Answer with explanation:
Outlier, in a data set are those real numbers called variates , if we consider two consecutive real numbers in that data set, when data is arranged in ascending or descending order the difference looks filthy,or ambiguous.
For, example , 13,45, 23.45, 35.45, 49.45,55.45, 80.45.
So, we can say that ,applying the above definition , 80.45 is an outlier.
Outliers affect the mean and Standard deviation.
→If you discard 50 % of the data , to get the better result in an experiment,the data set will become smaller and getting accurate result will be a task similar to catch a ruffian who is riding in a four wheeler and you are running behind him on footsteps.
→Similarly, Examining a smaller random sample of the population will not give accurate result.
Most of the Outliers lie either on right or left of Data set when arranged in ascending or descending order.
To overcome the effect of an outlier,we should consider large sample to get better result, as leaving some variates from right or left will have little effect on the result.
Option B: Examine a larger random sample of the population.
The graph shows the function f(x)=2x
What is the value of x when the f(x)=4?
A. 3
B. 1
C. 0
D.2
The value of x is option (D) 2
What is a function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.
Given,
f(x) = [tex]2^{x}[/tex]
we have to find the value of x when f(x) =4
f(x) = [tex]2^{x}[/tex] =4
[tex]2^{x}=4\\ 2^{x}=2^{2}[/tex]
Therefore value of x is 2
Hence, the value of x is option (D) 2
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Rewrite the equation below in standard form.
-3x+6y=12
A. 3x-6y=12
B. 3x-6y=-12
C. -x+2y=4
D. x-2y=-4
Polygon B is a scaled copy of Polygon A using a scale factor of 5. How many times larger is the area of Polygon B than the area of Polygon A?
Determine whether the sequence is arithmetic, geometric, both or neither.
16, 8, 4, 2
A. arithmetic
B. Goemetric
C. Neither
D. Both
I think its both because An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. Consecutive means one after the other. The constant value is called the common difference. Another way to think about an arithmetic sequence is that each term in the sequence is equal to the previous term plus the common difference and also A geometric sequence is a sequence in which the ratio of any two consecutive terms is constant. This constant value is called the common ratio. Another way to think about a geometric sequence is that each term is equal to the previous term times the common ratio. So when u look at it check out if the 16, 8, 4, and 2 see if they fit these terms
The ratios are constant (0.5), so the sequence is geometric.
Since the sequence is not arithmetic but is geometric, the correct answer is: B. Geometric
To determine whether the sequence 16, 8, 4, 2 is arithmetic, geometric, both, or neither, let's analyze the differences between consecutive terms and the ratios between consecutive terms.
Arithmetic Sequence:
An arithmetic sequence is a sequence in which the difference between consecutive terms is constant.
Calculating the differences:
8 - 16 = -8
4 - 8 = -4
2 - 4 = -2
The differences are not constant, so the sequence is not arithmetic.
Geometric Sequence:
A geometric sequence is a sequence in which the ratio between consecutive terms is constant.
Calculating the ratios:
8 / 16 = 0.5
4 / 8 = 0.5
2 / 4 = 0.5
The ratios are constant (0.5), so the sequence is geometric.
Since the sequence is not arithmetic but is geometric, the correct answer is:
B. Geometric
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a right rectangular prism is 6cm by 14cm by 5cm. what is the surface area of the right prism?
Final answer:
The surface area of a right rectangular prism with dimensions of 6cm by 14cm by 5cm is calculated by summing up the areas of all faces, resulting in a total surface area of 368cm².
Explanation:
To calculate the surface area of a right rectangular prism, we need to find the area of all the faces and add them together. For a prism with dimensions of 6cm by 14cm by 5cm, it has three pairs of identical faces: two faces that are 6cm by 14cm, two faces that are 6cm by 5cm, and two faces that are 14cm by 5cm.
Using the area formula for rectangles (Area = length × width), we find the areas of these faces:
For the 6cm by 14cm faces: Area = 6cm × 14cm = 84cm². Since there are two such faces, their combined area is 2 × 84cm² = 168cm².
For the 6cm by 5cm faces: Area = 6cm × 5cm = 30cm². Since there are two such faces, their combined area is 2 × 30cm² = 60cm².
For the 14cm by 5cm faces: Area = 14cm × 5cm = 70cm². Since there are two such faces, their combined area is 2 × 70cm² = 140cm².
