The absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign.
The absolute value is always a positive value and not a negative number. so those numbers are called absolute values.
It is represented as |a|, which defines the magnitude of any integer ‘a’.
It defines removing any negative sign in front of a number and thinking of all numbers as positive.
Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system.
When x itself is negative (x<0), then its absolute value is necessarily positive
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In ΔEFG, g = 4.3 cm, e = 9.1 cm and ∠F=116°. Find the length of f, to the nearest 10th of a centimeter.
The length of f in the triangle is 11.6 cm
What is cosine rule?In trigonometry, the Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
Cosine rule is therefore given as:
f² = g²+e²-2bccos F
f² = 4.3²+9.1²-2×4.3×9.1cos116
f² = 18.49+82.81-78.26(-0.44)
f² = 101.3+34.43
f² = 135.73
square root both sides
f = √135.73
f = 11.6 ( nearest tenth of centimeter)
therefore the length of f is 11.6cm
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Which relation is a function?
{(1, −7), (2, −8), (−2, 7), (1, 8)}
{(−2, 2), (−7, 7), (−1, 1), (−8, 8)}
{(−2, 1), (−2, 2), (−2, 7), (−2, 8)}
{(−2, 1), (−7, −1), (2, 8), (−7, −8)}
The second relation is a function
Mason is working two summer jobs, making $7 per hour babysitting and making $10 per hour clearing tables. In a given week, he can work at most 12 total hours and must earn no less than $90. If a represents the number of hours babysitting and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
the answer to this question is 107
eight children are divided into two teams each containing 4 children to play a game against each other. how many different divisions are possible? group of answer choices 35
8 children are divided into 2 teams each containing 4 children to play a game against each other. 105 different divisions are possible.
Permutation:
In mathematics, permutation refers to the process of placing all members of a set into an order or sequence. In other words, if the set is already ordered, the permutation of its elements is called permutation. Substitutions occur in more or less noticeable ways in almost all areas of mathematics. They often occur when different orders are considered in a particular finite set.
Combination:
Combining is a way of selecting items from a collection, and (unlike permutation) the order of selection does not matter. In smaller cases you can count the number of combinations. Combining refers to combining n things, taken k times at once, without repetition.
According to the Question:
The first team can be chosen in ⁸C₂ = 28 ways.
After that, there are 6 people left, from which there are ⁶C₂ = 15 ways to choose the second team.
Then, there are 4 people left, out of which ⁴C₂ = 6 ways he can choose the third team. There is only one way to choose the fourth and final team from the remaining two.
In the above procedure, each occasion of splitting eight into her two his four teams counted as 4!= 24 times.
Thus,
The number of ways to divide a group of 8 people into 4 teams of 2 people = 28 × 15 × 6 / 24
= 105
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the eifell tower 324 m tall. the height was halved repeatedly to make a model around30 cm. what power of 2 was the height divided by
The power of two by which the height was divided is given as follows:
Tenth power of 2.
How to obtain the power of two by which the height was divided?The power of two by which the height was divided is obtained applying the proportions in the context of this problem.
The equation that relates the heights and the scale factor is given as follows:
New height = Old height / Scale factor.
The parameters for this problem are given as follows:
Old height: 324 m.New weight: 30 cm = 0.3 m, as 1 m = 100 cm.Then the scale factor is obtained as follows:
Scale factor = 324/0.3
Scale factor = 1080.
The tenth power of 10 is given as follows:
2^10 = 1024.
Which is close to 1080, and hence the height was divided by the tenth power of 2.
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so for this i just need to know how to find the area and perimeter
Answer:
Step-by-step explanation:
x=7
Answer: Area: 364 Perimeter: 80
Step-by-step explanation:
Since 2x=14, x=7. Then you plug 7 into 3x+5, so 3(7)+5=26. Then for area you do 14*26=364, and for perimeter you simply do (26+14)2=80
A circle has a diameter of 7.6 cm
workout the circumferences of the circle
give your answer correct to 3 significant figures
The circumference of the circle is 23.864
In order to calculate the circumference of a circle, you need to multiply the Diameter of the circle with value of π (pi) which is 3.14.
