The answer is D. I and II only. The number of people who chose A as their favorite brand could be 30 or 35 since x is rounded to the nearest integer, which is 3. However, it cannot be 45 since 3 is the nearest integer.
1. x is rounded to the nearest integer, which is 3
2. If x is equal to 30, then the number of people who chose A as their favorite brand would be 30
3. If x is equal to 35, then the number of people who chose A as their favorite brand would be 35
4. If x is equal to 45, then the number of people who chose A as their favorite brand would be 45
5. Since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45
6. Therefore, the answer is D. I and II only.
1,150 respondents were asked to select their preferred brand among brands A, B, and C of laundry detergent. x% of those polled indicated that A was their preferred brand. The outcome is 3 if x is rounded to the nearest integer. This means that x could be 30, 35, or 45. However, since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45. Therefore, the answer is D. I and II only, meaning that the number of people who chose A as their favorite brand could be 30 or 35. This is because if x is equal to 30, then the number of people who chose A as their favorite brand would be 30 and if x is equal to 35, then the number of people who chose A as their favorite brand would be 35.
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Given the function h of x equals negative 2 times the square root of x, which statement is true about h(x)?The function is decreasing on the interval (0, [infinity]).The function is decreasing on the interval (–[infinity], 0).The function is increasing on the interval (0, [infinity]).The function is increasing on the interval (–[infinity], 0).
The function is decreasing on the interval (0, [infinity])
The function h of x equals negative 2 times the square root of x is a decreasing function on the interval (0, ∞). This means that as the value of x increases, the value of h(x) decreases. On the interval (-∞, 0), the function is increasing. This means that as the value of x decreases, the value of h(x) increases. The graph of the function looks like a parabola that opens downward and is symmetric around the y-axis. The graph is a concave down curve, and the y-intercept is at (0, 0). As the value of x gets closer to 0, h(x) approaches negative infinity. As x approaches infinity, h(x) approaches 0. This means that the range of h(x) is (-∞, 0].In order to determine if the function is increasing or decreasing on a given interval, we need to look at the sign of the derivative of the function on the interval.
The derivative of h(x) is -2/sqrt(x).
For the interval (0, [infinity]), the derivative of h(x) is negative, indicating that the function is decreasing.
For the interval (–[infinity], 0), the derivative of h(x) is positive, indicating that the function is increasing.
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A firm’s current profits are $900,000. These profits are expected to grow indefinitely at a constant annual rate of 2 percent. If the firm’s opportunity cost of funds is 4 percent, determine the value of the firm: a.The instant before it pays out current profits as dividends. b.The instant after it pays out current profits as dividends
Answer: a. The value of the firm the instant before it pays out current profits as dividends can be calculated using the Gordon Growth Model, which is given by the formula:
Value = Dividends / (Cost of Equity - Growth Rate)
Where Dividends = Current Profits, Cost of Equity = Opportunity Cost of Funds, and Growth Rate = Constant Annual Growth Rate.
Substituting the given values into the formula, we get:
Value = 900,000 / (0.04 - 0.02) = 900,000 / 0.02 = 45,000,000
b. The instant after it pays out current profits as dividends, the firm's value will be reduced by the amount of the dividends paid out. So, the value of the firm after paying out the dividends will be:
Value = 45,000,000 - 900,000 = 44,100,000
Step-by-step explanation:
What is the equation of the line that passes through the point (4, -1) and has a
slope of -2?
Answer:
y = - 2x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (4, - 1 ) into the partial equation
- 1 = - 2(4) + c = - 8 + c ( add 8 to both sides )
7 = c
y = - 2x + 7 ← equation of line
Based on the results, after trying for a while, you expect your weight to decrease by at least 10% of your current weight in the next two months. If you currently weigh 70Kg. Determine the amount of weight (in Kg) that you expect to lose?
y = (x^2/2) + x + 2; [-5, 3]
For each problem, approximate the area under the curve over the given interval using 4 left endpoint rectangles
The area under the curve over the given interval [-5, 3] can be approximated using 4 left endpoint rectangles.
