If -4 -1 and 1 1 are eigenvectors of a matrix corresponding to the eigenvalues and , respectively, then and x.
Are the eigenvalues and eigenvectors of matrix A the same?An eigenvalue is connected to each of A's eigenvectors. Consequently, we can refer to this eigenvector as X1 if 1 is an eigenvalue of A and AX=1X. Remember that X must not be 0 in order to be an eigenvector. Eigenvectors have a geometric meaning as well.A nonzero vector x such that Ax x for some scalar is an eigenvector of a n n matrix A. If there is a nontrivial solution x of Ax x, the scalar is referred to as an eigenvalue of A; the associated x is referred to as an eigenvector.To learn more about eigenvectors refer to:
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The length of a rectangle i 4 inche more than it width. The area of the rectangle i equal to 4 inche le than 2 time the perimeter. Find l and w
12 inches in length and 3 inches in width when a rectangle's length is 4 inches longer than its width.
Given that,
A rectangle's length is 4 inches longer than its width. The area of rectangle is equal to 4 inches less than 2 times the perimeter of rectangle.
We have to find what is the length and width of rectangle.
We know that,
Let take length as l and width as w.
l=4w
Area of rectangle is l×w
Perimeter of rectangle is 2(l+w)
So,
l×w=2(2(l+w))-4
l×w=4(l+w)-4
Take l as 4w
4w×w=4(4w+w)-4
4w²=4(5w)-4
4w²=20w-4
4w²-20w+4=0
w²-5w+1=0
w=3
So,
l=4w
l=12
Therefore, 12 inches in length and 3 inches in width when a rectangle's length is 4 inches longer than its width.
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find the number of solutions to the equation 3x-1=1/3(9x-5)
Answer:
No Solution
Step-by-step explanation:
-1 is not equal to -5/3
the increasing annual cost (including tuition, room, board, books and fees) to attend college ) to attend college has been widely discussed in many publications including money magazine. the following random samples show the annual cost of attending private and public colleges. data are in thousands of dollars. click on the datafile logo to reference the data. round degrees of freedom to the preceding whole number. private colleges 52.8 43.2 45.0 33.3 44.0 30.6 45.8 37.8 50.5 42.0 public colleges 20.3 22.0 28.2 15.6 24.1 28.5 22.8 25.8 18.5 25.6 14.4 21.8 a. compute the sample mean and sample standard deviation for private and public colleges. round your answers to two decimal places.
For private colleges:
The sample mean for a private college is 42.70 and the sample standard deviation is = 6.72.
For public colleges:
The sample mean for a private college is 22.30 and the sample standard deviation is = 4.53.
What is a standard deviation?
The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.
For Private:
sample mean=42.70
sample standard deviation =6.72
For Public:
sample mean=22.30
sample standard deviation =4.53
Hence,
For private colleges:
The sample mean for a private college is 42.70 and the sample standard deviation is = 6.72.
For public colleges:
The sample mean for a private college is 22.30 and the sample standard deviation is = 4.53.
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help for 50 points!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The slope of the line given the information in the table is 1.
What is the slope?The slope is found in linear functions. The slope measures the rate of change of the dependent variable with respect to the independent variable. In this question, the independent variable is x and the dependent variable is y.
Slope = change in the value of y / change in the value of x
Slope = (0 - - 1) / (1 - 0) = 1
Slope = (1 - 0) / (2 - 1) = 1
Slope = (2 -1 ) / (3 - 2) = 1
Based on the value of the slope, it means that for every one percent change in the value of x, the value of y changes by 1%.
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Answer:
Step-by-step explanation:
look at the x and axis and the irrational fractions and you should find your slope
The King family went out to eat. They ordered three combo meals, two sodas, and one iced tea. Write an expression representing their bill. Then, determine the cost of the dinner for the entire family.
½ Pound Cheeseburger - $3.50
Grilled Chicken Sandwich - $4.00 Combo Meal (with fries) - $5.25
Soda - $2.00
Iced Tea - $2.25
Milkshake - $3.75
Brownie a La Mode $4.00
The expression for their bill will be;
B = 3c + 2s + i
While the cost for the entire family for dinner will be $22.