In the given question,
given, d = 7.6cm
formula : C = d x π
therefore, C = 7.6 x 3.14 = 23.864cm
Write the answer correctly to 3 significant figures.
Alternatively, Circumference can also be calculated by using the value of the radius of the circle. We know, Radius = Diameter/2
Therefore, C = ( 2 x r ) x π
Symbols:
π = pi ( value = 3.14)
d = diameter
r = radius
C = circumference
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5 question
Directions: Read through Scenario and answer questions 1-15 using July’s Cost for Services fee schedule.
Scenario: July is self-employed and works as an esthetician. She does eyelashes, waxing services, brow lamination, facials and massages.
According to the information we can infer that July earns $675 per week (answer 1), $715 every weekend (answer 2); $5,560 per month (answer 3), $3,050 for additional services (answer 4), and $8,610 as a year's total (answer 5).
How much does July make per week (answer 1)?To calculate how much does July make per week we have to take into account the following information:
Services that July currently make every week.
3 natural looks lashes2 volume lashes2 brow laminations2 full face waxing1 bikini waxTo calculate the total earned by July we have to multiply the price of each service by the number of customers of each one. Additionally, we have to add all results as shown in the following.
3 * $65 = $1952 * $85 = $1702 * $80 = $1602 * $45 = $901 * $60 = $60$195 + $170 + $160 + $90 + $60 = $675
How much does July make on the weekend (answer 2)?To calculate how much does July make per weekend we have to take into account the following information:
Services that July currently make every weekend.
2 body massages2 natural look lash extensions3 mega volume extensions2 facialsTo calculate the total earned by July we have to multiply the price of each service by the number of customers of each one. Additionally, we have to add all results as shown in the following.
2 * $85 = $170
2 * $65 = $130
3 * $95 = $285
2 * $65 = $130
$170 + $130 + $285 * $130 = $715
How much does July make on a given month (answer 3)?To calculate how much July makes on a given month we have to add the weekend earnings with week earnings and multiply it by four (taking into account that a month has four weeks).
$715 + $675 = $1,390
$1,390 * 4 = $5,560
How much would July make for additional services alone per year (answer 4)?To calculate the total earned by July for additional services we have to calculate the total value of these services and multiply it by five.
2 * $185 = $370
3 * $80 = $240
$240 + $370 = $610
$610 * 5 = $3,050
How much would July make in a year for her regular services plus the additional services mentioned in question #4 (answer 5)?To calculate how much would July make in a year for her regular services plus the additional services of the question 4, we have to add both values.
$5,560 + $3,050 = $8,610
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how to prove the median of a trapezoid is parallel to the bases and equal in length to the average of their lengths?
The median of a trapezoid is parallel to the bases and equal in length to the average of their lengths. This is due to the midpoint theorem and the definition of the average.
The median of a trapezoid is a line segment that connects the midpoints of the non-parallel sides of the trapezoid. By the definition of a trapezoid, the two parallel sides (the bases) are of equal length.To prove that the median of a trapezoid is parallel to the bases and equal in length to the average of their lengths, we will make use of the midpoint theorem and the definition of the average.First, let's look at the midpoint theorem: If two points are the midpoints of two sides of a trapezoid, then the line connecting them is parallel to the bases. Now, let's look at the definition of the average: The average of two numbers is equal to the sum of the numbers divided by two.Now, let's apply these two concepts to the median of a trapezoid. As stated above, the median of a trapezoid connects the midpoints of the non-parallel sides of the trapezoid. By the midpoint theorem, the line connecting the midpoints of the non-parallel sides of the trapezoid is parallel to the bases. Next, we need to prove that the median of a trapezoid is equal in length to the average of the lengths of the bases. We can do this by noting that the length of the median of a trapezoid is equal to the sum of the lengths of the bases divided by two. This is because the median line segment connects the midpoints of the bases, so the length of the median is equal to half the sum of the lengths of the bases.Therefore, we can conclude that the median of a trapezoid is parallel to the bases and equal in length to the average of their lengths.Learn more about median here
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the price of fuel may increase due to demand and decrease due to overproduction. marco is studying the change in the price of two types of fuel, A and B, over time.
