The system of inequalities to represent the maximum amount of flooring needed and the maximum amount of money Samuel wants to spend is x + y <= 2000 and 4.50x + 8.25y <= 10000.
Let x be the number of square feet of carpet and y be the number of square feet of hardwood.
The most amount of flooring area he can cover is 2000 square feet. So the first inequality represents the maximum amount of flooring area that Samuel can cover:
x + y <= 2000
The carpet is $4. 50 per square foot and the hardwood is $8. 25 per square foot and Samuel has a budget of $10,000. So the second inequality represents the maximum amount of money that Samuel wants to spend:
4.50x + 8.25y <= 10000
So the system of inequalities is:
x + y <= 2000
4.50x + 8.25y <= 10000
This system represents the possible combinations of carpet and hardwood that Samuel can use while staying within his budget and the maximum amount of flooring area he can cover.
To know more on inequalities
https://brainly.com/question/19526736
#SPJ4
Find a general solution of the system x' (t) = Ax(t) for the given matrix A. x(t) = (Use parentheses to clearly denote the argument of each function.)
The general solution of the system x' (t) is[tex]X(t)=c_1\left(\left[\begin{array}{c}-5 \\2\end{array}\right] \cos 3 t-\left[\begin{array}{l}1 \\0\end{array}\right] \sin 3 t\right)[/tex][tex]+c_2\left(\left[\begin{array}{c}1 \\0\end{array}\right] \cos 3 t+\left[\begin{array}{c}-5 \\2\end{array}\right] \sin 3 t\right)\end{gathered}[/tex]
The given system of equation is X'A=X
where
[tex]$$A=\left[\begin{array}{cc}-15 & -39 \\6 & 15\end{array}\right]$$[/tex]
Eigenvector of a square matrix is defined as a non-vector in which when a given matrix is multiplied, it is equal to a scalar multiple of that vector. Let us suppose that A is an n x n square matrix, and if v be a non-zero vector, then the product of matrix A, and vector v is defined as the product of a scalar quantity λ and the given vector, such that:
Av =λvWhere
v = Eigenvector and λ be the scalar quantity that is termed as eigenvalue associated with given matrix A
The values of A are given by
[tex]$|A-\lambda I|=0 \\\left|\begin{array}{cc}-15-\lambda & -39 \\6 & 15-\lambda\end{array}\right|=0 \\[/tex]
[tex](-15-\lambda)(15-\lambda)-(6)(-39)=0 \\[/tex]
[tex]\Rightarrow-(15+\lambda)(15-\lambda)+(6)(39)=0 \\[/tex]
[tex]\\\Rightarrow(15+\lambda)(15-\lambda)-(6)(39)=0 \\\\\Rightarrow 225-\lambda^2-234=0 \\[/tex]
[tex]\Rightarrow-\lambda^2-9=0 \\[/tex]
[tex]\Rightarrow \lambda^2=-9 \\[/tex]
[tex]\Rightarrow \lambda=\pm 3 i[/tex]
Now, eigen vector u corresponding to [tex]$\lambda=3 i$[/tex] is given by
[tex]$$\begin{gathered}{[A-3 i I] u=O} \\{\left[\begin{array}{cc}-15-3 i & -39 \\6 & 15-3 i\end{array}\right]\left[\begin{array}{l}u_1 \\u_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\\\\end{gathered}$$[/tex]
Applying [tex]R_2 \rightarrow R_2-6 R_1[/tex]
