The rabbit covers a distance of 30 meters in 10 seconds at a constant speed of 3m/s.
As we know that distance is equal to speed multiplied by time, we can use this formula to calculate the distance covered by the rabbit in 10 seconds. Given that the speed of the rabbit is constant at 3m/s, we can use this value to calculate the distance it covers in 1 second.
So, distance covered by rabbit in 1 second = Speed of rabbit = 3m/s
Now we can use this value to find the distance covered by the rabbit in 10 seconds, which is equal to 10 times the distance covered by the rabbit in 1 second.
Distance covered by rabbit in 10 seconds = 3m/s x 10 seconds
= 30 meters
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I'll give Brainliest to whoever answers correctly and the answer is for 25 points
Answer:
y= (5/3)x -4/3
Step-by-step explanation:
Slope obtained from the two points of the graph.
m=5/3
Points: A(-1,-3). B(2,2)
m=(y2-y1)/(x2-x1)
m=(2-(-3))/(2-(-1))
m=5/3
Replacing in the equation form: y=mx+b
y=(5/3)x+b
2=(5/3)2+b
2=10/3 +b
2-10/3= b
6/3 - 10/3 = b
b= -4/3
Joining all the terms we obtain:
y= (5/3)x -4/3
Answer: The slope is 5/3
Step-by-step explanation:
the poin at (2,2) is 5 up and 3 right of the point at (
-1,-3)
give the position of C on this number line
The position of C on the number line is 1/8th position.
Define the term number line?A number line is a visual representation of the real numbers as points or marks on a straight line. The number line is usually represented horizontally, with zero in the middle and positive numbers to the right of zero and negative numbers to the left of zero.
From the given number line, there are total 8 points between 0 to 1
That means, it's fractions of 8.
Location of point C is on the 1st point,
So, position of C on this number line = (1/8) ÷ (1-0) = 1/8
Therefore, In the number line, C is located in the 1/8th place.
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a chess club with 80 memberd is electing a new presidentm jose received 52 votes. what percentage of the club members voted for Jose?
Answer:
Step-by-step explanation:
(52 divided by 80) multiplied by 100
that will give you the answer
If repeated samples of size n are taken from a normal population with an unknown variance, then the statistic ______ follows the t distribution with n-1 degrees of freedom
In summary, when repeated samples of size n are taken from a normal population with an unknown variance, the statistic t follows the t-distribution with n-1 degrees of freedom.
If repeated samples of size n are taken from a normal population with an unknown variance, then the statistic t follows the t distribution with n-1 degrees of freedom. When a sample of size n is taken from a normal population with a known variance and mean, the sample mean follows a normal distribution with a mean of μ and a variance of σ2/n. This distribution is known as the sampling distribution of the mean.
However, when the variance is unknown, the sampling distribution of the mean can no longer be calculated using the normal distribution. In this scenario, the sample mean is calculated using a t-distribution instead of a standard normal distribution.The t-distribution is similar to the standard normal distribution. However, it is more spread out and flatter than the standard normal distribution. As a result, the t-distribution has thicker tails than the standard normal distribution, which makes it more suitable for analyzing small samples of data.
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GIVING BRAINLIST SO HURRY!!!!
What is the median of the data set represented by the dot plot?
Answer:
14
Step-by-step explanation:
scores 10 10 12 13 14 15 18 19 19 Median score is the one in the middle
compute the determinants in exercises 9-14 by cofactor expansions. at each step, choose a row or column that involves the least amount of computation. [\begin{array}{ccc}6&3&2&4&0\\9&0&-4&1&0\\8&-5&6&7&1\\3&0&0&0&0\\4&2&3&2&0\end{array}\right]
Answer:
Step-by-step explanation:
Please help me with my math
Answer:
[tex]\textsf{$\boxed{\checkmark}\;\;y$-value\;of\;vertex\;is\;$-1$}[/tex]
[tex]\textsf{$\boxed{\checkmark}$\;\;Minimum\;value\;occurs\;at\;$y = -1$}[/tex]
Step-by-step explanation:
Given equation:
[tex]y=x^2+8x+15[/tex]
As the given equation is quadratic with a positive leading coefficient, it is a parabola that opens upwards. Therefore, its vertex is its minimum point. This means that the minimum value of the range is the y-value of the vertex.