the price f(x), in dollars, of fuel A after x months is represented by the function below:
f(x) = 2.27(0.88)^x
part A: is the price of fuel A increasing or decreasing and by what percentage per month? justify your answer
part B: the table below shows the price g(m), in dollars, of fuel B after m months:
m (number of months): 1 | 2 | 3 | 4
g(m) (price in numbers): 3.44 | 3.30 | 3.17 | 3.04
which type of fuel recorded a greater percentage change in price over the previous months? justify your answer
a) The price of fuel A is decreasing by a percentage of 12% per month.
b) The greater percentage decay is of type A fuel.
How to model an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the parameters are given as follows:
a is the initial value.b is the rate of change.For a decaying exponential function, we have that:
b = 1 - r, |b| < 1.
In which r is the decay rate.
For fuel type A, the decay rate is given as follows:
1 - r = 0.88
r = 0.12.
For fuel type B, the parameter b is given as follows:
b = 3.30/3.44
b = 0.96.
Hence the decay rate is of:
1 - r = 0.96
r = 0.04.
(which is a lower decay rate than the 0.12 of fuel type A).
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the roots of the polynomial 10x3 - 39x2 29x - 6 are the height, length, and width of a rectangular box (right rectangular prism). a new rectangular box is formed by lengthening each edge of the original box by 2 units. what is the volume of the new box?
The volume of the new box is 30 units^3.
We can infer the roots are rational integers from the response options, thus this polynomial ought to be simple to factor. The coefficients of x must multiply by 10, hence they must be in some sequence of 5,2,1 or 10,1. Since we can try each one separately, we can express the factored form as follows:
(5x-p)(2x-q)(x-r)
Due to the fact that p, q, and r must multiply to 6, they must be either 3,2,1 or 6,1,1 in some sequence. Once more, we may test each one in a different place to determine if they multiply properly.
When we multiply the x-terms and attempt (5x-2)(2x-1)(x-3), the answer is 29. Try adding the x^2 terms together; they equal -39. Consequently, the roots are [tex]\frac{2}{5} , \frac{1}{2} and 3.[/tex] Now if you add 2 to each root, you get the volume is
=> [tex]\frac{12}{5} X \frac{5}{2} X 5 =30[/tex]
Therefore, The volume of the new box is 30 units^3.
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The four triangles at right are placed in a bag. If you reach into the bag without looking and pull out one triangle at random, what is the probability that: Homework Help ✎
The triangle is scalene?
The triangle is isosceles?
At least one side of the triangle is 6 cm?
Probability of scalene triangle, isosceles triangle and at least one side of the triangle is 6 cm are 1/4, 1/2 and 1/2 respectively
How to determine the probability of having a scalene triangle?Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.
A probability of 0 means that an event is impossible, a probability of 1 means that an event is certain to occur.
A scalene triangle is a triangle with no equal sides.
An isosceles triangle is a triangle with two equal sides.
An equilateral triangle is a triangle with all 3 sides equal.
Check the attached image to see how I labeled the triangles
Triangle 1 is isosceles (two sides with 6 cm each)
Triangle 2 is scalene
Triangle 3 is isosceles (two sides with 10 cm each)
Triangle 4 is equilateral (three sides with 4 cm each)
Probability (Scalene triangle) = 1/4
Probability ( isosceles triangle) = 2/4 = 1/2
Probability ( At least one side is 6 cm) = 2/4 = 1/2
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The grain silo pictured above has a radius of 1.7 m. How much paint is required to
completely cover the sides and top of the grain silo once?
The amount of paint required for the grain silo is calculated to be
106.61 m²
How to find the paint required to cover the grain siloThe figure is made up of 2 objects a cylinder and the conical cover. Therefore, we solve for total surface area TSA of the cylinder and the cone and add
TSA for cylinder
= 2πr (h + r)
where
h = 6.2 m
r = 1.7 m
= 2π * 1.7 (6.2 + 1.7)
= 26.86π
TSA for cone
= πr (l + r)
where
l = slant height = 1.9 m
r = 1.7
= π * 1.7 (1.9 + 1.7)
= 6.12π
how much paint required = TSA for cone + TSA for cylinder
how much paint required = 6.12π + 26.86π
how much paint required = 32.98π
how much paint required = 103.61 m²
the thickness of the painting will say the volume of paint
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What is a infinitely many in math?
In mathematics, having an infinitely large amount or cardinality is referred to as having an infinity many.
Endless sets actually have an infinite number of components. If a set has continuity on both sides or is unbounded from start to finish, we can refer to it as infinite. For instance, the set of whole numbers W = 0, 1, 2, 3, etc. is an infinite set since it has an unlimited number of items. The set of real numbers is one of the uncountably infinite sets. Dots are used to symbolize the elements of an infinite set to denote the set's infinity.
There are some properties of infinite many solutions.
The superset of an infinite set is also infinite.
The subset of an infinite set may or may not be infinite.
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Give the domain and range. A relation. An arrow goes from 1 to negative 1, from 2 to 0, from 3 to 1. a. domain: {1, 2, 3}, range: {1, 0, 1} b. domain: {–1, 0, 1}, range: {1, 2, 3} c. domain: {1, 0, 1}, range: {1, 2, 3} d. domain: {1, 2, 3}, range: {–1, 0, 1} Please select the best answer from the choices provided A B C D
The domain and the range of the relation are given by the following option:
d. domain: {1, 2, 3}, range: {–1, 0, 1}.
How to obtain the domain and the range of the relation?The domain of a function is the set that contains all the input values, which are the values from which the arrow departs.
The range of a function is the set that contains all the output values, which are the values from which the arrow arrives.
Considering these definitions and the description of the set, the correct option is given by option d.
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how many gallons will daniel need? help please thank you
Measure wall height from floor to ceiling. Exclude baseboards and moldings. Measure length of each wall including doors and windows.
What exactly is the wall formula?Walls. Use the basic formula of Length x Width = Area to determine the area of a wall. Then, using the same approach, calculate the individual area of windows and doors. After you’ve taken all of these measurements, deduct the area of the windows and doors from the overall wall area. Methods of longwall and shortwall Long walls are those that run the length of the room, whereas short walls are those that run perpendicular to the length of the room.
Next, consider which unit of measurement is most appropriate for measuring a wall. Very tiny units such as inches, centimeters, and millimeters can be ruled out. We can also eliminate.
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Evaluate 8.5 x plus 7.9 y when x equals 7 and y equals 8
Answer:
=x^2+1 (Graph Example), 4x+2=2 (x+6) (Solve Example) Algebra Calculator is a calculator that gives step-by-step help on algebra problems. See More Examples ». x+3=5. 1/3 +
Step-by-step explanation:
Answer:
y=x^2+1
Step-by-step explanation: 4x+2=2 (x+6)
Marcel just started her own business making cookies. She sells the cookies in boxes, charging $15.00 per box. It costs her $50.00 to buy the supplies. She wants to calculate how many boxes she must make to earn a profit of at least 245.00.
Answer:
Step-by-step explanation:
To calculate how many boxes of cookies Marcel needs to make to earn a profit of $245.00, we need to use the following formula:
Profit = (Revenue - Expenses) / Number of boxes
We know that the revenue is $15.00 per box and the expenses are $50.00. We also know that the profit should be at least $245.00.
So we can substitute these values into the formula and solve for the number of boxes:
$245.00 = ($15.00 - $50.00) / x
Where x is the number of boxes.
To solve for x, we'll need to multiply both sides of the equation by x:
$245.00*x = ($15.00 - $50.00)
$245.00*x = -$35.00
x = -$35.00/$245.00 = -0.142857143
The number of boxes is a negative value which is not possible, so Marcel will not earn a profit of $245.00. She will need to increase her revenue or decrease her expenses to reach a profit of $245.00.
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on yellow, P(not yellow).
Answer: P(not yellow) = 6/8
Step-by-step explanation:
It is correct 100%
Answer:
0.625 in decimal form
What is the area of triangle abc?
Therefore , the solution of the given problem of triangle comes out to be area of triangle = 0.25 unit square.
What does a triangle actually mean?Triangles are polygons because they have four sides or more. Its form is simple and geometric. An angle square with the letters ABC is known as a triangle. When the sides remain not collinear, Euclidean geometry generates a singular plane or square. Having three parts and three corners makes a triangle a polygon. The corners of a triangle are where the three sides meet. Angles in a triangle add up at 180 °.
Here,
Given:
So , the vertices are of unit length :
=> Area of triangle = 1/2 * b*h
=> Area of triangle = 1/2 * 1 * 0.5
=> Area of triangle = 0.25 unit square.
Therefore , the solution of the given problem of triangle comes out to be area of triangle = 0.25 unit square.
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I. The sum of the probabilities in a probability distribution can be any number between 0 and 1. II. The probability of the union of two events is the sum of the probabilities of those events. III. The probability that an event happens is equal to 1 minus the probability that the event does not happen.
None of the above gives the complete set of true responses for the probability that the event does not happen.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
None of the above provides the entire set of accurate replies for the likelihood that the event does not occur.
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You have a set of cards labeled one through ten. Event A is drawing an odd card. Event B is drawing a four or higher. What is the P (A∩B)0.900.700.200.50
The value of probability P(A ∩ B) = 3/10 = 0.3.
Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.
Probability is used in many fields such as statistics, finance, economics, and science to make predictions and decisions based on uncertain information
Event A is drawing an odd card, which means that the odds are 5/10 or 1/2.
Event B is drawing a four or higher, which means that the odds are 7/10.
Event A ∩ B means that we are interested in the probability of drawing an odd card and drawing a card of four or higher at the same time. There are 3 cards that are both odd and four or higher, which are 5,7, and 9. So the probability of drawing one of these cards is 3/10.
Therefore, The value of probability P(A ∩ B) = 3/10 = 0.3.
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when mr. adams calculated his students' algebra test scores, he noticed that two students had extremely low scores. which measure of central tendency is affected most by the scores of these two students?
Mean has been affected most by the scores of these two students.
A bunch of scores is averaged to form the mean. The total scores were divided by the total scores. When population samples are tiny, the mean is susceptible to extreme scores.
When you add up all the individual scores and divide that total by the number of students, you obtain the mean, which is the arithmetic average score.
The average performance of a group of students on a test is represented by their mean scale score. A mean scale score is derived specifically by summing together the scores of each individual student and dividing that amount by the number of scores. It is additionally known as an average.
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do most teens recycle? to find out, an ap statistics class asked an srs of 100 students at their school whether they regularly recycle. in the sample, 55 students said that they recycle. is this convincing evidence that more than half the students at the school would say they regularly recycle? the dotplot shows the results of taking 200 srss of 100 students from a population in which the true proportion who recycle is 0.50.
More data needs to be collected to be able to conclude if more than half the students regularly recycle as the dotplot shows the results are variable.
1. Calculate the proportion of students who reported recycling in the sample:
55/100
= 0.55
2. Calculate the sample size:
100 students
3. Calculate the standard error: SE
= sqrt(0.50*(1-0.50)/100)
= 0.05
4. Calculate the 95% confidence interval:
CI = 0.55 +/- 1.96*SE
= 0.55 +/- 0.098
= (0.45, 0.65)
5. Compare the confidence interval to the true population proportion: 0.50 is not included in the CI, therefore we cannot conclude that more than half the students would say they regularly recycle.
We cannot conclude that more than half of the students would say they regularly recycle because the 95% confidence interval (0.45, 0.65) does not include the true population proportion (0.50). Therefore, more data needs to be collected to be able to draw a conclusion.