The formula for this is A = ∑f(xi)∆x. Where A is the area, f(x) is the function, xi is the left rectangles. of the interval, and ∆x is the width of the interval. For this problem, the function is f(x) = (x^2/2) + x + 2 and the given interval is [-5, 3]. So, the left endpoints of the intervals are x1 = -5, x2 = -1, x3 = 3, and x4 = 7 and the width of each interval is ∆x = 4. Plugging these values into the formula, A = (f(-5)∆x) + (f(-1)∆x) + (f(3)∆x) + (f(7)∆x). Simplifying, A = (9*4) + (6*4) + (12*4) + (26*4). Thus, the area under the curve over the given interval is A = 360.
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Type the expression that results from the following series of steps: Start with x , subtract 4, divide by 5, then add 9.
Answer:
Step-by-step explanation:
x-4/5+9
Suppose y = c1ekx + c2e-kx where k > 0 is a constant, and c1 and c2 are arbitrary constants. Find the following. Enter c1 as c1 and c2 as c2
The c1 and c2 are arbitrary constants.
What is the arbitrary constant?
y=mx+c is the general equation of a straight line in two dimensions, where m and c are arbitrary constants that represent the gradient of the line and the y-intercept. And ∫2x dx=x 2+c where c is an arbitrary constant whose value can be determined by a boundary condition.
y = c1ekx + c2e-kx is a general solution to the homogeneous linear differential equation y' + ky = 0. This means that any specific solution to this equation can be obtained by plugging in appropriate values for c1 and c2.
The general solution y = c1ekx + c2e-kx is a linear combination of ekx and e-kx.
The differential equation y' + ky = 0 is a first-order, linear differential equation.
The general solution y = c1ekx + c2e-kx is valid for all values of x.
The general solution y = c1ekx + c2e-kx is a sum of two linearly independent solutions to the differential equation.
The general solution y = c1ekx + c2e-kx is a particular solution if c1 and c2 are determined by initial or boundary conditions.
The general solution y = c1ekx + c2e-kx is a general solution if c1 and c2 are arbitrary constants.
The general solution y = c1ekx + c2e-kx is a unique solution if c1 and c2 are determined by initial or boundary conditions, otherwise, it is not unique.
The general solution y = c1ekx + c2e-kx is a solution to the homogeneous differential equation y' + ky = 0, it does not contain any particular solution for the non-homogeneous differential equation.
Hence, The c1 and c2 are arbitrary constants.
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For which of the following functions is the chain rule an appropriate method to find the derivative with respect to x ?y=sin(3x2)y=extanxy=18x4−2x
The chain rule tells us where to search the derivative of a composite function.
d/dx[f(g(x))] =f'[f[g(x)g'(x).
A function is composite if you can write it as f(g(x)) In other words, it is a function within a function, or a function of a function.
Following steps should be followed to find chain rule:
1: Recognize the chain rule: The function needs to be a composite function, which implies one function is nested over the other one.
2: Know the inner function and the outer function respectively.
3: Determine the derivative of the outer function, dropping the inner function
4: Obtain the derivative of the inner function Step
5: Multiply the outcomes from step 4 and step 5 respectively.
6: Simplify the obtained chain rule derivative.
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B is the set of integers greater than or equal to -3 and less than or equal to 0
Integers higher than or equal to -3 and less than or equal to 0 make up the set of numbers (-3 , -2 , -1, 0)
Explain about the set of integers?The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.
The formal definition of the set Z of integers is as follows: Z = {..., -3, -2, -1, 0, 1, 2, 3, ...} Unknown or unidentified integers are denoted in mathematical equations by lowercase, italicised letters from the "late middle" of the alphabet. P, q, r, and s are the most prevalent.
The category of whole numbers and the negative of natural numbers is known as integers. Thus, integers can be either positive or negative, including 0.
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In each of the following situations, data are obtained by conducting a statistical study. Classify each statistical study as experimental or correlational. Statistics students collect data on the shower length and gender of the person taking the shower for a random sample of showers. The manager of a tuna canning factory is interested in finding out which set of machine settings results in a smaller variance of the fill weight of the tuna cans. She uses one set of machine settings for the day shift and a second set of settings for the night shift. The next day she uses the second set of settings for the day shift and the first set of settings for the night shift. Data are collected on the fill weights of the tuna cans. For a sample of college students using the ATM in the campus center, data are collected on the dollar amount withdrawn.