Adding up all these areas gives us the total surface area of the prism:
Total Surface Area = 168cm² + 60cm² + 140cm² = 368cm²
Therefore, the surface area of the right rectangular prism is 368cm².
the measures of the legs of a right triangle can be represented by the expressions 6x^(2)y 9x^(2)y. Use the Pythagorean Theorem to find a simplified expression for the hypotenuse.
Answer:
h^2=a^2+b^2.
h^2=(6x^2y)^2+(9x^2y)^2.
h^2=36x^4y^2+81x^4y^2.
h^2=117x^4y^2.
h=sqrt(117x^4y^2).
=3 √13 x^2y
After applying Pythagoras' theorem the length of the hypotenuse we get is approximately 10.8 x²y unit.
Use the concept of the triangle defined as:
A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.
And the Pythagoras theorem for a right-angled triangle is defined as:
(Hypotenuse)²= (Perpendicular)² + (Base)²
Given that,
Base = 6x²y
perpendicular = 9x²y
Now apply the Pythagorean theorem,
(Hypotenuse)²= (6x²y)² + (9x²y)²
(Hypotenuse)²= 36x⁴y² + 81x⁴y²
(Hypotenuse)²= 117x⁴y²
Take square root on both sides we get,
Hypotenuse = √117 x²y
Hypotenuse ≈ 10.8 x²y
Hence,
The length of the hypotenuse is approximately 10.8 x²y unit.
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Weights were recorded for all nurses at a particular hospital, the mean weight for an individual nurse was 135 lbs. with a standard deviation of 15. If 19 nurses are selected at random, find the probability that the mean weight is between 125 and 130 lbs
Which equation illustrates the identity property of multiplication ? (X+yi)×z=(xz+yzi) (x+yi)×0=0 (x+yi)×(z+wi)=(z+wi)×(x+yi) (x+yi)×1=(x+yi)
The expression that shows identity property of multiplication is (x+yi)×1=(x+yi), the correct option is D.
What is the identity property of multiplication?According to the identity property of multiplication, the product of 1 and a number is the number itself.
The expressions in the question are
(X+yi)×z=(xz+yzi)
(x+yi)×0=0
(x+yi)×(z+wi)=(z+wi)×(x+yi)
(x+yi)×1=(x+yi)
The only expression that shows this property is (x+yi)×1=(x+yi).
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a rectangular corn hole area at the recreation center has a width of 5 feet and a length of 10 feet. if a uniform amount is added to each side, the area is increased to 84 square feet. what is the amount added to each side
Answer:
the answer is add 2 feet on each side!
Step-by-step explanation:
For a large sporting event the broadcasters sold 6969 ad slots for a total revenue of $131131 million. what was the mean price per ad slot?
Mr. Maddox asked four students to create a number line to help find the sum of fractions 3 2/3 + 1 3/4 + 2/3
Answer with explanation:
Question asked by Mr.Maddox to find the sum of fractions with the help of number line :
[tex]\rightarrow 3 \frac{2}{3}+1 \frac{3}{4}+\frac{2}{3}\\\\ \text{Using Associative Property}\\\\\rightarrow a+(b+c)=(b+c)+a\\\\\rightarrow [\frac{2}{3}+ 1\frac{3}{4}]+3 \frac{2}{3}\\\\\rightarrow [\frac{2}{3}+\frac{7}{4}]+\frac{11}{3}\\\\\rightarrow \frac{21+8}{12}+ \frac{11}{3}\\\\\rightarrow\frac{29+44}{12}\\\\ \rightarrow\frac{73}{12}\\\\\rightarrow 6\frac{1}{12}[/tex]
a rotation of a figure can be achieved by consecutive ___ of the figure over given lines
Calculate the rise and run and find the slope ( -9,2) and (-1,6)
What is the fifth term of the sequence?
an=5⋅2n−1
Enter your answer in the box.
a5=
Answer:
The fifth term of the sequence is:
49
Step-by-step explanation:
We are given the general term([tex]n^{th}[/tex] term) of the sequence as:
an=5.2n-1
We have to find the fifth term
i.e. we have to find the value of an for n=5
a5=5×2×5-1
=50-1
=49
Hence, the fifth term of the sequence is:
49
If A(0, 0), B(3, 4), C(8, 4), and D(5, 0) are the vertices of a quadrilateral, do the points form a rhombus? Justify your answer.
The given points do not form a rhombus.
What is a rhombus?A rhombus is a quadrilateral that has four equal sides.
Some of the properties we need to know are:
- The opposite sides are parallel to each other.
- The opposite angles are equal.
- The adjacent angles add up to 180 degrees.
We have,
To determine if the given points form a rhombus, we need to check if the sides are congruent (have equal length) and if the opposite angles are congruent (have equal measure).
First, we can find the lengths of all four sides of the quadrilateral using the distance formula:
AB = √((3 - 0)² + (4 - 0)²) = 5
BC = √((8 - 3)² + (4 - 4)²) = 5
CD = √((5 - 8)² + (0 - 4)²) = 5
DA = √((0 - 5)² + (0 - 4)²) = 5
Since all four sides have the same length of 5 units, the quadrilateral satisfies the property of having congruent sides.
Next, we need to check if the opposite angles are congruent.
We can do this by finding the slopes of the two diagonals and checking if they are perpendicular. If the slopes are perpendicular, then the opposite angles are congruent.
The slope of diagonal AC can be found as:
m(AC) = (4-0)/(8-0) = 1/2
The slope of diagonal BD can be found as:
m(BD) = (0-4)/(5-3) = -2/2 = -1
Since the product of the slopes is:
m(AC) x m(BD) = (1/2) x (-1) = -1/2
which is not equal to -1, the diagonals are not perpendicular and the opposite angles are not congruent.
Therefore,
The given points do not form a rhombus.
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What is the sum of the first 7 terms of the series −4+8−16+32−... ?
The height of a statue is 276 inches. What is the hieght of the statue in meters? Round your answer to the nearest hundredth.
We can convert inches to meters with the following conversion formula:
1 inch = 0.0254 meters
Now we have to find how many meters are there in 276 inches.
So multiplying 0.0254 with 276 would give us the answer.
276 inches = 0.0254 *276 = 7.0104 meters.
Answer : There are 7.0104 meters in 276 inches.
What is 0.3 percent as a fraction
Find the general solution of the given second-order differential equation. 3y'' + 2y' + y = 0
Final answer:
The general solution to the given second-order differential equation, 3y'' + 2y' + y = 0, is found using the characteristic equation method, resulting in complex roots. The solution is expressed in terms of sine and cosine functions multiplied by an exponential decay factor.
Explanation:
To find the general solution of the given second-order differential equation, 3y'' + 2y' + y = 0, we first convert it into its characteristic equation. This is done by substituting y = ert into the differential equation, where r is the root of the characteristic equation and t is an independent variable. This approach transforms the given differential equation into a quadratic equation.
The characteristic equation for this differential equation is 3r2 + 2r + 1 = 0. Solving this quadratic equation using the formula r = [-b ± sqrt(b2 - 4ac)] / 2a, where a=3, b=2, and c=1, gives the roots of the characteristic equation. In this case, the discriminant (b2 - 4ac) is less than zero, indicating complex roots.
The roots can be found to be r = -1/3 ± i(sqrt(2)/3). Therefore, the general solution to the differential equation is y(t) = e-t/3[C1cos(sqrt(2)t/3) + C2sin(sqrt(2)t/3)], where C1 and C2 are constants determined by initial conditions.
The general solution is [tex]\( y(t) = e^{-\frac{t}{3}} (C_1 \cos\left(\frac{\sqrt{2} t}{3}\right) + C_2 \sin\left(\frac{\sqrt{2} t}{3}\right)) \)[/tex].
To solve the second-order linear homogeneous differential equation [tex]\( 3y'' + 2y' + y = 0 \)[/tex], we follow these steps:
1. Write the characteristic equation associated with the differential equation.
2. Solve the characteristic equation for its roots.
3. Write the general solution based on the roots of the characteristic equation.
Step 1: Write the Characteristic Equation
The given differential equation is:
[tex]\[ 3y'' + 2y' + y = 0 \][/tex]
We assume a solution of the form [tex]\( y = e^{rt} \)[/tex]. Substituting [tex]\( y = e^{rt} \)[/tex] into the differential equation, we get:
[tex]\[ 3(r^2 e^{rt}) + 2(r e^{rt}) + e^{rt} = 0 \][/tex]
Dividing through by [tex]\( e^{rt} \)[/tex] (which is never zero), we obtain the characteristic equation:
[tex]\[ 3r^2 + 2r + 1 = 0 \][/tex]
Step 2: Solve the Characteristic Equation
The characteristic equation is a quadratic equation:
[tex]\[ 3r^2 + 2r + 1 = 0 \][/tex]
To find the roots of this quadratic equation, we use the quadratic formula:
[tex]\[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where [tex]\( a = 3 \)[/tex], [tex]\( b = 2 \)[/tex], and [tex]\( c = 1 \)[/tex].
