4^2 + 3^2) = 5
YZ = XZ * sin(Y) = 5 * sin(Y)
Since we know the value of XZ and YZ, we can use the tangent function to find the value of tan(Y):
tan(Y) = YZ / XZ = sin(Y) / cos(Y) = YZ / 5 = 3 / 4 = 0.75
So, the value of tan(Y) = 0.75.
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connsider the rectangle with a width of 18 in and a length of 39 in, write a ratio of the length to the width and simplify
Answer: 13:6
Ratio of length to width = 39:18
Divide both by 3 to simplify
13:6
Written as a simplified polynomial in standard form, what is the result when (x+5) 2 is subtracted from 1 1? Answer:
The expression for the simplified polynomial would be - x² - 10x - 24.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the polynomial ( x + 5 )² is subtracted from 1. The simplified polynomial can be written as:-
Polynomial = 1 - ( x + 5 )²
Polynomial = 1 - ( x² + 10x + 25 )
Polynomial = 1 - x² - 10x - 25
Polynomial = -x² - 10x - 24
Hence, the polynomial can be written as -x² - 10x - 24.
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How do you know when an expressionis in its simplest form?
Answer:
Uma expressão está e sua forma mais simples quando não há mais nenhuma simplificação possível. Isso significa que não há mais nenhum termo que possa ser combinado ou cancelado, e que todos os termos estão na sua forma mais simples. Além disso, todos os fatores e expoentes devem estar na sua forma mais simples.
-5x + -4 + 1 - 4x
show your work to combine "like terms"
Answer:
-9x + -3
Step-by-step explanation:
1. Primeiro, vamos penteinar SO prazoos que possuem um mesmamã variável, ou seja, -5x e -4x:
-5x - 4x
2. Agora, vamos penteinar SO prazoos que possuem o mesmo coeficiente, ou seja, 1 e -4:
-5x - 4x + 1 -
4 3. Por fim, vamos penteinar SO prazoos que possuem o mesmo coeficiente, ou seja, -4 e 1:
-5x - 4x + -4 + 1
What goes in the blank box?
On solving the linear equation y = 3/2x - 29, the missing value for x is obtained as 14.66.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The table shows the points (18,-2) and (16,-5).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[-5 - (-2)]/[16 - 18]
(-5 + 2)/(-2)
-3/-2
3/2
So, the slope point is obtained as m = 3/2.
The equation becomes - y = 3/2x + b
To find the value of b substitute the values of x and y in the equation -
-2 = 3/2(18) + b
-2 = 27 + b
b = -2 - 27
b = -29
So, the value for b is -29.
Now, the equation becomes -
y = 3/2x - 29
To find the missing value substitute the value of y = -7 in the equation -
-7 = 3/2x - 29
3/2x = -7 + 29
3/2x = 22
x = 22 × 2/3
x = 44/3
x = 14.66
Therefore, the value of x = 14.66.
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1. Which of the following could be used to find the value of z in the figure? 38° x ft 32 ft 52° 25 ft
Answer:
The value of z can be found using the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. In other words, if a, b, and c are the lengths of the sides of a triangle opposite angles A, B, and C, respectively, and A, B, and C are the angles opposite sides a, b, and c, respectively, then: a/sin(A) = b/sin(B) = c/sin(C). This can be used to solve for the unknown side length.
5% of batteries produced at a factory are defective. Use the binomial model to find the probability that 1 battery in a pack of 16 is defective.
The probability that 1 battery in a pack of 16 is defective is approximately 0.3706 or 37.06%.
How to evaluate using the binomial modelThe binomial model can be used to calculate the probability of a specific number of successful outcomes (in this case, defective batteries) in a fixed number of trials (in this case, 16 batteries) with a constant probability of success (in this case, 5%) for each trial.
The probability of 1 defective battery in a pack of 16 can be calculated using the formula:
P(X = 1) = (¹⁶C₁) × (0.05)¹ × (0.95)⁽¹⁶⁻¹⁾
where (¹⁶C₁) is the binomial coefficient, which is equal to 16.
So;
P(X = 1) = (¹⁶C₁) × (0.05)¹ × (0.95)⁽¹⁶⁻¹⁾
P(X = 1) = 16 × 0.05 × 0.95¹⁵
P(X = 1) = 0.3706
Therefore, the probability that 1 battery in a pack of 16 is defective is approximately 0.3706 or 37.06%.
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The number of papers ms. Motley grades increases exponentially as
time goes on. On the first day she grades 9 papers , on the second day she grades 27 papers and on the third day she grades 31 papers
How many will she grade in five days?
After many days will it take her to grade 6,000 papers?
The number of papers that Ms. Motley will grade in five days would be = 46 papers (approximately).
How to calculate the number of paper?The number of papers Ms. Motley graded in first day = 9 papers
The number of papers Ms. Motley graded in the second day = 27 papers
The number of papers Ms. Motley graded in the third day = 31 papers
The average number of she graded for the three days is calculated as follows;
9+27+31 = 67/3 = 27.3 papers.
If in 3 days = 27.3 papers
5. days = X papers
Make X papers the subject of formula;
X papers = 5× 27.3/3
= 136.5/3
= 45.5 papers
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two rooms in a tiny house share a wall the area of the living room is 54. The area of the bedroom is 42. the expression 54+42 represents the total area in square feet. Write and equivalent express to represent the total area as a product using the GCF as one of those factors
54+42=_(_+7)
If two rooms in a tiny house share a wall the area of the living room is 54. The expression to represent the total area as a product using the GCF as one of those factors is: 6×3+ 6× 8 and 6(3 + 8).
