Matrix A belongs to the permutation and Markov classes.
This is the case for matrix A, as it has one 1 in each row and column and 0s everywhere else. Matrix A is also a Markov matrix, which means that all the entries are non-negative and the sum of each row is equal to 1. This can be seen by summing each row, which yields 1+0+0 = 1, 0+1+0 = 1, and 1+0+0 = 1.
Matrix B belongs to the orthogonal, projection, and diagonalizable classes. Matrix B is orthogonal, which means that it is a square matrix whose columns and rows are orthonormal unit vectors (i.e. the dot product of any two columns or rows is 0). This is the case for matrix B, as the dot product of any two columns or rows yields 0. Matrix B is also a projection matrix, which means that it is a square matrix whose columns are all of unit length (i.e. the dot product of any two columns or rows is 1). This can be seen by taking the dot product of any two columns or rows, which yields 1. Finally, matrix B is diagonalizable, which means that it can be transformed into a diagonal matrix using a similarity transformation. This can be seen by calculating the eigenvalues and eigenvectors of matrix B, which yields the same diagonal matrix.
To learn more about Matrix here:
brainly.com/question/29132693
#SPJ4
You want the banner you are creating form one piece of cloth to be a golden rectangle. The clothe will be cut from a bolt that is 54 in wide. What are the dimensions
of the largest banner that you can make? Golden Ratio 1.618/1
54 in by
The dimensions of the largest banner are 54 inches by 87.372 inches.
What is a golden rectangle?A dividable rectangle is referred to as a "golden rectangle." into shapes that are similar to the original square and rectangle. Repeated golden rectangles form a pattern. displayed to the right. Each produced golden rectangle is duplicated and divided once more. All of the golden rectangles are like the original rectangle in shape.
Given a golden rectangle,
width of rectangle = 54 inch
let length be l,
according to the golden ratio,
l/b = 1.618/1
l = 1.618b
l = 1.618*54
l = 87.372 inches
Hence the dimensions are 54 inches by 87.372 inches.
Learn more about golden rectangle;
https://brainly.com/question/27915841
#SPJ1
what is the resultant image of point A(-12,3) , after a scale factor 1/3 and a rotation of 270 degrees?
The resultant image of point A(-12,3) , after a scale factor 1/3 and a rotation of 270 degrees is (1, 4).
What is dilation?In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object with respect to a specific scale factor, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/3 centered at the origin as follows:
Ordered pair A (-12, 3) → Ordered pair A' (-12 × 1/3, 3 × 1/3) = Ordered pair A' (-4, 1).
By applying a rotation of 270° about the origin to the given figure, the location of A" is given by:
(x, y) → (y, -x)
Ordered pair A' (-12, 3) → Ordered pair A'' = (1, -(-4) = (1, 4).
Read more on rotation here: brainly.com/question/28854313
#SPJ1
draw the recursion tree for ()=4( 2) , where c is a constant, and provide a tight asymptotic bound
The tight asymptotic bound for the function f(n) = 4f(n/2) + c is T(n) = O(n²).
A recursion tree is a graphical representation of a recursive function that shows the repeated calls of the function. The tree is constructed by expanding each call of the function into a separate node.
For the given function f(n) = 4f(n/2) + c, the recursion tree is attaced below:
f(n/4) f(n/4) f(n/4) f(n/4)
The height of the tree is log2(n), and at each level, there are 4 calls of the function. Hence, the total number of nodes in the tree would be [tex]4^{log2(n)} = n^2[/tex].
The tight asymptotic bound for the function can be found using the Master Theorem, which states that for a recurrence relation of the form T(n) = aT(n/b) + f(n), if f(n) = O([tex]n^c[/tex]) for some constant c, then T(n) = O([tex]n^d[/tex]), where d = max(c, log b(a)).
For this function, a = 4, b = 2, and c = 1. Hence, d = max(1, log2(4)) = max(1, 2) = 2. Thus, the tight asymptotic bound for the function is T(n) = O([tex]n^2[/tex]).
To learn more about the asymptotic bound, visit:
brainly.com/question/4084552
#SPJ4
on a railway line, peak ridership occurs between 7:00 am and 5:00 pm. the fairness of a passenger survey could be improved by over-sampling data from which group?
The fairness of a passenger survey could be improved by oversampling data from the group of passengers who travel during peak ridership hours between 7:00 am and 5:00 pm.
This will ensure that the survey adequately represents the population of interest and provides accurate results.