Substitute the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] into the quadratic formula:
[tex]\[ r = \frac{-2 \pm \sqrt{2^2 - 4 \cdot 3 \cdot 1}}{2 \cdot 3} \][/tex]
[tex]\[ r = \frac{-2 \pm \sqrt{4 - 12}}{6} \][/tex]
[tex]\[ r = \frac{-2 \pm \sqrt{-8}}{6} \][/tex]
[tex]\[ r = \frac{-2 \pm 2i\sqrt{2}}{6} \][/tex]
[tex]\[ r = \frac{-1 \pm i\sqrt{2}}{3} \][/tex]
Thus, the roots of the characteristic equation are:
[tex]\[ r_1 = \frac{-1 + i\sqrt{2}}{3} \][/tex]
[tex]\[ r_2 = \frac{-1 - i\sqrt{2}}{3} \][/tex]
Step 3: Write the General Solution
Since the roots are complex conjugates [tex]\( r_1 = \alpha + i\beta \)[/tex] and [tex]\( r_2 = \alpha - i\beta \)[/tex] with [tex]\( \alpha = -\frac{1}{3} \)[/tex] and [tex]\( \beta = \frac{\sqrt{2}}{3} \)[/tex], the general solution to the differential equation is of the form:
[tex]\[ y(t) = e^{\alpha t} (C_1 \cos(\beta t) + C_2 \sin(\beta t)) \][/tex]
Substitute [tex]\( \alpha \)[/tex] and [tex]\( \beta \)[/tex]:
[tex]\[ y(t) = e^{-\frac{t}{3}} \left( C_1 \cos\left( \frac{\sqrt{2} t}{3} \right) + C_2 \sin\left( \frac{\sqrt{2} t}{3} \right) \right) \][/tex]
Thus, the general solution of the differential equation [tex]\( 3y'' + 2y' + y = 0 \)[/tex] is:
[tex]\[ y(t) = e^{-\frac{t}{3}} \left( C_1 \cos\left( \frac{\sqrt{2} t}{3} \right) + C_2 \sin\left( \frac{\sqrt{2} t}{3} \right) \right) \][/tex]
where [tex]\( C_1 \)[/tex] and [tex]\( C_2 \)[/tex] are arbitrary constants.
Choose yes or no to tell if the fraction 3/8 will make each equation true
It says to check if [tex] \frac{3}{8} [/tex] satisfy each equation or not.
Checking first equation :-
96 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{96 * 3}{8} [/tex]
⇒ [tex] \frac{288}{8} [/tex] = 36
⇒ 36 = 36. First equation is "YES".
Checking second equation :-
38 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{38 * 3}{8} [/tex]
⇒ [tex] \frac{114}{8} [/tex] = [tex] \frac{57}{4} [/tex]
⇒ [tex] \frac{57}{4} [/tex] ≠ 14. Second equation is "NO".
Checking third equation :-
16 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{16 * 3}{8} [/tex]
⇒ [tex] \frac{48}{8} [/tex] = 6
⇒ 6 = 6. Third equation is "YES".
Checking fourth equation :-
56 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{56 * 3}{8} [/tex]
⇒ [tex] \frac{168}{8} [/tex] = 21
⇒ 21 = 21. Fourth equation is "YES".
Which function has an inverse that is also a function?
Answer:
C){(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
Step-by-step explanation:
The one-to-one function has inverse where the inverse is also function.
That is, there should be unique output for each input values.
Look at the options, Option C) only has unique output for each input values.
Therefore, the answer C){(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
Hope this will helpful.
Thank you.
Find the derivative of the function. f'(x)= arccsc 8x
The derivative of the function f'(x)= arccsc 8x is f'(x)= -1/(|8x|√((8x)² - 1)). We achieved this result by using the rules for derivatives of arcsine, arcsecant and arccosecant along with the chain rule for differentiation of composite functions.