[tex]& {\left[\begin{array}{cc}1 & \frac{-39}{-15-3 i} \\0 & 0\end{array}\right]\left[\begin{array}{l}u_1 \\u_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\[/tex]
[tex]& \Rightarrow u_1+\frac{39}{15+3 i} u_2=0 \\[/tex]
[tex]& \Rightarrow u_1=-\frac{13}{5+i} u_2=-\frac{13}{5+i} * \frac{5-i}{5-i} u_2=-\frac{13(5-i)}{26} u_2=-\frac{5-i}{2} u_2 \\[/tex]
Thus, by choosing [tex]$u_2[/tex]=1 eigenvector corresponding to [tex]$\lambda=3 i$[/tex] is [tex]$$u=\left[\begin{array}{c}-\frac{5-i}{2} \\1\end{array}\right]$$[/tex]
[tex]R_1 \rightarrow \frac{1}{-15+3 i} R_1 \\[/tex]
[tex]{\left[\begin{array}{cc}1 & \frac{-39}{-15+3 i} \\6 & 15+3 i\end{array}\right]\left[\begin{array}{l}v_1 \\v_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\[/tex]
Applying [tex]R_2 \rightarrow R_2-6 R_1 \\[/tex]
[tex]{\left[\begin{array}{cc}1 & \frac{-39}{-15+3 i} \\0 & 0\end{array}\right]\left[\begin{array}{l}v_1 \\v_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\[/tex]
[tex]\Rightarrow v_1+\frac{39}{15-3 i} v_2=0 \\\Rightarrow v_1=-\frac{39}{15-3 i}[/tex]
[tex]\begin{gathered}\Rightarrow v_1+\frac{39}{15-3 i} v_2=0 \\\v_2=-\frac{13(5+i)}{26} \\\Rightarrow v_1==-\frac{5+i}{2}\end{gathered}$$[/tex]
Thus, by choosing [tex]$v_2=1$[/tex] eigenvector corresponding to [tex]$\lambda=-3 i$[/tex] is
[tex]$$v=\left[\begin{array}{c}-\frac{5+i}{2} \\1\end{array}\right]$$[/tex]
Hence, the general solution is given by
[tex]X(t)=c_1 e^{3 i t} u+c_2 e^{-3 i t} v \text { [using } e^{i t}=\cos t+i \sin t \\[/tex]
[tex]X(t)=c_1\left[\begin{array}{c}-\frac{5-i}{2}(\cos 3 t+i \sin 3 t) \\(\cos 3 t+i \sin 3 t)\end{array}\right]+c_2\left[\begin{array}{c}-\frac{5+i}{2}(\cos 3 t-i \sin 3 t) \\(\cos 3 t-i \sin 3 t)\end{array}\right] \\[/tex]
[tex]X(t)=c_1\left[\begin{array}{c}-\frac{5}{2}(\cos 3 t+i \sin 3 t)+\frac{i}{2}(\cos 3 t+i \sin 3 t) \\(\cos 3 t+i \sin 3 t)\end{array}\right][/tex][tex]+c_2\left[\begin{array}{c}-\frac{5}{2}(\cos 3 t-i \sin 3 t)-\frac{i}{2}(\cos 3 t-i \sin 3 t) \\(\cos 3 t-i \sin 3 t)\end{array}\right] \\[/tex]
[tex]X(t)=c_1\left[\begin{array}{c}-\frac{5}{2} \cos 3 t-\frac{5 i}{2} \sin 3 t+\frac{i}{2} \cos 3 t-\frac{1}{2} \sin 3 t \\\cos 3 t+i \sin 3 t\end{array}\right][/tex][tex]+c_2\left[\begin{array}{c}-\frac{5}{2} \cos 3 t+\frac{5}{2} i \sin 3 t-\frac{i}{2} \cos 3 t-\frac{1}{2} \sin 3 t \\\cos 3 t-i \sin 3 t\end{array}\right ][/tex]
[tex]X(t)=c_1\left(\left[\begin{array}{c}-5 \\2\end{array}\right] \cos 3 t-\left[\begin{array}{l}1 \\0\end{array}\right] \sin 3 t\right)[/tex][tex]+c_2\left(\left[\begin{array}{c}1 \\0\end{array}\right] \cos 3 t+\left[\begin{array}{c}-5 \\2\end{array}\right] \sin 3 t\right)\end{gathered}[/tex]
Therefore, the general solution of the system X(t) is [tex]X(t)=c_1\left(\left[\begin{array}{c}-5 \\2\end{array}\right] \cos 3 t-\left[\begin{array}{l}1 \\0\end{array}\right] \sin 3 t\right)[/tex][tex]+c_2\left(\left[\begin{array}{c}1 \\0\end{array}\right] \cos 3 t+\left[\begin{array}{c}-5 \\2\end{array}\right] \sin 3 t\right)\end{gathered}[/tex].