Oversampling is the method of selecting respondents so that some groups make up a larger share of the survey sample than they do in the population. Oversampling small groups can be difficult and costly, but it lets polls to shed light on groups that would otherwise be too small to report on.
Oversampling and undersampling are methods used in data mining and data analytics to change unequal data classes to create balanced data sets. Oversampling and undersampling are also known as resampling.
To know more about oversampling, here
https://brainly.com/question/20308973
#SPJ4
Describe the translation thank you
The translation needed to obtain the graph of g(x) = 9^{x - 2} from the graph of f(x) = 9^x is shift 2 units right.
What is a horizontal translation?In Mathematics, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.By translating the exponential function f(x) = 9^x two (2) units to the right, we have the following:
f(x) = 9^x → g(x) = f(x - (2))
g(x) = 9^{x - 2}.
Read more on translation here: brainly.com/question/26869095
#SPJ1
Circumference: C = πrd or C = 2mr
Area: A= r² or A = π(r) (r)
REMEMBER: Each square box of the grid measures 1 unit (un) long and 1 unit (un) high!
What is the circumference of Circle G?
Use 3.14 for pl. Show your work here:
What is the area of Circle G? Use 3.14 for pl.
Show your work here:
Answer: 31.4
Step-by-step explanation: the circumference is 31.4 because the radius is 5, you multiply by 2 to get a diameter that is 10, then multiply that by 3.14 because in this question pi=3.14.
a sample of five households is selected, and the size of each household is recorded. the median size is 3 and the mode is 2. what is the mean?
The relation between mode, mean and median is:
mode=3median-2mean
Now, to find mean:
2mean=3median-mode
mean=7/2 = 3.5
Let we wish to evaluate the mean μ of a population. In real practice we would typically take just one sample. Imagine still that we take sample after sample, all of the same size n, and compute the sample mean x¯ every time.
The sample mean x is a random variable: it differs from sample to sample in a way that cannot be predicted with sureness. We will write X¯ when the sample mean is idea of as a random variable and write x for the values that it takes.
The random variable X¯ has a mean, denoted μX¯, and a standard deviation, denoted σX¯. Here is an example with such a small population and small sample size that we can indeed write down every single sample.
To know more about Mean:
https://brainly.com/question/30112112
#SPJ4
The number line below is divided into equal parts.
Fill in the missing fractions and percentages.
Note that your fractions don't need to be in simplest form.
The remaining fractions and percentages can be represented
as
0 1/4 2/4 3/4 1
|--------------|--------------|--------------|--------------|
0% 25% 50% 75% 100%
What is a number line?Real numbers are represented by a straight line known as a number line. The distance between the dots on the line, which correlates to the magnitude of the numbers, is how the numbers are typically represented. Positive or negative numerals can be used, and they are normally marked at regular intervals.
Given that,
The number line is divided into equal parts,
The missing parts are
0 1/4 2/4 3/4 1
|--------------|--------------|--------------|--------------|
0% 25% 50% 75% 100%
This is how we can fill in the remaining fractions and percentages.
To learn more about Number lines check:
brainly.com/question/24644930
#SPJ1
Alexander was able to cover 25% of 150 km journey in the morning. What percent of journey is still left to be covered?
Answer:
the answer would be 75% of the journey
need the answers for all pls
From the given table it is visible that the value of s(5)=4.2
What is value function?When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The amount that the function assumes for these argument values is the value of a function, given the value(s) assigned to its argument(s).
functions with return values and arguments. Functions with arguments and no return values.... This function takes arguments and returns a value.
functions with return values and no arguments.
without return values and without arguments
Function value can mean: The result of applying a function to an argument in mathematics. a closure in computer science.
To learn more about function refers to:
https://brainly.com/question/13581879
#SPJ1
5. Rachel used 5 ½ cups of sugar to make cherry cobbler. If each cobbler uses 1/3 cup of sugar, how many cobblers can she make?
Answer: 1 1/6
Step-by-step explanation:
The following plane is in 3-space with equation
c1x+c2y+c3z+c4 =0
that passes through three noncollinear points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) is given by the determinant equation
x y z 1
x1 y1 z1 1 = 0.
x2 y2 z2 1
x3 y3 z3 1
What does this determinant equation become if the three distinct points are collinear?