Explanation:To find the derivative of the function f'(x)= arccsc 8x, we will first need to understand that the derivative of the arcsine of x, also known as the inverse sine of x, is 1/(√(1 - x²)). Similarly, the derivative of arcsecant of x, known as the inverse secant of x, is 1/(|x|√(x² - 1)).
However, here we have arccosecant of x, known as the inverse cosecant of x. With this, we find that the derivative of arccosecant of x is -1/(|x|√(x² - 1)). Now in context of our function, where we replace x with 8x, we get f'(x)= -1/(|8x|√((8x)² - 1)).
We used the rules mentioned as well as the mutation rule ( df (u) = [du f(u)] dx ). This mutation rule is also known as the chain rule in differentiation, which allows us to differentiate composite functions. The function present here is a composite function where we have 8x in place of x in the arccosecant function.
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a test is worth 90 points and contains 25 questions. multiple-choice questions are worth 3 points each and word problems are worth 4 points. How many of each type of question are there?
How can I solve the following equation x3+x2+x+1=0?
Please can some body please help me with this math problem on IXL. I just want to get done with tthis IXL, because i have been doing it forever now
If two events a and b are independent and you know that p(a) = 0.75, what is the value of p(a | b)?
Marcia bake 2 pans of brownies. Her family ate 1 1/5 pans. what fraction of a pan of brownies was left?
we know that
To find out the fraction of a pan of brownies that was left subtract [tex]1\frac{1}{5}[/tex] from [tex]2[/tex]
remember that
[tex]1\frac{1}{5}=(1*5+1)/5=\frac{6}{5}[/tex]
so
[tex]2-\frac{6}{5} =(2*5-6)/5=\frac{4}{5}[/tex]
therefore
the answer is
the fraction of a pan of brownies that was left is [tex]\frac{4}{5}[/tex]
At Brown Elementary School, 80% of all fifth graders ride the bus to school. If 124 fifth graders ride the bus to school, how many fifth graders are there at the school?
Answer: The total number of fifth graders in the school is 155.
Step-by-step explanation: Given that at Brown Elementary School, 80% of all fifth graders ride the bus to school.
If 124 fifth graders ride the bus to school, we are to find the number of fifth graders in the the school.
Let, 'n' be the total number of fifth graders in the school.
Then, according to the given information, we have
[tex]80\%\times n=124\\\\\\\Rightarrow \dfrac{80}{100}\times n=124\\\\\\\Rightarrow \dfrac{4}{5}n=124\\\\\\\Rightarrow n=\dfrac{124\times 5}{4}\\\\\\\Rightarrow n=31\times5\\\\\Rightarrow n=155.[/tex]
Thus, the total number of fifth graders in the school is 155.
The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below: Car A: y = 44x + 26 Car B: y = 36x + 66 After how many hours will the two cars be at the same distance from their starting point and what will that distance be?
5 hours, 346 miles 5 hours, 246 miles 3 hours, 246 miles 3 hours, 346 miles
The answer is:
5 hours, 246 miles.
Why?Since we know the equations that represent the distances of both cars at certain times (function of time), we can calculate the time that they will be at the same distance by making their equation equal.
So, we are given the equations:
A-
[tex]y=44x+26[/tex]
B -
[tex]y=36x+66[/tex]
Now, by making both equation equal, we can calculate the time that they will have the same distance, so, we have:
[tex]44x+26=36x+66[/tex]
[tex]44x-36x=66-26[/tex]
[tex]8x=40[/tex]
[tex]x=\frac{40}{8}=5[/tex]
Hence, we have that they will have the same position after 5 hours.
Then, to calculate the distance, we need to substitute the obtained time in any of the given equations, so, substituting into A, we have:
[tex]y=44x+26[/tex]
[tex]y=44*5+26=220+26=246[/tex]
We have that the distance will be 246 miles.
Hence, we have that the answer is:
5 hours, 246 miles.
Have a nice day!
write 2/5 and 1/3 as equivalent fractions using a common denominator
The equivalent fractions with the same denominator are 6/ 15 and 5 /15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two fractions are 2/5 and 1/3. The two equivalent expressions with the common base will be written as:-
2/5 = ( 2 x 3 ) / ( 5 x 3 )
2//5 = 6 / 15
1/3 = ( 1 x 5 ) / ( 3 x 5 )
1 / 3 = 5 / 15
Therefore, the two fractions are 6/ 15 and 5 /15.
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