The x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a. Therefore, the x-value of the vertex of the given equation is:
[tex]\implies x=\dfrac{-8}{2(1)}=-4[/tex]
To find the y-value of the vertex, substitute x = -4 into the equation:
[tex]\begin{aligned}\implies y&=(-4)^2+8(-4)+15\\&=16-32+15\\&=-16+15\\&=-1\end{aligned}[/tex]
Therefore, the minimum y-value of the function is y = -1, so the range is y ≥ -1.
Therefore, the following are true statement about the given equation:
y-value of vertex is -1Minimum value occurs at y = -1This is a modification of A7 - Quadratic Approximation. Create a Matlab function called myta which takes four arguments in the form myta(f,n,a,b). Heref is a function handle, n is a nonnegative integer, and a and b are real numbers. The Matlab function should find the nth Taylor Polynomial to f(x) at x = a and plug in x = b, then it should return the absolute value of the difference between this value and f(b). The the nth Taylor Polynomial to f (x) is the function g(x) = f(a) + f'(a)(x – a) += f'(a)(x – a)? + 1 1 f''(a)(x – a)3 + + f(n)(a)(x – a)". 1 3! n! 3 Here are some samples of input and output for you to test your code. When you submit your code the inputs will be different. Here vpa is being used to show lots of digits
As we have defined the Matlab function called myta which takes four arguments in the form myta(f,n,a,b).
The purpose of the function is to find the nth Taylor polynomial of the function f(x) at x = a and evaluate it at x = b. Then, it should return the absolute value of the difference between this value and f(b).
Now that we have the nth Taylor polynomial of f(x) at x = a, we can evaluate it at x = b and calculate the absolute difference between this value and f(b).
function result = myta(f,n,a,b)
syms x; % define x as symbolic variable
g = f(a); % initialize g as f(a)
for i=1:n % iterate from 1 to n
deriv = diff(f,x,i-1); % calculate the ith derivative of f
term = deriv*(x-a)^(i-1)/factorial(i-1); % calculate the ith term of the Taylor series
g = g + term; % add the ith term to g
end
result = abs(g - f(b)); % calculate the absolute difference between g(b) and f(b)
end
This code calculates the absolute difference between g(b) and f(b) using the "abs" function and assigns it to the output variable "result".
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Help help please brainlist please ill mark
Answer:
Second choice
∠BCA ≅ ∠DCA
Step-by-step explanation:
This logically follows from the fact that both ∠BCA and ∠DCA are right angles from the previous step. And the reason given is "All right angles are ≅)
So they are congruent
Find m ∠ JKL using the picture
The value of m∠JKL is 34°
How to find the value of m∠JKL?An angle formed by a tangent and a secant intersecting outside a circle is equal to one-half the difference of the measures of the intercepted arcs.
Based on the theorem above, we can say:
m∠JKL = 1/2 * (159 - 91)
m∠JKL = 1/2 * 68
m∠JKL = 34°
Therefore, the value of m∠JKL in the circle is 34°.
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Find the first five terms of the sequence a(n)=3n-1
Answer:
-1, 2, 5 , 8 , 11 or 2, 5, 8, 11 , 14
Step-by-step explanation:
Assume n starts from 0
a(0) = 3 (0) -1 = -1
a(1) = 3 (1) -1 = 2
a(2) = 3 (2) -1 = 5
a(3) = 3 (3) -1 = 8
a(4) = 3 (4) -1 = 11
notice If we Assume n starts from 1
a(1) = 3 (1) -1 = 2
a(2) = 3 (2) -1 = 5
a(3) = 3 (3) -1 = 8
a(4) = 3 (4) -1 = 11
a(5)= 3 (5) -1 = 14
Notice a sequence can start from any N. But the most common ones are n=0 or n=1
Choose the true statement 
Answer: First one (the one you selected in the photo)
Step-by-step explanation:
If you need help draw a number line.
-8 is not equal to 8, as one is negative and the other is positive.
On a number line, -8 is to the left, meaning it is less, so the second one is false.
This means the first one is correct.
An assignment of probabilities to events in a sample space must obey which of the following? They must obey the addition rule for disjoint events. They must sum to 1 when adding over all events in the sample space. The probability of any event must be a number between 0 and 1, inclusive. All of the above
An assignment of probabilities to events in a sample space must obey all of the following: They must obey the addition rule for disjoint events, They must sum to 1 when adding over all events in the sample space, and The probability of any event must be a number between 0 and 1, inclusive. Hence, the correct option is All of the above.
What is probability?Probability is the branch of mathematics that deals with the likelihood of a random event occurring. Probability is concerned with quantifying the probability of different results in a certain event.
The possibility that a specific event will occur is calculated using probability. Probability is calculated using several methods in mathematics, including axioms, probability spaces, events, random variables, and expectation values.
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Can you help me with this question please.
Answer:
[tex]x = 4\sqrt{3}[/tex]
Step-by-step explanation:
The triangle is right-angled
In a right-angled triangle, the following equality holds
[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]
[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]
Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]
Find the definite integral of f(x)=
fraction numerator 1 over denominator x squared plus 10 invisible times x plus 25 end fraction for x∈[
5,7]
Over the range [5, 7], the definite integral of f(x) = 1 / (x² + 10x + 25) is around -1/60.
To find the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7], we can use the following formula:
∫[a,b] f(x) dx = F(b) - F(a)
where F(x) is the antiderivative of f(x).
First, we need to find the antiderivative of f(x):
∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx
To do this, we can use a technique called partial fraction decomposition:
1 / (x² + 10x + 25)
= A / (x + 5) + B / (x + 5)²
Multiplying both sides by the denominator (x² + 10x + 25), we get:
1 = A(x + 5) + B
Setting x = -5, we get:
1 = B
Setting x = 0, we get:
A + B = 1
A + 1 = 1
A = 0
Therefore, the partial fraction decomposition of f(x) is:
1 / (x² + 10x + 25) = 1 / (x + 5)²
Now we can find the antiderivative:
∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx = ∫ 1 / (x + 5)² dx
Using the substitution u = x + 5, du = dx, we get:
∫ 1 / (x + 5)² dx = -1 / (x + 5) + C
where C is the constant of integration.
Now we can evaluate the definite integral over the interval [5, 7]:
∫[5,7] f(x) dx = F(7) - F(5)
∫[5,7] f(x) dx = [-1 / (7 + 5) + C] - [-1 / (5 + 5) + C]
∫[5,7] f(x) dx = [-1 / 12 + C] - [-1 / 10 + C]
∫[5,7] f(x) dx = -1 / 12 + C + 1 / 10 - C
∫[5,7] f(x) dx = -1 / 60
Therefore, the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7] is approximately -1/60.
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a tank is being filled with water at the rate of gallons per hour with t>0 measured in hours. if the tank is originally empty, how many gallons of water are in the tank after 5 hours?
After 5 hours, the tank will have 50 gallons of water.
To solve this problem, use the following equation:
Gallons = Rate x Time
In this case, the rate is 5 gallons per hour and the time is 5 hours, so the equation becomes:
Gallons = 5 x 5
Therefore, the tank will have 50 gallons of water after 5 hours.
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A phlebotomist measured the cholesterol levels of a sample of 25 people between the ages of 35 and 44 years old. Here are summary statistics for the samples:
The 90% confidence interval for [tex]$\mu_W - \mu_M$[/tex] is approximately [tex]$-13.2 \pm 27.1$[/tex], or (-40.3, 13.9).
The answer is (c) [tex]13.2 \pm 33.1[/tex], which is not correct.
Which is the confidence interval?
A confidence interval is a range around a measurement that conveys how precise the measurement is.
We can use the two-sample t-interval formula to find the confidence interval for the difference in means:
[tex]$\bar{x}_W - \bar{x}M \pm t{\alpha/2, \nu} \sqrt{\frac{s_W^2}{n_W} + \frac{s_M^2}{n_M}}$[/tex]
where [tex]$\bar{x}_{W}$[/tex] and [tex]$\bar{x}M$[/tex] are the sample means, [tex]$s_W$[/tex] and [tex]$s_M$[/tex] are the sample standard deviations, [tex]$n_W$[/tex] and [tex]$n_M$[/tex] are the sample sizes, [tex]$\nu$[/tex] is the degrees of freedom, and [tex]$t{\alpha/2, \nu}$[/tex] is the critical value from the t-distribution with [tex]$\nu$[/tex]degrees of freedom and a level of significance of [tex]$\alpha=0.1$[/tex] (since we want a 90% confidence interval, which corresponds to a 10% level of significance).
Plugging in the values, we get:
[tex]$\bar{x}_W - \bar{x}M \pm t{0.05/2, 23} \sqrt{\frac{s_W^2}{n_W} + \frac{s_M^2}{n_M}}$[/tex]
[tex]$\begin{aligned} &= 213.6 - 226.8 \pm t_{0.025, 23} \sqrt{\frac{45.3^2}{14} + \frac{49.4^2}{11}} \ &= -13.2 \pm 2.074 \times 13.102 \ &= -13.2 \pm 27.115 \end{aligned}$[/tex]
Therefore, the 90% confidence interval for [tex]$\mu_W - \mu_M$[/tex] is approximately [tex]$-13.2 \pm 27.1$[/tex], or (-40.3, 13.9).
The answer is (c) [tex]13.2 \pm 33.1[/tex], which is not correct.
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complete question:
A phlebotomist measures the cholesterol levels of a sample of 25 people between
the ages of 35 and 44 years old. Here are summary statistics for the samples.
Cholesterol levels (mg per 100mL)
Women 35-44 years old
Men 35-44 years old
Sample mean
tilde x_{W} = 213.6
overline x_{M} = 226.8
Sample standard deviation
s_{W} = 45.3
s_{M} = 49.4
Sample size
n_{W} = 14
nu = 11
Assume that the conditions for inference have been met. Let mu_{w} ^ (- mu_{u}) be the difference in mean
cholesterol levels (in milligrams per 100 ml) in women and men of those ages.
Which of the following is a 90% confidence interval for mu_{W} ^ (- mu_{M})
Use a calculator to calculate the interval. (State your calculator settings for partial credit)
(a) - 13.2 plus/minus 33.1
(b) -13.2±29.7
(c) 13.2 plus/minus 33.1
(d) 13.2 plus/minus 29.7
(e) 13 plus/minus 33.1
Answer:
-13.2+- 33.1
Step-by-step explanation:
Please please please help me!!!!!
The volume of the sphere which is equivalent to the lung capacity is approximately =2,571 cm³
How to calculate the volume of the sphere?To calculate the volume of a sphere the formula used = V = 4/3 πr³
Radius = 8.5 cm
First cube the radius = 8.5³ = 614.125
The, multiply r³ by π = r³×π = 614.125× 3.14= 1928.3525
Take this answer and multiply it by 4 = 4×1928.3525= 7713.41
Last, divide this answer by 3 = 7713.41/3 = 2571.136666
Therefore the volume of the balloon = 2,571 cm³(approximately)
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Please help with the highlighted red on part(c) as well as part(d).
Use the formula (2) above and the results from part (b) to write the general solution of our system (4). Write this solution in your document. What happens to the system as t gets large?
Consider the system of differential equations
dx/dt = 3x+4y
dy/dt = -x - 2y
The solution of the system goes to infinity as t gets large.
Consider the given system of differential equations: dx/dt = 3x + 4ydy/dt = −x − 2yNow, find the solution of the system:(2) dx/dt + 2 dy/dt = 7xObserve the second equation and multiply it by 2:2 dy / dt = −2x − 4y(3) dx/dt + 2 dy/dt = 3x − 4ySubstitute the value of dy/dt from (3) into (2):(2) dx/dt + 3x − 4y = 7xSimplify this equation:dx/dt − 4x = 4yTake the laplace transform of both sides: Laplace{dx/dt − 4x} = Laplace{4y} ⇒ sX(s) − x(0) − 4X(s) = 4Y(s) ⇒ X(s) = {4Y(s)}/{s − 4}Now, find the Laplace transform of y(s):(1) dy/dt = −x − 2y ⇒ Laplace{dy/dt} = −Laplace{x} − 2Laplace{y} ⇒ sY(s) − y(0) = −X(s) − 2Y(s) ⇒ Y(s) = {−X(s)}/{s + 2}Substitute the value of X(s) in the above equation, we get:Y(s) = {−4Y(s)}/[(s − 4)(s + 2)]Simplify this equation:Y(s) = {A}/{s − 4} + {B}/{s + 2}Now, find the values of A and B:Multiplying the above equation by (s − 4) and (s + 2), we get:Y(s) = A(s + 2) + B(s − 4)Simplify this equation:Y(s) = (A + B)s + 2A − 4BAs per the equation (3), we can say A + B = 0, 2A − 4B = −4On solving, we get A = 2, B = −2Therefore, the value of Y(s) is:Y(s) = {2}/{s − 4} − {2}/{s + 2}Now, substitute the value of X(s) and Y(s) in the following equation:dx/dt − 4x = 4yThe solution of the above differential equation is:x(t) = {2}/{3}e^{4t} − {5}/{3}e^{-2t}The above is the general solution of the given system of differential equations.Now, find what happens to the system as t gets large?As t gets large, the term {5}/{3}e^{-2t} will tend to zero and {2}/{3}e^{4t} will tend to infinity.
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juan mcdonald is willing to pay $900 for a new ipad. he offers to pay $800 for an ipad at the apple store. it costs apple $700 to produce this ipad. a voluntary economic transaction between juan and apple occur because would be better off due to the transaction. a. will not; only apple b. will; both juan and apple c. will not; only juan d. will; neither juan nor apple
In the following question, option B, Juan McDonald is willing to pay $900 for a new iPad. he offers to pay $800 for an iPad at the apple store. it costs apple $700 to produce this iPad. A voluntary economic transaction between "Juan and Apple" will occur because it would be better off due to the transaction.
What is a voluntary economic transaction? Voluntary economic transactions involve willing buyers and willing sellers, and they usually involve the exchange of goods and services in return for money. In a free-market economy, people have the freedom to make voluntary economic transactions, and government intervention is minimal. What are the benefits of voluntary economic transactions? The benefits of voluntary economic transactions include the following: They are beneficial to both parties involved in the transaction.
The buyer obtains what they require, while the seller obtains the money they require. The exchange of goods and services for money encourages individuals to create, produce, and sell more. The economy is stimulated by increased economic activity, which leads to more job creation, more employment opportunities, and more revenue for the government. Juan McDonald is willing to pay $900 for a new iPad. He offers to pay $800 for an iPad at the Apple store. It costs Apple $700 to produce this iPad.A voluntary economic transaction between Juan and Apple will occur because it would be better off due to the transaction. So, the answer is option B: will; both Juan and Apple.
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a woman with blood type a has three children with a man who has blood type ab. the first child has blood type b. what is the probability that the second child born to the couple will have blood type ab?
The probability that the second child born to the couple will have blood type AB is 1/2.
What is Blood Grouping?Blood grouping is the categorization of blood into groups depending on the type of antigen and antibody present on the surface of red blood cells (RBCs).
The ABO blood grouping system, which includes A, B, AB, and O blood types, is the most well-known blood grouping system.
Blood group Rh (Rhesus) grouping system is another well-known blood grouping system that can be determined.
Therefore, the probability that the second child born to the couple will have blood type AB is 1/2.
50 percent of the offspring of this couple will inherit the gene for the ABO blood type A from the mother, while the remaining 50% will inherit the gene for the blood type B from the father.
The probability of inheriting the gene for blood type AB is thus 1/2 for a child born to these parents.
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a) Is the value of -42 different from the value of (-4)²? What purpose do the brackets serve? b) Is the value of -23 different from the value of (-2)³? What purpose do the brackets serve?
a) The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.
b) The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.
What is exponent?Exponents are mathematical notation used to indicate that a quantity is being multiplied by itself a certain number of times. The exponent is usually written as a superscript to the right of the base number.For example, in the expression 2³, the base number is 2 and the exponent is 3. This means that 2 is being multiplied by itself three times, resulting in a value of 8. Exponents can also be negative or fractional, indicating that the base number is being divided by itself a certain number of times.
In the given question,
a) The value of -42 is different from the value of (-4)². The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.
b) The value of -23 is different from the value of (-2)³. The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.
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you roll a fair 6 66-sided die. what is p(not 5 ) p(not 5)start text, p, (, n, o, t, space, 5, end text, )?
when we Roll a fair 6 66-sided die. then the probability of P (not 5) is 65/66
The concept used a die is a tool used for games and gambling. The die is a cube with six faces, each of which has a different number of dots from one to six. The roll of a die is a random event, which means that it is unpredictable, and each roll is independent of any other roll.
Let's solve the question that is P(not 5)
Since the die is fair, we have 66 sides on the die. Each of the sides has a probability of 1/66 of being rolled. P(not 5) means that we need to determine the probability of rolling a number that is not 5.
We know that a 66-sided die has 65 numbers other than 5.
Therefore, the probability of rolling a number that is not 5 is 65/66.
P(not 5) = 65/66
So, the probability of not rolling a 5 is p(not 5) = 65/66.
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What is an equation of the line that passes through the point (4,1) and is perpendicular to the line 2x-y= 4?
Answer:
Point-Slope Form: y - 1 = -1/2(x - 4) or Standard Form: y = -1/2x + 3
Step-by-step explanation:
For a line to be perpendicular, you take the negative inverse of the slope of 2x - y = 4. To do this, rearrange the y to one side and you get y = 2x - 4. The slope of the line is 2. So, taking the negative inverse would be -1/m (with m being slope of the the equation given in the problem. This would give you -1/2.
Using point slope formula, y - y1 = m(x - x1), you can plug in the point given, (4,1) and the slope you found to get y - 1 = -1/2(x - 4). For standard form, isolating the y gets you y = -1/2x + 3.
You can check your answer by using Desmos by putting in the line 2x - y = 4, the point (4,1), and the equation you got as your answer. You will see that the equation is perpendicular to 2x - y = 4 and passes through point (4,1). Your equation of the line is y - 1 = -1/2(x - 4) or y = -1/2x + 3
ax+by=ac
make 'a' as the subject
The required equation in terms of 'a' is: a = (ac - by)/x.
What is Subject in equation?The number being calculated is the formula's subject. On one side of the equals symbol, it is identifiable as the letter on its own.
According to question:To make 'a' the subject of the equation:
Ax + by = ac
we can start by isolating 'a' on one side of the equation.
Ax = ac - by
Then, we can divide both sides by 'x':
a = (ac - by)/x
Therefore, the equation in terms of 'a' is:
a = (ac - by)/x
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Complete questiion:
Find the subject of the equation ax+by=ac.
solve the differential equation by variation of parameters, subject to the initial conditions y(0)
The differential equation by variation of parameters, subject to the initial conditions y(0) can be found by homogeneous equation and by integrating it.
The solution to the differential equation by variation of parameters, subject to the initial conditions y(0), can be found by following these steps:
1. Separate the equation into homogeneous and particular parts.
2. Solve the homogeneous equation for its particular solution.
3. Construct a new auxiliary equation from the particular solution, integrating the particular solution with respect to the parameters.
4. Solve the auxiliary equation, again with respect to the parameters, and then integrate the result with respect to x.
5. Substitute the particular solution and the new parameters back into the original equation to solve it completely.
6. Substitute the initial condition y(0) to solve for the constants of integration.
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If Karel starts at Street 1 and Avenue 1, facing East, where will Karel be, and what direction will Karel be facing after running the following code? (Assume the world is 10x10 in size)move();turnLeft();putBall();turnLeft();turnLeft();turnLeft();move();turnLeft();
After running the given code, Karel will be at Street 2 and Avenue 2, facing North.
Here is a step-by-step explanation of what the code does:
move(); - Karel moves one block east, to Street 1 and Avenue 2.
turnLeft(); - Karel turns left to face north.
putBall(); - Karel puts a ball at Street 1 and Avenue 2.
turnLeft(); turnLeft(); turnLeft(); - Karel turns left three times to face south.
move(); - Karel moves one block south to Street 2 and Avenue 2.
turnLeft(); - Karel turns left to face east.
So after executing this code, Karel will be at Street 2 and Avenue 2, facing North.
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What value of z should we use when making a 93% confidence interval for p? A. 1.48 B. It's impossible to make a 93% CI. C. 2.70 D. 1.81
The value of z that should be used when making a 93% confidence interval for p is Z=1.81 that is option D.
The z score is a measure of how many standard deviations a raw score is below or above the population mean. It will be positive if the value is more than the mean and negative if it is less than the mean. It is often referred to as the standard score. It represents the number of standard deviations an entity has from the mean.
To utilise a z-score, both the mean and the population standard deviation must be known. The z score calculates the likelihood of a score occuring within a standard normal distribution. It also allows us to compare scores from various samples. A table for the values of, representing the values of the cumulative distribution function of the normal distribution, is known as a
At 93% confidence, the significance level is,
ɑ= 1-0.93
ɑ= 0.07
Divide alpha by 2,
ɑ/2= 0.07/2= 0.035
Now, from the ‘normal probability’ table, the z value corresponding to the inverse probability of 0.035 is 1.81.
As a result, the z value is 1.81 at 93% confidence level.
z= 1.81
The value for z score is 1.81
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Determine the overall resistance of a 100-meter length of 14 AWA (0.163 cm diameter) wire made of the following materials. a. copper (resistivity = 1.67x10-8 O•m) b. silver (resistivity = 1.59x10-8 O•m) c. aluminum (resistivity = 2.65x10-8 O•m) d. iron (resistivity = 9.71x10-8 O•m)
On the material was used, the 100-meter flex of 14 AWA wire's entirety would range. If the silver and copper cable are in 0.0013 and 0.0014, aluminum spans 0.002 and 0.004, and iron is between 0.007 and 0.008
What is a case of resistance?A force that works to slow something down or halt its progress: The air/wind drag slowed the vehicle down. the extent to which a material obstructs an electric charge from passing through it: There is little reluctance in copper.
The resistance (R) of a wire is given by the formula:
R = (ρ x L) / A
where:
ρ is the resistivity of the material
L is the length of the wire
A is the wire's cross-sectional size.
The cross-sectional area (A) of a wire with diameter d is given by the formula:
A = π x (d/2)²
where pi is a number in mathematics. (approximately equal to 3.14).
For a 100-meter length of 14 AWA wire with diameter 0.163 cm, we first need to convert the diameter to meters:
d = 0.163 cm = 0.00163 m
The cross-sectional area of the wire is then:
A = π x (0.00163/2)² = 2.087 x 10⁻⁶ m²
Using this value of A and the given resistivities, we can calculate the resistance for each material:
For copper:
R_copper = (1.67 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00134 Ω
For silver:
R_silver = (1.59 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00128 Ω
For aluminum:
R_aluminum = (2.65 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁶ m²) = 0.00199 Ω
For iron:
R_iron = (9.71 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00735 Ω
Therefore, the overall resistance of the 100-meter length of 14 AWA wire made of these materials would depend on which material was used. If copper or silver were used, the resistance would be relatively low, around 0.0013-0.0014 Ω. If aluminum were used, the resistance would be higher, around 0.002 Ω. If iron were used, the resistance would be much higher, around 0.007 Ω.
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find bases for the null spaces of the matrices given in exercises 9 and 10. refer to the remarks that follow example 3 in section 4.2.
In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.
The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.
The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.
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