An experimental design involves changing an independent variable and observing the impact on a dependent variable. The results are unaffected by other variables because they are controlled.
What are experimental or correlational statistical study?An experimental design involves changing an independent variable and observing the impact on a dependent variable. The results are unaffected by other variables because they are controlled. Variables are measured in a correlational design without any of them being changed. Without influencing or modifying any of the variables, a correlational study design examines associations between two (or more) variables. This particular quantitative research method is non-experimental. These determine the three categories of correlational research: Archival research, survey research, and observational study conducted naturally.Experimental research is an investigation carried out using two sets of variables and a scientific methodology. You use the first set as a standard against which to compare the differences in the second set. For instance, experimental techniques are used in quantitative research.We would learn them all and associate each song with a certain pizza truck if there were several different pizza trucks in the region, each with its own distinctive melody. In this case, "jingle" and "distance of the truck" are the two variables that are established as having a relationship by correlational study.To learn more about correlational statistical study refer to:
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which correctly explains the number of solutions of the following system of linear equations -2x+2y=10
y=x+5
For the system of equations, there are infinitely many solutions exist.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The system of equations are,
⇒ - 2x + 2y = 10 .. (i)
⇒ y = x + 5 .. (ii)
Here, From (i) equation,
⇒ - 2x + 2y = 10
Take 2 as common,
⇒ 2 (- x + y) = 10
⇒ - x + y = 5
⇒ y = x + 5
Which is same as equation (ii).
Hence, There are infinitely many solutions exist.
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consider the following set of requirements for a university database that is used to keep track of students' transcripts. the university keeps track of each student's name, student number, social security number, current address and phone, permanent address and phone, birthdate, sex, class (freshman, sophomore, ..., graduate), major department, minor department (if any), and degree program (b.a., b.s., ..., ph.d.). some user applications need to refer to the city, state, and zip of the student's permanent address, and to the student's last name. both social security number and student number have unique values for each student. each department is described by a name, department code, office number, office phone, and college. both name and code have unique values for each department. each course has a course name, description, course number, number of semester hours, level, and offering department. the value of the course number is unique for each course. each section has an instructor, semester, year, course, and section number. the section number distinguishes different sections of the same course that are taught during the same semester/year; its values are 1, 2, 3, ..., up to the number of sections taught during each semester. a grade report has a student, section, letter grade, and numeric grade (0, 1, 2, 3, 4 for f, d, c, b, a, respectively). using a modeling tool, complete the following. design a conceptual schema for this company (see chapter 1, page 13 for an example) draw an er diagram for that schema. specify key attributes of each entity type and structural constraints on each relationship type. note any unspecified requirements and make appropriate assumptions to make the specification complete. what to submit submit a word or pdf document containing both the conceptual schema and the er diagram. additional resources summary of the notation for er diagrams try one of the following er modeling tools to complete this assignment. gitmind - free online mind mapping diagrams.net dbdiagram.io start date jan 9, 2023 7:00 pm due date jan 23, 2023 11:59 pm
The conceptual schema and the E-R diagram are attached.
(i) Before making the E-R diagram we discuss the entity relational model for the given problem. So the E-R diagram is the graphical representation of different entities and attributes.
Assumptions for the given problem:
(i) University: a university has its name, address, email id, and mobile number
the university gives admission to students and also university and different departments.
(ii) Student: a student has attributes name, contact number, and social security number as the primary number, address, student number, birth date has its name, department, sex, class, department, and degree program.
(iii) Department: the department has its name, department code, office number, phone
(iv) Courses: each course has its name, description, course number, number of semester hours, level, and offering department.
(v) Section: section has an instructor, semester, year, course, section number
(vi) Grade report: a grade report contain a student section, letter grade, and numeric grade
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Use De Morgan’s Law to find the indicated set
Answer:
C' U (A U B')
Step-by-step explanation:
Using DeMorgan's laws
(C ∪ A' ∩ B)' = C' U (A' ∩ B)'
(A' ∩ B)' = (A')' U B' = A U B'
So (C ∪ A' ∩ B)' = C' U (A U B')
The following shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and area of the shaded part. Give your answer as a completely simplified exact value in terms of pi. (no approximations) FIRST PERSON TO ANSWER GETS 100 POINTS
Answer:
Perimeter = 8π cm
Area = (32π - 64) cm²
Step-by-step explanation:
ABCD is a square.
