Matrices A and B are non-invertible matrices that can be added together to form an invertible matrix. To find these matrices, we can use the following steps:
Step 1: Choose a matrix A that is not a diagonal matrix and is not invertible. One example of such a matrix is
[tex]A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right][/tex]
Step 2: Choose a matrix B that is not a diagonal matrix, is not invertible, and is not a scalar multiple of matrix A. One example of such a matrix is
[tex]B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right][/tex]
Step 3: Add the matrices A and B together to form the matrix A+B. This matrix will be invertible, as shown below:
[tex]A+B = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]+\left[\begin{array}{ccc}0&0\\1&1\end{array}\right]=\left[\begin{array}{ccc}1&1\\1&1\end{array}\right][/tex]
Step 4: Verify that the matrix A+B is invertible by finding its determinant. The determinant of a 2x2 matrix is given by:
det(A+B) = (1)(1) - (1)(1) = 0
Since the determinant of the matrix A+B is not equal to zero, the matrix is invertible.
Therefore, the matrices [tex]A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right][/tex] are non-invertible matrices that can be added together to form an invertible matrix [tex]A+B =\left[\begin{array}{ccc}1&1\\1&1\end{array}\right][/tex].
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105 is 33 1/3 of what number?
Answer:
≈ 315
Step-by-step explanation:
To find the number that 105 is 33 1/3 of, we can use algebra.
Let x be the number we are looking for. Then we can write the equation:
105 = (33 1/3)% of x
To solve for x, we can first convert the percentage to a decimal by dividing by 100:
33 1/3% = 33 1/3 ÷ 100 = 0.3333
Substituting this in the equation, we get:
105 = 0.3333x
To solve for x, we can divide both sides by 0.3333:
x = 105 ÷ 0.3333
Using a calculator, we get:
x ≈ 315
Therefore, 105 is 33 1/3 of 315.
What is the volume of this figure?
Answer:
112cm³
Step-by-step explanation:
Let us ignore the bottom part of the figure and first find only the volume of the cuboid at the top
from the figure we know that
length of the cuboid is 10 cm
Width is 2 cm
height is 5 cm
now the formula for Volume of cuboid is Length×Width×Height
so,
Volume of the Upper Cuboid = 10×2×5= 100cm³ ---(1)
Now we will ignore the cuboid on top and find the volume of the one at the bottom
From the figure, we know that its dimensions are
length = 2cm
height = 3cm
width = 2cm
Volume of the lower cuboid = 2×2×3 = 12cm³ ---(2)
Adding (1) and (2)
100cm³ + 12 cm³ = 112cm³
Therefore the volume of the given figure is 112cm³
The volume of the box is 112 cm³.
We have,
The figure can be considered as two boxes.
Now,
One box:
Volume.
= Length x Width x height
= 10 x 2 x 5
= 100 cm³
Another box:
Volume.
= Length x Width x height
= 2 x 2 x 3
= 12 cm³
Now,
The volume of the box.
= 100 + 12
= 112 cm³
Thus,
The volume of the box is 112 cm³.
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C) what’s the probability of a random sample of 150 bowlers will have an average score greater than 165?
The probability that a random sample of 150 bowlers will have an average score greater than 165 is 0
Describe Probability?Probability is a branch of mathematics that deals with the study of random events or outcomes. It is used to measure the likelihood or chance of an event occurring, ranging from impossible (0 probability) to certain (1 probability).
The basic concept of probability involves determining the ratio of the number of favorable outcomes to the total number of possible outcomes. This ratio is expressed as a fraction, decimal, or percentage.
For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2 or 0.5 or 50%, and the probability of getting tails is also 1/2 or 0.5 or 50%.
To give the probability that a random sample of 150 bowlers will have an average score greater than 165
P( [tex]\bar X[/tex]> 165) = P(z > (165 - 157)/(12/√(150)))
= P(z > 8.16)
= 0 [since from z table]
= 0
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Solve the equation by a method of your choice:
x2 - 2x - 3 = 0
If there are two solutions, separate the solutions by a comma.
Answer:
{x = -1, 3}
Step-by-step explanation:
See picture below :)
" The expressions Q(t)=t+12
Q
(
t
)
=
t
+
12
and P(t)=t2+9t+36
P
(
t
)
=
t
2
+
9
t
+
36
models the unit price ′P(t)′
′
P
(
t
)
′
and quantity of goods ′Q(t)′
′
Q
(
t
)
′
sold from a shop in a given ′t′
′
t
′
month. Using this model, Calulate the total revenue of the shop for a year.
