The equation Ax=b has infinitely many solutions. The non-trivial solution to Ax=0 is [tex]\mathbf{v}-\mathbf{w}=\left[\begin{array}{ccc}-4\\5\\2\end{array}\right][/tex] .
If x is in [tex]\mathbb{R}^n[/tex] and matrix A is m×n matrix with the columns denoted as a₁, a₂, ...aₙ, then, the product of these two is denoted as Ax. Then, the equation Ax=b is a matrix equation.
Given the matrixes [tex]\textbf{v}=\left[\begin{array}{c}1\\2\\3\end{array}\right][/tex] and [tex]\textbf{w}=\left[\begin{array}{c}5\\-3\\1\end{array}\right][/tex] .
a) Then, Av=b and Au=b.
Now, A(av+(1-1)w)=aAv+(1-a)Aw, a∈ [tex]\mathbb{R}[/tex].
=aAv+(1-a)Aw
=ab+(1-a)b
=b
Thus, we consider a(v)+(1-a)b=b is considered as a solution of Ax=b for any a∈ [tex]\mathbb{R}[/tex]. Therefore, the equation Ax=b has infinitely many solutions.
b) Now, let's write A(v-w)=Av-Aw
=b-b
=0
Therefore, (v-w) is also a solution of Ax=0. Then, [tex]\mathbf{v}-\mathbf{w}=\left[\begin{array}{ccc}-4\\5\\2\end{array}\right][/tex] is considered a non-trivial solution to the homogenous system Ax=0.
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The complete question -
Suppose that A is a matrix and b is a vector in [tex]\mathbb{R}^2[/tex]. Suppose further that [tex]\textbf{v}=\left[\begin{array}{c}1\\2\\3\end{array}\right][/tex] and [tex]\textbf{w}=\left[\begin{array}{c}5\\-3\\1\end{array}\right][/tex] are both solutions to the equation Ax = b.
(a) How many solutions does the equation Ax = b have? Explain your answer.
(b) Find a nontrivial solution to the homogeneous system Ax = 0. Justify that it is indeed a solution.
4. You are adding a cement patio to your back yard. Calculate the volume of cement
needed to pour a patio of the following dimensions including the fire pit. Be sure to calculate all
volumes needed to submit a complete answer. Use 3.14 = π Show all your work.
6 in
11 ft
I
13 ft
3ft
1.5 ft
2.5 ft
879.21 cubic feet is the volume of the cement needed to pour a patio of the following dimensions including the fire pit.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Firstly let us find the volume of the cylinder, whose radius is 1.5 ft, height is 3ft.
Volume of cylinder=πr²h
=3.14×1.5²×3
=21.21 cubic feet.
Now let us find the volume of fire pit.
Volume of fire pit=Length×width×height
=11×13×6
=858 cubic feet.
The total volume = 21.21+858
=879.21 cubic feet.
Hence, 879.21 cubic feet is the volume of the cement needed to pour a patio of the following dimensions including the fire pit.
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Can you help me with this?
The measure of angle y is 116 ⁰.
What is the measure of angle y?
First we need to find the value of angle DCO and the value of angle DOC.
∠ DCO = 90 - 58⁰ ( angle subtended by diameter of a circle )
∠ DCO = 32⁰
line OC = OD = radius of the circle
∠ DCO = ∠ DOC = 32⁰
Now, the measure of angle y is calculated as follows;
∠ ODC + ∠ DCO + ∠ DOC = 180 ( sum of angles in a triangle )
y + 32 + 32 = 180
y + 64 = 180
y = 180 - 64
y = 116⁰
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two airlines report their number od delayed flights each months for one year.airlines A has an LQR of 83.5 and airplines B has an LQR of 22. what airlines is the most consistent in not having delays? explain
PLS i need help
Airline B is the most consistent in not having delays.
What airlines is the most consistent in not having delays?To determine which airline is the most consistent in not having delays, we need to compare their LQRs (Linearity of Quality Ratios). The LQR is a measure of how consistent a process or system is over time, with higher LQR indicating greater consistency.
In this case, airline A has an LQR of 83.5, while airline B has an LQR of 22. This means that airline B is more consistent in not having delays, as it has a higher LQR.
