Answer:
"Sighs" should be "Sighed"
Yesterday the lightning auto club had two races. in both races, the same five cars - car a, car b, car c, car d, and car e - finished in the top five spots. in the second race, car c finished first, car a moved up 1 spot from the first race, car b moved down 2 spots from the first race, and car d and car e switched places from where they finished in the first race. which car finished second in the first race? note: no two cars tied in either race.
Based on the information provided in the question:
Car b finished in the second position in the first race.
Velocity:
Velocity is the directional velocity of a moving object, observed from a given frame of reference and indicating the rate of change of position measured at a given time reference (eg 60 km/h northward). Velocity is a fundamental concept in kinematics, a branch of classical mechanics that describes the motion of bodies.
Velocity is a physical vector quantity. Both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is called velocity, and its magnitude is a consistent derived unit measured in the SI (metric) system as meters per second (m/s or m⋅s−1). For example, "5 meters/second" is a scalar, but "5 meters/second east" is a vector. An object is said to be accelerating if its velocity, direction, or both change.
According to the question:
Let tₐ = time of finish of car A in sec
Let \(t_b\)= time of finish of car B in sec
Let \(t_c\) = time of finish of car C in sec
Let \(t_d\) = time of finish of car D in sec
Let \(t_e\) = time of finish of car E in sec
According to the above information:
(1) \(t_a = t_d -1\)
(2) \(t_b= t_e -6\)
(3) \(t_e =t_a +3\)
(4) \(t_a = t_c+5\)
Now,
From (3),
(3) \(t_a = t_e -3\)
and
(2) \(t_e =t_b+6\)
and
(1)\(t_d =t_a +1\)
Therefore, the series would be
Car C, Car B, Car A, Car D, Car E
the above series is the position of race from 1st to last.
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If the simple interest on $6,000 for 9 years is $4,320, then what is the interest rate?
The rate is ?
Answer:
6.48%
Step-by-step explanation:
the rule of the simple interest is:
I=PRT
but here we want the rate, and we have I and P and T
so put the rate on 1 side, and all the given numbers in other side
the rule will be like this:
R=I/PT
R=4320/6000×9
R=6.48%
help with this HW problem
y"- 2y' + 5y = 1 + t + δ(t-2), y(O) = 0, y'(0) = 4
The solution to the given differential equation is y(t) = -1/2e^t + 2te^t + 1/2 + δ(t-2), where δ(t) is the Dirac delta function.
To solve the given differential equation, we will first find the complementary solution, which satisfies the homogeneous equation y'' - 2y' + 5y = 0. Then we will find the particular solution for the inhomogeneous equation y'' - 2y' + 5y = 1 + t + δ(t-2).
Step 1: Finding the complementary solution
The characteristic equation associated with the homogeneous equation is r^2 - 2r + 5 = 0. Solving this quadratic equation, we find two complex conjugate roots: r = 1 ± 2i.
The complementary solution is of the form y_c(t) = e^rt(Acos(2t) + Bsin(2t)), where A and B are constants to be determined using the initial conditions.
Applying the initial conditions y(0) = 0 and y'(0) = 4, we find:
y_c(0) = A = 0 (from y(0) = 0)
y'_c(0) = r(Acos(0) + Bsin(0)) + e^rt(-2Asin(0) + 2Bcos(0)) = 4 (from y'(0) = 4)
Simplifying the above equation, we get:
rA = 4
-2A + rB = 4
Using the values of r = 1 ± 2i, we can solve these equations to find A and B. Solving them, we find A = 0 and B = -2.
Thus, the complementary solution is y_c(t) = -2te^t sin(2t).
Step 2: Finding the particular solution
To find the particular solution, we consider the inhomogeneous term on the right-hand side of the differential equation: 1 + t + δ(t-2).
For the term 1 + t, we assume a particular solution of the form y_p(t) = At + B. Substituting this into the differential equation, we get:
2A - 2A + 5(At + B) = 1 + t
5At + 5B = 1 + t
Matching the coefficients on both sides, we have 5A = 0 and 5B = 1. Solving these equations, we find A = 0 and B = 1/5.
For the term δ(t-2), we assume a particular solution of the form y_p(t) = Ce^t, where C is a constant. Substituting this into the differential equation, we get:
2Ce^t - 2Ce^t + 5Ce^t = 0
The coefficient of e^t on the left-hand side is zero, so there is no contribution from this term.