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Find the equation of the tangent line to the curve f(x) = 4x^3 - 2x^2 + 3x - 10 when x=4
Answer:
Is your question complete? there's no y term
Answer:
Refer to the image attached.
Step-by-step explanation:
I need the answer for this question
Answer:
[tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
Rate of change = [tex]\frac{Change in Y value}{Change in X value}[/tex]
Pick any two sets of 'X' and 'Y' value
I chose (-4, 6) as [tex](X_{1} ,Y_{1} )[/tex]and (12, -2) as [tex](X_{2} ,Y_{2} )[/tex] :
Rate of change = Slope / Gradient of graph = [tex]\frac{Y_{2} -Y_{1} }{X_{2} - X_{1} }[/tex]
= [tex]\frac{-2 - (6)}{12 - (-4)}[/tex]
= [tex]\frac{-2 - 6}{12 + 4}[/tex]
= [tex]\frac{-8}{16}[/tex]
= [tex]\frac{- 1}{2}[/tex]
What is the name of the fee charged by a financial institution for withdrawing money from an account before the maturity date?
O A. Surrender charge
O B. Liquidity fee
O C. Early redemption fee
Surrender charges safeguard against such losses. Surrender costs on some annuities and insurance products can apply for as short as 30 days or as long as 15 years. If you cash in your investment in year one, the surrender cost for annuities and life insurance is typically 10%.
The surrender period is the amount of time that an investor must wait before withdrawing cash from an annuity without penalty. Surrender periods can last many years, and withdrawing funds before the conclusion of the surrender term may result in a surrender charge, which is basically a delayed sales cost.
The longer the surrender time, in general, but not always, the better the annuity's other terms.
The surrender period is the period during which an investor may withdraw funds from an annuity without incurring a surrender charge.
The surrender term can last many years, and annuitants may face large fines if they remove their invested assets before the time has finished.
Other financial instruments include a surrender period as well B-share mutual funds and entire life insurance plans are two examples.
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One scuba diver’s elevation changed by −15 5/8
feet every minute. This was 114
times the rate of change for a second scuba diver.
What was the rate of change in elevation of the second scuba diver in feet per minute?
Answer:
Step-by-step explanation:
The rate of change in elevation of the second scuba diver in feet per minute would be -15 5/8 / 114 = -0.137 feet per minute.
Tyrone is converting startfraction 45 over 50 endfraction to a percent. which method should he use to find the percent? divide the numerator and denominator of the fraction by 2. subtract 40 from the numerator and denominator of the fraction. multiply the numerator and the denominator of the fraction by 2. add 50 to the numerator and denominator of the fraction.
40% first you turn it into a decimal, then u multiply it by 100 to get your percent.
For solving this question we will use the Unitary method
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The term "unitary method" refers to a process where the value of one item is initially determined before determining the values of any other items.
The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
2/5 = 0.4
0.4 x 100 = 40% first u turn it into a decimal, then u multiply it by 100 to get ur percent
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The full question will be
Tyrone is converting StartFraction 45 Over 50 EndFraction to a percent. Which method should he use to find the percentage?
Which of the following method solves initial values problem by using sloped at two points ?
A. Euler method
B. Heuns method
C. RK method
D. picards method
The method that solves initial values problem by using sloped at two points is Heuns method.
Therefore the answer is B. Heuns method.
The Heun's method, also known as the improved Euler method, is a numerical method used to solve initial value problems for ordinary differential equations. It is a second-order method, which means that it uses the slope at two points (the starting point and one other point) to estimate the solution at a future point.
Heun's method is an explicit method which is an extension of the Euler method, by using the slope at the midpoint between the current and the next steps to improve the accuracy of the solution.
Euler method is a first-order method which estimates the solution at a future point by using the slope at one point only.
RK method is a family of methods that ranges from first-order to fourth-order method, but it uses a combination of the slopes at different points to estimate the solution.
Picard's method is a method of solving differential equations that is based on the idea of repeatedly applying a function to an initial value until a fixed point is reached. It's a method that does not use slopes.
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