To understand why this is the case, we need to understand how the LQR is calculated. The LQR is calculated as the ratio of the process variation to the specification (or tolerance) width. In this case, the process variation is the number of delayed flights each month for one year, and the specification width is the maximum number of delays that the airline deems acceptable.
Assuming that both airlines have the same maximum acceptable number of delays, airline B has a higher LQR because it has less process variation in its number of delayed flights. This suggests that airline B has more consistent operational performance and is less prone to delays than airline A.
Therefore, based on the given LQRs, we can conclude that airline B is the most consistent in not having delays.
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Pls help me thank you so much
Answer:
Step-by-step explanation
Area of rectangle = width * length
18a^3b^6=6a^2b^3* length
length=18a^3b^6/6a^2b^3= 3ab^3
1 mile long to 800 feet
Answer:
0.1515
Step-by-step explanation:
1 mile = 5,280 feetTo convert 1 mile to 800 feet, we can set up a proportion:
[tex] \frac{1 mile}{5,280 feet} = \frac{x \: miles}{800 feet} [/tex]
where x is the number of miles equivalent to 800 feet. To solve for x, we can cross-multiply:
[tex]{5,280 feet}^{x miles} = {800 \: \: feet}^{1 mile}[/tex]
Dividing both sides by 5,280 feet, we get:
[tex]x miles = \frac{800 feet}{5,280 feet} \\ x miles = 0.1515151515 miles[/tex]
Therefore, 1 mile is equivalent to approximately 0.1515 miles or 800 feet is equivalent to approximately 0.1515 miles.
A. Is there a GCF?
B. Is the polynomial a special case? If so, name the special polynomial.
16p^2 − 9
A. There are no common factors that can be factored out from both terms of the polynomial 16p² − 9.
B. The polynomial 16p² − 9 is a special case known as the difference between two squares. It can be written as:
(4p)² - 3²
What is polynomial?Pοly (which means "many") and Nοminal (which means "terms") are the twο terms that make up pοlynοmial. An expressiοn that cοnsists οf variables, cοnstants, and expοnents and is cοmbined using mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn is referred tο as a pοlynοmial (Nο divisiοn οperatiοn by a variable). The expressiοn is divided intο three categοries: mοnοmial, binοmial, and trinοmial depending οn hοw many terms are included in it.
This can be factored further using the difference of two squares formula:
(4p - 3)(4p + 3)
Therefore, the polynomial 16p² − 9 is a special case of the difference between two squares.
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Complete question:
Answer the following questions for the expression provided.
16p² − 9
A. Is there a GCF?
B. Is the polynomial a special case? If so, name the special polynomial.
Solve for v. Round your answer to the nearest tenth.
Answer:
47.5
Step-by-step explanation:
What is the law of sines?The law of sines states that for any triangle:
side A (which is opposite to angle A) divided by sin(angle A) = side B (which is opposite to angle B) divided by sin(angle B).
Let's see if we can use this in the problem.
We have 2 angles, 1 side, and 1 variable for the side. we can set up an equation this way;
58/sin(39degrees) = v/sin(31degrees)
isolate v:
58sin(31degrees)/sin(39degrees) = v
We can plug this into a graphing calculator to get:
47.46740892
We round to the nearest 10th to get
47.5
I need to be able to explain this can someone help?
3(2x+5) + 2x = x+50
Hint: x+50
-x
x=5
the research hypothesis posits that the treatment association between two variables will be greater than zero (h1: rxy > 0). what would be concluded for r(29) = .267, p > .05?
Based on the given information, we cannot reject the null hypothesis that there is no significant treatment association between the two variables (H0: rxy = 0).
The correlation coefficient (r) is 0.267, which indicates a positive but weak relationship between the two variables. However, the p-value is greater than 0.05, which means that the result is not statistically significant at the 5% level of significance. Therefore, we fail to reject the null hypothesis (H0) and conclude that there is no significant treatment association between the two variables. This suggests that the treatment did not have a significant effect on the relationship between the two variables.