The equation of a plane in 3-space with equation c1x + c2y + c3z + c4 = 0 can be determined by passing through three non-collinear points (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). This is given by the determinant equation:
Copy code
| x y z 1 |
| x1 y1 z1 1 | = 0.
| x2 y2 z2 1 |
| x3 y3 z3 1 |
However, if the three distinct points are collinear, meaning they lie on the same line, then the determinant equation becomes undefined as the determinant of a 3x3 or smaller matrix with linearly dependent rows or columns is equal to zero. This means that there is no plane that passes through three collinear points as a plane requires at least three non-collinear points to be defined.
Here you can learn more about matrix with linearly dependent
https://brainly.com/question/30326376#
#SPJ11
The radius of a semicircle is 2 feet. What is the semicircle's area?
The area of the semicircle is 3.14 square feet.
The formula for area of a semicircle is A = ([tex]\pi[/tex]* r^2) / 2
Here A = Area
r = Radius
Given:
Given that the radius of the semicircle is 2 feet.
We need to Find out the area of the semicircle.
The value of [tex]\pi[/tex] is 3.14
A = ([tex]\pi[/tex] * 2^2) / 2
Substituting π = 3.14 and r = 2, we get;
A = (3.14 * 4) / 2
A = 6.28 / 2
A = 3.14 square feet
Learn more about semicircle
https://brainly.com/question/15822332
y-3x=5
y=3x +5
Determine the number of solutions of the system. Explain the reasoning.
The number of solutions of the system y = 3x + 5 is one because it is a linear equation.
What is linear equations?An equation in which is the highest power of to the variables 1 is knowns as the linear equation. Mathematically: it is an algebraic equations that can be also written in the form of ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.
Linear equations are equations in which the variables are raised to the power of 1, and the graph of the equation is a straight line. As a result, there is only one solution to the equation, which is when the line intersects the x-axis. This means that the equation has only one set of x- and y-coordinates, where x is the independent variable and y is the dependent variable, that satisfy the equation. The x-coordinate of the solution is the same as the value of x that makes the equation true and the y-coordinate is the value of y for this same x-value.
To know more about Linear equation click-
https://brainly.com/question/2030026
#SPJ1
Please help quick help
The perimeter of the actual triangle is 74 and option D is the correct answer.
What is scale factor?The scale factor is the difference in size between the original item's scale and that of the new object, which is a representation of it (bigger or smaller).
Given that the scaled dimension of the triangular face has the following dimensions:
PQ = 12
QR = PQ(1 + 25/100) = 12(125/100) = 15
PR = 2/3 (QR) = 2/3 (15) = 10
The scaling factor is 1/2 hence the actual dimensions of the triangle would be:
Original segments (1/2) = Scaled segment
Scaled (2) = Original
Using the above we have:
PQ = (12)(2) = 24
QR = (15)(2) = 30
PR =(10) (2) = 20
The perimeter of the triangle is the sum of all it sides:
P = 24 + 30 + 20
P = 74
The perimeter of the actual triangle is 74 and option D is the correct answer.
Learn more about scale factor here:
https://brainly.com/question/30215119
#SPJ1
Help pls just need to simplify
researchers are studying two populations of wild horses living in the western regions of a country. in a random sample of 32 horses taken from the first population, the mean age of the sample was 21 years. in a random sample of 41 horses from the second population, the mean age of the sample was 19 years. is the sampling distribution of the difference in sample mean ages approximately normal?
Yes, the sampling distribution of the difference in sample mean ages is approximately normal.
This is because the Central Limit Theorem states that the sampling distribution of the mean of any sample of size n will be approximately normal, provided that the samples are drawn from a population with a finite variance. Furthermore, the sample sizes in this case (32 and 41) are both greater than 30, which is the minimum sample size needed for the CLT to be valid.
The Central Limit Theorem is a fundamental theorem of statistics that states that the sampling distribution of the means of any sample of size n drawn from a population with a finite variance will be approximately normal, regardless of the shape of the population’s probability distribution.
Learn more about the Central Limit Theorem :
https://brainly.com/question/13652429
#SPJ4
suppose he starts with the same square of card, but changed the 4 inches to a different measurement. what is the largest volume he can make the box
The volume of the box will be 3136 cu. inches and the largest volume the box can be made of is also the same.
The amount of space occupied by a three-dimensional object as measured in cubic units.
The given square after getting folded turns into a box of 28*28*4 inches. The volume of the box can be determined by using the formula of volume of the cuboid.
Volume of the cuboid = 28*28*4
Volume of the cuboid =3136 cu. inches
The largest volume that the box can have is 3136 cu. inches as when increasing the height, the length or the width will decrease and so does the volume.
