(a) A basis for a subspace is a set of linearly independent vectors that span the subspace. To find a basis for this subspace, we can use the following steps:
Write the given set of vectors as the rows of a matrix, with each vector as a row.
Use row-reduction (Gaussian elimination) to put the matrix in row-echelon form.
The non-zero rows of the row-echelon form matrix form a basis for the subspace.
So, we get the matrix:
| 6a - 2c | -5b - 5c | -6a + 5b + 2c | -6a + 2c |
Using row-reduction, we can simplify the matrix to:
| 1 - 1/3 | 0 | 1/3 | -1/3 |
The non-zero rows are {[ 1 - 1/3 0 1/3 -1/3 ]}
So, a basis for the subspace is:
{[ 1 - 1/3 0 1/3 -1/3 ]}
(b) The dimension of a subspace is the number of linearly independent vectors in a basis for the subspace. In this case, the basis for the subspace has only one vector, so the dimension of the subspace is 1.
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Will give you brainly! :) Thank you for taking time out of your day to answer this!
The probability values are P(30 ≤ Amount ≤ 59) = 0.43, P(Amount ≥ 60 or Amount < 30) = 0.57 and P(Amount ≥ 40) = 0.45
Calculating the probability valuesAt least $30 but not more than $59
This means that we use the money spent from 30 to 59
So, we have
30 to 59 = 76 + 58 + 67
30 to 59 = 201
Total = 85 + 98 + 201 + 84
Total = 468
Next, we have
P(30 ≤ Amount ≤ 59) = 201/468
P(30 ≤ Amount ≤ 59) = 0.43
At least $60 or less than $30
This means that we use the money spent less than 30 and greater than or equal to 60
So, we have
At least $60 or less than $30 = 84 + 85 + 98
At least $60 or less than $30 = 267
Next, we have
P(Amount ≥ 60 or Amount < 30) = 267/468
P(Amount ≥ 60 or Amount < 30) = 0.57
At least $40
This means that we use the money spent greater than or equal to 40
So, we have
At least $40 = 58 + 67 + 84
At least $40 = 209
Next, we have
P(Amount ≥ 40) = 209/468
P(Amount ≥ 40) = 0.45
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Write the equation of a line perpendicular to the one above that passes through (-2, 9). You may use either slope intercept or point slope form.
Answer:
-3x + 3
Step-by-step explanation:
To find the equation of a line perpendicular to the line passing through (-2, 1) and (4, 3), we need to determine the slope of the original line first. Then, we can use the negative reciprocal of that slope to find the slope of the perpendicular line. Finally, we can use the point-slope form to write the equation of the perpendicular line.
Step 1: Find the slope of the original line.
Slope (m) = (change in y) / (change in x)
m = (3 - 1) / (4 - (-2))
m = 2 / 6
m = 1/3
Step 2: Determine the slope of the perpendicular line.
The slope of the perpendicular line is the negative reciprocal of the original line's slope.
Perpendicular slope = -1 / (1/3)
Perpendicular slope = -3
Step 3: Use the point-slope form to write the equation.
The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (-2, 9) and the perpendicular slope (-3), we can write the equation as:
y - 9 = -3(x - (-2))
y - 9 = -3(x + 2)
y - 9 = -3x - 6
y = -3x + 3
Therefore, the equation of the line perpendicular to the line passing through (-2, 1) and (4, 3) and passing through (-2, 9) is y = -3x + 3.
at ghs the ratio of students to teachers is about 14.5 to 1 approximately how many teachers would there be if the school had an enrollment of 205 students
Answer:
14
Step-by-step explanation:
14.5 to 1
205/14.5 = 14
3.3.4√20+5-43 calculate
Here are the steps to calculate the expression √20 + 5 - 43 :
Step 1: Simplify the square root of 20:
[tex]\sqrt{20}[/tex]
Step 2: Calculate the value of the square root:
[tex]\sqrt{20} = 2\sqrt{5}[/tex]
Step 3: Substitute the value of the square root into the expression:
[tex]2\sqrt{5} + 5 - 43[/tex]
Step 4: Perform addition:
[tex]2\sqrt{5} + 5 = 2\sqrt{5} + \frac{5}{1} = \frac{2\sqrt{5} + 5}{1}[/tex]
Step 5: Perform subtraction:
[tex]\frac{2\sqrt{5} + 5}{1} - 43 = \frac{2\sqrt{5} + 5 - 43}{1}[/tex]
Step 6: Simplify the numerator:
[tex]\frac{2\sqrt{5} - 38}{1}[/tex]
Step 7: Simplify the expression:
[tex]2\sqrt{5} - 38[/tex]
Therefore, the calculation √20 + 5 - 43 simplifies to 2√5 - 38.