The calculations are as follows:
t = r * √(n-2)/√(1-r²)t = 0.267 * √(29-2)/√(1-0.267²) = 1.15Degrees of freedom (df) = n-2 = 29-2 = 27Using a two-tailed test at α = 0.05, the critical t-value is ±2.052
Since 1.15 < 2.052 and the p-value > 0.05, we fail to reject the null hypothesis that there is no significant treatment association between the two variables.
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Derrick has a chance to win a new music player. He must Pick one of the 2 winning tokens from a bag that holds 15 tokens what is the probability that Derek picks a winning token
Answer:
13.3
Step-by-step explanation:
Derrick has a chance of winning 2 out of the 15 tokens in the bag. So the probability of Derrick picking a winning token can be calculated as:
Probability of winning = Number of winning tokens / Total number of tokens
Probability of winning = 2/15
Therefore, the probability of Derrick picking a winning token is 2/15 or approximately 0.133 or 13.3%.
Do not round your answer. Type in just the number.
0. 48 is 10% of 1. 6.
The answer by using percentage method is 0.16 (not rounding the answer).
The statement "0.48 is 10% of 1.6" means that 0.48 is one-tenth (10%) of 1.6. To understand this relationship, we can use basic arithmetic.
To find out what 10% of 1.6 is, we can multiply 1.6 by 0.1 (which is equivalent to dividing 1.6 by 10).
10% of 1.6 = 1.6 x 0.1
= 0.16
Therefore, we can see that 0.48 is equal to 10% of 1.6:
0.48 = 0.16 x 3
In other words, 0.48 is three times (3x) the value of 10% of 1.6.
Overall, understanding percentages and their relationship to numbers is an important part of basic mathematics, and can be useful in many real-world situations such as calculating discounts, taxes, and interest rates.
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If the area of △PQR is A, give the expressions that complete the equation for the measure of ∠R
In Triangle PQR where angle Q is a right angle. QR measures 33 point 8; PQ measures 57 point 6; measure of angle P is unknown. Then the measure of ∠R = 30.4 degrees.
Measures of Angle:
An angle is formed when two lines or rays meet at a common point. Common points are called vertices.
Angles are measured using basic geometric tools such as protractors and compasses. This tool allows you to find precise measurements of angles. A protractor helps provide accurate measurements of angles, while compasses help construct angles.
Angles are measured in three ways: degrees, radians, and revolutions. In geometry, an angular measure can be defined as the measure of the angle formed by two rays or two arms at a common vertex.
Given that:
QR = 33.8 and PQ = 57.6, and
Q is the right angle, then
tan R = opposite / adjacent
= QR / PQ = 33.8 / 57.6 = 0.586.
Therefore,
tan R = 0.586
Angle R = tan⁻¹ (0.586) = 30.4 degrees.
Complete Question:
How would you solve the following geometry problem?: ∆PQR, find the measure of ∡P. In Triangle PQR where angle Q is a right angle. QR measures 33 point 8; PQ measures 57 point 6; measure of angle P is unknown. Answers: 30.4° 35.9° 54.1° 59.6° What I did: equation: tan(x) = 33.8/57.6 tan(x)=0.56 But I know that isn't correct.
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Janelle spent:
Harper and Dean raced each other in
gym class. Harper ran 100 m in 14. 56
seconds. Dean ran the same distance in
15. 12 seconds. How much faster was
Harper than Dean?
Number model:
Estimate:
Harper and Dean raced each other in gym class. Harper ran 100 m in 14. 56
seconds. Dean ran the same distance in 15. 12 seconds. Therefore, Harper 0.56 second faster than Dean.
Distance:
Distance is a numerical or sometimes qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria. Since spatial cognition is a rich source of conceptual metaphors in human thought, the term is also often used metaphorically to refer to a measure of the amount of difference between two similar objects (such as statistical distance or distance between changing probability distributions) text strings) or some degree of separation (like the distance between people in a social network). Most of these concepts of distance, whether physical or metaphorical, are formalized in mathematics using the concept of metric spaces.
In the social sciences, distance can refer to qualitative measures of separation, such as social or psychological distance.
Given that:
Harper ran 100 m in 14. 56 seconds. Dean ran the same distance in 15. 12 seconds.
Now, The faster Harper ran than dean is:
15.12- 14.56 = 0.56 seconds.
Therefore, Harper 0.56 second faster than Dean.