What is a mathematical expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
The structure of an expression is:
Expression is (Number/variable, Math Operator, Number/variable)
Types of Algebraic ExpressionsAlgebraic expressions are classified on the basis of the number of terms in the expression.
The various types of algebraic expressions are:
Monomial expressions contain only one term.Binomial expressions contain two unlike terms. Trinomial expressions contain only three unlike terms.Polynomial expressions have two or more terms. This includes binomials and trinomials too and all other expressions with four or more terms.Solution:
From the question;
Let c = Combo Meal (with fries) - $5.25
s = Soda - $2.00
i = Iced Tea - $2.25
The family ordered 3 combo meals, 2 sodas and 1 iced tea
So, expressing it;
Bill = 3c + 2s + i
Substituting the prices for the meals
Bill = 3(5.25) + 2(2) + 2.25
Bill = 15.75 + 4 + 2.25
Bill = $22
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If 50% of a number is 120 and 80% of the same number is 192, find 30% of that
number.
Answer: the answer is 72
Step-by-step explanation:
if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240
Now we need to determine 30% of 240 and the procedure explaining it as such
Step 1: In the given case Output Value is 240.
Step 2: Let us consider the unknown value as x.
Step 3: Consider the output value of 240 = 100%.
Step 4: In the Same way, x = 30%.
Step 5: On dividing the pair of simple equations we got the equation as under
240 = 100% (1).
x = 30% (2).
(240%)/(x%) = 100/30
Step 6: Reciprocal of both the sides results in the following equation
x%/240% = 30/100
Step 7: Simplifying the above obtained equation further will tell what is 30% of 240
x = 72%
Therefore, 30% of 240 is 72
I hope this helps
Answer:
72
Step-by-step explanation:
You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.
SolutionThe 30% you want will be the difference between 80% and 50%:
80% -50% = 30%
192 -120 = 72
30% of the same number is 72.
What is the solution to the inequality 2n-5 > 1
Answer:
n > 3
Step-by-step explanation:
2n - 5 > 1
Add 5 on both sides
2n > 6
Divide by two on both sides to isolate n
n > 3
Let the random variable b represent the number of books a student buys at the next book fair. What is the expected value of b ?.
The expected value of the random variable b is given as follows:
2.404 books.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.
From the histogram given by the image at the end of the answer, the distribution is given as follows:
P(X = 1) = 0.285.P(X = 2) = 0.333.P(X = 3) = 0.168.P(X = 4) = 0.136.P(X = 5) = 0.063.P(X = 6) = 0.015.Then the expected value of the random variable b is obtained as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.
Missing InformationThe histogram is given by the image at the end of the answer.
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simplify (8^(5))/(8^(-9))
1.8^-45
2.8^-4
3.8^14
4.8^45
The expression (8^(5))/(8^(-9)) is simplified to 8^14. Option 3
What are index forms?Index form of a number can simply be described as that number written in the form of an exponential expression.
The number can also be written as a single number which is raised to another number.
Some rules of indices to note;
Multiplying index form results in addition of their powersDivision results in subtraction of their powersGiven that;
(8^(5))/(8^(-9))
Then, we have;
8^5-(-9)
8^5+9
Add the powers
8^14
Hence, the value is 8^14
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f(x) =
2/9x2+18x-216
Answer:
Domain: all real numbers
Step-by-step explanation:
The function is:
[tex] f(x) = \dfrac{2}{9}x^2 + 18x - 216 [/tex]
The domain of a function is the set of values of the x-coordinates of the points of the function.
In this function, there is no restriction on x, so the domain is all real numbers.
Simplify -1(15+4-27) over 16
Answer:
1/2
Step-by-step explanation:
-1(15+4-27)/16
Add 15 and 4 to get 19.
Now you have -1(19-27)/16
Subtract 27 from 19 to get −8.
