Answer:
⇒ π and √ 78
Rational number:
A number that can be expressed exactly by a ratio of two integers. Integer is usually defined as one of the positive or negative numbers 1, 2, 3, etc., or zero. An example of a rational number is a repeating decimal. A repeating decimal is a decimal numeral that, after a certain point, consists of a group of one or more digits repeated as infimum, as 2.33333.... or 23.0218181818...
Irrational number:
A number that cannot be exactly expressed as a ratio of two integers. An example is a infinite decimal which is a nonterminating decimal, a decimal numeral that does not end in an infinite sequence of zeros (contrasted with terminating decimal). Example: 2.3459810212901....
_________________________
Rational numbers.
The number 9/15 is equal to 0.6 which is a terminating decimal and is therefore, rational.
18 is a whole number and integer making it rational.
9 is a integer and a whole number = rational.
169 is a integer and whole number = rational.
_____________________________________
Irrational numbers.
√78 ≈ 8.831760866
This decimal is a nonterminating decimal that does not terminate nor repeat making it irrational.
Now onto Pi/π which is the 16th letter of the Greek alphabet and is a known-irrational number. The ratio itself: 3.141592+. The letter is used as the symbol for the ratio of the circumference of a circle to its diameter.
So, why is PI irrational?It relates to how pi is computed. Pi is equal to the circumference of a circle, which may be calculated by placing an n-gon within a circle. However, when the sides of the n-gon are raised, the value of pi varies every time you divide it by the diameter of the circle, therefore it is impossible to get the exact value of pi. Additionally, irrational numbers never finish or repeat their decimal expansion, therefore they cannot be tallied as 2, 3, and so on.
_____________________________________
Therefore, the number that are irrational is π and √78.
Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as
A data set having two values that have the highest and equal frequencies will have a bimodal distribution. Hence, option D is the right choice.
A symmetric distribution occurs when the mean, median, and mode all occur at the same location and the values of the variables occur at regular intervals.The few low scores in a negatively skewed distribution tend to push the mean to the left, thus the mean is typically lower than the median.The mode is consistently less than the mean and median in a positively skewed distribution.A continuous probability distribution having two distinct modes, that is, two separate values with the highest and equal frequencies is referred to as a bimodal distribution.Thus, a data set having two values that have the highest and equal frequencies will have a bimodal distribution. Hence, option D is the right choice.
The given question is incomplete. The complete question is:
"Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as:
A. Symmetric distribution
B. Negatively skewed distribution
C. Positively skewed distribution
D. Bimodal distribution."
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Larry likes skeet shooting. a clay disc is shot into the air and the participant tries to shoot it. he rarely misses, because he knows that the flight of the disc can be modeled by a quadratic function. the discs are released from a firing mechanism that sits at ground level and shoots the disc on average a horizontal distance of 120m. the average maximum vertical height that the disc reaches is 40 m.
a)The functions that represent the flight of the clay disc in Factored Form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]
b)The function in its standard form is,[tex]\rm y =- \frac{1}{90} x^3 + \frac{4}{3} x[/tex].
c) The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
The given points represent on the graph is;
x = 0 , y = 0
x = 120 , y = 0
x = 60 , y = 40
The standard equation is;
[tex]\rm y = a(x-h)^2 +k \\\\ y = a(x-60)^2 +40 \\\\ 0 = sA(120-60) +40\\\\ 0= a \times 3600 + 40 \\\\ 3600 a = -40 \\\\ a = - \farc{1}{90}[/tex]
Substitute the value as;
[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]
b)
The above equation in the standard form is found as;
[tex]\rm y = \frac{-1}{90}(x^2 +3600 -120 x )+40 \\\\ y =- \frac{1}{90}(x^2 -40 + \frac{4}{3}x +40 \\\\ y = \frac{-1}{90} x^2 + \frac{4}{3}x[/tex]
c)The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.
Hence, the functions that represent the flight of the clay disc in the factored form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]
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WILL MARK BRAINLIEST!!! According to the synthetic division below, which of the following statements are true? Check all that apply.
According to the given synthetic division, the statements that are true are; Options A, C and E
How to carry out Synthetic Division?
In the synthetic calculation we use the coefficient of the dividend
with the factors of the function.
Therefore;
3 , -13 , 4 are the coefficient of the dividend 3x² - 13x + 4
Therefore, the divisor is 4 and as such x = 4 is a root of f(x) = 3x² - 13x + 4
Also, it means that (x - 4) is a factor of the dividend F(x) = 2x² - 2x - 12
- The quotient is the last line of the synthetic division. Thus, the coefficients of quotient are 3, -1.