For more such questions on Eigenvector
https://brainly.com/question/29658558
#SPJ4
34 entre 250.6 con operacion
De acuerdo con la información del enunciado, el resultado de esta operación matemática (división) es 0,13
¿Cómo solucionar la división?Para solucionar la división, debemos realizar el siguiente procedimiento:Identificar las partes de la división (dividendo y divisor), en este caso como el divisor es más grande, debemos añadir un cero y una coma en el cociente para añadir un cero en el dividendo.Una vez hemos agregado un cero al dividendo, debemos identificar un número que al multiplicarlo con el divisor no de menor o igual al dividendo, en este caso sería 1, porque 250.6 * 1 = 250.6Entonces debemos hallar la diferencia entre 250.6 y 340, este procedimiento se hace con una resta y daría 89,4.Una vez hallamos este número, debemos identificar otro número para el cociente que multiplicado por 250,6 no de inferior o igual a 894, en este caso sería 3, 3 * 250,6 = 751.8En este paso debemos realizar otra resta para identificar la diferencia entre estos dos número. 894 - 751,8 = 142,2Esta división da como resultado un número decimal de varios valores por lo que podemos repetir este procedimiento tantas veces sea necesario dependiendo de la exactitud de nuestras necesidades.
Aprenda más sobre división en: https://brainly.com/question/29292671
#SPJ1
the length of each side of a square is 3 inches more than the length of each side of a smaller square. the sum of the areas of the squares is 149 inches squared. find the length of the side of the smaller square.
The length of the side of the smaller square is 7 inches.
Let x be the length of the side of the smaller square.
The length of each side of a square is 3 inches more than the length of each side of a smaller square. Thus the length of the side of the larger square is
(x + 3) inches.
The area of the smaller square is
x^2 square inches.
The area of the larger square is
(x + 3)^2 square inches.
We can set up the equation:
x^2 + (x + 3)^2 = 149
Expanding and simplifying the equation gives:
x^2 + x^2 + 6x + 9 = 149
Combining like terms:
2x^2 + 6x - 140 = 0
Using the quadratic formula, we can solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-6 ± √(6^2 - 4 * 2 * (-140))) / 2 * 2
x = (-6 ± √(36 + 1120)) / 4
x = (-6 ± √(1156)) / 4
x = (-6 ± √(596)) / 4
x = (-6 ± 34) / 4
x = -10 or x = 7
The side length of the smaller square can't be negative, so x = 7 inches.
To know more on quadratic formula
https://brainly.com/question/11540485
#SPJ4
at what point do the curves r1(t) = t, 3 − t, 15 + t2 and r2(s) = 5 − s, s − 2, s2 intersect?
Therefore , the solution of the circle comes out to be the parametric curves cross at position (4, 1, 32).
What is a circle?Each point in the plane that is a certain distance from some other point forms a circle (center). Thus, it is an arc composed of points that also are spaced apart from one another in the plane. Additionally, at every angle, it is radial symmetric about the center. In the closed, two-dimensional plane of a circle, every pair of endpoints is uniformly separated from the "center." By drawing lines through the circle, one can create a line of circular symmetry. Additionally, it rotates equally at all angles about the center.
Here,
This is what we get when we use the parametric values in both r2 and r1 as functions of t:
Curve 1: x1(t), y(t), and z(t) = 48-12
Figure 2: Curve 2:
x2(t)=8-t, y2(t)=t-3, 22(t) = 12
Where they meet, they are equal, so:
x1(t) Equals x2(t),
where t=8-t 2t8 and t=4
(x(t), y(t), z(t)) = using curve 1 (t,5-t,48-12)
Following that,
(x(4), y(4), 2(4)) = (4,5-4, 48-42) = (4,1,32)
They get together at point (4, 1, 32).
Therefore , the solution of the circle comes out to be the parametric curves cross at position (4, 1, 32).
To know more about circle visit:
https://brainly.com/question/29142813
#SPJ4
WILL MAKE BRAINLIEST! Find the solution to the system of equations. Round to the nearest tenth if necessary.
Answer:
The solution to the system of equations g(x) = x - 1 and f(x) = x^2 - 5 is the point where the two functions intersect, which is the point (1,0).
To confirm this, we can substitute x = 1 into each equation and see that they both equal 0:
g(1) = 1 - 1 = 0
f(1) = 1^2 - 5 = -4 + 1 = -3 = 0
So (1,0) is the solution to the system of equations.
2x^4 = 50 how do you solve this using factoring?
