Therefore , the solution to the given problem of algorithm comes out to be it fall under the category of undecidable questions, which is a subtype of unsolvable problems.
Define algorithm.An algorithm is a process for carrying out a computation or resolving a challenge. Algorithms work as a detailed set of guidelines that lead hardware- or software-based routines through a series of predetermined actions step by step. Algorithms are frequently used in all areas of IT.
Here,
A problem is considered undecidable if there is no algorithm that can be created that will consistently return a true or false answer for each input value.
Only issues that should have a yes-or-no response (such as: does my code contain a bug?) fall under the category of undecidable questions, which is a subtype of unsolvable problems.
Therefore , the solution to the given problem of algorithm comes out to be it fall under the category of undecidable questions, which is a subtype of unsolvable problems.
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What is the perimeter of 4?
The perimeter of a shape with 4 sides is equal to the sum of its sides multiplied by itself, which in this case is 4 multiplied by 4, resulting in a perimeter of 16.
Step 1: Calculate the length of each side by multiplying 4 by 4.
Step 2: Add the lengths of each side together to get the perimeter.
Step 3: The perimeter of the shape with 4 sides is equal to 16.
The perimeter of a shape is the sum of the lengths of its sides. To calculate the perimeter of a shape with 4 sides, you need to find the length of each side. To do this, you can multiply the length of one side by itself. For example, if the length of one side is 4, the length of each side would be 4 multiplied by 4, which is 16. Therefore, the perimeter of a shape with 4 sides is equal to 16. To calculate the perimeter of a different shape with an unknown number of sides, you can add up the lengths of each side to get the total perimeter. This is a useful way to measure the size of a shape and can be used to calculate the area of a shape by dividing the perimeter by the number of sides.
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Which graph best represents a function with a domain of all real numbers greater than or
equal to 1 and less than or equal to 2?
The graph best represents a function with a domain of all real numbers greater than or equal to 1 and less than or equal to 2 are area between equation x + y [tex]\geq[/tex] 1 and x + y [tex]\leq[/tex] 2 .
Which function has a domain that includes all real numbers?The collection of all potential inputs for a function is known as its domain. For instance, the domain of f(x)=x2 is all real numbers, and the domain of g(x)=1/x is all real numbers other than x=0.
How do you plot all real values on a graph?The real numbers are all the numbers that make up the real number line, per definition. Thus, all real numbers can be graphed by simply drawing a number line. The number line is a graph of all real numbers since it contains all of the rational numbers.
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55 pecans put them in 2 buckets where one has 15 more than the other
The number of pecans in each bucket will be 20 and 35.
How to illustrate the expression?From the information, there are 55 pecans are put in 2 buckets where one has 15 more than the other. An expression show the relationship between the variables.
In this case, 55 pecans put them in 2 buckets where one has 15 more than the other.
This will be:
x + x + 15 = 55
2x + 15 = 55.
Collect the like terms
2x = 55 - 15
2x = 40
Divide
x = 20
The other number will be:
x + 15.
= 20 + 15
= 35
The numbers are 20 and 35.
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55 pecans are put in 2 buckets where one has 15 more than the other. What is the amount in each bucket.
The foundation for a new high school building is rectangular in shape, and the area is [tex]5x^3 + 4x^2 - 10x - 8[/tex] square meters. Factor by grouping to find expressions for the dimensions of the building
The dimensions of the building are (x² - 2)(5x + 4). The result is obtained by using the expression for the dimensions.
How to factor by grouping?Grouping is a specific technique used to factor polynomial equations. You can use it with quadratic equations and polynomials that have four terms. The method is slightly different.
Here is how to factor by grouping:
Look at the equation and find the master product (ac).Find the factors of ac that the sum is equal to b.Split the center term into two factors.Group the terms to form pairs.Factor out each pair and factor out the shared parentheses.The area of the new high school building in a rectangular shape is 5x³ + 4x² - 10x - 8. Factor by grouping to find the dimensions!
Follow the steps on how to factor by grouping.