Therefore:
AB = BC = CD = DA = 8 cmArea = 8 × 8 = 64 cm²PerimeterThe perimeter of the shaded part is the sum of two congruent quarter circles, i.e. half the length of the circumference.
The arcs AC are quarter circles of a circle with radius 8 cm.
Therefore the perimeter of the shaded area is:
[tex]\implies \sf Perimeter=Half\;circumference=\dfrac{1}{2} \cdot 2\pi r=\pi r=8\pi\;cm[/tex]
AreaTo find the area of the shaded area, subtract the two unshaded areas from the area of the square.
As the two unshaded areas are congruent we only need to find the area of one unshaded area.
The area of one unshaded area is the area of the square minus the area of the sector ADC (which is a quarter of a circle with radius 8 cm).
[tex]\begin{aligned}\implies \textsf{Area of one unshaded area}&=\textsf{Area of square}-\textsf{Area of $\frac{1}{4}$ circle}\\&=64-\dfrac{1}{4} \pi r^2\\&=64-\dfrac{1}{4} \pi \cdot 8^2\\&=64-\dfrac{1}{4} \pi \cdot 64\\&=(64-16 \pi)\; \sf cm^2\end{aligned}[/tex]
Now we have found the area of one unshaded area, to calculate the area of the shaded area simply subtract two unshaded areas from the area of the square:
[tex]\begin{aligned}\implies \textsf{Shaded area}&=64-2(64-16\pi)\\&=64-128+32\pi\\&=(32\pi-64)\; \sf cm^2 \end{aligned}[/tex]
5. give an example of tangents in the real world that have not been presented in this lesson. explain how you know the tangent and the radius in your example are perpendicular.
Part A: The path of the ball in relation to the curved path of the thrower
Part A: The path the ball takes is perpendicular to the hand, bat, or feet at the point of last contact
Part A:
A real-world example of tangents is the direction of a ball immediately after it is released and the circular path of the motion, that provides the force input that is given to the ball to cause it to move in the required direction
The tangent is the path the ball takes immediately after it is moving without contact with the bat, hand, or feet that causes it to move.
The circular path is the motion of the hand, leg, bat, or feet that makes before the ball is released.
The radius is the hand, leg, or bat that rotates in a circular path, so as to move the ball
Part B:
The radius, such as the leg kicking a ball is perpendicular to the tangent which is the path of the ball because a kick sends the ball into the air, the orientation of the leg at the point the ball leaves is perpendicular to the angle of elevation with which the ball is launched.
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. MATHEMATICS: 1. Given that x + y =3/4 and x - y =5/2 find the value of 2y + x
Step-by-step explanation:
[tex]x = \frac{13}{8} \\ y = \frac{ - 7}{8} \\ 2y + x = - \frac{14}{8} + \frac{13}{8} = - \frac{1}{8} [/tex]
Answer:
-1/8
Step-by-step explanation:
x + y = 3/4
x -y = 5/2
2x = 13/4 3/4 + 5/2 = 3/4 + 10/4 = 13/4 Next divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{\frac{13}{4} }{2}[/tex] [tex]\frac{13}{4}[/tex] ÷[tex]\frac{2}{1}[/tex] = [tex]\frac{13}{4}[/tex] x [tex]\frac{1}{2}[/tex] = [tex]\frac{13}{8}[/tex]
x = [tex]\frac{13}{8}[/tex]
plug in 13/8 for x in either of the two original equations.
x + y = 3/4
13/8 + y = 3/4 Subtract 13/8 from both sides
y = -7/8 3/4 - 13/8 = 6/8 - 13/8 = -7/8
Check:
substitute x = 13/8 and y = -7/8 back into the original two equations to see if the equations ae true
x + y = 34
13/8 - 7/8 = 3/4
6/8 = 3/4
3/4 = 3/4 Checks
x - y = 5/2
13/8 - (-7/8) = 5/2
13/8 + 7/8 = 5/2
20/8 = 5/2
5/2 = 5/2 Checks
Find the value of 2y + x
2(-7/8) + 13/8
-14/8 + 13/8
-1/8
You want to know the opinions of American school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association (the largest teachers union) and mail a questionnaire to 2,500 teachers chosen at random from this list. In all 1,347 teachers return the questionnaire. In this situation, the sample is: a. the 1,347 teachers who mailed back the questionnaire b. the 2,500 teachers to whom you mailed the questionnaire. call members of the National Education Association. d. all American school teachers. e. all American school students.