- The quotient is 1 degree less than the dividend and so the degree of the dividend is 2.
- The degree of the quotient is 1 and so the he quotient is 3x - 1.
Thus, options A, C and E are correct
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4. Which of the following uses the reciprocal property to rewrite
We can actually deduce here the one that uses the reciprocal property to rewrite [tex]\frac{x}{6} = \frac{28}{3\\}[/tex] is: C. [tex]\frac{6}{x} = \frac{3}{28}[/tex].
What is reciprocal?A reciprocal of a number is defined as the number that when it is multiplied by the number, the result is 1. Thus, we deduce here that the product of a number and its reciprocal gives one.
Thus: x/6 x 6/x = 1
Also, if 28/3 x 3/28 = 1
Thus, we see that they use the reciprocal property.
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The shorter leg of a right triangle is 5cm shorter than the longer leg. The hypotenuse is 5cm longer than the longer leg. Find the side lengths of the triangle.
Answer:
15, 20, 25
Step-by-step explanation:
added in the picture
Which graph represents the following system of inequalities? x < - 2x + 4; y < x + 3; x < 3
Graph C represents the following system of inequalities. For clarification refer to the attachment.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
Given relations;
x < - 2x + 4
y < x + 3
x < 3
Hence graph C represents the following system of inequalities.
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which of the following number is not a cube number
A) 10000
B)3125
C)64
D)729
Answer:
3125
Step-by-step explanation:
³√3125 comes around 14 not a whole no so not a perfect cubeAnd
10000=10³64=4³729=9³What is one of the solutions to the following system of equations?
x² + y² = 25
y - 3x = -5
Answer:
x = 0 y = -5
x = 3 y = 4
Step-by-step explanation:
x² + y² = 25
y - 3x = -5
-----------------------
y = 3x-5
x² + y² = 25
x² + (3x-5)² = 25
(3x-5)(3x-5) = 9x² -15x -15x + 25
x² + 9x² -15x -15x + 25 = 25
x² + 9x² -15x -15x = 0
x² + 9x² - 30x = 0
10x² - 30x = 0
x(10x-30)=0
x = 0
10x-30=0
x = 3
y - 3x = -5
y - 3(0) = -5
y = -5
y - 3(3) = -5
y - 9 = -5
y = 4
Answer:
(4,3) and (0,-5) are both solutions where we have (x,y).
Step-by-step explanation:
Here are simplified steps:
https://www.symbolab.com/solver/matrix-calculator/x%5E%7B2%7D%2By%5E%7B2%7D%3D25%3B%20y-3x%3D-5?or=input
Symbolab is an excellent tool for just most math.
One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
$\begin{align*}
&-x^2 + 18x + 81 \\
&3x^2 - 6x + 9 \\
&8x^2 - 32x + 32 \\
&25x^2 - 30x - 9 \\
&x^2 - 14x + 196
\end{align*}$
Answer:
Step-by-step explanation:
The quadratic expression having repeated root is 8x² - 32x + 32.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
We have to find the root of each quadratic expression.
-x² + 18x + 81 = 0x² - 18x - 81 = 0
Discriminant = [tex]\sqrt{(-18)^2-(4*-81)}[/tex] = [tex]\sqrt{648}[/tex]
x = (18 + √648) / 2 or x = (18 - √648) / 2
Distinct roots
3x² - 6x + 9x² - 2x + 3
Discriminant = [tex]\sqrt{(-2)^{2}-(4*3) }[/tex] = [tex]\sqrt{-8}[/tex]
x = (2 + [tex]\sqrt{-8}[/tex]) / 2 or x = (2 - [tex]\sqrt{-8}[/tex]) / 2
Distinct roots
8x² - 32x + 32
x² - 4x + 4Discriminant = [tex]\sqrt{(-4)^{2}-(4*4) }[/tex] = 0
x = (4 + 0)/ 2 or x = (4 - 0) / 2
x = 2 or x = 2
Repeated roots
Hence the quadratic expression having repeated roots is 8x² - 32x + 32.
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The radius of a sphere is 3 inches. Which represents the volume of the sphere? 12Ï€ cubic inches 36Ï€ cubic inches 64Ï€ cubic inches 81Ï€ cubic inches.
Answer: 113 inches cubed
Step-by-step explanation:
Volume of a sphere = 4/3 Pi r^3
Radius = 3 inches
Volume = 113 inches cubed
Hope I helped!
A, B and C are the vertices of a triangle.
A has coordinates (1,4)
B has coordinates (3, 0)
C has coordinates (-3,-2)
D is the midpoint of AB.
E is the midpoint of AC.
Prove that DE is parallel to BC.
You must show each stage of your working.
PLEASE HELP ASAP THANK YOU
Answer:
see below
Step-by-step explanation:
To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.
The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.
D (2,2)
You could also see this on a graph, see image.
E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.
E is (-1,1)
Then we are able to calculate the slope of DE and BC.
To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.
Slope of DE:
(2-1)/(2--1)
= 1/3
Slope of BC:
(0--2)/(3--3)
=2/6
=1/3
The slopes of BC and DE are equal, so the segments are parallel.
(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)
What is the domain of the function y=3 In x graphed below?
Answer:
x>0
Step-by-step explanation:
points exist on the right of the graph so the domain is x>0
55. The Cone Problem Begin with a circular piece of paper with
4-in. radius as shown in (a). Cut out a sector with an arc length o
x. Join the two edges of the remaining portion to form a cone
with radius r and height h, as shown in (b).
4 in.
4 in.
(a)
(b)
(a) Explain why the circumference of the base of the cone is
8T X
(b) Express the radius r as a function of x.
(c) Express the height has a function of x.
(d) Express the volume V of the cone as a function of x.
pls helpppp
The circumference of the base of the cone is 8π - x since the base is equal to go the arc length of the remainder of the circle.
How to calculate the values?The radius r as a function of x will be:
8π - x = 2πr
r = (8π - x)/2π
r = 4 - x/2π
The height has a function of x will be:
r² + h² = 16
h² = 16 - r²
where r = 4 - x/2π
h = √16 - ✓(4 - x/2π)²
h = 4✓(4 - x/2π)²
The volume V of the cone as a function of x will be:
= 1/3 πr²h
= π/3(4 - x/2π)² 4✓(4 - x/2π)²
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Work out the value of (2^3)^2
Answer:
2⁶
Step-by-step explanation:
law of indices states multiplication of powers in and out of bracket 3×2=6
[tex]\text{Let's work out:: 2 to the power of 3 to the power of 2 }\\\text{We can start by raising 2 to the power of 3:: 2*2*2=8, then raising that}\\\text{to the power of 2:: 8*8=64}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{The value is 64}[/tex]
How many other states have a similar law? all 50 states 48 states 40 other states 52 states
Answer:
all 50 states
Step-by-step explanation:
Complete the flow chart to prove 3 is congruent to 4
The flow chart is complete and the answers are given below.
What is meaning of Congruent Figures ?Those figures that have same shape and size are called Congruent Figures.
The flow diagram will be completed as follows
∠2 ≅ ∠4 ( vertical angle theorem )
∠1 ≅ ∠2 ( Given )
∠1 ≅ ∠ 3 ( Vertical Angle Theorem)
∠3 ≅ ∠4 ( Transitive Property of congruence)
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How would you answer this question?
Answer:
32
Step-by-step explanation:
the pattern of sticks from the first 3 diagrams is
7 , 12 , 17 ,..
note the pattern increases by 5 each time , then continue by adding 5 to the previous value.
4th = 17 + 5 = 22
5th = 22 + 5 = 27
6th = 27 + 5 = 32
Common types of data patterns that can be identified when examining a time series plot include all of the following except ______.
Answer:
Vertical is the answer
What are the solutions of x^2-3x+3=0
Therefore the solution to this equation is imaginary given by x = [tex]\rm \dfrac { 3 \pm \sqrt{-3}}{2}[/tex]
What is a Quadratic Equation ?A Quadratic equation is an equation that can be written in the form of
ax² +bx+c = 0
The solution of the given quadratic equation
x² -3x +3 = 0
the roots of the equation is given by
[tex]\dfrac { -b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
here a = 1 , b = -3 , c = 3
Substituting the values
The solution is
[tex]\rm \dfrac { 3 \pm \sqrt{(-3)^2 -4*1 *3}}{2}[/tex]
Therefore the solution to this equation is imaginary
given by
x = [tex]\rm \dfrac { 3 \pm \sqrt{-3}}{2}[/tex]
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Lightning quickly heats the air causing it to expand, which produces the sound of thunder. Sound travels approximately 1 mile in 5 seconds. Knowing D = rt, how far away is a thunderstorm when you notice a 3- second delay between the flash of lightning and the sound of thunder? Lightning quickly heats the air causing it to expand , which produces the sound of thunder . Sound travels approximately 1 mile in 5 seconds . Knowing D = rt , how far away is a thunderstorm when you notice a 3 second delay between the flash of lightning and the sound of thunder ?
Answer:
every second it travels 1/5 of a mile after 3 seconds you are 3/5 miles away
Hope This helps!
Given the following formula, solve for a.
Answer:
A
Step-by-step explanation:multiply both sides by two, then subtract b and c from both sides to get a on the right side by itself
Answer:
О A a = 2s - b - c
Step-by-step explanation:
S = (a+b+c)/2
2s = a + b +c
2s - b - c = a
Dan makes $72 working 8
hours. How much does he
make per hour?
Answer:
9 dollars per hour
Step-by-step explanation:
We want to use a ratio to find the rate in dollars per hour
72 dollars / 8 hours
Simplify by dividing the top and bottom by 8
9 dollars / 1 hour
9 dollars per hour
Step-by-step explanation:
72$ Per 8 hours, is the same as getting 9$ per hour. How this is possible is simple, All you do when you get a question like this, is that you divide the dollars by the hour, minutes, seconds, etc.
Problem-Connection:
As from this Question we Have 72$ per 8 hours, so we divide 72/8 which results in 9. So Dan Earns 9$ Per Hour.
Answer:
Dan Earns 9$ Per hour.
Your welcome!
Brainly will be greatly appreciated!
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
Option C is equal to 7^1/3
Hi, so this isn't an equation but could somebody explain what domain and range are please? I'm not doing great with understanding it for whatever reason and it would be super helpful if you could dvmb it down a little bit please
Answer:
Step-by-step explanation:
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
For example, "whatis.com" could be a domain with records for "www.whatis.com" and "www1.whatis.com,"
A circle of radius 1 is inscribed within a square. What is the probability that a randomly-selected point with the square is also within the circle?
A circle of radius 1 is inscribed within a square. What is the probability that a randomly-selected point with the square is also within the circle?
[tex] {p}^{2} > {p}^{2} \: \: and \: \: p {1}^{2} - \: p {2}^{2} \: < \frac{1}{3} [/tex]
Step-by-step explanation:
HOPE ITS HELP
Directions: Find the inverse of each number.
Additive
-3 =
14 =
-28 =
-1/5 =
Multiplicative
2/3 =
6/18 =
5 =
11 =
Answer:
Step-by-step explanation:
Additive inverse:
-3=3
14=-14
-28=28
-1/5=1/5
Multiplicative Inverse:
2/3=3/2
6/18=18/6
5=1/5
11=1/11
Answer:
inverse of -3 is +3
inverse of 14 is -14
inverse of -28 is 28
inverse of -1/5 is 1/5
inverse of 2/3 is 3/2
inverse of 6/18 is 18/6
inverse of 5 is 1/5
inverse of 11 is 1/11
Step-by-step explanation:
Because inverse mean switch it. or opposite of digit
if plus digit then negative digit .
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
By the Pythagorean theorem,
[tex]a^{2}+12^{2}=13^{2}\\\\a^{2}+144=169\\\\a^{2}=25\\ \\ a=\boxed{5}[/tex]
What is the difference of the polynomials?
(x² + x³ + x² + x) - (x²-x³+x²-x)
© 2x2
O 2x³+2x
O x6 +x²
O 2x5+2x²
Answer:
2x³ + 2x
Step-by-step explanation:
(x² + x³ + x² + x) - (x² - x³ + x² - x)
= x² + x³ + x² + x - x² + x³ - x² + x
Gathering like terms...
x³ + x³ +x² + x² -x² - x² + x + x
= 2x³ + 2x
The difference of the polynomials is 2(x³+x).
What is a polynomial?A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Given are two polynomials (x² + x³ + x² + x) and (x²-x³+x²-x), we need to find the difference,
So,
(x² + x³ + x² + x) - (x²-x³+x²-x)
= x² + x³ + x² + x - x²+x³-x²+x
= 2x²-2x²+x³+x³+x+x
= 2x³+2x
= 2(x³+x)
Hence the difference of the polynomials is 2(x³+x).
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The absolute value of 5.8 is _________.
Answer:
5.8
Step-by-step explanation:
Games Made x
(in 1000s)
Profit y
(in $1000s)
4
6
8
10 12
118 142 150 142 118
Which type of function best models the data in the
table? Justify your choice.
The type of function that best models the data in the table is the quadratic function
How to determine the function type?The table of values is represented as:
x: 4 6 8 10 12
y : 118 142 150 142 118
From the above table, we can see that:
The y values increase from 118 to 150The y values then decrease to 118The x values increaseThis is only possible in a quadratic function
Hence, the type of function that best models the data in the table is the quadratic function
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