5x³ + 4x² - 10x - 8
= (5x³ + 4x²) - (10x - 8)
= x²(5x + 4) - 2(5x - 4)
= (x² - 2)(5x + 4)
Hence, the dimensions of the building are (x² - 2)(5x + 4).
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What are the factors of the expression 2x^2 5x 12?
[tex](x- (\frac{-5+71i }{4}))[/tex] and [tex](x- (\frac{-5-71i }{4}))[/tex] are factors of the quadratic expression.
2x^2 + 5x + 12
Consider given quadratic expression.
2x^2 + 5x + 12
Let f(x) = 2x^2 + 5x + 12
Assume f(x) = 0
2x^2 + 5x + 12 = 0
using the Quadratic Formula where
a = 2, b = 5, and c = 12
[tex]x = \frac{-b\pm \sqrt{b^2 - 4ac} }{2a} \\\\\\x = \frac{-5\pm \sqrt{5^2 - 4(2)(12)} }{2\times2} \\\\\\x = \frac{-5\pm \sqrt{25 - 96} }{4} \\\\\\x = \frac{-5\pm \sqrt{-71} }{4}[/tex]
The discriminant b^2 - 4ac < 0.
So, there are two complex roots.
[tex]x = \frac{-5\pm71i }{4}[/tex]
This means, [tex](x- (\frac{-5+71i }{4}))[/tex] and [tex](x- (\frac{-5-71i }{4}))[/tex] are factors.
2x^2 + 5x + 12
= [tex](x- (\frac{-5+71i }{4}))[/tex] × [tex](x- (\frac{-5-71i }{4}))[/tex]
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The temperature in knowlton is 2.5 C colder than the terminal elmwood. Which equation shows the temperature, in C, in knowlton? 9 - 2.5 = 6.5 or 9 + 2.5 = 11.5 or -9 - 2.5 = - 11.5 or -9 + 2.5 = -6.5
The equation representing the asked situation is (9 - 2.5) = 6.5
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, The temperature in Knowlton is 2.5 C colder than the terminal Elmwood.
We know, that, if temperature is colder in any area A than another area B then, A will have less temperature than B.
Therefore, temperature in Knowlton is less than that of in Elmwood.
Therefore, if the temperature in Elmwood is 9 the temperature in Knowlton will be 9-2.5 = 6.5
Hence, the required equation is 9-2.5 = 6.5
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write the rule x= 10, -4, 0, 5, -2
y= 29, -13, -1, 14, -7
10=29
-4=-13
0=-1
5=14
-2=-7 help asap!!
The rule for the given set of data is y = 3x - 1.
What is rule in function?The relationship between dependent and independent variables, expressed as an equation, is referred to as a function rule. In order to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, one must follow a specific function rule.
A function rule can be defined as the procedure that transforms an input value into an output in plain English.
Lets put two of the points in slope formula
y - y₁ = m(x - x₁)
29 - (-13) = m(10 - ( -4))
42 = m14
m = 42/14
m = 3
Now lets make the equation
y - 29 = m(x - 10)
y = 3x - 30 + 29
y = 3x - 1
Thus, the rule for the given set of data is y = 3x - 1.
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Number 7 says find the measure of the angle indicated I could fit the question in with it! If you could help!
The measure of angle E if The measure of angles is 2x + 13, 11x - 6 and 89°, is 37°.
What is the angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Given:
The measure of angles is 2x + 13, 11x - 6 and 89°,
Use the exterior angle theorem and find the value of x as shown below,
2x + 13 + 89 = 11x - 6
2x + 102 = 11x - 6
9x = 108
x = 12
Thus, the measure of ∠ E = 2 × 12 + 13
∠ E = 24 + 13
∠ E = 37°
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What ordered pair is a solution to the system of linear equations?
Solutions of a system of an equations are given with the values of the variables which make all the equations true in which a solution of a system of given two linear equations is represented in an ordered pair (x, y) as explained with example below:
An example of a system of two linear equations in an ordered pair , in order to show the two equations that are arranged together to form a system of equations in an linear form .
let , 2x + y = 7,
x- 2y = 6
A linear equation which consists of two variables, as 2x + y = 7, has an infinite number of solutions. in which the graph of a equation is a line. we know that every point on the line is a required solution to the equation and every solution of an equation is a point on the line.
