pi or π is a Greek word and its value is approximately 3.14 and it is an irrational number.
It is given that the letter is pi or π.
We have to write the history of pi and its importance to the study of geometry.
What is pi or π ?
pi or π is the ratio of the circumference of any circle to the diameter of that circle.
We know that ;
pi or π is a Greek letter. In decimal form, the value of pi is approximately 3.14 and it is an irrational number.
According to Petr Beckmann's A History of Pi, William Jones first used this Greek letter for some purpose in 1706. Around 30 years later, it became a standard symbol for mathematical notation.
Also ; it has been known for at least 4,000 years what Pi means. According to the history of Pi , who claims that by 2000 B.C , "the Babylonians and the Egyptians were aware about the existence and significance of this constant,"
Also ; every circle has the same ratio of circumference to diameter. Both the Babylonians and the Egyptians approximated the value of pi numerically, and later mathematicians in ancient Greece, especially Archimedes, improved these approximations.
Pi is a fundamental concept that appears in all branches of mathematics. It is a crucial concept that facilitates understanding of both universal truths and some mathematical concepts.
Thus , pi or π is a Greek word and its value is approximately 3.14 and it is an irrational number.
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The area of a rectangular garden is 24x^2 - 64x. The width is 8x. Find the length in terms of X.
The length of the garden will be - L = 3x - 8.
We have a rectangular garden.
We have to determine its length.
What is the Area of Rectangle?The area of rectangle is -
A = L x B
According to the question -
Area = [tex]24x^{2} -64x[/tex]
Width = [tex]8x[/tex]
Therefore -
Area = Length x Width
Length = Area / width
Length = [tex]$\frac{24x^{2} -64x}{8x} = 3x -8[/tex]
Hence, the length of the garden will be - L = 3x - 8.
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12x)^0 (6x^-4)
please can someone solve this i need it now!!! :(
After simplification, the value of the given expression (12x)⁰(6x⁻⁴) is 6/x⁴.
What are expressions?A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression)So, (12x)⁰(6x⁻⁴):
(12x)⁰(6x⁻⁴)6 × 1/x⁴6/x⁴Therefore, after simplification, the value of the given expression is 6/x⁴.
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Use completing the square to solve for x in the equation (x minus 12) (x + 4) = 9.
The solution fo the equation by completing the square is x = 12.544 or -4.544
What is completing the square method?Completing the square method is a method of solving quadratic equations in which the equation is converted into a perfect square binomial.
How to use completing the square to solve the equation?Given (x - 12)(x + 4) = 9
Expanding the brackets, we have
x² - 12x + 4x - 48 = 9
x² - 8x - 48 = 9
x² - 8x - 48 - 9 = 0
x² - 8x - 57 = 0
To complete the square, we add half the square of the coefficient of x to both sides. so,
x² - 8x - 57 = 0
x² - 8x - 57 + (-8/2)² = 0 + (-8/2)²
x² - 8x - 57 + (-4)² = 0 + (-4)²
x² - 8x + (-4)² - 57 = 0 + (-4)²
(x - 4)² - 57 = 16
(x - 4)² = 16 + 57
(x - 4)² = 73
Taking square roots, we have
x - 4 = ±√73
x - 4 = ±8.544
x = 4 ± 8.544
x = 4 + 8.544 or x = 4 - 8.544
x = 12.544 or -4.544
So, the solution fo the quadratic equation by completing the square is x = 12.544 or -4.544
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Answer:
Step-by-step explanation:
x=+/-square root 73
HELP ASAP ASAP ASAP ASAP
Answer:
Step-by-step explanation:
somewhat
The roller coaster at the state fair cost 7 tickets per ride. If you had 833 tickets, how many times could you ride it.
Answer:119 times
Step-by-step explanation:
833/7=119
The expression 4·125‾‾‾‾√3gives the perimeter of the base of a cube with a volume of 125 cubic inches. What is the length, in inches, of the perimeter of its base?
The length, in inches, of the perimeter of its base is 5in
Volume of a cubeA cube is a three dimensional object with 6 faces and 12 edges.
The formula for calculating the volume of a cube is expressed according to the equation;
V = l³
l = ∛V
where
l is the side length of the cube
Given the following parameters
V = 125in³
Substitute
125 = l³
l = ∛125
l = 5in
Hence the length, in inches, of the perimeter of its base is 5in
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What are the domain and range of the function represented by the set of
ordered pairs?
{(-13, 9), (-7,-5), (5, 14), (11,-10)}
The function's domain and range as represented either by set of ordered pairs:
Domain = (-13 , -7 , 5 , 11)
Range = (9 , -5 , 14 , 11)
What is function's domain and range?Range and domain The domain of something like a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the collection of values that the function can take. This is the set of values that the function returns after we enter an x value.
According to the data:The set of ordered pairs = {(-13, 9), (-7,-5), (5, 14), (11,-10)}.
(x,y)
x=input
y=output
As a result, the domain consists only of the first numbers.
range refers to all of the second numbers.
x=domain
y=range
So,
Domain = (-13 , -7 , 5 , 11)
Range = (9 , -5 , 14 , 11)
The function's domain and range as represented either by set of ordered pairs:
Domain = (-13 , -7 , 5 , 11)
Range = (9 , -5 , 14 , 11)
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The table shows the results of an experiment in which a spinner numbered 1-4 was spun.
What is the experimental probability that the spinner will land on a 4?
Answer:
1/4 or 25% or 0.25
Step-by-step explanation:
Find the 13th term of the geometric sequence 7, 21, 63
Answer: 3720087
Step-by-step explanation:
n=term number
an=term value
terms: 7, 21, 63...
term number: 1, 2, 3, ...
7 is 1st term. 21 is 2nd term. 63 is 3rd term.
21/7=3
63/21=3
Common change in each term is multiplication by 3
Hence, the formula can be expressed in exponents.
an=3^(n-1) * 7 where n is the term number, an is the term value, and 7 is the 1st term in the sequence.
an=3^(13-1) * 7
an=3^12 * 7
an=531441 * 7
an=3720087
A boat is cruising at a speed of 24 miles per hour. The captain plans to cruise at this speed for the next 9 miles, plus or minus 3 miles. What is the minimum number of hours the boat will cruise at? Maximum number of hours?
Answer:
Minimum 1/4 Hour Maximum 1/2 Hour
Speed is the ratio of distance and time.
The maximum number of hours the boat will cruise is 1/2 hours.
The minimum number of hours the boat will cruise is 1/4 hour.
What is speed?Speed is the ratio of distance and time.
It tells us how fast a body is moving.
We have,
Boat speed = 24 miles per hour.
Speed = distance / time
Distance = 9 miles
Time = distance / speed
Minimum number of hours:
Distance = 9 - 3 = 6 miles
Time = Distance / Speed = 6 / 24 = 1/4 hours
Maximum number of hours:
Distance = 9 + 3
Time = Distance / Speed = 12 / 24 = 1 / 2 hours
Thus,
The maximum number of hours the boat will cruise is 1/2 hours.
The minimum number of hours the boat will cruise is 1/4 hour.
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Help me pls
thanks
please show work!
Answer:
7. ) 3 3/4 9.) 3 1/8 11.) 7/16 13.) 5 13/15 15.) 7 1/2
Step-by-step explanation:
Number 7, first make 4 1/6 into an improper fraction.
6x4+1= 25/6
25/6x9/10
225/60
Simplified- 3 3/4
Number 9, make 4 3/8 into an improper fraction.
4x8+3= 35/8
35/8x5/7
175/56
Simplified- 3 1/8
Number 11, make 2 5/8 into an improper fraction.
2x8+5= 21/8
21/8x1/6
21/48
Simplified- 7/16
Number 13, make 1 3/5 and 3 2/3 into an improper fraction.
1x5+3= 8/5, 3x3+2=11/3
8/5x11/3
88/15
Simplified- 5 13/15
Number 15, make 3 1/3 and 2 1/4 into an improper fraction.
3x3+1= 10/3, 2x4+1=9/4
10/3x9/4
90/12
Simplified- 7 1/2
Hope that helped! :D
Please someone help I’ve been stuck on this forever
Which expression shows a way to factor 36+48
The expression for 36+48 is 12(3 + 4).
What is factor?A number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.
Given:
36+48
Now, factorise 36 and 48
36=2*2*3*3
48=2*2*2*2*3
So, the common factor is 12.
Hence, the for the factor is 12(3 + 4)
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An urn contains 5 red 6 blue and 8 green balls. if a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) of the same color? (b) of different colors?
The probability that each of the balls will be; a) P( of the same color) = 0.08875. b) P ( of different color) = 0.247678
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
The Number of red balls = 5
The number of blue balls = 6
The number of green balls = 8
The Total number of balls = 5 + 6 + 8 = 19
Then with three balls selected at random, by using combination method ;
nCr = n!/(n-r)!r!
a) P( of the same color) = 5C3 + 6C3 + 8C3 / 19C3
= 86/969 = 0.08875
b) P ( of different color) = 5C1 X 6C1 X 8C1 /19C3
= 240/969 = 0.247678
Hence, The probability that each of the balls will be; a) P( of the same color) = 0.08875. b) P ( of different color) = 0.247678
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Tamika is preheating her oven before using it to bake. Tamika wants to predict the
final temperature after a minutes. She wrote the equation y = 45x + 67, where y
represents the final temperature in degrees Fahrenheit. What could the number 67 in
Tamika's equation represent?
In Tamika's equation y = 45x + 67, 67 represents temperature in degree Fahrenheit.
What is a equation?An equation is a mathematical statement that compares two mathematical expressions by equating them and on both sides the quantities are of same type . Like we cannot compare a length quantity with a temperature quantity.
Given that Tamika wants to predict the final temperature after some minutes of preheating her oven. She wrote the equation y = 45x + 67, where y represents the final temperature in degrees Fahrenheit.
y = 45x + 67
In this equation as y is temperature so the expression 45x + 67 is of temperature in degrees Fahrenheit too and each term of this expression is also temperature in degrees Fahrenheit.
Therefore , 67 represents temperature in degree Fahrenheit.
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how much is a 47 mile taxi ride
The fare for 47 miles is $32.9
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Total miles= 36 miles
Total fare = 25.20
fare for 1 miles
= 25.20/36
=0.7
Now, for 47 miles the fare will be
=0.7*47
=$32.9
Hence, the fare for 47 miles is $32.9
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Which of the following is a counterexample for this conditional statement?
If a number is positive, then it is spelled without the letter 'e'.
6
1
2
4
Explanation:
The number 1 is spelled as "one", which clearly has an "e" in it. This contradicts the original statement that we don't need this letter.
The other numbers of 6 (six), 2 (two), and 4 (four) don't involve "e"s at all. So they can be ruled out.
a. A line passes through (-5,0) and (0,7) . What is an equation of the line in point-slope form?
7 - 0 = 7/5(0 - (-5)) is the equation in slope intercept form for the line passes through points (-5,0) and (0,7).
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope.
We have been asked to write an equation of the line in point-slope form
of a line which passes through (-5,0) and (0,7)
We know that point-slope form = y₂ - y₁ = m(x₂ - x₁)
But first we will find slope(m)
We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (-5,0) and (0,7)
⇒ m = [tex]\frac{7- 0}{0 - (-5)}[/tex]
⇒ m = [tex]\frac{7}{5}[/tex]
⇒ m = 7/5
After we substitute the given information we get
7 - 0 = 7/5(0 - (-5))
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Use the given information to determine whether LM is a perpendicular bisector, median, and/or an altitude of Δ J K L .
LM ⊥ JK
Since LM ⊥ JK, LM is an altitude by the definition of altitude. We don't know if it is a perpendicular bisector because it is not evident that M is the midpoint of JK.
What is meant by the altitude of a triangle?An altitude of a triangle is a line segment through a vertex that is perpendicular to a line containing the base in geometry. The extended base of the altitude is the line that contains the opposite side. The intersection of the extended base and the altitude is known as the altitude's foot.
A triangle's altitude is the perpendicular drawn from the triangle's vertex to the opposite side. The altitude, also known as the triangle's height, forms a right-angle triangle with the base.
Since LM ⊥ JK, LM is an altitude by the definition of altitude. We don't know if it is a perpendicular bisector because it is not evident that M is the midpoint of JK.
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The hockey stick that Erik wants to purchase is $95.00. He knows the price will increase by 15% by the end of next month. Erik needs to calculate the new price of the hockey stick. He solved the problem using the steps below
The new price of the hockey stick based on the information is $109.25.
How to calculate the value?From the information, the hockey stick that Erik wants to purchase is $95.00. He knows the price will increase by 15% by the end of next month.
Therefore, the new price will be:
= $95 + (15% × $95)
= $95 + (0.15 × $95)
= $95 + $14.25
= $109.25
Therefore, the new price of the hockey stick is $109.25.
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The hockey stick that Erik wants to purchase is $95.00. He knows the price will increase by 15% by the end of next month. Erik needs to calculate the new price of the hockey stick. What will the new price be?
uhh i need help someone help me pls
O
O
-100
What is the probability of flipping tails on the coin and spinning a 2 on the spinner?
8
Tails
414
4
3
(T.1)
(T.2)
(T.3)
(T.4)
Answer:
a 50% chance of getting tails
but about the spinner It depends on what kind of spinner it is and how many sides/numbers/etc
does it have
Q(4, 2) R(5, 1) S(3,7). If the triangle is reflected across the y-axis, what will S' be?
Answer:
S' (- 3, 7 )
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
S (3, 7 ) → (- 3, 7 )
The total cost to buy gloves for the football team can be found using the function \(p=24.99g+5.69\), where \(g)\ is the number of gloves bought. If there are at least \(7\) players but no more than \(14\) players on the football team, what is the domain of the function for this situation
The domain of the given function is a 180.62 to 355.55.
According to the statement
We have to find that the linear equation domain.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The total cost to buy gloves for the football team can be found using the function \(p=24.99g+5.69\), where \(g)\ is the number of gloves bought. If there are at least \(7\) players but no more than \(14\) players on the football team
Then
p=24.99g+5.69
Now find the value of the g is
p=24.99g+5.69
Here the domain of the g]function is a From 1 to 14.
Then
For 7
p=24.99(7)+5.69
p=174.93+5.69
p = 180.62.
And for 14
p=24.99(14)+5.69
p=349.86+5.69
p = 355.55.
So, The domain of the given function is a 180.62 to 355.55.
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he graph of the function f(x) = (x − 3)(x + 1) is shown. On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0). Which describes all of the values for which the graph is positive and decreasing? all real values of x where x < −1 all real values of x where x < 1 all real values of x where 1 < x < 3 all real values of x where x > 3
Answer:
real x values is x < -1
Step-by-step explanation:
Assuming that g(x) = 1/3 f(x) and h(x) = -g(x) + 4, fill in the following table.
Please, someone help me on this.
Answer:
Step-by-step explanation:
The values of functions are as follows:
g(-6) = -6
g(0) = 5
g(7) = 8
h(-6) = 10
h(0) = -1
h(7) = -4
Given, that function g(x) = f(x)/3 and function h(x) = -g(x) + 4
Now to calculate the function values on different values of x.
g(x) = f(x)/3
h(x) = -g(x) + 4
1 )
When x = -6
f(-6) = -18
g(-6) = f(-6)/3
g(-6) = -18/3
g(-6) = -6
h(-6) = -g(-6) + 4
h(-6) = 6 + 4
h(-6) = 10
2)
When x = 0
f(0) = 15
g(0) = f(0)/3
g(0) = 15/3
g(0) = 5
h(0) = -g(0) + 4
h(0) = -5 + 4
h(0) = -1
3)
When x = 7
f(7) = 24
g(7) = f(7)/3
g(7) = 24/3
g(7) = 8
h(7) = -g(7) + 4
h(7) = -8 + 4
h(7) = -4
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True or false? Any two right triangles with the same hypotenuse have the same area.
Explain your reasoning.
The statement that any two right triangles with the same hypotenuse have the same area is false.
Hypotenuse is defined as the longest side of a right-angled triangle.
let us take two triangles ΔXYZ & ΔDEF with same hypotenuse
for ΔXYZ let, XY(height)=7cm, YZ(base)=24cm, XZ(hypotenuse)=25cm.
for ΔDEF let, DE(height)=15cm, DF(base)=20cm, DF(hypotenuse)=25cm.
Area of a Right Angled Triangle is given by [tex]=\frac{1}{2} *base*height[/tex]
For ΔXYZ
Area=(1/2)*base*height
= (1/2)*24*7
=12*7
=84 ......(1)
For ΔDEF
Area=(1/2)*base*height
= (1/2)*20*15
=10*15
=150 .......(2)
From equation (1) & (2) we can conclude that two triangles having same hypotenuse may not have same area.
Therefore , the statement that any two right triangles with the same hypotenuse have the same area is false.
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State whether following sentence is true or false. If false, replace the underlined term to make a true sentence.
A permutation is an arrangement of objects in which order is NOT important.
False , A permutation is an arrangement of objects in which order is NOT important.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.This sentence is false.
A permutation is an arrangement of objects in which order is NOT important.
True sentence is -
State whether following sentence is true or false. If false, replace the underlined term to make a true sentence.
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The least preferable and reliable method of selecting people to participate in a research study is:_____.
The least preferable and reliable method of selecting people to participate in a research study is convenience sampling.
Convenience sampling is a type of sampling in which you include people who are easy to reach. Convenience sampling is included in non-probability sampling because it doesn't include a random selection of the participants. Convenience sampling can be used when you need to conduct a study quickly or when you are on a shoestring budget as it is inexpensive compared to other methods of sampling.
It is the least preferable method because of the inability to generalize the result of the survey to the population as a whole. In addition to this, there is a possibility of under or over-representation of the population as a whole. The biggest problem with convenience sampling is dependence as the sample items are connected to each another in some way. This dependency interferes with statistical analysis.
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is the following relation a function?
Answer:
relation
Step-by-step explanation:
To be a function each element from set x has only one unique element in y.
In our case x = 0 has two outcomes y = 1 and y = 3, so is a relation.
f(x) = y
f(-2) = 5
f(0) = 1 and f(0) = 3
f(5) = 8
f(7) = 5
Some memory aids:
Think about if we count how many likes we got on a social media post at the end of the day, then we can not have different numbers for same post yet we can have the same number of likes on different posts to be a function.
f(post 0) = 1 like and f(post 0) = 3 likes ❌ not a function because same post has different numbers of likes at the end of the day -not possible
f(post -2) = 5 likes and f(post 7) = 5 likes ✅ could be a function because different posts can have the same number of likes at the end of the day