To know more about Volume of the cuboid, here
brainly.com/question/1549540
#SPJ4
you are choosing between two health clubs. Club A offers membership for a fee of $21 plus a monthly fee of $22. Club B offers membership for a fee of $12 plus a monthly fee of $25. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
After the second month, the charge will remain the same. 14 + 28 (2) = $70 would be the final price.
How to find the calculation?The first club offers a lower membership cost but a higher monthly fee in this instance, while the second club offers the polar opposite.
The computation would then be as follows to determine how long it would take for the total cost of each health club to equalize:
Example:
1 club fee equals 2 clubs fees
14+ 28x= 24+ 23x
28x-23x= 24-14
5x= 10 \sx=2
After the second month, the charge will remain the same. 14 + 28 (2) = $70 would be the final price.
The Complete Question.
To Learn more About final price Refer To:
https://brainly.com/question/28829803
#SPJ1
If A + B + C = π, express cos (A + B) in terms of angle C.
Answer:
te te te te te te te rog vreau să mă iai la un cont decent în privat de la școală dar trebuie să se poate mai bine tu nu mi-ai spus sa te sun se va întâmpla la un cont decent și a ride la un moment de la card memorie micro
Step-by-step explanation:
trebuie sa faci așa 4629+(703)-105
Answer:
cos(A + B) = - cosC
Step-by-step explanation:
using the addition identity
cos(x ± y) = cosxcosy ∓ sinxsiny
given
A + B + C = π ( subtract C from both sides )
A+ B = π - C
then
cos(A + B)
= cos(π - C)
= cosπ cosC + sinπ sinC
= - 1 × cosC + 0 × sinC
= - cosC + 0
= - cosC
Spray drift is a constant concern for pesticide on Spray Droplet Size and Deposition t investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the nomal distribution with mean 1050 m and standard deviation 150 μa reasonable model for droplet size for water (the "control and agricultural producers. The The paper "Effects of 2,4-D and was ) sprayed through a 760 ml/min nozzle.
(a) What is the probability that the size of a single droplet is less than 1470 μm? At least 950 μm? (Round your answers to four decimal places.)
less than 1470 μm __
at least 950 μm __
(b) What is the probability that the size of a single droplet is betweet 950 and 1470 μm? (Round your answer to four decimal places)
(c) How would you characterize the smallest 2% of all droplets? (Round your answer to two decimal places.) The smallest 2% of droplets are those smaller than ___ μm in size.
(d) If the sizes of five independently selected droplets are measured, what is the probabity that at least one exceeds 1470 μm? (Round your answer to four decimal places,) You may need to use the appropriate table in the Appendix of Tables to answer this question
(a) P(X < 1470) = 0.8849, P(X >= 950) = 0.7487, (b) the probability that the size of a single droplet is between 950 and 1470 μm is 0.6336, (c) the smallest 2% of all droplets are those smaller than 827 μm in size, and (d) the probability that at least one exceeds 1470 μm is 0.3995.
(a) To find the probability that the size of a single droplet is less than 1470 μm or at least 950 μm, we need to use the standard normal distribution table. To do this, we first need to convert the droplet size to a standard normal variable.
Let X be the droplet size. Then we have:
Z = (X - 1050)/150
The probability that the size of a single droplet is less than 1470 μm is equal to the cumulative distribution function of Z evaluated at Z = (1470 - 1050)/150 = 1.2:
P(X < 1470) = P(Z < 1.2) = 0.8849 (rounded to four decimal places)
The probability that the size of a single droplet is at least 950 μm is equal to 1 minus the cumulative distribution function of Z evaluated at Z = (950 - 1050)/150 = -0.6:
P(X >= 950) = 1 - P(Z < -0.6) = 0.7487 (rounded to four decimal places)
(b) To find the probability that the size of a single droplet is between 950 and 1470 μm, we subtract the cumulative distribution function of Z evaluated at Z = (950 - 1050)/150 = -0.6 from the cumulative distribution function of Z evaluated at Z = (1470 - 1050)/150 = 1.2:
P(950 <= X <= 1470) = P(Z <= 1.2) - P(Z <= -0.6) = 0.8849 - 0.2513 = 0.6336 (rounded to four decimal places)
(c) To find the smallest 2% of all droplets, we find the value of Z such that P(Z <= Z) = 0.02. Using the standard normal distribution table, we find that Z = -2.33. Then, we convert Z back to the original variable X:
X = Z * 150 + 1050 = -2.33 * 150 + 1050 = 827 (rounded to two decimal places)
So, the smallest 2% of all droplets are those smaller than 827 μm in size.
(d) To find the probability that at least one of five independently selected droplets exceeds 1470 μm, we use the cumulative distribution function of a binomial distribution with n = 5 and p = P(X > 1470). The cumulative distribution function of a binomial distribution with parameters n and p is given by:
1 - (1 - p)^n
Using the standard normal distribution table, we find that P(X > 1470) = 1 - P(Z < (1470 - 1050)/150) = 1 - 0.8849 = 0.1151. Then, we plug in n = 5 and p = 0.1151 into the cumulative distribution function formula:
P(at least one exceeds 1470 μm) = 1 - (1 - 0.1151)^5 = 0.3995 (rounded to four decimal places).
To know more about probability, here
https://brainly.com/question/23862234
#SPJ4
The fifth, ninth, sixteenth terms of a linear sequence (a.p.) are consecutive terms of an expodencial sequence (g.p.)
1. Find the common difference of the linear sequence in term of the first term.
2. Show that twenty-first , thirty-seventh and sixty-fifth terms of the linear sequence are consecutive terms of an exponential sequence whose common ratio is 7/4
The common difference is 7/4 and the required terms are 16a,28a,49a
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar2, ar3, ar4,...
Given here: The fifth, ninth, sixteenth terms of a linear sequence (a.p.) are consecutive terms of an expodencial sequence (g.p.)
5th term of the ap: a+4d
9th term: a+8d
16th term: a+15d
In a gp, the square of any term is equal to the product of the terms before and after it:
(a+8d)²=(a+4d).(a+15d)
[tex](a^2+16ad+64d^2)=a^2+19ad+60d^2\\4d^2-3ad=0\\d(4d-3a)=0[/tex]
(i) ANSWER: d = (3/4)a
(ii) 21st term: a+20d = a+15a = 16a
37th term: a+36d = a+27a = 28a
65th term: a+64d = a+48a = 49a
28a/16a = 7/4; 49a/28a = 7/4; this sequence is geometric with common ratio 7/4
Hence, The common difference is 7/4 and the required terms are 16a,28a,49a
Learn more about a G.P series here:
https://brainly.com/question/4853032
#SPJ1
Gabriella measured a line to be 11.1 inches long. If the actual length of the line is 11.6 inches, then what was the percent error of the measurement, to the nearest tenth of a percent
Answer:
10%
Step-by-step explanation:
11.6/11.1 = 0,1045045
Which line of best fit tends to underestimate the bite force and would NOT make
good predictions on the relationship of body mass and bite force of crocodiles?
Sol's Line
Taylor's Line
Patti's Line
Marrisa's Line
Taylor's Line Best Fit does not accurately anticipate the relationship between crocodile body mass and bite force and has a tendency to overestimate the bite force.
An infinite sum of terms that are expressed in terms of the function's derivatives at a single point is the Taylor series, also known as the Taylor expansion, of a function. Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions.
What is the line's Taylor form?P1(x) = (a)+ f'(x a) The function close to x = an is best approximated linearly by the tangent line. The curve and tangent line have the same first derivative, or slope, at the point where x = a. This close estimate is a Taylor polynomial of degree 1 is referred to as P1 (x).
To know more about Taylor's Line visit:-
https://brainly.com/question/12784768
#SPJ1
The pictures below are my questions please let me know if there’s a problem!! :)
Answer:
Step-by-step explanation:
(1) Yes, the table is proportional
4.5/25 = 5.4/30 = 6.3/35 = 7.2/40
= 0.18
For a $50 bill the donation will be
50 X 0.18 = $9
Hence, 0.18 times of the dinner bill is donated to charity
(2) Yes, this is also proportional
a1 = 0.47
a2 = 0.68
a3 = 0.89
a4 = 1.10
d = a2 -a1 = a3 -a2 = a4 - a3
= 0.21
For a 6 ounce letter the A.P will be a6 so
a6 = a + 5d
= 0.47 + 5(0.21)
= 0.47 + 1.05
= 1.52
Hence , For every ounce of weight the cost gets increased by 0.21 the weight
What is the value of 110% of of of 64?
Answer:
The answer would be 70.4
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Jon and Felipe just had business cards made. Jon's printing company charged a one-time setup fee of $10 and then $20 per box of cards. Felipe, meanwhile, ordered his online. They cost $21 per box. There was no setup fee, but he had to pay $9 to have his order shipped to his house. By coincidence, Jon and Felipe ended up spending the same amount on their business cards. How much did each spend? How many boxes did each buy? Jon and Felipe each spent $ on business cards, buying boxes.