Therefore, the particular solution is y_p(t) = At + B + δ(t-2). Plugging in the values we found earlier (A = 0, B = 1/5), we have y_p(t) = 1/5 + δ(t-2).
Step 3: Finding the general solution
The general solution is the sum of the complementary and particular solutions:
y(t) = y_c(t) + y_p(t)
y(t) = -2te^t sin(2t) + 1/5 + δ(t-2)
In summary, the solution to the given differential equation is y(t) = -1/2e^t + 2te^t + 1/2 + δ(t-2).
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(No links or urls please) Write an equation of a circle that passes through the following points- see image
Step-by-step explanation:
Step-by-step explanation:
The general equation for a circle is
\( {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \)
where (h, k) is the coordinates of the center of the circle and r is the radius. Since the circle passes through (4, 4) and (-4, -4), its center is located at the origin, which means its equation becomes
\( {x}^{2} + {y}^{2} = {( \sqrt{ {4}^{2} + {4}^{2} } )}^{2} = 32\)
Ferris wheel makes 6 revolutions per ride. It
has a diameter of 45 feet. How far would someone
travel during one ride?
Answer:
270
Step-by-step explanation:
so u would take 6 and 45 and multiplay
I’m not good at math and I have a question that says what is 1.10 x 10^6 power can someone help me??
Answer:
It will be 1,100,000
Hope it helps!
Answer:
1,110,000 in standard form
Step-by-step explanation:
To write this number in standard form, put the most significant digit in the number place indicated by the exponent of 10, then put the digits right of it in the corresponding number places to the right of the most significant digit.
__
You will notice that number place values increase the exponent of the base (10) by 1 unit for each place going left. The exponent decreases by 1 unit for each place going right. This is true for a place-value number system in any base.
How do you find the scale factor of a dilation with a center of dilation?
The scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).
What is dilation?
A dilation is a transformation that creates an image that has the same shape as the original but is larger.
• An enlargement is a dilation that produces a larger image.
• A reduction is a dilation that produces a smaller image.
• A dilation expands or contracts the original figure.
A dilation is a stretch or a shrink in the size and location of a figure or point.
The scale factor in a dilation is the amount by which the figure is stretched or shrunk.
The center of dilation is a reference point used to appropriately scale the dilation of a figure. Given a point on the pre-image, \((x_1, y_1)\)and a corresponding point on the dilated image \((x_2, y_2)\)and the scale factor,
k, the location of the center of dilation, \((x_0,y_0)\) is
\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\)
Hence, the scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).
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Can someone answer quick!!!
Answer:
Step-by-step explanation:
answer what?
Looking to receive help on practice question 103, thank you!
To convert the given polar equation to rectangular form, here are the steps.
1. Remember that sec θ = 1/cos θ. This means, the given polar equation can also be written as:
\(r=\frac{-3}{\cos \theta}\)2. We can multiply cos θ to both sides of the function to remove the cos θ in the right side.
\(\begin{gathered} r(\cos \theta)=\frac{-3}{\cos\theta}(\cos \theta) \\ r\cos \theta=-3 \end{gathered}\)3. Since we know that x = r cos θ, we can say that x = -3. This is the rectangular form of the equation.
\(x=-3\)Determine whether each relation represents a function. If it is a function, state the domain and range. a) {(1,4),(2,5),(3,6),(4,7)} b) {(−3,9),(−2,4),(0,0),(1,1),(−3,8)}
a) The relation {(1,4),(2,5),(3,6),(4,7)} represents a function. Domain: {1,2,3,4}. Range: {4,5,6,7}.b) The relation {(−3,9),(−2,4),(0,0),(1,1),(−3,8)} does not represent a function due to multiple outputs for input -3.
a) The relation {(1,4),(2,5),(3,6),(4,7)} represents a function because each input value (x) has a unique output value (y). The domain of the function is {1,2,3,4}, which includes all the x-values. The range is {4,5,6,7}, which includes all the corresponding y-values. In this case, for each x-value, there is only one y-value associated with it.
b) The relation {(−3,9),(−2,4),(0,0),(1,1),(−3,8)} does not represent a function because the input value -3 is associated with two different output values, 9 and 8. In a function, each input value should have a unique output value, but in this case, the input -3 has two different outputs, violating the definition of a function.Therefore, the relation in (a) represents a function with a defined domain and range, while the relation in (b) does not represent a function due to the presence of multiple outputs for a single input.
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5/3g = 2g - 2/3g + 2
The solution to given equation 5/3g = 2g - 2/3g + 2 is g = 6
In this question, we have been given an equation 5/3g = 2g - 2/3g + 2
We need to solve given equation.