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A computer costs $800. It loses 14 of its value every year after it is purchased. Write an equation representing the value, v, of the computer, t years after it is purchased. Response area Use your equation to find v when t is 5. Response area What does this value of v mean? Response area
Answer: (I think might be wrong:/ )
(n - 1) x 3/4
And is 14 like $14 or 1/4? but someone asked this so here is what i found
The value of the computer at time 0 is $800
The value of the computer at time 1 is $600
The value of the computer at time 2 is $450
The value of the computer at time 3 is $337.50
The value of the computer at time t is (n - 1) x 3/4
Depreciation
When an asset depreciates, it means that the asset declines or reduces in value, it means that is value becomes smaller as the years goes by.
Calculation of the decline in value
Value of the computer can be represented with this equation: cost of the computer in the previous year x (1 - rate of decline)
Value of the computer at time 0 = $800
Value of the computer at time 1 = $800 x (3/4) x 1 = $600
Value of the computer at time 2 = $600 x 3/4 = $450
Value of the computer at time 3 = $450 x 3/4 = $337.50
Suppose that a motorboat is moving at 46 ft/s when its motor suddenly quits, and that 8 s later the boat has slowed to 26 ft/s. Assume that the resistance it encounters while coasting is proportional to its velocity, so that dv/dt = - kv. How far will the boat coast in all? The boat will coast feet
The boat will coast for a distance of 644.99 ft
The equation for velocity is given by
[tex]v(t) = v_{0} e^{-kt}[/tex]
It is given that the initial velocity of the motorboat is 46 ft/s
Hence,
v₀ = 46 ft/s
Hence we get
[tex]v(t) = 46 e^{-kt}[/tex]
Now we are given the time to be 8 sec hence putting this in the velocity equation will give us
[tex]v(8) = 46 e^{-8k}[/tex]
Now according to the question, v(8) = 26 hence we get
[tex]26 = 46 e^{-8k}[/tex]
Solving this will give us the value of k to be
[tex]e^{-8k} = \frac{13}{23}[/tex]
[tex]or, -8k = log13 - log23[/tex]
[tex]or, k = \frac{log23-log13}{8}[/tex]
The position function is given by
[tex]x(t) = x_{0} + (\frac{v_{0}}{k} ) (1-e^{-kt})[/tex]
Now the distance travelled by boat will be
[tex]\lim_{t \to \infty} (\frac{46}{k} ) (1-e^{-kt})[/tex]
[tex]= \lim_{t \to \infty} (\frac{46X8}{log23 - log 13} ) (1-e^{-\frac{log23-log13}{8} t})[/tex]
[tex]=\frac{368}{log23 - log13}[/tex]
= 644.99 ft
Hence, the boat will coast for a distance 644.99 ft
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PLS HELP AND HURRY! FIRST TO GIVE THE CORRECT ANSWER GETS BRAINLIEST! PLS HELP AND HURRY!!!!!!!!!!
Graph the data set.
{(0, 0), (−1, −3), (−2, −6), (−3, −9), (−4, −12)}
Which kind of model best describes the data?
A. exponential
B. cubic
C. quadratic
D. linear
Answer:
Step-by-step explanation:
Its a cubic graph.
Tyra rewrote the quadratic equation 2²10x-24 as a product of polynomials. Her work is shown:
Step 1: x²-10x-24
Step 2: x²-4x-6x-24
Step 3:(x²-4x)+(-6x-24)
Step 4:x(x-4)-6(x-4)
Step 5:(x-4)(x-6)
Tyra made an error when rewriting the quadratic equation as a product of polynomials. [DROP DOWN 1] is the step where Tyra made the mistake. [DROP DOWN 2] is the correct product of polynomials.
The response we have is as follows to the query that was asked Therefore, the quadratic equation 2x² - 10x - 24 can be factored into (x - 2)(x - 3).
What is quadratic equation?A quadratic formula in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of the second rank guarantees that the it has at least a single option according to the Central Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one term in it needs to be squared. One of the common formulas for solving quadratic problems is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical factors or variables a, b, and c.
ax² + bx + c = 0
a = 2, b = -10, and c = -24.
2x² - 10x - 24.
-24 as -6x + 4x.
2x² - 4x - 6x + 4x - 24.
(2x² - 4x) + (-6x - 24)
2x(x - 2) - 6(x + 4).
(x - 2)(2x - 6).
(x - 2)(x - 3).
Therefore, the quadratic equation 2x² - 10x - 24 can be factored into (x - 2)(x - 3).
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Use the figure below to answer the following questions:
A. What 3-D shape does the net below form? ____________________
B. What is the formula to find the surface area of Use the figure below to answer the following questions:
A. What 3-D shape does the net below form? ____________________
B. What is the formula to find the surface area of this shape? vshape? Use the figure below to answer the following questions:
A. What 3-D shape does the net below form? ____________________
B. What is the formula to find the surface area of this shape?
To calculate the surface area of the net pictured, you would need to know the base and height of the triangle, as well as the length of the prism.
What is surface area?Surface is a physical property of an object which is the outermost layer of the object. It can be solid, liquid, or gas, and it is usually the first thing we touch or see. It can also be the outermost layer of the atmosphere. Surface can be measured by its texture, smoothness, roughness, color, and other qualities. Surface can be studied through microscopy, spectroscopy, and other techniques. Surface can be used to identify and classify materials, as well as to study their properties.
The net below forms a triangular prism. A triangular prism is a three-dimensional shape with two parallel faces that are triangles, and three rectangular faces. The formula for finding the surface area of a triangular prism is SA = 2b(h + l) + 3lh, where b is the base of the triangle, h is the height of the triangle, and l is the length of the prism. Therefore, to calculate the surface area of the net pictured, you would need to know the base and height of the triangle, as well as the length of the prism.
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Find the x-intercepts, the y-intercept, and the coordinates of the vertex of the parabola
y = (x − 50)^2 − 100
Answer:
Vertex: (50, -100)
X-intercepts: (40, 0), (60, 0)
Y-intercept: (0,2400)
What is vertex-form?For a parabolic equation, written in y = a(x-h) +k format, it is in vertex form. This is because we can derive the vertex just by looking at the equation; and from this the vertex is (h, k). In our equation, h is 50, and y is -100, so our vertex is (50, -100).
The x-intercept value of a function is the value of x when y is zero. It is a dot on the x-axis. We can use this by plugging it into the equation.
0 = (x-50)^2 -100
100 = (x-50)^2
+/- 10 = x -50
X = 40, x = 60
So our two x-intercepts will be (40,0) and (60,0)
Like the x-intercept, it is the y-value of a function when the x-value is zero. We can plug this in:
y = (0-50)^2 -100
Y = 2500 - 100
Y = 2400
So our y-intercept is (0,2400)
Vertex: (50, -100)
X-intercepts: (40, 0), (60, 0)
Y-intercept: (0,2400)
Q2. ) A solid cube of Al with each side 1. 0 meter is converted into metallic powders of spherical shape by gas atomization process. What is the percent increase in total surface area if the diameter of each particle is 100 um
The percent decrease in total surface area is 99.8%.
What is the surface area of the cube?The initial surface area of the cube can be calculated by using the formula:
A = 6s^2
where;
A is the surface area and s is the length of the side of the cube.A = 6 x (1.0 m)^2 = 6.0 m^2
To calculate the total surface area of the metallic powders, we need to first calculate the number of particles produced from the cube. We can do this by using the formula:
N = (V / Vp)
where;
N is the number of particles, V is the volume of the cube, and Vp is the volume of each particle.V = s^3 = (1.0 m)^3 = 1.0 m^3
Vp = (π/6) x (0.1 m)^3 = 5.24 x 10^-4 m^3
N = (1.0 m^3) / (5.24 x 10^-4 m^3)
N = 1.91 x 10^6 particles
The total surface area of the metallic powders can be calculated by using the formula:
A' = N x πd^2 / 4
where;
A' is the total surface area and d is the diameter of each particle.d = 100 μm = 0.0001 m
A' = (1.91 x 10^6) x π x (0.0001 m)^2 / 4 = 0.015 m^2
The percent increase in total surface area is then:
% increase = (A' - A) / A x 100%
% increase = (0.015 m^2 - 6.0 m^2) / 6.0 m^2 x 100%
= -99.8%
Therefore, the percent decrease in total surface area is 99.8%. This makes sense as the metallic powders have a larger surface area compared to the solid cube, but the total surface area is still less than the sum of the surface area of each particle due to the spaces between the particles.
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a circle of radius r has area a = r2. if a random circle has a radius that is uniformly distributed on the interval (0, 1), what are the mean and variance of the area of the circle?
Based on the provided information, the mean of the area of the circle is 1/3 and the variance is 4/45.
The mean and variance of the area of a circle with a uniformly distributed radius on the interval (0,1) can be found using the expected value and variance formulas for continuous random variables.
The expected value (mean) of a continuous random variable X is given by:
E[X] = ∫xf(x)dx
Where f(x) is the probability density function of X. In this case, since the radius is uniformly distributed on the interval (0,1), the probability density function is f(x) = 1 for 0 ≤ x ≤ 1.
The expected value of the area of the circle is therefore:
E[A] = ∫a*f(a)da = ∫r^2*1dr = (1/3)r^3 for 0 ≤ r ≤ 1 = (1/3)(1)^3 - (1/3)(0)^3 = 1/3
The variance of a continuous random variable X is given by:
Var[X] = E[X^2] - (E[X])^2
The expected value of the square of the area of the circle is:
E[A^2] = ∫a^2*f(a)da = ∫r^4*1dr = (1/5)r^5 for 0 ≤ r ≤ 1 = (1/5)(1)^5 - (1/5)(0)^5 = 1/5
Therefore, the variance of the area of the circle is:
Var[A] = E[A^2] - (E[A])^2 = 1/5 - (1/3)^2 = 4/45
So the mean of the area of the circle is 1/3 and the variance is 4/45.
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A student can ride his bicycle at an average speed of 6 mph. If he cycles for 4 hours, how far can he travel Sedit 15 miles
A student can ride his bicycle at an average speed of 6 mph. If he cycles for 4 hours, how far can he travel 24 miles.
The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.
We can use the formula:
[tex]Distance = rate * time[/tex]
To solve this problem.
The rate is given as 6 miles per hour, and the time is given as 4 hours.
So, we have:
distance = 6 * 4
Simplifying, we get:
distance = 24 miles
So, the student can travel 24 miles if he cycles for 4 hours at an average speed of 6 mph.
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Worth 15 points!!! And Brainiest!!! An Ohio park has a triangle sandbox.
Max wants to create a smaller sandbox at his backyard having the same angles as the park sandbox. Drawings of both sandboxes are shown. Show all work below to gain full credit with this problem.
a) proportion and calculations for finding x (5 points)
b) proportion and calculations for finding y (5 points)
c) perimeter of Todd's sandbox (5 points)
Do all 3. Show all work!!
Step-by-step explanation:
To figure out how much smaller Max's sandbox is, we will divide 25 by 10, 25/10 = 2.5. Max's sandbox is 2.5 times smaller than the one in the park.
To find x we will divide 15 by 2.5 to keep the proportions the same, 15/2.5 = 6, so x = 6 feet.
To find y, we will do the same but with 12.5, 12.5/2.5 = 5, so y = 5 feet.
To find the perimeter, we will add all the sides together, 10 + 6 + 5 = 21, so the perimeter of Max's sandbox is 21 feet.
Hope this helps!
consider a predicate p. suppose that we proved p(-2) and p(0). find the set of integers k for which p(k) is proved true if we also prove that p(k)^p(k 2)=> p(k-2)
The set of integers for which p(k) is true is all even integers for which p(k) is proved true if we also prove that p(k)^p(k 2)=> p(k-2).
Considering that p(- 2) and p(0) are valid and expecting that p(k)^p(k+2) => p(k-2), we can decide the arrangement of numbers k for which p(k) is valid by acceptance. In particular, we can show that p(k) is valid for all even numbers k by enlistment, as follows.
To begin with, since p(- 2) and p(0) are valid, the base instance of k = - 2 is valid.
Then, expect that p(k) is valid for some even number k. Then, at that point, utilizing the given ramifications, we have p(k+2) is valid.
At long last, utilizing a similar ramifications once more, we have that p(k-2) is valid. Accordingly, by acceptance, we have shown that p(k) is valid for all even numbers k.
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All of the following represent examples of a biased sample of students in a small high school except _____.
selecting every sixth name from a list of all the students
randomly selecting ten names from a list of all the students
randomly selecting ten names from a list of all the ninth graders
randomly selecting ten names from a list of all the boys
If we know the temperature in degrees Celsius, C, we can find the temperature in degrees Kelvin, K, using this equation: K=C+273. 15
Complete the table with temperatures in Kelvin or in Celsius
If we know the temperature in degrees Celsius, C, we can find the temperature in degrees Kelvin, K, using this equation: K=C+273 (option 1)
To convert a temperature from degrees Celsius to degrees Kelvin, you simply add 273 to the temperature in degrees Celsius. This is because the Kelvin scale is an absolute temperature scale where 0 K represents the theoretical minimum temperature, known as absolute zero, at which all matter would have zero thermal energy.
The Celsius scale, on the other hand, is a relative temperature scale that uses the freezing and boiling points of water as reference points. The formula K = C + 273 allows us to convert from one scale to the other.
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Complete Question:
If we know the temperature in degrees Celsius, C, we can find the temperature in degrees Kelvin, K, using this equation:
K=C+273K=C+269K=C+278K=C+276Find the equilibria for each of the following differential equations and determine the values of a for which the equilibrium is locally stable. (Enter your answer using inter (a) y-1+ ay caly table when a i i the , 00 (0, x ) is locally stable when a is in the interval . (b)-e-ay is locally stable when a is in the interval a, oo)x is locally stable when a is in the interval-00,0)x -0 is locally stable when a is in the interval 0, (0,00) X . is locally stable when a is in the interval (-00,0) x
a) If a < 0, then y'' < 0, which means that the equilibrium is locally stable. Therefore, the equilibrium is locally stable when -1 < a < 0.
b) If a > 0, then y'' > 0, which means that the equilibrium is unstable. Therefore, the equilibrium is locally stable when a < 0.
c) y' is always positive to the right of any equilibrium point and always negative to the left, which means that all equilibria are unstable.
d) y' is negative to the left of the equilibrium point and positive to the right, which means that the equilibrium is locally stable.
e) y' is positive to the right of the equilibrium point and negative to the left, which means that the equilibrium is locally unstable.
(a)[tex]y' = y - 1 + ay[/tex]
To find the equilibrium, we set y' = 0 and solve for y:
[tex]y - 1 + ay = 0\\y(1 + a) = 1\\y = 1/(1 + a)[/tex]
To determine the stability of the equilibrium, we need to compute the derivative of y' with respect to y and evaluate it at the equilibrium point:
[tex]y'' = a[/tex]
When y"< 0, which happens when a < 0, the equilibrium is said to be locally stable. As a result, when -1 < a < 0, the equilibrium is locally stable.
(b)[tex]y' = -e^{(-ay)}[/tex]
To find the equilibrium, we set y' = 0 and solve for y:
[tex]-e^{(-ay)} = 0\\y = 0[/tex]
To determine the stability of the equilibrium, we again compute the derivative of y' with respect to y and evaluate it at the equilibrium point:
[tex]y'' = a e^{(-ay)}[/tex]
If a > 0, the equilibrium is unstable because y" > 0, indicating that a > 0. As a result, when a 0, the equilibrium is locally stable.
(c) [tex]y' = x[/tex]
To find the equilibrium, we set y' = 0 and solve for y:
x = 0
y = any constant
This means that there are infinitely many equilibria, one for each value of y.
To determine the stability of each equilibrium, we compute the derivative of y' with respect to y and evaluate it at the equilibrium point:
[tex]y'' = 0[/tex]
Since y'' is always 0, we cannot use it to determine the stability of the equilibria. Instead, we need to examine the sign of y' in the neighborhood of each equilibrium point. If y' is positive (resp. negative) on one side of the equilibrium point and negative (resp. positive) on the other side, then the equilibrium is unstable (resp. stable). In this case, we can see that All equilibria are unstable because y' is always positive to the right of any equilibrium point and always negative to the left.
