The inverse of a function, denoted f^-1(x), is a function that "undoes" the original function. In other words, if f(x) = y, then f^-1(y) = x.
To find the inverse of a function from a table of values, we simply switch the x and y values. So, for the given table of values:
x | 1 | 2 | 3 | 4 | 5 | 6
---|---|---|---|---|---|---
f(x) | 7 | 9 | 3 | 0 | 4 | 1
The inverse function f^-1(x) would have the table of values:
x | 7 | 9 | 3 | 0 | 4 | 1
---|---|---|---|---|---|---
f^-1(x) | 1 | 2 | 3 | 4 | 5 | 6
Now, to find f^-1(0), we simply look for the value of x that corresponds to f^-1(x) = 0. From the table, we can see that f^-1(0) = 4.
Therefore, the answer is f^-1(0) = 4.
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The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor. This is an example of
a. Nominal data
b. Ordinal data
c. Interval data
d. Quantitative data
The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor is an example of Ordinal data.
Ordinal data is a type of data that is used to rank or order objects or individuals. It is a type of categorical data that can be ranked or ordered, but cannot be measured numerically. In this case, the machines are ranked based on their design quality, which is an example of ordinal data. Other examples of ordinal data include movie ratings, letter grades, and customer satisfaction ratings.
Therefore, the correct answer is option b. Ordinal data.
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Given to find the Determinant of the following 5*5 Matrix:
let A=
EXPLANATION
Firstly to find the Determinant of a Matrix of order n*n the easiest way is to Convert the given matrix into Upper Triangular form
where Upper Triangular form means the values in the matrix which are below to the Diagonal elements are 0.
After Converting it to the Upper Triangular Matrix, the product of the Diagonal elements gives the Determinant of the Matrix
So the Given Matrix Should be Converted into the Upper Triangular Matrix in the form:
To find the determinant of the given 5x5 matrix A, we need to convert it into an upper triangular form.
This means that all the values below the diagonal elements should be 0. Once we have the upper triangular form, we can find the determinant by taking the product of the diagonal elements.
To convert the given matrix into an upper triangular form, we can use elementary row operations. We can subtract multiples of the first row from the other rows to make the values below the first element 0. Then we can do the same for the second row, third row, and so on until we have an upper triangular matrix.
Once we have the upper triangular matrix, we can find the determinant by taking the product of the diagonal elements. The determinant of the given matrix A is the product of the diagonal elements of the upper triangular matrix.
So the steps to find the determinant of the given matrix A are:
1. Convert the given matrix into an upper triangular form using elementary row operations.
2. Take the product of the diagonal elements of the upper triangular matrix to find the determinant.
By following these steps, we can find the determinant of the given 5x5 matrix A.
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HELPPPP MEEEE I NEED TO TURN IN THIS LATE MATH HOMEWORK
Answer:
enter the step by step answer u did and then add the number the match and enter them in the box and u shall be done
Step-by-step explanation:
HELP ASAP
Use the square below
N
K
Find the mZOKL
Find the m/MOL
M
L
For the given square, m∠OKL=45° and m∠MOL=90°.
What is a Square?A square is a regular quadrilateral in Euclidean mathematics because it has four equal sides and four equal angles (right angles, 90-degree angles). It can also be explained as a rectangle with two adjacent sides that are of identical length. It is the only regular polygon whose diagonals are all the same length and whose internal, central, and exterior angles are all equal (90°).
What are Angle Bisectors?In mathematics, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal sections. An angle bisector is a beam that divides an angle into two identical segments of the same length.
Angle bisector points are equally spaced from both angle lines.
Any angle, including acute, obtuse, and right angles, can have an angle bisector traced to it.
In the given square,
The diagonals NL and KM are angle bisectors of ∠K, ∠L, ∠M and ∠N.
Therefore, ∠OKL= 90/2
∠OKL=45°
We know that, in a square, diagonals are equal and bisect each other at right angles.