-1(-8)/16
Reduce the fraction 16/−8 to lowest terms by extracting and canceling out 8.
-(-1/2)
Simplify
1/2
Answer:
1/2
Step-by-step explanation:
⁻¹⁽¹⁵⁺⁴⁻²⁷⁾⁄₁₆
Calculate:
-(15 + 4 - 27) / 16
-(19-27)/16
-(-8) / 16
= 8/16
Simplify:
= 1/2
This graph shows the revenue, cost, and profit functions of a company. How can this company become profitable?
A graph shows the Price per Unit on the x-axis and dollars on the y-axis. A downward parabola revenue vertex at (25, 12,000) intercepts the origin and x-axis at (30, 0) linear function costs intercept the y axis at (0, 13,000).
A.
by increasing its production
B.
by increasing its prices
C.
by reducing its costs
D.
by reducing its prices
Based on this graph which shows the revenue, cost, and profit functions of a company, the way in which this company can become profitable is: C. by reducing its costs.
What is a profit?In Mathematics, a profit can be defined as a measure of the amount of money that is generated when the cost price is deducted from the selling price (revenue) of a good or service, which is usually provided by producers.
Mathematically, the profit made by an entrepreneur or business organization can be calculated by using this mathematical expression:
Profit = Revenue - Cost
In this scenario, the most effective and efficient way in which this company can become profitable is simply by reducing (lowering) its costs because it is incurring more cost than the amount of revenue it generates.
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a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 402402 gram setting. is there sufficient evidence at the 0.020.02 level that the bags are overfilled? assume the population is normally distributed. state the null and alternative hypotheses for the above scenario.
Yes there is sufficient evidence that the alternative hypothesis is;
bag filling machine works incorrectly at the 402 gram setting which is;
H_o ; μ ≠ 402
Null hypothesis; H_o ; μ = 402
Alternative hypothesis; H_o ; μ ≠ 402
The null hypothesis states that there is no difference in the test which is denoted by H_o. However, the sign of null hypothesis is denoted by the signs of = or ≥ or ≤.
Meanwhile, the alternative hypothesis is one that defers from the null hypothesis. This therefore implies a significant difference in the test. Thus, the signs of alternative hypothesis is denoted by; < or > or ≠.
Now, the question we have is a two tailed test. Thus;
The null hypothesis is;
bag filling machine works correctly at the 402 gram setting which is;
H_o ; μ = 402
The alternative hypothesis is;
bag filling machine works incorrectly at the 402 gram setting which is;
H_o ; μ ≠ 402
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Find the equation of a line that passes through the point (0,-1) and has a gradient of 2.
Leave your answer in the form
y=mx+c
Answer:
Step-by-step explanation:
y = 2x - 1
when you sub in 0 in x and -1 in y, the y-intercept is -1.
Multiple (3x+y) by (4x+2y)
Answer:
12x² + 10xy + 2y²
Step-by-step explanation:
(3x + y)(4x + 2y) =
= 12x² + 6xy + 4xy + 2y²
= 12x² + 10xy + 2y²
H(d) models the basketball's height (in meters) at a horizontal distance of dd meters from Kaori. What does the statement H(R)=4H(R)=4 mean
The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.
It is given that Kaori is taking a free-throw. H(d) models the basketball's height (in meters) at a horizontal distance of d meters from Kaori.
The given statement is H(R) = 4H.
Here we have H(R) instead of H(d) and it shows the height of basketball. So it clear that the height of basketball's is 4H because H(R)=4H at d = R
Since d represents the horizontal distance from Kaori, therefore the horizontal distance from Kaori is R.
Thus, Answer: The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.
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estimate using compatibl numbers.
241 divided by 34
alexis likes to go for boat rides along a river with her family. in still water, the boat travels about 7 kilometers per hour. in the river, it takes them the same amount of time t to go upstream 4 kilometers as it does to travel downstream 8 kilometers. if the speed of the river is r, which of the following expressions represents the time it takes to travel 4 kilometers upstream?