You want to know the opinions of American school teachers about establishing a national test for high school graduation then correct option is D) all American school teachers.
In statistics, A population is a very large set of individuals or values that belong to a specified group established by researcher.
A sample is a subset of population that represents the entire population in research.
Given : We want to know the opinions of American school teachers about establishing a national test for high school graduation.
Clearly , by the above definition
Population = all American school teachers.
You obtain a list of the members of the National Education Association and mail a questionnaire to 2500 teachers chosen at random from this list.
sample = 2500 teachers chosen at random from this list.
Hence, the intended population is all American school teachers.
Thus , the correct answer is D) all American school teachers.
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1. You are the manager of a small store that specializes in hats, sunglasses, and other accessories. You are considering a sales promotion of a new line of hats and sunglasses. You will offer the sunglasses only to those who purchase two or more hats, so you will sell at least twice as many hats as pairs of sunglasses. Moreover, your supplier tells you that, due to seasonal demand, your order of sunglasses cannot exceed 100 pairs. To ensure that the sale items fill out the large display you have set aside, you estimate that you should order at least 210 items in all. Assume that you will lose $3 on every hat and $2 on every pair of sunglasses sold. Given the constraints above, how many hats and pairs of sunglasses should you order to lose the least amount of money in the sales promotion? [Using Graphic method]
Graphical techniques are widely used to assess whether the data support the fractionation of a single source or the mixture of two putative sources.
For 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.
What is meant by Graphic method?To determine if the data support the mixing of two potential sources or the fractionation of a single source, graphical approaches are frequently used.
To better interpret their data, researchers now employ a variety of graphical tools, including scatterplots, box plots, and histograms. Graphs are excellent for illustrating trends, patterns, and correlations between variables as well as for displaying and summarizing vast volumes of numerical data.
We generate a graph for each equation in order to solve systems of equations or simultaneous equations graphically. Then, we search for the intersection of the two graphs. The system of equations would have a solution at the coordinates of the point of intersection.
Let x be the number of hats and y be the number of pairs of sunglasses.
The constraints exists:
2y = x (because for every 2 hats sold, 1 pair of sunglasses is sold)
y <= 100 (because the supplier can only provide 100 pairs of sunglasses)
x + y >= 210 (because you want to sell at least 210 items in total)
x, y >= 0 (because the number of items sold cannot be negative)
Lose in every hat is $3 and in Pair of Sunglasses is $ 2
Total loss in promotion or cost of promotion is
3x + 2y
For least purchase,
x + y = 210
⇒ x + x/2 = 210
⇒3x/2 = 210
⇒ x =140
y = 140/2 = 70
So, for 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.
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For 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.
What is meant by total?
Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A car that has been totalled in an accident is irreparably damaged.the outcome of addition. For instance, adding 3 and 2 balls results in a total of 5 balls. Another illustration: The result of 12 + 4 + 6 = 22 is 22. Math is enjoyable.When you add up or count up all of something's components, you obtain the entire number or cost of that thing.Let x be the number of hats and y be the number of pairs of sunglasses.
The constraints exists:
2y = x (because for every 2 hats sold, 1 pair of sunglasses is sold)
y <= 100 (because the supplier can only provide 100 pairs of sunglasses)
x + y >= 210 (because you want to sell at least 210 items in total)
x, y >= 0 (because the number of items sold cannot be negative)
Lose in every hat is $3 and in Pair of Sunglasses is $ 2
Total loss in promotion or cost of promotion is
3x + 2y
For least purchase,
x + y = 210
⇒ x + x/2 = 210
⇒3x/2 = 210
⇒ x =140
y = 140/2 = 70
So, for 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.
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What is the reference angle for the given angle measure drawn in standard position?