To solve a system of two linear equations in an ordered pair , we want to find the values to particular variables that are solutions to both linear equations. In other words, we are expecting for the ordered pairs (x, y) that make both equations valid . These type of equations are known as solutions to a system of equations.
hence , the solutions of a system of equations are the values of the variables that make all the valid and obeyed equations are true. and solution of a system of two linear equations is represented always in an ordered pair (x, y) .
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A photographer takes 12 different photographs. There are 3 sunsets, 4 oceans, and 5 mountains.
How many possible arrangements are there if all the photographs of the mountains are next to each other?
Answer:
4838400 arrangements--------------------------------------------------
Permutation of 5 mountain photographs:
P(5, 5) = 5! = 120Since all are next to each other, the mountain photographs count as one item along with the other 3 + 4 = 7 photographs and therefore the permutation for this is:
P(8,8) = 8! = 40320Total arrangements is:
120*40320 = 4838400Estimate the area of the circle. Round to the nearest whole number. A) 3 square units B) 6 square units C) 9 square units D) 12 square units
The area of the circle is A. 3 square units
How to determine the area of the circleThe formula for determining the area of a circle is expressed as;
A = πr² or 1/4πd²
Given that;
A is the area of the circleπ takes the value 3.14 or 22/7r is the radius of the circled is the diameter of the circleAlso, the formula for calculating the radius of a circle is given as;
Radius = diameter/2
Substitute the value, we have;
Radius = 2/2
Radius = 1
Substitute the value into the formula
Area, A = 3. 14 × (1)²
Find the square
Area, A = 3. 14 square units
Hence, the value is 3 square units. Option A
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The complete question
Estimate the area of the circle, given the diameter as 2 unit. Round to the nearest whole number. A) 3 square units B) 6 square units C) 9 square units D) 12 square units
Please help I’m going to fail this grade
The result of the operation between two mixed numbers are listed below:
99 / 104 4 / 3 6 / 5 52 / 25 57 / 53 33 / 100 1 / 2 8 / 5 4 4 / 3How to solve an operation between mixed numbers
Mixed numbers are real numbers with special notation to transform improper fractions into a combination of integers and fractions. That is:
a b / c = a + b / c
Where a, b, c are integers and c is a non-zero number.
The procedure to simplify the operation is described below:
Transform mixed numbers into improper fractions. Divide the resulting two fractions. Simplify the expression.Case 1
1 3 / 8 ÷ 1 4 / 9
(1 + 3 / 8) ÷ (1 + 4 / 9)
(11 / 8) ÷ (13 / 9)
(11 / 8) / (13 / 9)
99 / 104
Case 2
2 1 / 3 ÷ 1 3 / 4
(2 + 1 / 3) ÷ (1 + 3 / 4)
(7 / 3) ÷ (7 / 4)
(7 / 3) / (7 / 4)
28 / 21
4 / 3
Case 3
4 1 / 5 ÷ 3 1 / 2
(4 + 1 / 5) ÷ (3 + 1 / 2)
(21 / 5) ÷ (7 / 2)
42 / 35
6 / 5
Case 4
5 1 / 5 ÷ 2 1 / 2
(5 + 1 / 5) ÷ (2 + 1 / 2)
(26 / 5) ÷ (5 / 2)
(26 / 5) / (5 / 2)
52 / 25
Case 5
9 1 / 2 ÷ 9 4 / 6
(9 + 1 / 2) ÷ (9 + 4 / 6)
(19 / 2) ÷ (58 / 6)
114 / 106
57 / 53
Case 6
2 2 / 10 ÷ 6 2 / 3
(2 + 2 / 10) ÷ (6 + 2 / 3)
(22 / 10) ÷ (20 / 3)
(22 / 10) / (20 / 3)
(66 / 200)
33 / 100
Case 7
2 1 / 4 ÷ 4 1 / 2
(2 + 1 / 4) ÷ (4 + 1 / 2)
(9 / 4) ÷ (9 / 2)
(9 / 4) / (9 / 2)
18 / 36
1 / 2
Case 8
2 2 / 3 ÷ 1 2 / 3
(2 + 2 / 3) ÷ (1 + 2 / 3)
(8 / 3) ÷ (5 / 3)
(8 / 3) / (5 / 3)
8 / 5
Case 9
5 3 / 5 ÷ 1 2 / 5
(5 + 3 / 5) ÷ (1 + 2 / 5)
(28 / 5) ÷ (7 / 5)
(28 / 5) / (7 / 5)
28 / 7
4
Case 10
4 2 / 3 ÷ 3 1 / 2
(4 + 2 / 3) ÷ (3 + 1 / 2)
(14 / 3) ÷ (7 / 2)
(14 / 3) / (7 / 2)
28 / 21
4 / 3
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The Yellow Cab Company charges just $1.25 per mile, but it costs $6.00 to get in the cab. Express Cab charges no fee to get in the cab, but $2.00 per mile for the ride. For what number of miles is the cost the same?
Answer: 8 miles
Step-by-step explanation:
1.25m+6=2m
--1.25m. -1.25m
6=.75
6/.75m=8 mile
s
What i the equation of the line that pae through the point (−8, −10) and (6, 3)? Write your anwer in lope-intercept form
The equation of the line that passes through the points (−8, −10) and (6, 3)in slope-intercept form is y = (13/14) x - 18/7.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
Given the two points, (−8, −10) and (6, 3), get the slope of the line using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - -10) / (6 - -8)
m = 13 / 14
Using the slope-intercept form, plug in the value of the slope and one point to determine the y-intercept, b.
y = mx+ b
-10 = (13/14)(-8) + b
b = -18/7
Substitute the value of the slope and y-intercept in the slope-intercept form.
y = mx + b
y = (13/14) x - 18/7
Hence, the equation of the line in slope-intercept form is y = (13/14) x - 18/7.
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50% of 188 is equal to what number?
Answer:
Step-by-step explanation:
a.50%=[tex]\frac{1}{2}[/tex]
b.so 50% of 188 means 188·[tex]\frac{1}{2}[/tex]=94
answer is 94
What is the domain and range of a composite function?
The domain of a composite function is the set of all possible inputs for both functions, and the range is the set of all possible outputs.
A composite function is the combination of two or more functions. The domain of a composite function is the set of all possible inputs for both functions. This means that the domain is the set of all the possible inputs that can be used in either of the functions that make up the composite function. The range of a composite function is the set of all possible outputs. This means that the range is the set of all the possible outputs that can be obtained by the combination of the two or more functions. When graphing a composite function, it is important to remember that the domain and range of the composite function are the union of the domain and range of the individual functions in the composite function. The domain and range of a composite function can be determined by first determining the domains and ranges of the individual functions and then combining them.
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What are the angles of a 5 12 13 triangle?
The angles of a 5-12-13 triangle are A = 81.19°, B = 48.76°, and C = 9.98°.
The angles of a triangle are determined by the triangle's side lengths. This is known as the Law of Cosines. To determine the angles of a 5-12-13 triangle, we can use the Law of Cosines formula:
Cos(A) = (b² + c² - a²) / 2bc
In this equation, A is the angle opposite side a, b is the angle opposite side b, and c is the angle opposite side c. In a 5-12-13 triangle, a = 5, b = 12, and c = 13.
Using the Law of Cosines formula, we can calculate the angle A:
Cos(A) = (12² + 13² - 5²) / 2(12)(13)
Cos(A) = (144 + 169 - 25) / 156
Cos(A) = 278 / 156
Cos(A) ≈ 1.78
Using a calculator, we can calculate the angle A:
A = cos-1 (1.78)
A ≈ 81.19°
Using the same Law of Cosines formula, we can calculate the other two angles of the triangle:
Cos(B) = (a² + c² - b²) / 2ac
Cos(B) = (5² + 13² - 12²) / 2(5)(13)
Cos(B) = (25 + 169 - 144) / 65
Cos(B) = 50 / 65
Cos(B) ≈ 0.77
Using a calculator, we can calculate the angle B:
B = cos-1 (0.77)
B ≈ 48.76°
We can also calculate the angle C:
Cos(C) = (a² + b² - c²) / 2ab
Cos(C) = (5² + 12² - 13²) / 2(5)(12)
Cos(C) = (25 + 144 - 169) / 60
Cos(C) = 10 / 60
Cos(C) ≈ 0.17
Using a calculator, we can calculate the angle C:
C = cos-1 (0.17)
C ≈ 9.98°
Therefore, the angles of a 5-12-13 triangle are A = 81.19°, B = 48.76°, and C = 9.98°.
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A football team consists of 20 each freshmen and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that
On solving the provided question, we can say that Probability ( At least one of the students is a senior) = 0.4632 approx
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
P(All four players are senior) = 0.00033 approx
P(There is one each: freshman, sophomore, junior and senior) = 0.0944 approx.
P(There are 2 sophomores and 2 freshman) = 0.0568 approx
P( At least one of the students is a senior) = 0.4632 approx
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There are 2 pitchers of iced tea. The iced tea in the 1st one was made with 4 tea bags and 1.25 quarts of water. The iced tea in the second pitcher was made with 5 tea bags and 2 quarts of water. Which pitcher has a higher concentration of tea? Why?
Answer:
Pitcher 2
Step-by-step explanation:
Pitcher 1 = 4 x 1.25 = 5ml concentration
Pitcher 2 = 5 x 2 = 10ml concentration
therefore, pitcher 2 has more concentration :)
hope this helped
The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
Ponies
3
Rabbits
8
Sheep
6
Write the ratio of ponies to sheep.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio, if
possible.
Answer:
1/2
Step-by-step explanation:
You are comparing ponies to sheep, so you put the ponies on top(3)
and the sheep on the bottom(6)
3/6 reduces to 1/2
Eva gets £42 a month for her allowance. Out of this, for every £5 she spends, she saves £1 how much money does she spend in a month
Answer:
Eva spends £35 in a month.
Step-by-step explanation:
We know that Eva gets £42 a month for her allowance and for every £5 she spends, she saves £1.
We are looking to find out how much money does she spend in a month.
To calculate this, we can use the following formula:
Spent money = Allowance - (Allowance / (5 + 1))
Plugging in the known values:
Spent money = 42 - (42 / (5 + 1))
Spent money = 42 - (42 / 6)
Spent money = 42 - 7
Spent money = 35
So, Eva spends £35 in a month.
Elijah currently owes a total of $1,649.70 on his revolving credit accounts. What is Elijah's debt-to-credit ratio if the total of his revolving credit limits is $6,345.00? Round the final answer to the nearest whole percent.
a
26%
b
38%
c
41%
d
50%
a. 26%
sorry if wrong...
What is 200/51 equal to
Answer:
Approx 3.92
Step-by-step explanation:
[tex]w + 29 = 250 \div 5 - 20[/tex]
Find the value of w
Answer:
I don't know I am sorry bro
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer:
The values are 13 and 1
I hope this is correct
Find each measure for the given set of data: 11, 13, 17, 20, 22, 25, 27, 31, 31, 33
The values of mean ,median, range and inter quartile range could be 23,23.5,22,14 respectively.
What is mean ?
mean can be defined as the ratio of sum of the total observations and the number of total observations.
Given set of data
11,13,17,20,22,25,27,31,31,33
Mean = 11 +13+17+20+22+25+27+31+31+33/10
= 230/10
=23
Hence mean = 23
The (n/2)th term= the 5th term
=22
The (n/2+1) term = The 6th term
= 25
The median = 22+25/2
=23.5
Range = Highest term - lowest term
=33- 11
=22
Here lower half {11,13,17,20,22}
The middle number of lower half is first quartile.
Q₁ = 17
And lower half is{25,27,31,31,33}
The middle number of upper half is third quartile.
Q₃=31
Interquartile Range =Q₃-Q₁
=31-17
=14
Hence, The values of mean ,median, range and inter quartile range could be 23,23.5,22,14 respectively.