[tex] {2x}^{4} = 50 \\ = > {x}^{4} = \frac{50}{2} \\ = > {x}^{4} = 25 \\ = > {x}^{4} - 25 = 0 \\ = > ( {x}^{2} + 5)( {x}^{2} - 5) = 0 \\ = > {x}^{2} - 5 = 0 \\ > (x - 5)(x + 5) = 0 \\ = > x = 5 \: \: and \: \: - 5[/tex]
Answer:
5, -5
Hope it helps.
Please send your query through comment section.
A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X1 and X2 as given in the table. Consequently, .
If the data from X2 is higher than the data from X1, then the researcher can conclude that using an octane booster increases gasoline mileage
X1: Gas mileage before using octane booster
X2: Gas mileage after using octane booster
The researcher is comparing X1 and X2, to determine if using an octane booster increases gasoline mileage.
1. The researcher selected a random sample of seven cars and drove them for two weeks without using the octane booster (X1).
2. The researcher then drove the same seven cars for two weeks with the octane booster (X2).
3. The researcher then compared the data from X1 and X2 to see if there was an increase in gasoline mileage.
4. If the data from X2 is higher than the data from X1, then the researcher can conclude that using an octane booster increases gasoline mileage.
Learn more about data here
https://brainly.com/question/14893265
#SPJ4
A graphic artist uses a program to draw geometric shapes in a given pattern. The program uses an algorithm that draws the shapes based on input from the artist. The table shows the approximate number of steps the algorithm takes to draw different numbers of shapes.
Based on the values in the table, which of the following best characterizes the algorithm for drawing n
shapes, where n
is a very large number?
answer choices
The algorithm runs in a reasonable amount of time because it will use approximately n
steps to draw n
shapes.
The algorithm runs in a reasonable amount of time because it will use approximately N 2 steps to draw n shapes.
The algorithm runs in an unreasonable amount of time because it will use approximately n steps to draw n shapes.
The algorithm runs in an unreasonable amount of time because it will use approximately N 2 steps to draw n shapes.
The algorithm completes in an acceptable amount of time because it will draw n forms in around n2 steps.
what is algorithm ?A mathematical algorithm is a process that describes a series of steps that can be used to accomplish a mathematical computation. A typical illustration of a mathematical algorithm would be the step-by-step process used in long division. A set of instructions called an algorithm is used to solve a problem or complete a task. An algorithm is a set of instructions that spells out how to carry out a task. An algorithm can be thought of as a series of detailed instructions that result in a predictable pattern in a set of numbers or in lines of code.
given
Which of the following best describes the algorithm for drawing n forms, where n is a very big number based on the numbers in the table.
Because it will take around n2 steps to draw n forms, the algorithm completes in a fair length of time.
To know more about algorithm visit :-
https://brainly.com/question/29289479
#SPJ4
A town with 1800 homes was surveyed. of the 360 who answered the survey, 48 did not have computers at home. On the basis of the survey, estimate how many total homes do not have computers at home.
URGENT!!!!!!!
Answer:
here
Step-by-step explanation:
18000 divided by 360, then multiply that new number with 48. i believe that is the correct math...
Answer:
240
Step-by-step explanation:
48/360*1800
240
a $300 trampoline is 25% off . what is the sale price of the trampoline ?
Answer: The sale price would be 225.00
The selling price of the trampoline will be $225.
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
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 there is a 25% discount on the price $300. The discounted price will be calculated as:-
Discounted price = 300 x 0.75
Discounted price = $225
Therefore, the selling price of the trampoline will be $225.
To know more about percentages follow
https://brainly.com/question/24304697
#SPJ2
two arithmetic sequences and both begin with and have common differences of absolute value , with sequence increasing and sequence decreasing. what is the absolute value of the difference between the st term of sequence and the st term of sequence ?
The difference between the 51st term of a and the 51st term of b is 1000.
the nth term of an arithmetic series is given by [tex]a_{n}= a_{0}+(n-1)*d[/tex]
where [tex]a_{0}[/tex] is the first term of the arithmetic series, [tex]a_{n}[/tex] is the nth term of the series and d is the common difference
Given that,
[tex]a_{0}=b_{0}=30[/tex]
Common difference of both series that have absolute value = 10
common difference of series a is 10 as this series is increasing
similarly, the common difference of series b is -10 as it is decreasing
Putting the values in the above equation we get:
[tex]a_{51}= a_{0}+(n-1)*d\\[/tex]
=> 30 + (51-1)*10
=> 30 + 500 = 530
Thus, the value of [tex]a_{51}[/tex] is 530.
[tex]b_{51}= b_{0}+(n-1)*d\\[/tex]
=> 30 + (51-1)*-10
=> 30 -500 = -470
Thus, the value of [tex]b_{51}[/tex] is -470.
so we have to find the value of [tex]a_{51}-b_{51}[/tex] which is 530 - (-470) =530 +470 =1000
Therefore, The difference between the 51st term of a and the 51st term of b is 1000.
To know more about arithmetic series visit: brainly.com/question/16415816
#SPJ4
The Parkers are getting a new pet. Alan wants a cat, but his sister Jessica wants a dog. Both want a fair method to determine who gets to choose the new pet. Alan devised a method using the given spinner. They will spin the arrow twice and record the outcomes. If the product of the outcomes is even, Alan gets to choose the new pet. If the product of the outcomes is odd, Jessica gets to choose the new pet. Determine if the method is fair. If it is not, how can it be adjusted to make it fair?
A. The method is not fair. This can be resolved by using the sum of the two outcomes instead of the product.
B. The method is not fair. This can be resolved by using the same method with a spinner with only two same-sized sections instead of four.
C. The method is fair.
D. The method is not fair. This can be resolved by finding the product of the outcomes of three spins instead of two.
The method proposed is not fair, it can be adjusted by giving each sibling equal chance of winning.
What is algebra ?
Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It includes the study of operations such as addition, subtraction, multiplication, division, and the extraction of roots, as well as the properties of operations such as commutativity, associativity, and distributivity.
The method proposed by Alan is not fair because it does not take into account the probability of each outcome. The product of the outcomes being even or odd does not guarantee an equal probability of winning for both siblings. To make it fair, each sibling should have an equal chance of winning. A fair method could be to have the arrow spun once, and the sibling whose number is spun gets to choose the new pet. Another fair method could be to have a coin flipped, and the sibling whose side of the coin is facing up gets to choose the new pet.
So , The method proposed is not fair, it can be adjusted by giving each sibling equal chance of winning.
To learn more about algebra visit : brainly.com/question/24875240
#SPJ4
Question 3 (20 points) Solve this problem. Round answer to the nearest hundredths place. 81.7 x2.68
So,
The skateboard cost $67.
The protective helmet cost $25.
To find the percent that the price of the skateboard was out of the total amount, add 67 and 25 and divide 67 by the result.
Step 1:
67 + 25 = 92
Step 2:
67/92 = 0.728 or 72.8%.
The correct option is B.
Answer:200
Step-by-step explanation: when you multiply 81.7x2.68 it equals to 218.948 which to the nearest hundreth is 200
write an explicit rule for the sequence {-7,-1,5,11,17}. what is the position number for the term 47?
The position number for term 47 is 269.
This is an arithmetic sequence since each term has a common difference. Let us test it.
The difference between 1st and 2nd terms is
-7 + d = -1
d = -1 + 7
= 6
Now we check the difference for term
The difference between 3rd and 4th terms is
5 + d = 11
d = 11 – 5
= 6
So the difference is the same so we can apply a common equation for arithmetic sequence
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )
Where :
[tex]a_{n}[/tex] = number at term n
[tex]a_{1}[/tex] = first number of sequence
d = difference for each number sequence
n = term
From the question, we need to find the number at position term 47
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )
[tex]a_{47}[/tex] = -7 + 6 ( 47 - 1 )
= -7 + 6 ( 46 )
= -7 + 276
= 269
Learn more about arithmetic sequence here
https://brainly.com/question/27079755
#SPJ4
in a group of 10 people, each person shakes hands with everyone else once. how many handshakea re there
The possible number of handshakes in a group of 10 people, where each person shakes hands with everyone else once are equal to 45.
Number of people in the group = 10
Each person shakes hands with everyone else once. When n people shake hands with each other, the total number of handshakes = ⁿC₂
where C denotes the combination , is represent an arrangement of objects in different ways without care of order.
Total number of handshakes = ¹⁰C₂
= 10!/2!(10 - 2)! = 10!/2!×8!
= 10×9×8!/(2×1)8!
= (10×9)/2
= 45 handshakes.
In other words, when 10 people are shaking hands, each one will shake hands with 9 others. Then, the total possible number of handshakes in a group = 10 × 9 = 90
(but remember the point that , when A shakes hands with B, B is also shaking hands with A, i.e., we are counting one handshake twice, one from A's side and the other from B's side).