The reference angles are given as -
- 34π/3 → π/3- 5π/12 → π/12 17π/6 → π/6What is a radian?The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics
Given are the angles as shown in the figure.
We can write the reference angles as -
{ 1 } -- 34π/3 → -34 x π/3 → π/3
- 34π/3 → π/3
{ 2 } -- 5π/12 → -5x π/12 → π/12
- 5π/12 → π/12
{ 3 } -17π/6 → 17 x π/6 → π/6
17π/6 → π/6
Therefore, the reference angles are given as -
- 34π/3 → π/3- 5π/12 → π/12 17π/6 → π/6To solve more questions on reference angles, visit the link below -
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What is the result when -3x - 4 is subtracted from -4x - 3?
how many total atoms of each element are present in the following formulas?
3 CaCl₂
Tap in the fields to enter the answers directly OR
tap on the Number Pad icon to use our built-in Number Pad.
To ascertain an element's molar mass, use the periodic table. Calculate the quantity of moles by dividing the supplied mass in grammes by the molar mass.
How many types of atoms are in an element?One type of atom makes up each individual element. Protons, neutrons, and electrons, three additional subatomic particles, make up atoms. Chemical reactions allow elements to interact with one another to create molecules.The number of atoms can be calculated by multiplying the number of moles by Avogadro's number. An atom's atomic number is equal to the quantity of protons in its nucleus or the quantity of electrons in an electrically neutral atom.CaCl2 contains 3 atoms. We can determine the number of atoms in a compound by counting the subscripts after each ingredient. Counting moles is the initial step in calculating the number of atoms.To learn more about element's refer to:
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A three-column table is given.
Part 8 B D
Part 10 15 45
Whole A C 72
What is the value of C in the table?
18
24
27
71
The value of C in the table will be 24.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, a table of proportional data below,
Part 8 B D
Part 10 15 45
Whole A C 72
Since the two-part will be proportional to the whole.
thus,
=> c /72 = 15/45
=> C = 72/3
=> C = 24
Therefore, the value of C in the given table will be 24 as pe the proportionality.
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In a class there are 42 students. the numbers of girls is 2times the numbers of boys. how many boys and girls are there in the class
Answer: 14 boys & 28 girls
Step-by-step explanation:
the number of girls= 2x
the number of boys= x
now create an algebraic equation:
x + 2x = 42
3x = 42
x = 14 (boys)
multiply 14 by 2 as the number of girls is two times the number of boys.
14 x 2 = 28 girls
6x + 4y = 7Kx + 8y = 7What is the value of K?
The value of K in the given equations 6x+4y=7 and Kx+8y=7 is k=(-4y/x)+6.
What are equations?Two things are equal, according to an equation.
It will be written with the equals sign "=" as in x+2=6.
What is on the left (x + 2) is equal to what is on the right ((6)), according to that equation.
A remark like "this equals that" can be compared to an equation.
So, we have the equations:
6x + 4y = 7
Kx + 8y = 7
Now, we know that both equations are equal to 7. so, we can write it as:
6x + 4y = Kx + 8y
Solve with subject K as follows:
6x + 4y = Kx + 8y
Kx - 6x = 4y - 8y
(K-6)x = -4y
k-6 = -4y/x
k = (-4y/x) + 6
Therefore, the value of K in the given equations 6x+4y=7 and Kx+8y=7 is k=(-4y/x)+6.
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use the method of mathematical Induction to Prove that 4+9+14+19+_ _ + (5n-1) = n/₂ (3+5n) for all natural numbers n
Mathematical induction, .∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.
To prove mathematical induction?Assume that Pn is 4 + 9 + 14 +... + (n/2)(5n + 3)=(5n -1).
First, establish that P1 is accurate when n equals 1.
LHS= 4
RHS
= 1/2(5 + 3)
= 1/2(8)
= 4
= LHS
Is P1 true.
2) Assume Pn to be accurate, i.e., 4 + 9 + 14 +... + ( 5n -1)= (n/2)(5n +3)
3) Establish Pn+1 as true in the induction stage.
Replace (n+1) on both sides of n to obtain Pn+1.
Pₙ₊₁: 4 +9 +14 +...+(5n -1)+ [5(n+1) -1]=
Establish the RHS and LHS's parity.