A researcher performed an experiment with two groups. She found the difference of the means for each group. Then
she combined the groups, chose two new groups, and found the difference between the means of those groups. She
repeated this process 200 times. The normal distribution of the difference in the means she found is given below. How
great would the difference in means between the first two groups have to be in order to be considered significant?
At least 8
O At least 10
At least 9
At least 7
Answer:
Step-by-step explanation:
To determine the significance level for the difference in means between the first two groups, we need to refer to the provided normal distribution. However, you haven't provided the details or parameters of the normal distribution, such as the mean and standard deviation. Without this information, it is not possible to determine the exact significance level required.
In hypothesis testing, the significance level, typically denoted as α (alpha), is chosen by the researcher before conducting the experiment. It represents the threshold at which the researcher considers the results to be statistically significant. Commonly used significance levels are 0.05 (5%) or 0.01 (1%).
Please provide the necessary parameters or more information about the normal distribution to determine the specific significance level for the difference in means between the first two groups.
b) tan 2A cot A-1 = sec 2A
The trigonometric equation is tan 2A cot A-1 = sec 2A
We have to prove the trigonometric equation
tan 2A cot A-1 = sec 2A
Now let us take LHS
tan 2A cot A-1
2tanA/1-tan²A - 1 . cotA - 1
2-1+tan²A/1-tan²A
1+tan²A/1-tan²A
sec2A
Hence, the trigonometric equation is tan 2A cot A-1 = sec 2A
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The product of a number and five added to 17
Answer:
The phrase "The product of a number and five added to 17" can be represented mathematically as:
5x + 17
In this expression, 'x' represents the unknown number. The product of the number and five is calculated by multiplying the number by 5, and then 17 is added to the result.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
d. 465 degrees (not my own answer, see below)
Step-by-step explanation:
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b) Find the sum of all the numbers between 0 and 207 which are exactly divisible by 3.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
5/4 = h/44, so h = 55
The height of the tree is 55 feet.
D is correct.
You roll a 6-sided number cube and toss a coin. Let event A = Toss a heads.
What outcomes are in event A?
What outcomes are in event AC?
1. Event A includes the outcomes of H and T,
2. while event AC includes all the possible outcomes of rolling a number cube, which are 1, 2, 3, 4, 5, and 6.
1. Event A is defined as tossing a heads on a coin, regardless of the outcome of rolling a number cube. Therefore, the outcomes in event A are H (heads) and T (tails), since either of these outcomes could occur when rolling a number cube and tossing a coin.
2. Event AC is the complement of event A, i.e., it is the set of outcomes that are not in event A. Since event A contains H and T, the outcomes in event AC are the remaining outcomes that are not in event A, which are all the possible outcomes when rolling a number cube: 1, 2, 3, 4, 5, and 6.
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A kid's size small T-shirt is designed to fit children
who weigh between 43 and 55 pounds.
a. Write an inequality to describe w, the weight
of a child who has outgrown the small T-shirt.
9 √
b. Write an inequality to describe y, the weight
of a child who is not ready for the small T-shirt
yet.
A) The inequality that the weight of a child who has outgrown the small T-shirt is w > 55. B) The inequality that the weight of a child who is not ready for the small T-shirt yet. Is y < 43
How to determine the inequalitiesa. To describe the weight (w) of a child who has outgrown the small T-shirt, we can use the inequality:
w > 55
This inequality states that the weight of a child (w) must be greater than 55 pounds for them to have outgrown the small T-shirt.
b. To describe the weight (y) of a child who is not ready for the small T-shirt yet, we can use the inequality:
y < 43
This inequality states that the weight of a child (y) must be less than 43 pounds for them to not be ready for the small T-shirt yet.