How to find the total area?Living room area = 54 square feet
Area of the bedroom = 42 square feet
Total area of the two rooms = 54 + 42
Total area of the two rooms = 66 square feet
So, the expressions that represent the total area of the two rooms is: 6×3+ 6× 8 and 6(3 + 8).
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Answer:
54+42=6(9+7)
Step-by-step explanation:
Find the smallest value of m such that the product of 189m is a perfect square
Answer: 7
Step-by-step explanation:
First, we need to prime factorize the number 189,
189 = 3 × 3 × 3 × 7 × m
From the factors we can see that there is no pair of same numbers for 7, so if we replace m with 7, we can get a perfect square.
Hence the answer is 7
rhombus is inscribed in rectangle as shown. segments and are parallel to . segments and are parallel to . if and what is the area of rectangle ?
The perimeter of the rectangle WXYZ is 96 cm.
Here we see that
WXYZ is a rectangle (given)
Therefore,
∠WZY = 90 = ∠WZS
Since JS is parallel to PZ and JP is parallel to SZ, we get
JPSZ as a rectangle. Similarly, PKWQ, SYMR, and XQRL are rectangles.
JS = PZ
or, JS = PW + WZ
or, JS = KQ + WZ
or, WZ = JS - KQ
or, WZ = 52 - 25
or, WZ = 27
The side of the rhombus PS is a diagonal of rectangle JSPZ
Therefore length of the diagonal PS = √(JP² + JS²)
= √(52² + 39²)
= 65 cm
Hence for PWKQ,
PK = √(PQ² - KQ²)
= √(65² - 25²)
= 60 cm
For triangles ΔPWQ and ΔSYR,
the corresponding sides are parallel to each other. Hence we can say that
PW/YR = WQ/SY = PQ/RS
Therefore,
60/SY = 65/65 [Since they are the sides of a rhombus]
or, SY = 60 cm
Now, SY = SZ + ZY
or, SY = JP + ZY [Opposite sides of a rectangle are equal]
or, ZY = 60 - 39
or, ZY = 21
Hence the perimeter of WXYZ
2(length + width)
= 2(27 + 21)
= 96 cm
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Complete Question
Rhombus PQRS is inscribed in a rectangle JKLM, as shown. Segments PZ and XR are parallel to JM. Segments QW and YS are parallel to JK. If JP = 39 cm, JS = 52 cm, and KQ = 25 cm, what is the perimeter of rectangle WXYZ?
PLEASE HELP ITS DUE TODAY AND WOULD GIVE A LOT OF POINTS IF SOMEONE SHOWS THE ANSWER ANY SPAM ANSWERS WILL BE REPORTED!
To find the slope of the line given the points (0,2) and (1,0), we can use the formula: m = (y2 - y1) / (x2 - x1).
m = (0 - 2) / (1 - 0) = -2
Using point-slope form, we can write the equation of the line as:
y - 2 = -2 (x - 0)
y = -2x + 2
To get the inequality we just need to change the equation to the inequality by replacing the equal sign with the inequality sign.
So the linear inequality for the points (0,2) and (1,0) is:
y >= -2x + 2
use the centroid therom and the fogure for exercises 5-8 QU RS and PT are medians of PQR rs = 21 VT=5 find each length
The length of RV is 14, SV is 7, TP is 15 and VP is 10. The solution has been obtained using centroid theorem.
What is centroid theorem?
According to the centroid theorem, the centroid of a triangle is located at a distance of 2/3 between the vertex and the midpoint of the sides.
In the given figure, V is the centroid of the triangle
The medians RS and PT intersect at V.
Now, since V divides each median in the ratio 2:1, therefore,
⇒VT = 1/3 of PT
⇒PT = 3*VT
Since, VT=5
⇒PT = 15 = TP
So, VP = PT - VT
⇒VP = 15-5
⇒VP = 10
Similarly,
⇒RV = 2/3 of RS
Since, RS = 21, therefore,
⇒RV = 2/3 of 21
⇒RV = 14
So, SV = RS-RV
⇒SV = 23-14
⇒SV = 7
Hence, the length of RV is 14, SV is 7, TP is 15 and VP is 10.
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The complete question is attached below
use the following equation to determine the ratio of the displacement thickness to the boundary layer thickness.
The formula the ratio of the displacement thickness to the boundary layer thickness is u = δ / 2
The term displacement thickness is defined as the distance by which the body surface should be shifted in order to compensate for the reduction in mass flow rate on account of boundary layer formation.
Here we need to find the way to determine the ratio of the displacement thickness to the boundary layer thickness.
As we all know that the boundary layer thickness. ideal fluid viscous force is neglected but in actual viscous stresses are prominent within the boundary layer.
AS we all also know that when fluid flows past a solid body the fluid particles adhere to the boundary and the condition of no-slip occurs.
Here the term non-slip conditions means the velocity of the fluid at body surface will be same as the velocity of body.
Then it can be calculated by using the following formula,
=> u = δ / 2
Complete Question:
Here by using the equation u/U = y/δ and to determine the ratio of the displacement thickness to the boundary layer thickness.
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