It takes 51.33 min or 6/7 hrs to travel upstream 4 km.
What is relative velocity?
it is the speed measured with respect to an observer whether he is moving or stationary and it might differ for different observers.
speed of boat = 7 km/hr
speed of river = r km/hr
speed upstream = 7-r km/hr
speed downstream = 7+r km/hr
time taken to go upstream 4 km = 4/(7-r)
time taken to go downstream 8 km = 8/(7+r)
as time taken is equal in both scenario:
4/(7-r) = 8/(7+r)
on solving we get:
r = 7/3 km/hr
put this value in time taken for upstream
4/(7-(7/3)) = 6/7 km/hr or 51.33 min
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Using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.
What is relative velocity?Think about two trains that are traveling in the same direction and at the same pace.
Even though the tracks, buildings, and trees on either side of the track indicate that both trains are moving, to the observer of one train, the other train appears to be stationary.
The other train seems to be moving at a constant speed.
So, we know that:
Speed of boat = 7 km/hr
Speed of river = r km/hr
Now,
Speed upstream = 7-r km/hr
Speed downstream = 7+r km/hr
Time taken to go upstream 4 km = 4/(7-r)
Time taken to go downstream 8 km = 8/(7+r)
As the time taken is equal in both scenarios:
4/(7-r) = 8/(7+r)
On solving we get:
r = 7/3 km/hr
Put this value in time taken for upstream as follows:
4/(7-(7/3)) = 6/7 km/hr or 51.33 min
Therefore, using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.
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Which value of x satisfies the equation
5/6 (3/8 - x) = 16
1) -19.575
2) -18.825
3) -16.3125
4) -15.6875
Answer:
(2) -18.825
Step-by-step explanation:
follow the law of BODMAS
First open the brackets to get;
5/16 - 5/6x = 16
Then collect liie terms;
5/6x = 5/16 - 16
5/6x = -251/16
x = -18.825
if the points below represent a direct variatin find the missing value (2, -6) and (5, y)
The missing value if the point is a direct variation is -15
How to determine the missing value?From the question, we have the following ordered pairs
(2, -6) and (5, y)
These ordered pairs are direct variation
A direct variation is represented as
k = y/x
This means that
y/5 = -6/2
Evaluate the quotient
y/5 = -3
Multiply both sides by 5
y = -15
Hence, the value of y is -15
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What is the solution to the system of equations?
1/3x-5=y
1/6x+y=4
Answers:
(18, 1)
(9/2, -7/2)
(-2, 17/3)
Answer:
A. (18, 1)
Step-by-step explanation:
Which polygon appears to be regular?
Answer:
Figure b
Step-by-step explanation:
the sides are equal
A line has a slope of 1/2 and includes the points (-4,-7) and (w,-3) What is the value of w?
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{w}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{w}-\underset{x_1}{(-4)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{1}{2}} \\\\\\ \cfrac{-3+7}{w+4}=\cfrac{1}{2}\implies \cfrac{4}{w+4}=\cfrac{1}{2}\implies 8=w+4\implies 4=w[/tex]
Given n sets a₁, a₂. Aₙ. The inclusion-exclusion principle states that the cardinatlity of a₁∪ a₂∪. ∪aₙ is the sum of the individual cardinalities minus the sum of the cardinalities of intersections of any two sets plus the sum of the cardinalities of intersections of any three sets minus the sum of the cardinalities of intersections of any four sets and so on. This alternating sum ends with the cardinality of the intersection of all n sets. How many terms are there in this formula that are intersections of 3 sets?.
There are total of 7 terms in the formula of intersection of 3 sets.
What is intersection?In set theory, the intersection of two sets A and B, denoted {A,B}, is the set containing all the elements of A that also belong to B, or all the elements that also belong to B.A cut operation is represented by the symbol ∩.The set A ∩ B - pronounced "intersection B" or "intersection of A and B" - is defined as the set consisting of all elements that belong to both A and B.A controlled intersection has signs, signals, and lane markings that tell drivers and others what to do.The most common controlled intersections are stop sign controlled intersections.Stop signs and traffic lights are also used depending on the flow of traffic passing through that particular intersection.The formula of the given sets is,
n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C).