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Write a ratio of the following in three ways.
Write your answers on the blanks.
1) 6 Weeks to 12 days_____
2) 10 decimeters to 10 centimeters_______
3) 4 days to 36 hours___
4) 4 months to 8 weeks___
5) 30 seconds to 6 minutes__
6) 24 girls to 16 boys___
7) 12 mangoes to 36 fruits__
8) 2. Years to 36 months__
9) 45 points to 9 games__
10) 468 students for 9 classrooms___
Ratios express the relationship between two or more quantities, they can be expressed in different forms such as 6:12, 42:12 and 3:1, 10:10, 100:10, and 10:1, 24:36 and 2:3.
1. 6 Weeks to 12 days:
6:12 (using the same unit of measurement, weeks)42:12 (converting weeks to days, 6 weeks x 7 days/week = 42 days)3:1 (simplifying the ratio to its simplest form)2. 10 decimeters to 10 centimetres:
10:10 (using the same unit of measurement, decimeters)100:10 (converting decimeters to centimeters, 10 decimeters x 10 centimeters/decimeter = 100 centimeters)10:1 (simplifying the ratio to its simplest form)3. 4 days to 36 hours:
4:36 (using the same unit of measurement, days)24:36 (converting days to hours, 4 days x 24 hours/day = 96 hours)2:3 (simplifying the ratio to its simplest form)4. 4 months to 8 weeks:
4:8 (using the same unit of measurement, months)16:8 (converting months to weeks, 4 months x 4 weeks/month = 16 weeks)2:1 (simplifying the ratio to its simplest form)5. 30 seconds to 6 minutes:
30:6 (using the same unit of measurement, seconds)180:6 (converting seconds to minutes, 30 seconds x 6 minutes/60 seconds = 0.5 minutes)30:1 (simplifying the ratio to its simplest form)6. 24 girls to 16 boys:
24:16 (using the same unit of measurement, girls and boys)3:2 (simplifying the ratio to its simplest form)7. 12 mangoes to 36 fruits:
12:36 (using the same unit of measurement, mangoes and fruits)1:3 (simplifying the ratio to its simplest form)8. 2 years to 36 months:
2:36 (using the same unit of measurement, years and months)6:36 (converting years to months, 2 years x 12 months/year = 24 months)1:6 (simplifying the ratio to its simplest form)9. 45 points to 9 games:
45:9 (using the same unit of measurement, points and games)5:1 (simplifying the ratio to its simplest form)10. 468 students for 9 classrooms:
468:9 (using the same unit of measurement, students and classrooms)52:1 (simplifying the ratio to its simplest form)To learn more about the ratio, visit:
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Select the correct answer. A body travels 10 meters during the first 5 seconds of its travel, and it travels a total of 30 meters over the first 10 seconds of its travel. What is its average speed during the time from t
The speed of travel will be 4 m/s.
How do you find the distance traveled in the Nth second?The formula for distance travelled in nth second is given by, Sn = u + a (n – ½).
The body's total distance travelled is equal to the sum of the 10 m it covered in the first five seconds and the 30 m it covered in the following five seconds. The total distance covered is 40 metres. This can be divided by the duration to determine the average speed. Therefore, the average speed is 4 m/s.
Total distance=10+30=40
speed=distance/time=40/10=4m/s
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True or False? A rectangle's area is found by adding the length of the sides and its perimeter is found by multiplying the base by the height.
Answer: The Answer is false!
Step-by-step explanation:
The area of a rectangle is found by multiplying the length by the width.
How do you verify inverse?
To verify the inverse we can use Horizontal Line Test.
Suppose F is a function.
F does not have an inverse if any horizontal line crosses the graph of f more than once. If no horizontal line crosses the graph of F more than once, then F does have an inverse. In mathematics, having an inverse is a very significant quality, and it has a name.
If and only if a function f has an inverse, then it is one-to-one. The following definition, which is also the one that is most frequently used, is equivalent. If f(a) = f(b) implies a = b for all a and b in its domain, then a function f is one-to-one.
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