By integration of monthly revenue we will get total revenue of the shop for a year is $51,600.
What is integration ?
Integration is a fundamental operation in calculus that involves finding the area under a curve, or the antiderivative of a function. It is the reverse operation of differentiation, which is used to find the rate of change of a function.
Integration is represented by the symbol ∫ (the integral sign), and the result of the operation is called the indefinite integral or antiderivative of the function. The antiderivative is a family of functions that differ only by a constant, known as the constant of integration.
Given by the question:
The monthly revenue can be calculated by multiplying the unit price and the quantity of goods sold in a given month. Therefore, the monthly revenue function is:
[tex]R(t) = P(t) * Q(t) = (t^2 + 9t + 36) * (t + 12)[/tex]
To find the total revenue over a year, we need to integrate the monthly revenue function over the interval [0,12] (since we are considering a year):
[tex]Total revenue = \int\limits^a_0 {R(t)} \, dt[/tex]
= [tex]\int\limits^a_b (t^2 + 9t + 36) * (t + 12) } \, dt[/tex]
= [tex]\int\limits^a_b {(t^3 + 21t^2 + 132t + 432) } \, dt[/tex]
=[tex][t^4/4 + 7t^3/3 + 66t^2 + 432t][/tex]evaluated from 0 to 12
=[tex](20736/4 + 12096 + 9504 + 5184) - (0 + 0 + 0 + 0)[/tex]
= [tex]51600[/tex]
Therefore, the total revenue of the shop for a year is $51,600.
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This is about Linear Features, If you know it I will be very grateful.
Answer:
Slope = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Slope of a graph = [tex]\frac{rise}{run}[/tex]
Steps to follow:
1. Select two points along this linear graph by reading them:
For example (0, 3) and (8, 7)
2. Draw a vertical line from Point (8, 3) to Point (8, 7). This line is considered as the rise
3. Draw a horizontal line connecting (0, 3) with (8, 3). This line represents the run
4. Substitute the x and y coordinates of the two points mentioned in Step 1 in the formula below:
Slope = [tex]\frac{y_{2} - y_{1}}{x_{2} -x_{1}}[/tex]
= [tex]\frac{7 - 3}{8 - 0}[/tex]
= [tex]\frac{4}{8}[/tex]
Divide the numerator and denominator by the Highest Common Factor ‘4’ to simplify the fraction:
= [tex]\frac{1}{2}[/tex]
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Answer:
Step-by-step explanation:
4x-22.2=1.90
22.20-4x=1.90
4x + 1.90 = 22.20
Write the linear equation in slope-intercept form from the given table.
The number of solutions of the system y = 3x + 5 is one because it is a linear equation.
What is linear equations?An equation in which is the highest power of to the variables 1 is knowns as the linear equation. Mathematically: it is an algebraic equations that can be also written in the form of ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.
Linear equations are equations in which the variables are raised to the power of 1, and the graph of the equation is a straight line. As a result, there is only one solution to the equation, which is when the line intersects the x-axis. This means that the equation has only one set of x- and y-coordinates, where x is the independent variable and y is the dependent variable, that satisfy the equation. The x-coordinate of the solution is the same as the value of x that makes the equation true and the y-coordinate is the value of y for this same x-value.
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Can someone check my wrong answers for me? thank u
Are you more likely to see a twelve-pack from the local brewery or a twelve-pack from the large chain with an average fill of 327.9 ml?
Local brewery.
a. At the local brewery the middle 95% of six-packs will have an average fill between ml 326.828 and 329.572 ml
b. At the large chain brewery, the middle 95% of six-packs will have an average fill between 326.824 ml and 329.176 ml.
How to solve thisX ζ N (328.2, 0.7^2)
YζN (328, 0.6^2)
P (X> 327.9) = 0.6659
P (Y> 327.9) = 0.5662
Since, P (X> 327.9) > P (Y> 327.9)
We are more likely to see 12-pack from the local brewery.
a. To find a, b such that P(a<x<b) = 0.95
a= 326.828
b= 329.572
b. To find c, d such that P(c<Y<d) = 0.95
c= 326.824
d= 329.176
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Last year at a certain high school, there were 50 boys on the honor roll and 80 girls on the honor roll. This year, the number of boys on the honor roll increased by 20% and the number of girls on the honor roll increased by 10%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
the total number of students on the honor roll increased by 13.8%.