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Which expressions are equivalent? Choose ALL that apply.
28
74
1) 7 to the fourth power
) 4 to the seventh power
7. 7. 7. 7
The equivalent expression to the given expression is, 7 to the fourth power.
What is equivalent expression?
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18.
Consider, the given expression
7 · 7 · 7 · 7
By using:
If a = b · b · b
Here there is multiplication of b 3 times.
So, [tex]a = b^3[/tex]
In the given expression 7 is occur 4 times,
Hence it becomes, [tex]7^4[/tex].
That is 7 to the fourth power.
Therefore, the equivalent expression to the given expression is, 7 to the fourth power.
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In an arithmetic sequence the seventh term is −13, the nineteenth term is 47 and the nth term is 217.
Find the value of n.
The value of n in the sequence is ≅ 15
How to solve an Arithmetic Progression?We should know that Arithmetic progression is a type of sequence in which the consecutive terms are gotten by the addition or subtraction of a constant term known as the common difference.
The given parameters are>
a+6d--13 ........................................ (1)
a+8d=47............................................ (2)
Subtracting equation 1 from [a+8d=47]-[a+8d=-13
⇒ 2d=60
d=30
Put d=30 in equation 1
a+6(30)=-13
a+180=-13
Collecting like terms
a=-13-180
a=-193
The nth term of an AP is given by
nth term = a+(n-1)d
where nth = 217
⇒ 217=-193+(n-1)30
Simplifying the expressing
217+223=30n
440/3=30n/30
n=14.7
Therefore n≅15
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solve for x: x/7 < or equal to -6
Step-by-step explanation:
x
— - 6 = 0
7
Subtracting a whole from a fraction
Rewrite the whole as a fraction using 7 as the denominator :
6 6 • 7
6 = — = —————
1 7
x - (6 • 7) x - 42
——————————— = ——————
7 7
x - 42
—————— = 0
7
x-42
———— • 7 = 0 • 7
7
x-42 = 0
x = 42 Answer
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if i have a b and then i get a 72% on a test that is 30% of my grade, what will my grade be?
Answer:
if you have about an 85 now than you shouldn’t go below a b
Step-by-step explanation:
In an AOL survey of Internet users, this question was posted online: "Have you ever been hit by a computer virus?" Among the 170,063 responses, 63% answered "yes."
The population will be _______.
Question 11 options:
170,063 responses.
all internet users.
63% answered "yes."
an AOL survey.
The population based on the information will be B. all internet users.
What is a population?In statistics, a population is a group of similar items or events that are relevant to a particular question or experiment. A statistical population can be a group of existing objects or a hypothetical and potentially infinite group of objects conceived as an experience-based generalization.
A population is any complete group that shares at least one characteristic. Populations are more than just individuals. People, animals, businesses, buildings, motor vehicles, farms, objects, or events are examples of populations.
In this case, In an AOL survey of Internet there wwe'r 170,063 responses, and 63% answered "yes. The population is the internet users.
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the cargo plane delivering the relief supplies must be at another location after dropping off the supplies at your site. this requires the unloading tasks to be completed in 70 minutes. the current process is taking 2 people to complete all tasks in 86 minutes
Total number of people required is 3 to complete it in 57.33 days.
What is indirect proportion ?Basically in this proportion, two quantities generally follow the opposite trend of each other like if one is increasing other one is decreasing.
As an example, if the time takes to run 10 m is inversely proportional to the speed you can run at - if you double your given speed, it takes you half as much long.
Initially,
Total People = 2
Total time taken = 86 minutes
Total time we have= 70 minutes
As people and time are inversely proportional to each other.
[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{86}[/tex]
x = (86 × 2) / 3
x= 57.33
Hence, total number of people required is 3 to complete it in 57.33 days.
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