5/3g = 2g - 2/3g + 2
5/3g - 2g = 2g - 2/3g + 2 - 2g ........(subtract 2g from both sides)
(5/3 - 2 )g + 2/3 g= - 2/3g + 2 + 2/3 g ........(add 2/3 g to each side)
-1/3g + 2/3 g = 2
1/3 g = 2
g = 2 * 3 ..............(multiply each side by 3)
g = 6
Therefore, the solution to given equation 5/3g = 2g - 2/3g + 2 is g = 6
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An angle in a rectangular coordinate system is in standard position if its vertex is at the_______.
An angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The angle is measured in a counterclockwise direction from the positive x-axis and is considered positive if it lies in the counterclockwise direction and negative if it lies in the clockwise direction.
The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located. An angle in a rectangular coordinate system is in a standard position if its vertex is at the origin of the plane. An angle is said to be in a standard position if its vertex is located at the origin of the coordinate system.
To summarize, an angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located.
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$200 is shared between two friends Mary and John in the ratio 3 : 2 respectively. What is the result?
Answer:
John: $80
Mary: $120
Step 1: Add the ratios (3 and 2).
=> 3 + 2 = 5
Step 2: Divide 200 by 5.
=> 200 ÷ 5
= 40
Step 3: Multiply.
=> Mary total: 40 x 3 = $120
=> John total: 40 x 2 = $80
Hoped this helped
If a nerve signal travels to and from the brain at a speed of 30 meters per second, how long would it take the signal to
travel 3 meters? Use this equation: time = distance/speed.
it takes 0.1 second to do 3 meters
PLEASE HELP QUICK. 10 points reward
Answer:
1/4
a-3/4
Step-by-step explanation:
i hope this helps and plz mark me brainliest
Professor is grading assignments and looking at the total number of errors, regardless of what the errors are (spelling, citations, etc.), over various semesters. She looks at 150 assignments each from 5 different semesters. After inspecting them, she find that 24% of the assignments have errors.
Compute the following:
Sp (estimate of the standard deviation). Reminder: Sp= √5-(1-D)/n
upper and lower control limits for p chart (total of two values). Reminder: UC and LCL=
p+/−(3∗Sp)
The estimate of the standard deviation (Sp) for the total number of errors in assignments from various semesters is approximately 0.044996 and the upper control limit (UC) is approximately 0.374988, and the lower control limit (LCL) is approximately 0.105012 for the p chart.
To compute the estimate of the standard deviation (Sp), we need to determine the proportion of assignments with errors in each semester and calculate the overall proportion of assignments with errors.
Given:
Number of semesters (n) = 5
Total number of assignments per semester (nupper) = 150
Proportion of assignments with errors (p) = 0.24
First, we calculate the proportion of assignments with errors for each semester:
Semester 1: p1 = (150 * 0.24) / 150
= 0.24
Semester 2: p2 = (150 * 0.24) / 150
= 0.24
Semester 3: p3 = (150 * 0.24) / 150
= 0.24
Semester 4: p4 = (150 * 0.24) / 150
= 0.24
Semester 5: p5 = (150 * 0.24) / 150
= 0.24
Next, we calculate the overall proportion of assignments with errors:
p = (p1 + p2 + p3 + p4 + p5) / n
= (0.24 + 0.24 + 0.24 + 0.24 + 0.24) / 5
= 1.2 / 5
= 0.24
Now we can compute the estimate of the standard deviation (Sp):
S = √((n - 1) * (1 - p) / n)
= √((5 - 1) * (1 - 0.24) / 150)
= √(4 * 0.76 / 150)
= √(0.304 / 150)
≈ √0.0020267
≈ 0.044996
Finally, we can compute the upper control limit (UC) and lower control limit (LCL) for the p chart using the formula:
UC = p + (3 * Sp)
LCL = p - (3 * Sp)
UC = 0.24 + (3 * 0.044996)
= 0.24 + 0.134988
≈ 0.374988
LCL = 0.24 - (3 * 0.044996)
= 0.24 - 0.134988
≈ 0.105012
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perform the indicated calculation. you may use a calculator. remember to round your answers according to the rules for significant figures. 138.2 km x 3.5 km
The result of Multiplying 138.2 km by 3.5 km is 483.7 km².