Step-by-step explanation:
Last year, there were a total of 50 + 80 = 130 students on the honor roll.
This year, the number of boys on the honor roll increased by 20%, which means there are now 1.2 * 50 = 60 boys on the honor roll.
The number of girls on the honor roll increased by 10%, which means there are now 1.1 * 80 = 88 girls on the honor roll.
The total number of students on the honor roll this year is 60 + 88 = 148.
The percentage increase in the total number of students on the honor roll is (148-130)/130 * 100% = 13.8%.
Rounding to the nearest tenth, we get that the total number of students on the honor roll increased by 13.8%.
Referring to the figure, find an expression for the area.
The area of the figure can be expressed using the formula A = (x + 1)2.
What is area?Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.
This formula is derived from the fact that the figure is a square with sides of length x + 1. Since a square is a special type of rectangle, the area of a square is simply equal to the product of its two sides, or (x + 1)2.
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PLEASE HELP
match each transformation with its coordinates
1) A(1,2),A'(-1,2) : a reflection across the y-axis
2) A(1,2), A'(-2,1): a rotation 270⁰ clockwise around the origin
3) A(1,2), A'(-1,4): a translation of 2 units left and 2 unit up
4) A(1,2),A'(-1,-2): a rotation 180⁰ around the origin
5) A(1,2),A'(-3,-7): a translation of 4 units left and 9 units down
What is the transformation of a point?
The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
The given point is A(1,2).
The rule of a rotation 180⁰ around the origin is (x,y)→(−x,−y).
Therefore, A(1,2)→A'(-1,-2).
A rule of translation of 2 units left and 2 unit up is (x,y)→(x-2,y+2)
Therefore, A(1,2)→A'(1-2,2+2) = A'(-1,4).
The rule of a reflection across the y-axis is (x,y)→(−x,y).
Therefore, A(1,2)→A'(-1,2)
A rule of translation of 4 units left and 9 units down is (x,y)→(x-4,y-9)
Therefore, A(1,2)→A'(1-4,2-9) = A'(-3,-7).
The rule of a rotation 270⁰ clockwise around the origin is (x,y)→(-y,x)
Therefore, A(1,2)→A'(-2,1)
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Answer:
Step-by-step explanation:
f(x) = 4x + 6.
Find x such that
f(x) = 26.
Answer:
x=5
Step-by-step explanation:
26=4x+6
20=4x
x=5
Using the graph given below state the value of lim
The value for the [tex]\lim_{x \to 3^{+}}[/tex]f(x) = 3.
What is limit in graph?A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value.
A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.
Given:
We have given the graph, from the graph we can se a red dot.
So, the [tex]\lim_{x \to 3^{+}}[/tex]f(x) = 3
Also, limit is defined as a value that a function approaches the output for the given input values.
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tan(−0.9)
Find an approximate value of the given trigonometric function by using the figure and a calculator.
tan(−0.9)
We can write tan(− 0.9) as -
tan(− 0.9) = -1.26.
What is tangent function?Tangent function is defined as the ratio of perpendicular and base. Mathematically, we can write -
tan(Ф) = p/b
tan(Ф) = perpendicular/base
Given is to find the value of tan(− 0.9).
We know -
1 radian = 57.2958 degrees
0.9 radian = 57.3 x 0.9 = 51.57 degrees
0.9 radian = 51.57 degrees ... { 1 }
So, we can write -
tan(− 0.9) = tan( - 51.57°) = - 1.26
Therefore, we can write tan(− 0.9) as -1.26.
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Let u and v be linearly independent unit vectors. Find the set of all possible values of u⋅v. Give your answer in interval notation.
If u and v be linearly independent unit vectors then the set of all possible values of u⋅v is zero.
What are Vectors?Vectors are used in science to describe anything that has both a direction and a magnitude.
Since u and v are unit vectors, their magnitudes are both 1.
|u + v|² = (u + v)⋅(u + v) = u⋅u + 2u⋅v + v⋅v
= 1 + 2u⋅v + 1
= 2 + 2u⋅v.
On the other hand, we also have:
|u + v|² = (u + v)⋅(u + v) = u⋅u + 2u⋅v + v⋅v = 2,
since u and v are linearly independent and hence orthogonal.
Equating the two expressions for |u + v|² we get:
2 + 2u⋅v = 2,
u⋅v = 0.