(d)[tex]y' = y - x^3[/tex]
To find the equilibrium, we set y' = 0 and solve for y:
[tex]y = x^3[/tex]
To determine the stability of the equilibrium, we compute the derivatives of y' with respect to y and x and evaluate them at the equilibrium point:
[tex]y'' = 1\\x'' = 0[/tex]
Since y'' is always positive and x'' is always 0, we can use the sign of y' as a function of x to determine the stability of the equilibrium. We can see that The equilibrium is locally stable because y' is negative to the left of the equilibrium point and positive to the right of it.
(e) [tex]y' = y - x[/tex]
To find the equilibrium, we set y' = 0 and solve for y:
y = x
To determine the stability of the equilibrium, we compute the derivatives of y' with respect to y and x and evaluate them at the equilibrium point:
[tex]y'' = 1\\x'' = 0\alpha[/tex]
Since y'' is always positive and x'' is always 0, we can use the sign of y' as a function of x to determine the stability of the equilibrium. We can see that The equilibrium is locally unstable because y' is positive to the right of the equilibrium point and negative to the left.
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See photo for question
Answer:
7.9
Step-by-step explanation:
The interior angle measurements for the given triangle is not given, therefore, use the following equation:
[tex]c^2 = a^2 + b^2[/tex]
In which:
a = side (x)
b = side (9)
c = hypotenuse (12)
~
Plug in the corresponding numbers and variable to the corresponding variables:
[tex]c^2 = a^2 + b^2\\(12)^2 = (x)^2 + (9)^2[/tex]
First, simplify. Find the powers of 9 and 12:
[tex](12)^2 = (x)^2 + (9)^2\\(12 * 12) = x^2 + (9 * 9)\\(144) = x^2 + (81)[/tex]
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
Subtract 81 from both sides of the equation:
[tex]144 = x^2 + 81\\144 (-81) = x^2 + 81 (-81)\\144 - 81 = x^2\\x^2 = 63\\[/tex]
Next, root both sides of the equation, to isolate the variable, x:
[tex]x^2 = 63\\\sqrt{x^2} = \sqrt{63} \\x = \sqrt{63} \\x = \sqrt{63} = \sqrt{3 * 3 * 7} = 3\sqrt{7}[/tex]
3√7 to decimal form = ~7.9 (rounded to the nearest tenths).
7.9 is your answer.
~
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how many ways are there to select an unordered group of eight numbers between 1 and 25 inclusive with repetition? in what fraction of these ways is the sum of these numbers even?
There are a total of 25⁸ ways to select an unordered group of eight numbers between 1 and 25 inclusive with repetition. This is because for each of the eight numbers, there are 25 options to choose from, and the choices are independent of each other.
To find the fraction of these ways in which the sum of the numbers is even, we need to use the principle of inclusion and exclusion. First, we count the total number of ways in which the sum of the numbers is odd. This is equal to the number of ways in which an odd number of the eight numbers are odd, and the rest are even. There are 12 odd numbers and 13 even numbers between 1 and 25 inclusive.
Using the binomial coefficient, the number of ways in which the sum of the numbers is odd is:
C(8,1) * 12¹* 13⁷ + C(8,3) * 12³ * 13⁵ + C(8,5) * 12⁵ * 13³ + C(8,7) * 12⁷ * 13¹ = 9,676,454,400
Therefore, the number of ways in which the sum of the numbers is even is:
25^8 - 9,676,454,400 = 6,400,821,094,400
And the fraction of these ways is:
6,400,821,094,400 / 25⁸ = 0.5351
So, approximately 53.51% of the ways to select an unordered group of eight numbers between 1 and 25 inclusive with repetition have an even sum.
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How many times larger is the 6 in 4.6 then the 6 in 0.036
How many times larger is the 6 in 4.6 than the 6 in 0.036: 1.3 times larger is the 6 in 4.6, and 166.6 times larger is the 6 in 0.036.
1.3 times larger is the 6 in 4.6
The answer you divide 6 by 4.6 which would get you 1.30.
so, the remainder would be 1
166.6 times larger is the 6 in 0.036
The answer you divide 6 by 0.036 which would get you 166.6
so, the remainder would be 166
To know how frequently bigger the number is than the other number, simply divide the main number continuously number.
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