Therefore, ∠MOL=90°
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Find the length of BD
40
Hot
16
02
A
01
BD 30 F
BD =
Answer:
[tex]\tt BD =12[/tex]Step-by-step explanation:
Ratio of corresponding sides are equal.
[tex]\tt \cfrac{BD}{FD} =\cfrac{AC}{EC}[/tex]
[tex]\tt \cfrac{BC}{30} =\cfrac{16}{40}[/tex]
[tex]\tt BD=30\left(\frac{2}{5}\right)[/tex]
[tex]\tt BC=6\cdot \:2[/tex]
[tex]\tt BD =12[/tex]
Therefore, the length of BD is 12.
___________________________
Hope this helps! :)
You are 14ft away from a flagpole and are looking up at if from an angle of 74.4 How is the flagpole ?
Answer:
23.4 ft tall
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given: Distance from the flagpole = 14 ft
Angle of elevation θ = 74.4°
To find: Length of the flagpole
Answer:
tan(74.4°) = [tex]\frac{L}{14}[/tex]
L = 14 tan(74.4°) = 50.142 ft
So the length of the pole is 50.142 ft.
Solve the given polynomial equation. Use the Rational Zero Theorem, Descates's Rule of Signs, and possib ald in obtaining the first root. x^(4)-4x^(3)-37x^(2)-56x-24=0
The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation (or zeros or roots of a polynomial function). The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials.
A polynomial doesn't need to have rational zeros. But if it has rational roots, then they can be found by using the rational root theorem.
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30,4 Find the value of x and y to the nearest tenth
In the given triangle of attached figure , the required value of x and y is given by option d. x=24.0,y=46.4 ( nearest tenth ).
Let us consider triangle name of the attached figure be ABC,
From vertex A perpendicular line intersect BC at point D.
From the attached figure,
Measure of ∠B = 45°
Measure of ∠C = 30°
Side length AC = 34 units
Side length AB = x units
Side length BC = y units
In triangle ADC,
sin C = AD / AC
Substitute the value we have,
⇒ sin 30° = AD / 34
⇒ AD = ( 1/2 )× 34
⇒ AD = 17
And cos C = CD / AC
Substitute the value we have,
⇒ cos 30° = CD / 34
⇒CD = 34 × cos 30°
⇒ CD = 34 × (√3 /2 )
⇒ CD = 29.45 units
In triangle ADB,
sin B = AD/ AB
⇒ sin 45° = 17 / x
⇒ x = 17 / sin 45°
⇒ x = 17 / ( 1/√2)
⇒ x = 17√2
⇒ x= 24.038 units
⇒ x= 24.0 units ( nearest tenth )
Now in triangle ABD,
cos B = BD/ AB
⇒ cos 45° = BD / 24.0
⇒ BD = 24 × cos 45°
⇒ BD = 24× (1/√2)
⇒ BD = 16.97units
y = BD + CD
= 16.97 + 29.45
= 46.42
= 46.4 units ( nearest tenth )
Therefore , the value of x and y from the attached figure is equal to option d. x=24.0,y=46.4.
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The above question is incomplete, the complete question is:
Find the value of x and y to the nearest tenth.
a. x=48.1,y=46.4
b. x=48.1,y=139.3
c. x=24.0,y=139.3
d. x=24.0,y=46.4
Figure is attached.
Plsssss help me I will give brainiest
Answer:
the first one: 1:39
the second one: 7:12
the third one: 10:24
Step-by-step explanation:
the short hand points to the hour and the long hand points to the minutes. when the long hand is at 1, that's 5 minutes and when it's at 2, that's 10 minutes and so on and so forth. and each of the little dash marks in between the numbers is 1 minute.
i hope this was correct, i'm not great with time
Question 1:
say 1:39am/pm OR one thirty-nineQuestion 2:
say 7:12am/pm OR seven twelveQuestion 3:
say 10:24am/pm OR ten twenty-fourWrite a division expression that reporesetns the weight of the steel structure divided bythe total weiught of the briudges material
The division expression that represents the weight of the steel structure divided by the total weight of the bridge's materials is 400 tons ÷ (1,000 tons + 400 tons + 200 tons) = 25%.