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some help is required
54° is the value of the given angle BAC.
As we know that the arc and angles formed by intersecting chords,
θ = (α + β)/2 .....(i)
According to the given figure, we have
θ = 10x+4
α =9x-12
β = 12x +15
Substitute the value in equation (1)
10x+4 = (9x-12+12x +15)/2
20x+8 = 21x +3
x = 8-3
x = 5
Thus,
∠BAC = θ
= 10*5+4
= 50 + 4
=54
Therefore, the value of the given angle will be 54°.
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Help me please I need help asap
1. Area of the smaller circle is 100πcm²
2. Area of the bigger circle 800πcm²
How to determine the valueThe formula for the circumference of a circle is expressed as;
Circumference = 2πr
Substitute the values, we get;
20π = 2πr
Divide by the coefficient of r, we get;
r = 10cm
Now, area of a circle is expressed as;
Area = πr²
Substitute the value of the radius
Area = π × 10²
Find the square
Area = 100πcm²
Area of the big circle = 8(area of the small circle)
substitute the values
Area of the big circle = 8(100π)
expand the bracket
Area of the big circle = 800 πcm²
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A triangle has side lengths of 2.83 meters, 4 meters, and 2.24 meters. The angles measure 45°, 63°, and 72°.
What type of triangle is this?
Answer:
ougylbhj,
Step-by-step explanation:
ulygkuyHold on, our servers are swamped. Wait for your answer to fully load
5. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SALGTRIG4 7.3.112.
A rectangle is to be inscribed in a semicircle of radius 4 cm as shown in the following figure.
10
4 cm-
(a) Find the function that models the area of the rectangle.
A(0) = 16 sin (20)
Need Help? Read It
MY NOTES
4
ASK YOUR TEACHER
(b) Find the largest possible area for such an inscribed rectangle. [Hint: Use the fact that sin(u) achieves its maximum value at u=/2.]
16
cm²
(c) Find the dimensions of the inscribed rectangle with the largest possible area. (Round your answers to two decimal places.)
smaller dimension 2
x cm
larger dimension 25
x cm
PR.
The Area function [tex]A(x) = 2x * \sqrt(16 - x^2).[/tex]
(a) For a rectangle inscribed in a semicircle of radius 4 cm, let half-length be x and height be y.
Therefore, the Area function [tex]A(x) = 2x * \sqrt(16 - x^2).[/tex]
(b) Maximum area occurs when x = [tex]4 * sin(\pi/4), so A(4 * sin(\pi/4)) = 16 cm^2.[/tex]
(c) Dimensions for the largest inscribed rectangle are smaller dimension (height) ≈ of 2.83 cm, a larger dimension (base) ≈ of 5.66 cm.
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Find the area of the composite figure
The area of the composite shape is 125units²
What is area of shape?The area of a figure is the number of unit squares that cover the surface of a closed figure.
A composite shape can be defines as a shape created with two or more basic shapes.
The composite shape can be divided into 2 equal squares and a rectangles.
Area of the square = l²
= 5× 5 = 25
For two squares it will be;
25 × 2
= 50 units²
area of the rectangle = l× w
where w is the width
A = 15 × 5
= 75 units²
Therefore the area of the composite shape = 50 + 75 = 125 units²
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Simplify > (x)3(−x3y)2
−x9y2
x5y2
−x6y2
x9y2
The simplified expression of the expression (x)³(−x³y)² is x⁹y²
Simplyfing the expression using the common factorFrom the question, we have the following parameters that can be used in our computation:
(x)3(−x3y)2
Express properly
So, we have
(x)³(−x³y)²
Open the brackets
(x)³(−x³y)² = x³ * x⁶y²
Multiply (x)³ and x⁶ in the expression
So, we have the following representation
(x)³(−x³y)² = x⁹y²
Hence, the simplified expression is x⁹y²
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Could someone help me with this? I have to double check I’m right thank you
Solving linear equations using matrices involves steps ranging from creating an augmented matrix, performing row operations, back substitution, and then interpreting results
To solve a system of linear equations using matrices:
Step 1: Write the system of linear equations in matrix form.
Represent the coefficients of the variables as a matrix (called the coefficient matrix), and the constants on the right side of the equations as another matrix (called the constant matrix).
Step 2: Create the augmented matrix.
Combine the coefficient matrix and the constant matrix into a single matrix by appending the constant matrix as an additional column. This combined matrix is called the augmented matrix.
Step 3: Perform row operations to achieve row-echelon form.
Use row operations (swapping rows, multiplying a row by a constant, or adding/subtracting rows) to manipulate the augmented matrix into row-echelon form. Row-echelon form has zeroes below the diagonal and non-zero elements on the diagonal.
Step 4: Perform back-substitution.
Starting from the last row of the row-echelon form matrix, solve for the variables using back-substitution. Substitute the values of the variables you find into the previous rows to determine the remaining variable values.
Step 5: Interpret the results.
Once you have solved all the variables, you have found the solution to the system of linear equations. If there are infinitely many solutions or no solutions, this will be indicated by the row-echelon form.
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need help fast pls!!!
The volume of solid figure is,
⇒ V = 113 cm³
We have to given that;
A solid figure is shown with a cylinder and a cone.
Now, We know that;
Volume of cylinder = πr²h
And,
Volume of cone = πr²h / 3
Where, 'r' is radius and 'h' is height.
Here, Height of cylinder = 7 cm
And, Radius of cylinder = 4/2 = 2 cm
Hence, WE get;
Volume of cylinder = πr²h
Volume of cylinder = 3.14 x 2² x 7
Volume of cylinder = 87.9 cm³
And, Height of Cone = 6 cm
Radius of Cone = 4/2 = 2 cm
Hence, WE get;
Volume of Cone = πr²h/3
Volume of Cone = 3.14 x 2² x 6 / 3
Volume of Cone = 25.1 cm³
Thus, The volume of solid figure is,
⇒ V = 87.9 cm³ + 25.1 cm³
⇒ V = 113 cm³
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The proof shows that ABCD is a square. Which of the following is the missing
reason?
E
B
AC BD
mZDEC = 90°
The missing reason in the proof is "mZDEC = 90°" or "Angle DEC is a right angle."
The missing reason in the proof is the statement "mZDEC = 90°". This statement implies that the angle DEC is a right angle, which is a crucial piece of information in proving that ABCD is a square.
In a square, all angles are right angles, so if we can establish that an angle in the figure is 90°, we can conclude that the figure is a square. In this case, the angle DEC being 90° is the key piece of evidence that supports the claim that ABCD is a square.
The statement "mZDEC = 90°" indicates that the measure of angle DEC is 90 degrees. This is significant because it confirms that one of the angles in the figure is a right angle, meeting the definition of a square.
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The number of miles on a car when the engine fails is normally distributed. The mean is 60,000 miles and the standar
deviation is 5000 miles. What is the probability the engine will not fail between 55,000 and 65,000 miles?
25%
40%
35%
32%
The probability that the engine will not fail between 55,000 and 65,000 miles, based on normal distribution probabilities, when the mean failure is 60,000 miles and standard deviation of 5,000 miles is e) 68%.
What is the normal distribution probability?Normal distribution probability is a continuous probability distribution with symmetrical values that mostly cluster around the mean.
We can compute the normal distribution probability using the normal distribution calculator.
Mean number of miles when a car's engine fails = 60,000 miles
Standard deviation = 5,000 miles
Sample cutoff = between 55,000 and 65,000 miles
The probability of the engine fail between 55,000 and 65,000 miles = 0.6827.
= 68%.
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Question Completion:a) 25%
b) 40%
c) 35%
d) 32%
e) 68%
1. Is there a right angle in the triangle shown by connecting the center of the earth, the
satellite & station 1? How do you know? *Assume that the line connecting the satellite
& station 1 is tangent to the earth*
The triangle shown in the figure formed by the line connecting the center of the Earth to the Station 1, the Station 1 to the Satellite, and the Satellite to the center of the Earth forms a right triangle.
What is a right triangle?A right triangle is a triangle that has a 90 degrees interior angle.
The line joining the center of the Earth and Station 1 is perpendicular to the line connecting the Satellite to Station 1, because, the line connecting the Satellite to Station 1 is a tangent and tangents to a circle are perpendicular to a radius of the circle at the point of tangency.
The triangle formed by connecting the center of the Earth to the Station 1, and connecting the Satellite to Station 1, and connecting the Satellite to the center of the Earth forms a right triangle, because the angle formed by the line connecting the center of the Earth to Station 1, forms a right angle with the tangent from the Satellite to the Station 1
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Three lines intersect to form six angles that measure in degrees in some of the angles are represented by expressions as shown in this. Based on the diagram write an algebraic equation that can be used to find the value of X show explain how you got your answer
1. The equation to be formed is 40 + 5x + 90 = 180
2. The value of x is 10
What is the sum of angles on a straight line?A straight line's total angles are always 180 degrees. Around the place where two lines join, they create four angles. The total of the angles on either side of a straight line, if those lines are straight and form one, is always 180 degrees.
We know that;
40 + 5x + 90 = 180 (Sum of angles on a straight line)
130 + 5x = 180
5x = 180 - 130
x = 50/5
x = 10
Thus the value of x is given as 10
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solve for v, PV/T=pv/t
No matter the values of P, V, T, p, and t, as long as the equation PV/T = pv/t holds true, the solution for v is always equal to V.
To solve for v in the equation PV/T = pv/t, we can manipulate the equation to isolate v on one side.
Starting with the given equation:
PV/T = pv/t
To isolate v, we can cross-multiply:
PVt = pVt
Next, we divide both sides of the equation by pt:
V = v
Therefore, the solution is v = V.
In other words, v is equal to V, which means they represent the same values.
This implies that v and V are interchangeable and can be used interchangeably in the equation.
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-49 = 7i, what number is the i.
Answer:
-7
Step-by-step explanation:
divide by 7 on both sides and you get i = -7
24. Find RT.
13
Ø
S
P
X
11
20
RT =
Show work need bothof these problems
24. The length RT is 18 units
25. The equation of the circle graphed is x² + (y - 3)² = 16
24. How to calculate the length RTThe length RT can be calculated using the intersecting secants equation
So, we have
11 * (11 + x) = 9 * (9 + 13)
So, we have
11 + x = 18
This gives
RT = 18
The equation of the circleThe equation of the circle graphed is represented as
(x - a)² + (y - b)² = r²
Where, we have
Center = (a, b) = (0, 3)Radius, r = 4 unitsSo, we have
(x - 0)² + (y - 3)² = 4²
Evaluate
x² + (y - 3)² = 16
Hence, the equation of the circle graphed is x² + (y - 3)² = 16
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Can someone answer this question
8/5 is the value that is not one of the possible rational zeros of the given polynomial.
Using the Rational Root Theorem, we need to consider the factors of the constant term (-8) divided by the factors of the leading coefficient (5).
The factors of -8 are ±1, ±2, ±4, ±8.
The factors of 5 are ±1, ±5.
Since the leading coefficient of the given polynomial is positive (5), the negative factors can be ignored.
So, the possible rational zeros are:
1/1, 2/1, 4/1, 8/1, 1/5, 2/5, 4/5, 8/5
Now, we can substitute each of these values into the polynomial and see if any of them result in a zero.
Upon checking, we find that 8/5 is not a zero of the polynomial 5x³ - 2x² + 20x - 8.
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Please help due 5 min!!!!
which are true please help
Answer:
All statements above are false
Step-by-step explanation:
You want to know which of the statements saying translation, rotation, and reflection change the measures of line segments or angles is true.
Rigid motionTranslation, rotation, and reflection are referred to as "rigid motion." That means all parts of the transformed figure keep their measures and positions relative to other parts of the figure. No lengths or angle measures are changed.
All of the (above) listed statements are false.
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