The total number of handshakes in actual way = 90/2 = 45 handshakes. Hence, the total number of handshakes in a group is 45.
To learn more about Combination formula, refer:
https://brainly.com/question/28065038
#SPJ4
a recipe calls for 3 3/8 tablespoons of sugar. if you want to make 1/2 the recipe, then how much sugar do you need?
If you want to make 1/2 the recipe, then [tex]1\frac{11}{16}[/tex] tablespoon of sugar you need.
In the given question, a recipe calls for [tex]3\frac{3}{8}[/tex] tablespoons of sugar.
If you want to make 1/2 the recipe, then we have to find how much sugar you need.
As given that;
1 recipe = [tex]3\frac{3}{8}[/tex] tablespoons of sugar
Before solving the question, we convert the mixed fraction into simple fraction.
To convert in simple fraction we multiply 3 by 8 then we add 3 on the result of multiplication of 3 and 8.
1 recipe = 27/8 tablespoons of sugar
We have to find sugar need for making 1/2 recipe.
1/2 recipe = [tex]\frac{27}{8}\times\frac{1}{2}[/tex] tablespoons of sugar
1/2 recipe = 27/16 tablespoons of sugar
1/2 recipe = [tex]1\frac{11}{16}[/tex] tablespoons of sugar
To learn more about conversion of fraction link is here
brainly.com/question/29264210
#SPJ4
Taylor earned $338.00 at her job when she worked for 20 hours. What was her hourly wage, in dollars per hour?
What is the answer.
Answer:
$338/20 = $16.90
Answer:
[tex]\$16.90 \textrm{ per hour}[/tex]
Step-by-step explanation:
To solve this, we simply have to divide the total amount of money that Taylor earned by the number of hours that she worked for.
[tex]\dfrac{\$338.00}{20 \textrm{ hr}} = \$16.90 \textrm{ per hr}[/tex]
Each number in the first table represents the points scored by a player on the AOP Academy basketball team. Make a frequency distribution, including relative frequency.
percent of total = frequency/total x 100%
1 5 8 10 11 12
1 6 9 10 12 13
3 7 9 11 12 13
4 8 10 11 12 14
For the relative frequencies below, round to the nearest hundredth. If applicable, include a leading zero.
Score Frequency Relative Frequency
Answer:
1 2 8.33%
3 1 4.17%
4 1 4.17%
5 1 4.17%
6 1 4.17%
7 1 4.17%
8 2 8.33%
9 2 8.33%
10 3 12.5%
11 3 12.5%
12 4 16.67%
13 2 8.33%
14 1 4.17%
total =24
what are the mean and standard deviation of the sampling distribution of the sample mean for samples of size 4 ?
On solving the provided question, we can say that standard deviation 15.4 is the mean of the sample means' sampling distribution.
What is standard deviation?Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each score from the mean.
If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size:
u = 15.4;
⊕ = 5.6
now
μ = 5.6[tex]\sqrt{5}[/tex] =
To know more about standard deviation visit:
https://brainly.com/question/23907081
#SPJ4
x race to power 4 minus 8x race to power 2 plus 1 equal to zero (Pls can anybody solve this)
Answer:
×⁴-8ײ+1
Explanation:
kaya yan ung sagot ksi hnd mo na sya mai-sosolve kasi mag kaiba ung upper right side nya kaya i coppy molng un^_^..hope its help...
Find the measure of each acute angle.
Answer:
Step-by-step explanation:
The sum of the angles in a triangle is 180
So, (19x-1)+(13x-5)+90(right angle) =180
32x+84=180
32x=96
x=3
19x3-1=56
13x3-5=34
answer : 56, 34
Find the slope of the line passing through the points (-6, -4) and (5, -4).
slope:
Find the slope of the line passing through the points (3, 3) and (3, -6).
slope:
you can use math away app
Simplify the expression. 3.8−4.9n−3n+6
Answer:
-7.9n+9.8
Step-by-step explanation:
add em
Answer:
9.8 - 7.9n
Step-by-step explanation:
To simplify, we need to have the least amount of terms possible. To do this here, we need to group like terms. We will start by rearranging our equation to group our like terms, like this:
3.8 + 6 - 4.9n - 3n
Then, we will combine our liker terms, giving us:
9.8 - 7.9n
That is the most simplified we can get. So our simplified equation is
9.8 - 7.9n.
Hope this Helped!
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x - 1)
b. y = f(²)
c.
d.
y - 1 = f(x)
²/₁ = f(x)
Answer:
c
Step-by-step explanation:
given f(x) then f(x) + c is a vertical translation of f(x)
• if c > 0 then a shift up of c units
• if c < 0 then a shift down of c units
here the red graph is i unit above the black graph , then c = + 1
and equation is
y = f(x) + 1 ( subtract 1 from both sides )
y - 1 = f(x)
Nina hired a car in the United States.
The cost of hiring the car was $294.
The exchange rate is £1 = $1.4.
Work out the cost of hiring the car in pounds.
The cost of hiring the car in pounds Nina hired is £210.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Nina hired a car in the United States. The cost of hiring the car was $294.
Now, To covert the dollar into pounds, we have to multiply the total amount in dollars by the unit conversion rate which is, £1 = $1.4 ⇒ $1 = £(1/1.4),
Therefore,
$294 is equal to £(294/1.4) = £210.
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ1
How much interest will you have in 6 months if you invest $1,000 at 3% compounded monthly
The interest that we will have in 6 months if you invest 1000 dollars at 3% compounded monthly is 15.09 dollars.
How to find compound interest?Let's find the compound interest that will if one invest 1000 dollars in 6 months at 3% rate compounded monthly.
using compound interest formula,
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
where
p = principalr = raten = number of timest = timeTherefore,
p = 1000
r = 3% = 3 / 100 = 0.03
t = 0.5
n = 12
Therefore,
[tex]A = 1000(1+\frac{0.03}{12} )^{12(0.5)}[/tex]
A = 1000(1 + 0.0025)⁶
A = $1,015.09
Therefore,
Interest = 1,015.09 - 1000 = $15.09
learn more on interest here:https://brainly.com/question/14295570
#SPJ1
Write an equation for the line that passes through (9, 12) and is perpendicular to y=4 .
The linear function that passes through (9, 12) and is perpendicular to y=4 is given as follows:
x = 9.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change of the function.b is the intercept, representing the value of y when x = 0.The line y = 4 is an horizontal line, hence a perpendicular line will be a vertical line, which has the format given as follows:
x = c.
The point is (9,12), meaning that the x-coordinate is of 9, and thus the constant c is given as follows:
c = 9.
Hence the equation is:
x = 9.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
a basket contains 15 apples, of which two are rotten. a sample of three apples is selected at random. in how many ways can two rotten apples be chosen?
There are 6 ways to choose two rotten apples out of a sample of three.
What is algebra ?
Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include the manipulation of equations and formulas using the rules of arithmetic, the solution of equations, and the study of the properties and behaviors of functions.
There are two rotten apples out of 15 total apples, so the probability of choosing a rotten apple is 2/15. The probability of choosing two rotten apples out of a sample of three is (2/15) * (1/14) * (3 choose 2) = (2/455) * 3 = 6/455. So there are 6 ways to choose two rotten apples out of a sample of three.
Hence , There are 6 ways to choose two rotten apples out of a sample of three.
To learn more about algebra visit : brainly.com/question/24875240
#SPJ4
Do absolute value functions pass the vertical line test?
No, absolute value functions do not pass the vertical line test.
The vertical line test is a way to determine if a graph represents a function. A graph represents a function if and only if no vertical line intersects the graph more than once.
An absolute value function is defined as:
y = |x|
The graph of this function is a V-shape, with the vertex at the origin. The graph of the function is defined for all x-values, but the graph is not a function because a vertical line can intersect the graph at two points, one for x and the other for -x, for example if the vertical line x=2, it will intersects the graph at (2,2) and (2,-2), thus it does not pass the vertical line test.
To know more on vertical line test
https://brainly.com/question/29263148
#SPJ4
please help me on this math question
Answer:
The formula for compound interest is: A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (the amount Alex has at the end of 7 years)
P = the initial investment (£4000)
r = the annual interest rate (x/100)
n = the number of times interest is compounded per year (let's assume it is compounded annually)
t = the number of years invested (7)
Plugging in the given values and solving for x:
5263.73 = 4000(1 + x/100)^7
So x = ((5263.73/4000)^(1/7))-1*100
x = 6.33% (approximately)
So, the interest rate is 6.33%.