The total weight of the bridge's materials is the sum of the weight of concrete, steel structure, glass, and granite, which is:
1,000 tons + 400 tons + 200 tons = 1,600 tons
Simplifying the expression by dividing both numerator and denominator by 400 tons gives:
Weight of steel structure / Total weight of bridge's materials = [tex]\frac{1}{4}[/tex]
Weight of steel structure / Total weight of bridge's materials
[tex]= \frac{400 tons}{1,000 tons + 400 tons + 200 tons}[/tex]
[tex]= \frac{400 tons}{1,600 tons}[/tex] = 0.25
Therefore, the weight of the steel structure is one-fourth (or 25%) of the total weight of the bridge's materials.
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The complete question is:
Write a division expression that represents the weight of the steel structure divided by the total weight of the bridge's materials. Concrete weighs 1,000 tons, Steel structure weighs 400 tons and glass and granite weighs 200 tons.
I need help doing the math homework
By algebra properties, the factor form of polynomials are listed below:
(a + b) · (a - b) (a + b) · (a² - a · b + b²) (a - b) · (a² + a · b + b²) (x² + 6) · (x + √6) · (x - √6) (4 · c + 1) · (16 · c² - 4 · c + 1) (k - 3) · (k² + 3 · k + 9) (∛54 · x + ∛250 · y) · [(∛54 · x)² - (∛54 · x) · (∛250 · y) + (∛250 · y)²] 3 · (m - 2 · √n) · (m + 2 · √n) · (m² + 4 · n) a · b² · (a + 1) · (a² - a + 1) · (a - 1) · (a² + a + 1) y² · (x - 7 · y) · (x² + 7 · x · y + 49 · y²) 9 · y · (y - ∛4) · [y² + ∛4 · y + (∛4)²] · (y + ∛4) · [y² - ∛4 · y + (∛4)²] (w - 4) · (w - 9) p · (p + 12) · (p - 7)How to factor polynomials
In this problem we need to factor 13 cases of polynomials, whose results must be derived by algebra properties. The factor form of the polynomial is:
Case 1:
a² - b²
(a + b) · (a - b)
Case 2:
a³ + b³
(a + b) · (a² - a · b + b²)
Case 3:
a³ - b³
(a - b) · (a² + a · b + b²)
Case 4:
x⁴ - 36
(x² + 6) · (x² - 6)
(x² + 6) · (x + √6) · (x - √6)
Case 5:
64 · c³ + 1
(4 · c + 1) · (16 · c² - 4 · c + 1)
Case 6:
k³ - 27
(k - 3) · (k² + 3 · k + 9)
Case 7:
54 · x³ + 250 · y³
(∛54 · x + ∛250 · y) · [(∛54 · x)² - (∛54 · x) · (∛250 · y) + (∛250 · y)²]
Case 8:
3 · m⁴ - 48 · n²
(√3 · m² - 4√3 · n) · (√3 · m² + 4√3 · n)
3 · (m² - 4 · n) · (m² + 4 · n)
3 · (m - 2 · √n) · (m + 2 · √n) · (m² + 4 · n)
Case 9:
a⁷ · b² - a · b²
a · b² · (a⁶ - 1)
a · b² · (a³ + 1) · (a³ - 1)
a · b² · (a + 1) · (a² - a + 1) · (a - 1) · (a² + a + 1)
Case 10:
x³ · y² - 343 · y⁵
y² · (x³ - 343 · y³)
y² · (x - 7 · y) · (x² + 7 · x · y + 49 · y²)
Case 11:
9 · y⁷ - 144 · y
y · (9 · y⁶ - 144)
y · (3 · y³ - 12) · (3 · y³ + 12)
9 · y · (y³ - 4) · (y³ + 4)
9 · y · (y - ∛4) · [y² + ∛4 · y + (∛4)²] · (y + ∛4) · [y² - ∛4 · y + (∛4)²]
Case 12:
w² - 13 · w + 36
(w - 4) · (w - 9)
Case 13:
p³ + 5 · p² - 84 · p
p · (p² + 5 · p - 84)
p · (p + 12) · (p - 7)
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A second year mathematics unit at a university in a foreign country has unpredictable patterns of administering weekly tests. There will be either no test, or one test, and if there is one, it is either a 15 minute minor test or a 30 minute major test. For any given week, if there was no test in the previous week, the probability that there will be a minor test is 0.6, and the probability that there will be a major test is 0.3. For a week where there was a minor test in the previous week, the probability of minor and major tests are 0.4 and 0.2 respectively. If there was a major test in the previous week, this week there will be a minor test with probability 0.3 and no test with probability 0.7. Let Xn be the Markov chain for the situation described above, with state space {0, 1, 2}, where 0 indicates no test, 1 stands for a minor test, and 2 indicating a major test. a) Write down the transition matrix for the Markov chain. b) Find the two-step transition probability matrix for the Markov chain. c) Given that there was no test this week, find the probability that there is a test in two weeks time. d) Compute P(X5 = 2|X3 = 1, X1 = 0).
Given that there was no test this week (X0 = 0), the probability that there is a test in two weeks time (X2 = 1 or X2 = 2) is given by the sum of the probabilities of the two possible states in the two-step transition probability matrix:
P(X2 = 1 or X2 = 2|X0 = 0) = P^2[0][1] + P^2[0][2] = 0.36 + 0.12 = 0.48
To compute P(X5 = 2|X3 = 1, X1 = 0), we can use the formula for conditional probability:
P(X5 = 2|X3 = 1, X1 = 0) = P(X5 = 2, X3 = 1, X1 = 0)/P(X3 = 1, X1 = 0)
= P(X5 = 2|X3 = 1)*P(X3 = 1|X1 = 0)*P(X1 = 0)/P(X3 = 1|X1 = 0)*P(X1 = 0)
= P(X5 = 2|X3 = 1)*P(X3 = 1|X1 = 0)/P(X3 = 1|X1 = 0)
= P(X5 = 2|X3 = 1)
= P²[1][2]
= 0.12
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What are the solutions for the equation 6x²-11x-7=0
The solutions for the equation 6x²-11x-7=0 are x = -1/2 and x = 7/3
How to determine the solutionIt is important to note that quadratic equations are defined as equations having the highest degree of x as 2.
From the information given, we have that the quadratic equation is given as;
6x²-11x-7=0
Now, multiply the coefficient of x squared with the constant value, then find the pair factors of the product that adds up to given the coefficient of x = -11
We have;
6x² - 14x + 3x - 7 =0
Group the expression in pairs
(6x² - 14x) + (3x - 7) = 0
Factor the expressions
2x(3x - 7) + 1(3x - 7) = 0
Then, we have;
(2x + 1) and (3x - 7) = 0
x = -1/2
x = 7/3
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Write and solve an equation for the following situation in order for a ladder to reach a height of 10 feet it needs to be placed at a 75
If the ground already has an elevation of 15 degree. The degree that the ladder need to be set is 65.4 degrees.
What degree does the ladder need to be set?Angle at which the ladder is set from the horizontal = x.
Angle between the ladder and the ground = (75 - 15 + x) degrees
Using trigonometry, we can write the equation:
tan(75 - 15 + x) = 10 / L
where:
L= length of the ladder.
Simplifying the left-hand side using the trigonometric identity for the tangent of the difference of two angles, we get:
tan(60 + x) = 10 / L
Multiplying both sides by L, we get:
L * tan(60 + x) = 10
Dividing both sides by tan(60 + x), we get:
L = 10 / tan(60 + x)
Using a calculator, we can evaluate the right-hand side to be:
L = 10 / tan(60 + x) ≈ 5.768 / tan(x)
So, the equation we need to solve for x is:
5.768 / tan(x) = L
Substituting the value of L obtained from the previous problem, we get:
5.768 / tan(x) = 2.68
Multiplying both sides by tan(x), we get:
5.768 = 2.68 tan(x)
Dividing both sides by 2.68, we get:
tan(x) ≈ 2.153
Using a calculator, we can find the value of x that satisfies this equation by taking the inverse tangent (tan^-1) of both sides:
x ≈ 65.4 degrees
Therefore, the ladder needs to be set at an angle of approximately 65.4 degrees from the horizontal in order to reach a height of 10 feet when the ground already has an elevation of 15 degrees and the ladder is placed at a 75-degree angle with the ground.
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The complete question is:
Write and solve an equation for the following situation in order for a ladder to reach a height of 10 feet it needs to be placed at a 75 degree to the ground . The ground already has an elevation of 15 degree. What degree does the ladder need to be set?
Find EG if FG = 8, EH = x - 1, and EG = x + 1
If FG = 8, EH = x - 1: EG = x + 1
How to find EG?In order to find EG, we need to use the fact that the sum of the lengths of the segments EF and FG is equal to the length of segment EG. That is,
EF + FG = EG
We are given that FG = 8, and we know that EH + HF = EF. Therefore,
EF = EH + HF
Putting this all together, we get:
EF + FG = EG
(EH + HF) + 8 = x + 1
EH + HF = x - 7
But we also know that EH = x - 1, so we can substitute that in:
x - 1 + HF = x - 7
Simplifying this equation, we get:
HF = -6
Now we can use the fact that the sum of the lengths of the segments EH and HF is equal to the length of segment EF. That is,
EH + HF = EF
(x - 1) + (-6) = EF
x - 7 = EF
Finally, we can substitute this value for EF into our original equation to find EG:
EF + FG = EG
(x - 7) + 8 = EG
x + 1 = EG
Therefore, EG = x + 1.
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W
W
The prism and pyramid above have the same width, length, and height. The volume of the prism is 63 cm³. What is the volume of the
pyramid?
OA. 42 cm³
OB. 189 cm³
OC. 84 cm³
OD.
21 cm³
Vοlume οf the Pyramid is 21 cm³
What is Prism and Pyramid?A prism is a sοlid shape with twο identical parallel bases and flat sides that cοnnect the bases. The sides οf a prism are usually rectangles, but they can alsο be triangles οr οther pοlygοns.
A pyramid is a sοlid shape with a pοlygοnal base and triangular sides that meet at a single pοint called the apex.
When a prism have same base area and height as that οf a pyramid the vοlume οf the prism is three times that οf the pyramid.
=> Vοlume οf prism = 3 Vοlume οf pyramid
Here we have
The prism and pyramid abοve have the same width, length, and height.
The vοlume οf the prism is 63 cm³
As we knοw,
Vοlume οf prism = 3 Vοlume οf pyramid
The vοlume οf the Pyramid = [ Vοlume οf prism ]/ 3
= [ 63 cm³]/3 = 21 cm³
Therefοre,
Vοlume οf the Pyramid is 21 cm³
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Assessment Math R. 14 Multiply using the distributive p Simplify the expression: (2w-5)(-7)
-14w + 35 is the simplified answer of (2w-5)(-7).
What is distributive property?The distributive property states that for two numbers a and b, a(b+c) = ab + ac. This means that multiplying a number by a sum is the same as multiplying each number in the sum by the original number.
To simplify the expression (2w-5)(-7) using the distributive property, we need to multiply each term inside the parentheses by -7.
The distributive property states that a(b + c) = ab + ac. In this case, a = -7, b = 2w, and c = -5.
So, using the distributive property, we can simplify the expression as follows:
(2w-5)(-7) = (-7)(2w) + (-7)(-5)
= -14w + 35
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At a temple to Sekhmet, there is a circular
reed bed to be planted with 4 different types
of reed, one in each of the four sections, as
shown here. The radius is 360cm and there
are two strings crossing at right angles of
lengths 560cm and 640cm.
Find out how far from the centre of the circle
the crossing point is
Therefore, the distance from the center of the circle to the crossing point of the two strings is 40sqrt(2) cm, or approximately 56.57 cm to two decimal places.
How far from the centre of the circle the crossing point is?The Pythagorean theorem can be used to calculate the distance between the circle's centre and where the two strings cross. Let A and B represent the spots where the threads converge, with O serving as the circle's centre. Next, we have:
OA2 plus OB2 equals AB2.
The circle's radius being equal to half the separation between the two strings, we get:
The equation OA = OB = sqrt((560/2)2 + (640/2)2) (156800)
And because the circle's diameter is twice its radius, we get the following equation: AB = 2 * radius = 2 * 360 = 720.
Now that we have the values, we can calculate:
2 * (156800) = AB2 => 2 * (156800) = 7202 => 313600 = 518400 - 2 * OA2 => OA2 = 102400 / 2 => OA = sqrt(51200) => OA = 40sqrt (2)
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probability please help!!!!!!
The probability of choosing the lists of students from the class is given by combinations C = 2400 ways
What are Combinations?The number of ways of selecting r objects from n unlike objects is given by combinations
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the total ways of choosing the students from the class be C
Now , the total number of boys = 12 boys
The total number of girls = 10 girls
And , the lists are in the order
A = { boy , girl , boy }
B = { girl , boy , girl }
The total number of ways C = A + B
From the combination of selecting boys and girls , we get
The total number of selecting A = 12 x 10 x 11 = 1320 ways
The total number of selecting B = 10 x 12 x 9 = 1080 ways
So , the total number of selecting the lists C = 2400 ways
Hence , the probability of choosing the lists of students from the class is given by C = 2400 ways
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The angles in a triangle are 3x – 7, 4x – 1, and 5x + 20.
Is the triangle right-angled?
Answer:
Yes, the triangle is right-angled since one of the angles is 90°
Step-by-step explanation:
The sum of the three angles of a triangle must add up to 180°
Here the three angles are 3x – 7, 4x – 1, and 5x + 20.
Adding them up gives
3x – 7 + 4x – 1 + 5x + 20 = 180
Grouping like terms:
3x + 4x + 5x - 7 - 1 + 20 = 180
12x + 12 = 180
12x = 180 - 12 = 168
x = 168/12 = 14
Substituting this value of x into each of the expressions:
3x – 7 = 3(14) - 7 = 42 - 7 = 35°
4x – 1 = 4(14) - 1 = 56 - 1 = 55°
5x + 20 = 5(14) + 20 = 70 + 20 = 90°
Since one of the angles is 90° it is indeed a right angled triangle
565 545 245 450 350How much money will they save monthly by the move to Oakland?
Benito and his family will save $1,315 by the move to Oakland.
Savings in house = $1200 - $565
= $635
Savings in food = $655 - $545
= $110
Saving in health care = $495 - $245
= $250
Saving in taxes = $625 - $450
= $175
Saving in necessities = $495 - $350
= $145
Total saving = $635 + $110 + $250 + $175 + $145
= $1,315.
Hence, Benito and his family will save $1,315 by the move to Oakland.
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Your question is incomplete, the complete question is:
Benito's family is thinking of relocating from Los Angeles to Oakland to save money. They set up a budget comparing the cost of living for both cities.
Oakland Los Angeles
Cost Housing $565 $1200
Food $545 $655
Health Care $245 $495
Taxes $450 $625
Other Necessities $350 $495
How much money will they save monthly by the move to Oakland? $1315, $1560, $1665, or $1765?
\[ \begin{array}{c} A=\left[\begin{array}{lll} -5 & 1 & -7 \end{array}\right] \\ B=\left[\begin{array}{llll} -8 & 7 & 5 & -5 \end{array}\right] \\ C=\left[\begin{array}{ll} -4 & -2 \end{array}\right]
A \times B \times C = \left[\begin{array}{ll} -40 & -60 \\ -68 & 70 \\ 6 & 0 \end{array}\right]
To find the product of the matrices A, B and C, we can use the following equation:
$$A \times B \times C = \left[\begin{array}{lll} (A \times B)_{11} & (A \times B)_{12} & (A \times B)_{13} \\ (A \times B)_{21} & (A \times B)_{22} & (A \times B)_{23} \\ (A \times B)_{31} & (A \times B)_{32} & (A \times B)_{33} \end{array}\right] \times C = \left[\begin{array}{ll} (A \times B \times C)_{11} & (A \times B \times C)_{12} \\ (A \times B \times C)_{21} & (A \times B \times C)_{22} \\ (A \times B \times C)_{31} & (A \times B \times C)_{32} \end{array}\right]$$
To find each element of the product, we use the following equation:
$$(A \times B \times C)_{ij} = \sum_{k=1}^{3} A_{ik} \times B_{kj} \times C_{ij}$$
Where $i$ and $j$ represent the row and column numbers respectively. For example, to find the element $(A \times B \times C)_{11}$, we have:
$$(A \times B \times C)_{11} = \sum_{k=1}^{3} A_{1k} \times B_{k1} \times C_{11} = (-5 \times -8 \times -4) + (1 \times 7 \times -4) + (-7 \times 5 \times -4) = -40$$
Therefore, the product of A, B and C is:
$$A \times B \times C = \left[\begin{array}{ll} -40 & -60 \\ -68 & 70 \\ 6 & 0 \end{array}\right]$$
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The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (Note: Ignore the percent symbol when entering your answer.
The percentage that is less than the average number of shoppers in the original store at any time is 60%.
Little's law:Little's law is a fundamental principle in queueing theory that relates the average number of customers in a stable system to the average time that a customer spends in the system.
The law states that the average number of customers N in the system is equal to the average rate of customer arrivals r multiplied by the average time W that a customer spends in the system:
N = rWHere we have
For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes.
=> Number of shoppers per minute = 1.5
=> Rate of shoppers per minute = 1.5
The manager estimates that each shopper stays in the store for an average of 12 minutes.
Hence, by Little’s law, the number of shoppers N = r × t
=> Number of shoppers = (1.5) × 12 = 18
Let the estimated average number of shoppers in the original store at any time be 45.
So, the number of shoppers is (45 - 18) less than the original i.e 27
Percentage [ 27/45 ] × 100 = 60%
Therefore,
The percentage that is less than the average number of shoppers in the original store at any time is 60%.
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data. Nina: 18 hours, 100%; Johannes: 10 hours, 80%; Al-Rahim: 2 hours, 50%; Caroline: 6 hours, 70%; Saul: 8 hours, 80%
The average percentage of time spent studying is 8.64%.
To find the average percentage of time spent studying, we need to first add up the total hours and total percentage of all the students. Then, we can divide the total percentage by the total hours to find the average percentage of time spent studying.
Total hours = 18 + 10 + 2 + 6 + 8 = 44 hours
Total percentage = 100% + 80% + 50% + 70% + 80% = 380%
Average percentage = Total percentage / Total hours = 380% / 44 hours = 8.64%
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Complete question
Find the average percentage of time spent on studying. data. Nina: 18 hours, 100%; Johannes: 10 hours, 80%; Al-Rahim: 2 hours, 50%; Caroline: 6 hours, 70%; Saul: 8 hours, 80%
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 22ft long and 14ft wide.
Find the area of the garden. Use the value 3.14 for pie , and do not round your answer. Be sure to include the correct unit in your answer.
Step-by-step explanation:
To find the area of the rose garden, we need to find the sum of the areas of the rectangle and the semicircle.
Area of rectangle = length x width = 22 ft x 14 ft = 308 sq ft
Area of semicircle = (1/2) x pi x radius^2, where radius = diameter/2
The diameter of the semicircle is the width of the rectangle, which is 14 ft. So the radius is 7 ft.
Area of semicircle = (1/2) x 3.14 x 7^2 = 3.14 x 24.5 = 77.03 sq ft
Total area of rose garden = area of rectangle + area of semicircle
= 308 sq ft + 77.03 sq ft
= 385.03 sq ft
Therefore, the area of the rose garden is 385.03 square feet.
A tabletop in the shape of a trapezoid has an area of 6,731 square centimeters. Its longer base measures 127 centimeters, and the shorter base is 85 centimeters. What is the height?
Answer:
[tex]\boxed{The \ height \ of \ the \ tabletop \ is \ 63.5 \ centimeters}[/tex]
Step-by-step explanation:
We are given that,
Length of the base = 127 centimeters
Width of the base = 85 centimeters
Area of the trapezoid shaped base = 6,731 square centimeters.
Since, we know,
[tex]\bold{Area \ of \ a\ trapezoid}=\frac{Length +Width}{2}\times Height[/tex]
So, we get,
[tex]6731=\frac{127+85}{2}\times Height[/tex]
i.e. [tex]6731=\frac{212}{2}\times Height[/tex]
i.e. [tex]6731=106\times Height[/tex]
i.e. [tex]Height=\frac{6731}{106}[/tex]
i.e. Height = 63.5 centimeters
Hence, the height of the tabletop is 63.5 centimeters.
Big ideas 7.5 question
Measure of angles ∠Q,∠T,∠R are 98°, 98°, 82° respectively.
What is isosceles trapezoid?An isosceles trapezoid can be defined as a trapezoid whose non-parallel sides and base angles have the same measure. That is, if the two opposite sides (bases) of a trapezoid are parallel and the two non-parallel sides are of equal length, it is an isosceles trapezoid.
Given,
Isosceles trapezoid QRST
m∠S = 82°
Base angles are equal in Isosceles trapezoid
m∠R = m∠S
m∠R = 82°
and
m∠Q = m∠T
Sum of all interior angles of a quadrilateral is 360°
m∠Q + m∠T + m∠R + m∠S = 360°
m∠Q + m∠Q + 82° + 82° = 360°
2 m∠Q = 360° - 164°
2 m∠Q = 196°
m∠Q = 98°
m∠T = 98°
Hence, 98°, 98°, 82° are measure of angles ∠Q,∠T,∠R respectively.
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A boat traveled 34 miles in two hours. At this rate , how many miles would the boat travel in 6 hours
Write three rational expressions that simplify to (x)/(x+1), none of which may have a monomial in either the numerator or denominator. Show that your expressions simplify.
Three rational expressions that simplify to (x)/(x+1) are:
1) (x+2-2)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1)
3) (3x+5-5-2x)/(x+2+1-2)
To simplify these expressions, we can combine like terms in the numerator and denominator:
1) (x+2-2)/(x+1) = (x)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1) = (-x+3)/(-x+3) = (x)/(x+1)
3) (3x+5-5-2x)/(x+2+1-2) = (x)/(x+1)
As shown, all three expressions simplify to (x)/(x+1), fulfilling the requirements of the question.
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Hamid wants to find out what people in Melworth think about the sports facilities in the town. Hamid plans to stand outside the Melworth sports centre one Monday morning. He plans to ask people going into the sports centre to complete a questionnaire. Carol tells Hamid that his survey will be biased. Give one reason why the survey will be biased.
Because it only covers those who are entering the sports centre, the survey will be prejudiced.
Why are surveys biased?This means that the survey will only reflect the opinions of those who are likely to have positive perceptions of the sports facilities and who are interested in using them. It does not include the viewpoints of those who do not use or hold a poor opinion of the sporting facilities.
Those who don't use the facilities, for instance, could have bad perceptions of the sports centre if it is renowned for being pricey or challenging to get to. The survey will miss important information if it simply polls visitors to the sports centre.
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