To perform the indicated calculation, we need to multiply 138.2 km by 3.5 km.138.2 km x 3.5 km = 483.7 km²
The result of multiplying 138.2 km by 3.5 km is 483.7 km².
When dealing with significant figures, we should consider the least precise measurement involved in the calculation, which in this case is 3.5 km (with two significant figures). Therefore, we should round the answer to the same number of significant figures, resulting in 480 km².
So, rounding according to the rules for significant figures, the result of the calculation 138.2 km x 3.5 km is approximately 480 km².
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Write as an algebraic expression the product of x and 9
A- x/9
B- x+9
C- 9x
D- x-9
Answer:
it would be C 9x because a product is the answer from a multiplication equation (:
Manvita deposits Rs. 5000 in her bank account after two days. She withdraws Rs.
3748 from it. If the amount deposited is a positive integer. How will you represent
the amount withdrawn and also find the balance amount in the account?
If the amount deposited is a positive integer , so the amount withdrawn is represented by -3748 and the balance amount in the Manvita's account is Rs 1252 .
In the question ,
it is given that
Money deposited by Manvita = Rs 5000 .
Money withdrawn by Manvita = Rs 3748 .
Since , amount deposited is a positive integer ,
So, the amount withdrawn will be a negative integer
Balance in Manvita's account = Money deposited + Money Withdrawn
Substituting the values , we get
Balance in Manvita's account = 5000 + (-3748)
= 5000 - 3748
= 1252
Therefore , if the amount deposited is a positive integer , so the amount withdrawn is represented by -3748 and the balance amount in the Manvita's account is Rs 1252 .
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Which of the following is the solution of the quadratic equation xଶ 3x − 10 0?
The solutions of the quadratic equation x^2 + 3x - 10 = 0 are x = 4 and x = -1.
The solution of the quadratic equation x^2 + 3x - 10 = 0 can be found by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where (a, b, and c) are 1, 3, and -10
So, the solutions of the equation x^2 + 3x - 10 = 0 are:
x = (-3 ± √(3^2 - 4(1)(-10)) ) / 2(1)
x = (-3 ± √(9 + 40)) / 2
x = (-3 ± √49) / 2
x = (-3 ± 7) / 2
x = (4, -1)
Complete question:
Which of the following is the solution of the quadratic equation x^2 - 3x − 10 = 0?
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Sonia and Angela work at the same store. Each week, Sonia works 5 more hours
than Angela. Sonia earns $10.00 per hour and Angela earns $8.00 per hour.
a) Write a simplified expression to represent the total number of hours Sonia and
Angela work in one week.
The length of one kind of fish is normally distributed. The average length is 2.5 inches, with a standard deviation of 0.4 inches. What is the probability that the average length of 100 randomly selected fishes is less than 2.4 inches
There is only a 0.62% chance that the average length will be less than 2.4 inches. Therefore, we can conclude that it is unlikely for the average length of 100 randomly selected fish to be less than 2.4 inches.
Use the central limit theorem, which states that the distribution of sample means will be approximately normal regardless of the distribution of the population, as long as the sample size is large enough.
In this case, we are given that the length of one kind of fish is normally distributed, with a mean of 2.5 inches and a standard deviation of 0.4 inches. We want to find the probability that the average length of 100 randomly selected fish is less than 2.4 inches.
To apply the central limit theorem, we need to calculate the mean and standard deviation of the sampling distribution of the sample mean. The mean of the sampling distribution will be equal to the population mean, which is 2.5 inches. The standard deviation of the sampling distribution can be calculated using the formula:
standard deviation = population standard deviation / square root of sample size
In this case, the population standard deviation is 0.4 inches, and the sample size is 100, so:
standard deviation = 0.4 / sqrt(100) = 0.04 inches
Now that we have the mean and standard deviation of the sampling distribution, we can use the z-score formula to find the probability of obtaining a sample mean of less than 2.4 inches:
z = (sample mean - population mean) / standard deviation
z = (2.4 - 2.5) / 0.04 = -2.5
Using a standard normal distribution table, we can find that the probability of obtaining a z-score of -2.5 or less is approximately 0.0062. This means that the probability of obtaining a sample mean of less than 2.4 inches is approximately 0.0062.
In other words, if we were to randomly select 100 fish from this population and calculate the average length, there is only a 0.62% chance that the average length would be less than 2.4 inches. Therefore, we can conclude that it is unlikely for the average length of 100 randomly selected fish to be less than 2.4 inches.
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Round 42.3952 to the nearest thousandth
Answer:
42.395
Step-by-step explanation:
to calculate the center line of a control chart you compute the ________ of the mean for every period.
The centre line of a control chart is calculated by computing the average (mean) of the data for every period.
In control chart analysis, the centre line represents the central tendency or average value of the process being monitored. It is typically obtained by calculating the mean of the data points collected over a specific period. The purpose of the centre line is to provide a reference point against which the process performance can be compared. Any data points falling within acceptable limits around the centre line indicate that the process is stable and under control.
The calculation of the centre line involves summing up the values of the data points and dividing it by the number of data points. This average is then plotted on the control chart as the centre line. By monitoring subsequent data points and their distance from the centre line, deviations and trends in the process can be identified. Deviations beyond the control limits may indicate special causes of variation that require investigation and corrective action. Therefore, the centre line is a critical element in control chart analysis for understanding the baseline performance of a process and detecting any shifts or changes over time.
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today, the number of children served under ideia represent approximately what percentage of all children in school? a. 8 b. 13 c. 20 a. 8
Today, the number of children served under IDEA (Individuals with Disabilities Education Act) represents approximately 13% of all children in school.
1. IDEA is a law that ensures educational services for children with disabilities.
2. The number of children served under IDEA includes those who receive special education and related services.
3. According to the National Center for Education Statistics, about 13% of all public school students receive special education services under IDEA.
4. This percentage represents the proportion of children with disabilities in school, as IDEA aims to provide them equal access to education.
So, the correct answer is b. 13.
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PLEASE ANSWER QUICKLY!!The diameter, D, of a sphere is 10.4 mm. Calculate the sphere's volume, V.
Use the value 3.14 for me, and round your answer to the nearest tenth. (Do not round any intermediate computations.
Answer:
About 588.7 mm^3
Step-by-step explanation:
The formula for the volume of a sphere is (4/3)*pi (or in this case 3.14)*r^3, where r is the radius.
We need the radius. We are given the diameter, 10.4.
The radius is half the diameter, so 10.4/2=5.2.
Use r=5.2 and put it into the formula:
(4/3)*3.14*5.2^3≈588.7
Answer:
1360
Step-by-step explanation:
\(4 \times 3.14 \times {10.4}^{2} \\ = 1358.4896\)
3x +2a+5x+4a
simplified
Answer:
a) 8x + 6a
b) 5p + 7q
Step-by-step explanation:
3x + 2a + 5x + 4a
Combine alike terms.3x + 5x + 2a + 4a = 8x + 6a
7p - 2p + 6q + q = 5p + 7q
Answer:
8x+6a
5p+7q
Step-by-step explanation:
1)
3x+2a+5x+4a
rearrange
3x+5x+2a+4a
simplify
8x+6a
2)
7p+6q-2p+q
rearrange
7p-2p+6q+q
simplify
5p+7q
Hope this helps! :)
Name the gigure from by joining the co-orfinatr (3,5),(2,5),(-3,2) and (2,2)
Yes, that is correct. The four points (3,5), (2,5), (-3,2), and (2,2) form a four-sided polygon or a quadrilateral. A quadrilateral is any four-sided polygon, and it can have different shapes and properties depending on the angles and sides of its vertices
The set of four points (3,5), (2,5), (-3,2), and (2,2) form a closed shape with four straight sides, known as a polygon. Specifically, this polygon has four sides and is therefore known as a quadrilateral.
Quadrilaterals can have different shapes and properties depending on the angles and sides of their vertices. In this case, the quadrilateral formed by these four points is a trapezoid.
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
The parallel sides of this trapezoid are formed by the line segments connecting (3,5) and (2,5), and (-3,2) and (2,2), while the non-parallel sides are formed by the line segments connecting (3,5) and (-3,2), and (-3,2) and (2,2).
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Question
The figure formed by joining the coordinates (3,5), (2,5), (-3,2), and (2,2) is a quadrilateral.
BONUS QUESTION: Is it true or false that each system of linear equations
has either one solution, no solutions OR an infinite number of solutions?
Answer:
true because I know hdhdnndnd
Step-by-step explanation:
ehbendndbdbdbbch
Answer:
true
Step-by-step explanation:
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Alex reads x pages in 4 hours. How many pages does he read
in 1 hour? ANSWER ME PLSS
x:4h
Find the unit rate of this equation.
\( \frac{x}{4} = h\)
Multiply both equations by 10, and simplify the results.
\( \frac{10x}{4} = 10h\)
\(2.5x = 10h\)
\(0.25x = h\)