Therefore, the only possible value for u⋅v is 0.
Hence, u and v be linearly independent unit vectors then the set of all possible values of u⋅v is zero.
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Question 43 Tim's age was three-quarters of Mary's age 5 years ago. If Tim will be five-sixth of Mary's age in 3 years, what is the sum of their ages right now? Available Options A.28 B.35 C.38 D.41 E.none
Answer:
E. none
Step-by-step explanation:
Let's use algebra to solve the problem:
Let's start by defining some variables. We'll use T for Tim's current age, and M for Mary's current age.
According to the first sentence of the problem, "Tim's age was three-quarters of Mary's age 5 years ago." In other words, we can write:
T - 5 = (3/4)(M - 5)
We can simplify and rearrange this equation to get:
4T - 20 = 3M - 15
4T = 3M + 5
According to the second sentence of the problem, "Tim will be five-sixth of Mary's age in 3 years." In other words, we can write:
T + 3 = (5/6)(M + 3)
Again, we can simplify and rearrange this equation to get:
6T + 18 = 5M + 15
6T = 5M - 3
Now we have two equations with two variables (4T = 3M + 5 and 6T = 5M - 3). We can use these equations to solve for T and M.
Multiplying the first equation by 2, we get:
8T = 6M + 10
Multiplying the second equation by 3, we get:
18T = 15M - 9
We can now solve for M by subtracting the first equation from the second:
10T = 21
T = 2.1
Substituting this value of T into one of the equations (e.g. 4T = 3M + 5), we can solve for M:
4(2.1) = 3M + 5
M = 8.3
Therefore, Tim's current age is 2.1 years and Mary's current age is 8.3 years.
The sum of their ages right now is T + M = 2.1 + 8.3 = 10.4 years.
So the sum of Tim and Mary's ages right now is 10.4 years.
A 24-hour digital clock shows the correct time at noon on Janurary 1. If the clock loses 15 minutes per day,after how many days will the clock show the correct time?
Answer:
24 days.
Step-by-step explanation:
Since the clock loses 15 minutes per day, it will show the correct time after gaining back 24 hours, equivalent to 1 day.
Therefore, the clock will show the correct time for the first time after 24 days, which is calculated as follows:
One day to gain back the first 15 minutes
One day to gain back the second 15 minutes
...
One day to gain back the 24th 15 minutes
So the answer is 24 days.
ical from a point 1.75m grove the ground and lom awa Laway from a Eleve tower the angle of of the top of the tower is to calculate the height of the tower
The height of the tower is 17.32 meters
What is height and distance?Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.
Given that, Ical is 10 meters away from a tower [since angle is not given let the angle of the top of the tower be 60°], we need to find the height of the tower, [see the figure attached]
The whole scene is making a right triangle, so using the concept of trigonometric ratios,
We get,
Tan 60° = height of the tower / distance of Ical from the tower
Tan 60° = height of the tower / 10
Height of the tower = 10 × Tan 60°
Height of the tower = 10 × √3
Height of the tower = 10√3
Height of the tower = 10 × 1.73
Height of the tower = 17.32
Hence, the height of the tower is 17.32 meters
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Which data set has two values for the mode?
2, 2, 2, 5, 6, 7, 9, 10
5, 6, 8,10, 11, 11, 15, 18
12, 12, 13, 13, 14, 14, 15, 15
21, 22, 22, 24, 25, 26, 28, 28
The data set: 21, 22, 22, 24, 25, 26, 28, 28 have two values of mode, which are, 22 and 28.
What is meant by the mode of a data set?
The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. Yet, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode. When the highest frequency was noted for more than one value in a data collection, there are many modes. The mode cannot be utilised in either of these examples to identify the distribution centre. Categorical variables can be summarised using the mode.
a)2, 2, 2, 5, 6, 7, 9, 10
Here most repeated value is only 2.
So the mode is 2.
b) 5, 6, 8,10, 11, 11, 15, 18
Here most repeated value is only 11.
So the mode is 11.
c)12, 12, 13, 13, 14, 14, 15, 15
Here the values 12,13,14 and 15 are repeated twice.
So this has 4 values as mode.
d) 21, 22, 22, 24, 25, 26, 28, 28
Here 22 and 28 are repeated twice.
So this data set has 2 values for the mode.
Therefore the data set: 21, 22, 22, 24, 25, 26, 28, 28 have two value of mode, which are, 22 and 28.