LHS = 4 +9 +14 +...+(5n -1)+ [5n +5-1]
Bold expression in (2) should be replaced with the value of Pn:
.∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.
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How do you solve this please
The number of students in the population would be:
Wear glasses - 165 students Wear contact lenses - 60 students No vision problem diagnosed - 525 students How to find the population ?The sample is directly related to the population of students so parts of the students can be found using the sample.
Students in population who wear glasses :
= Sample who wear glasses / Total sample x Total population
= 11 / 50 x 750
= 165 students
Students who wear contacts:
= 4 / 50 x 750
= 60 students
Students with no vision problems :
= 35 / 50 x 750
= 525 students
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The multiplicative inverse of -7/9 is
Answer:
9/-7
Step-by-step explanation:
the reason is all you have to do is reverse the fraction
Answer:
-9/7
Step-by-step explanation:
The multiplicative inverse of -7/9 is_____?
The multiplicative inverse of a number is defined as a number that when multiplied by the original number gives the product as 1
-7/9 × (- 9/7) = 1
Please help, thank you in advance! 15 POINTS!!!
The value of the probability of event C is 0.30.
How to determine the probabilityThe law of total probability states that
P(A U B U C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C).
Substitute the known values in the above equation, so, we have the following representation
P(A U B U C) = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02.
Also are given:
P(A U B U C)' = 0.33,
This implies that
P(A U B U C) = 1 - 0.33 = 0.67.
Substituting the values, we get:
0.67 = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02
0.67 = 0.24 + 0.26 + P(C) - 0.15 + 0.02
0.67 = 0.50 + P(C) - 0.13
0.80 = 0.50 + P(C)
P(C) = 0.80 - 0.50 = 0.30.
Hence, the probability is 0.30
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Chris buys 1.6 pounds of almonds and 2.8 pounds of cashews. Emily buys 0.7 pound of almonds and 1.5 pounds of cashews.
The total cost of the nuts that Chris and Emily buy can be found using the expression: (1.6a) + (2.8c) + (0.7a) + (1.5c) You can also use the expression (10.6a) + (2.8c) for the total cost of nuts that Chris buy.
What is pounds?pound, unit of avoirdupois weight, equal to 16 ounces, 7,000 grains, or 0.45359237 kg, and of troy and apothecaries’ weight, equal to 12 ounces, 5,760 grains, or 0.3732417216 kg. The Roman ancestor of the modern pound, the libra, is the source of the abbreviation lb. In medieval England several derivations of the libra vied for general acceptance.
Among the earliest of these, the Tower pound, so called because its standard was kept in the Royal Mint in the Tower of London, was applied to precious metals and drugs and contained 5,400 grains, or 0.350 kg, whereas the mercantile pound contained 6,750 grains, or 0.437 kg. The troy pound, believed to have originated in Troyes, France, superseded the lighter Tower pound in 1527 as the gold and silver standard. Increased trade with France led also to the adoption of the 16-ounce avoirdupois pound in the 16th century to replace the mercantile pound.
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Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept
f(x) = (x + 1)(x - 5)(x - 1)^2
The x-intercepts will be at x = 0 , -2 A line crosses the x-axis at the x-intercept, and the y-intercept is where the line crosses the y-axis.
What is polynomial function?A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5. A polynomial is a function that has the formula f(x) = anxn + anxn + anxn+1 +... + a2x2 + a1x + a0. The highest power of x in the formulation of a polynomial is its degree. Constant (non-zero) polynomials, linear polynomials, quadratics, cubic, and quartics, respectively, are polynomials of degree 0, 1, 2, 3, and 4.Given
f(x) = x²(x+2)
To find the x-intercepts ⇒ f(x) = 0
∴ x²(x+2) = 0
∴ x² = 0 OR x+ 2 = 0
∴ x = 0 or x = -2
So, the x-intercepts will be at x = 0 , -2
We must graph the function f in order to determine whether the graph crosses the x-axis, hits the x-axis, and then reverses at each intercept (x)
The attached figure represents the graph of f(x)
As shown in the figure:
1) The graph crosses the x-axis at x = -2
2) The graph touches the x-axis and turns around at x = 0
The complete question is,
Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work.
f(x) = x2(x + 2)
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