Jon bought 10.5 boxes of cards and Felipe bought 11 boxes of cards, and Jon and Felipe each spent $215 on business cards.
What is the system of equations?
A system of linear equations is a set of two or more equations that includes common variables. To solve a system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
Let x be the number of boxes of cards that Jon bought and y be the number of boxes of cards that Felipe bought.
The equation for Jon's cost is: 10 + 20x = y * (21 + 9)
The equation for Felipe's cost is: 21y + 9 = 10 + 20x
We will solve the system of equations using substitution.
Starting with the second equation, we can simplify: 21y + 9 = 10 + 20x
21y + 9 - 10 = 20x
21y - 1 = 20x
Dividing both sides by 21: y = (20/21)x + 1
We can now substitute this expression for y into the first equation:
10 + 20x = (20/21)x + 10 + 9
10 + 20x = (20/21)x + 19
10 = 19 - (20/21)x
Multiplying both sides by 21:
210 = 19 * 21 - 20x
Subtracting 19 * 21 from both sides:
210 - 19 * 21 = -20x
Divide both sides by -20:
x = 10.5
So, Jon bought 10.5 boxes of cards and Felipe bought (20/21) * 10.5 + 1 = 11 boxes of cards.
To find out how much each spent, we can plug these values back into either equation:
Jon's cost: 10 + 20 * 10.5 = 215
Felipe's cost: 21 * 11 + 9 = 250
So, Jon and Felipe each spent $215 on business cards, buying 10.5 boxes.
Hence, Jon bought 10.5 boxes of cards and Felipe bought 11 boxes of cards, and Jon and Felipe each spent $215 on business cards.
To learn more about the system of equations visit,
https://brainly.com/question/28405823
#SPJ1
Question Down below (PLS HELP FOR 50 BRAINLIST)
Pls anyone i would appreciate it
Just select Two answers in the picture showen below
The two inequalities that represent the constraints in this situation are
r + c >= 80 and 1.45r + 0.65c <= 200
How to determine the inequalityLet r be the number of roses and c be the number of carnations Victor buys.
So, we have
Total number of flowers: r + c >= 80
Victor has $200 to spend on flowers for the school celebration.
Roses cost $1.45 each and carnations cost $0.65 each.
So, we have
Total spending: 1.45r + 0.65c <= 200
Read more about inequality at
https://brainly.com/question/25275758
#SPJ1
If angle b is two more than three times angle c, angle b and c are complimentary what is the measure of each angle
Step-by-step explanation:
"∠B is 2 more than 3 times the measure of ∠C" translates into B = 3C + 2....(1)
"...∠B and ∠C are complementary angles" translates to B + C = 90...............(2)
Now, all that's left to do is to solve for B and C. So, we'll take equation (1) and substitute it into equation (2) as follows:
(3C + 2) + C = 90
4C + 2 = 90
4C = 88
C = 22
Plugging C = 22 back into either equation (1) or (2) gives us
B = 90 - 22 = 68 (or B = 3(22) + 2 = 68)
Thus, ∠B = 68º; ∠C = 22º
use property 8 to estimate the value of the integral ∫1147xdx.
Using property 8 and the midpoint rule, we have estimated the value of the integral ∫1147xdx to be approximately 14.
Property 8 of the definite integral states that if a < b and 0 < c < d, then:
∫baf(x)dx = ∫dcf(x)dx - ∫caf(x)dx
We can use this property to estimate the value of the integral ∫1147xdx. Let's choose c = 1 and d = 4, so that 0 < c < d and a < b. Then:
∫1147xdx = ∫447xdx - ∫11x dx
Next, we can use a numerical method, such as the midpoint rule or trapezoidal rule, to estimate the value of each of the integrals on the right side of the equation.
For example, using the midpoint rule with n = 4 subintervals for each integral:
∫447xdx ≈ (4 - 4/2) + (4 - 3/2) + (4 - 2/2) + (4 - 1/2) = 4 + 4 + 4 + 4 = 16
∫11x dx ≈ (1 - 1/2) + (1 - 2/2) = 1 + 1 = 2
So, our estimate of ∫1147xdx becomes:
∫1147xdx ≈ 16 - 2 = 14
Therefore, using property 8 and the midpoint rule, we have estimated the value of the integral ∫1147xdx to be approximately 14.
To learn more about the trapezoidal rule,
Visit; brainly.com/question/17218343
#SPJ4