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Answer:
D
Step-by-step explanation:
here is a pic for proof
My teacher gave me an extra credit assignment with 25 minutes left of class. It is extra credit, not a timed assessment. need done asap
Can you help me find the point of intersection for the question in the attached picture?
Answer:
y = x + 3 --- 1
y = 4x + 9 --- 2
By combining 1 and 2, we have
x + 3 = 4x + 9
3-9 = 4x-x
-6 = 3x
x = -2
Sub x = -2 into 1
y = (-2) + 3 = 1
Intersection = (-2,1)
Please help answer this question ASAP!!
Convert 59°C to degrees Fahrenheit. If necessary, round your answer to the nearest tenth. Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answer: Using the formula F=9/5C+32, we can convert 59°C to degrees Fahrenheit:
F = 9/5 * 59°C + 32
F = 118.2°F + 32
F ≈ 150.8°F
Therefore, 59°C is approximately equal to 150.8°F.
Step-by-step explanation:
Round 10.468 to the nearest hundredth
Answer:
Step-by-step explanation:
10.468 rounded to the nearest hundredth would be 10.47
4 = tenths place
6 = hundredths place
8 = thousandths place
8 >= 0.5 so 10.468 --> 10.47
Answer: 10.47
Step-by-step explanation: After the decimal, it goes tenths, hundredths, thousandths. So we're looking at the second place after the decimal, which is a 6, and the next number is 8. Think of it like 68, rounding up to the next ten, or 70. So that turns it into 10.470, and you get to drop the zero to make it 10.47.
In a sample of 900 U.S. adults, 192 think that most celebrities are good role models. Two U.S. adults are selected from this sample without replacement.
The probability that both adults think most celebrities are good role models is 0.046
What is probability?Probability is a branch of mathematics that deals with the study of random events or processes. It is the measure of the likelihood or chance of an event or outcome occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Given that the probability that the celebrities are good role models is 192/900
Then if we pick two adults without replacement; 192/900 * 192/899
= 0.046
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Missing parts;
In a sample of 900 U.S. adults, 192 think that most celebrities are good role models. Two U.S. adults are selected from this sample without replacement.Find the probability that both adults think most celebrities are good role models.
W>2w-9 solve the inequality
The solution to the given inequality w > 2w - 9 is w < 9.
What is inequality?Inequality is defined as mathematical pieces of information that have a minimum of two terms including variables or numbers that are not equal.
The "inequality" is given in the question, as follows:
w > 2w - 9
We have to solve the above inequality for w.
⇒ w > 2w - 9
Rearrange the term of variable w in the above inequality,
⇒ w - 2w > - 9
Apply the subtraction operation and solve for w:
⇒ - w > - 9
Multiply the negative sign and flip the sign of inequality:
⇒ w < 9
Thus, the solution to the given inequality is w < 9.
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write the system as a vector equation where the first equation of the system corresponds to the first row. select the correct choice below and fill in any answer boxes to complete your choice.
The system of equations can be represented as a vector equation A x = b, where A is the coefficient matrix, x is the variable vector, and b is the constant vector.
Using matrices and vectors, a system of linear equations can be expressed as a vector equation. Consider a set of n variables and m linear equations. It may be written as follows:
A x = b
where A is a m x n matrix of the coefficients of the variables, x is a n x 1 column vector of the variables, and b is a m x 1 column vector of the constants on the right-hand side of each equation.
To match the rows of the system of equations to the corresponding row of the matrix A and vector b in the vector equation, we can represent the system of equations as:
a 21 x 1 + a 22 x 2 +... + a 2n x n = b 2 a 11 x 1 + a 12 x 2 +... + a 1n x n = b 1
a mn x n = b m, where a m1 x 1 = a m2 x 2 +...
The vector form of this is as follows:
Beginning with "a 11" and "a 12," adding "cdots and a 1n," going on to "a 21" and "a 22," adding "cdots and a 2n," adding "vdots and vdots and ddots and vdots," ending with "a m1" and "a m2," adding "cdots and a mn,"
With A serving as the coefficient matrix, x serving as the variable vector, and b serving as the constant vector, the system of equations can thus be expressed as a vector equation, A x = b.
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Round 2.77247497243 to the nearest millionth.
Answer:
3.00000000000
Step-by-step explanation:
2.77247497343 is closer to 3.00000000000 than 2.00000000000
Solve for x.
Show work
Answer:
x=11.34
Step-by-step explanation:
