The set of ordered pairs that represents a function from A to B is {(1, -1), (3, 2), (4, 0), (2, 1)}. A function from A to B is a relation that assigns a unique element from B to each element in A.
In order for a set of ordered pairs to represent a function, each element in A must have exactly one corresponding element in B.
Let's analyze each set of ordered pairs:
1. {(1, -1), (3, 2), (2, -2), (4, 0), (2, 1)}: This set is not a function because the element 2 in A is assigned two different elements (-2 and 1) in B. Each element in A should have a unique corresponding element in B.
2. {(1, 2), (4, 0), (2, 1)}: This set is a function because each element in A is assigned a unique element in B.
3. {(1, 1), (2, -2), (3, 0), (4, 2)}: This set is a function because each element in A is assigned a unique element in B.
4. {(1, 0), (2, 0), (3, 0), (4, 0)}: This set is a function because each elementin A is assigned a unique element (0) in B.
Based on the analysis, the set of ordered pairs that represents a function from A to B is {(1, -1), (3, 2), (4, 0), (2, 1)}.
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Consider the initial value problem y" + 16 = 48t, y(0) = 5, y'(0) = 2. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(S). Do not move any terms from one side of the equation to the other (until you get to part (b) below). 48/s^2 help (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = (58^3+2s^2+48)/(s^2(s^2+16)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t).
a. To solve the initial value problem using Laplace transforms, we start by taking the Laplace transform of both sides of the given differential equation. The Laplace transform of y(t) is denoted as Y(s). The Laplace transform of the second derivative y"(t) can be expressed as s²Y(s) - sy(0) - y'(0), where y(0) and y'(0) are the initial conditions. The Laplace transform of 48t is simply 48/s².
Applying the Laplace transform to the given differential equation, we get:
s²Y(s) - sy(0) - y'(0) + 16Y(s) = 48/s²
Substituting the initial conditions y(0) = 5 and y'(0) = 2, we have:
s²Y(s) - s(5) - 2 + 16Y(s) = 48/s²
Simplifying this equation gives the corresponding algebraic equation in terms of Y(s).
b. Now, we solve the equation obtained in part (a) for Y(s). Rearranging the terms, we have:
(s² + 16)Y(s) = 48/s² + s(5) + 2
Combining like terms, we get:
(s² + 16)Y(s) = (48 + 5s² + 2s) / s²
Dividing both sides by (s² + 16), we obtain:
Y(s) = (48 + 5s² + 2s) / (s²(s² + 16))
So, Y(s) is equal to the Laplace transform of y(t).
c. To find y(t), we take the inverse Laplace transform of Y(s) obtained in part (b). We can use partial fraction decomposition and the properties of Laplace transforms to simplify the expression and find the inverse Laplace transform.
Taking the inverse Laplace transform of Y(s), we find:
y(t) = L^(-1){Y(s)} = L^(-1){(48 + 5s² + 2s) / (s²(s² + 16))}
The inverse Laplace transform can be calculated using tables or software, and it yields the solution y(t) to the initial value problem.
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Find the value of x
Answer:
dkeekek
Step-by-step explanation:
kddeejwkwnqnnwwnwwnwnwnwwnw
Answer:
use pythagoras theorem for solving this
value of x is 12 cm
Luba walked 5 miles in 1 1/2 hours. How fast did she walk in miles per hour?
A. 2/15 miles per hour
B. 9/10 miles per hour
C. 2 3/4 miles per hour
D. 3 1/3 miles per hour
Answer:
c or d sorry if I'm wrong
Step-by-step explanation:
I think it's your d because of the shortest answers and they're the only two that makes sense
HELP Me PLEASE I'M BEGGING. I GOT TO SEND IT TONIGHT
Answer:
1. -34
Step-by-step explanation:
Find the area of the shape shown below. Please help :(
Answer:
the area is 42 square units
Step-by-step explanation:
lets break it down
12 x 1 = 12
12 x 5 = 60
60 / 2 = 30
12 + 30 = 42
Find the area of the circle. Round your answer to the nearest hundredth. Use 3.14 or 22/7 for π (pi)
Answer:
3.14
Step-by-step explanation:
1x1xpi
1x3.14=3.14
there are 12 socks in flora drawer 9 are red and 2 are blue and 1 is green she take out one sock without looking at the color. What is the numerical probability of flora picking out a blue sock?
The numerical probability of Flora picking out a blue sock is 1 out of 6, or approximately 0.1667, or 16.67%.
To calculate the numerical probability of Flora picking out a blue sock, we need to consider the total number of socks and the number of blue socks in the drawer.
Given:
Total number of socks = 12
Number of red socks = 9
Number of blue socks = 2
Number of green socks = 1
The probability of Flora picking a blue sock can be calculated as the ratio of the number of blue socks to the total number of socks:
Probability of picking a blue sock = Number of blue socks / Total number of socks
Probability of picking a blue sock = 2 / 12
Simplifying the fraction, we get:
Probability of picking a blue sock = 1 / 6
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The cellphone Luke wants to buy is on sale for 15% off the original price. It was originally priced at $150. What is the amount of the discount?
1. Determine the value of y for y = x -2
x 9 -1 5 -7 3
y ? ? ? ? ?
Please help! (It's called functional relationships by the way) Will mark brainliest (If you send any cutt or tyink links that are scams, I WILL REPORT YOU SO DON'T ANSWER IF U DON'T KNOW!!!!!!!)
Answer: The answer is 3
Step-by-step explanation:
Hope this helps you! Have a good day! :)
Find the value of x.
Answer:
14
Step-by-step explanation:
kswkekddkkekekekeke
jskekekkeenenen
nnwkekekenr
wnwnene
snsn
wm
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Rosie bought a ring in the USA she paid 345 US dollars work out in pounds the amount rosie paid for the ring
Answer:
Step-by-step explanation:
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 35.5 for a sample of size 767 and standard deviation 15.2. Estimate how much the drug will lower a typical patients systolic blood pressure (using a 90% confidence leve). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
_____<µ<______
The tri-linear inequality that estimates how much the drug will lower a typical patient's systolic blood pressure using a 90% confidence level is 34.5 < µ < 36.5.
Given that the sample mean of a blood-pressure drug is 35.5 for a sample size of 767 and standard deviation 15.2, to estimate how much the drug will lower a typical patient's systolic blood pressure, we use the following formula of a confidence interval:
Confidence interval = sample mean ± margin of error,
where the margin of error = z(α/2) * (σ/√n),
σ = 15.2, the standard deviation
n = 767, sample size
α = 0.10, level of significance
z(α/2) = 1.645 (from a standard normal distribution table)
Plugging in the values,
Margin of error = 1.645 * (15.2 / √767)≈ 1.02
Confidence interval = 35.5 ± 1.02≈ 34.5 < µ < 36.5
Therefore, the blood-pressure drug will lower a typical patient's systolic blood pressure within the range of 34.5 and 36.5.
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Duncan has cups of sand. He divides the sand equally into 4 containers. He uses all the sand in 1 container to make pieces of sand art. It takes cups of sand to complete each piece of sand art. How many pieces of sand art does Duncan make? A. 1 2/3 B. 2 C. 4 D. 5 5/9
Answer:
4
Step-by-step explanation:
From the above question:
1/4 cup of sand = 1 sand art
1 cup of sand = x
Cross Multiply
x × 1/4 cup of sand = 1 cup of sand × 1 sand art
x = 1 cup of sand × 1 sand art/1/4 cup of sand
x = 1 ÷ 1/4
x = 1 × 4
x = 4 pieces sand art
Therefore, Duncan can make 4 pieces of sand art.
Twelve identical computers are to be distributed to an elementary, middle, high school and community college. How many ways are there to distribute the 12 computers to the four schools, if we assume that some schools might end up with none, but all 12 must be given out
There are 91 ways to distribute the 12 identical computers among the elementary, middle, high school, and community college, ensuring that all 12 computers are given out.
To find the number of ways to distribute 12 identical computers among four schools (elementary, middle, high school, and community college) while ensuring that all 12 computers are given out, we can use the concept of stars and bars or the balls and urns method.
Let's represent the distribution using stars and bars. We have 12 identical stars (representing the computers) and 3 identical bars (representing the separators between the four schools). The bars divide the stars into four groups, each representing the number of computers given to each school.
We need to determine the number of ways to arrange the 12 stars and 3 bars. This can be calculated using the formula:
Number of ways = (n + k - 1) choose (k - 1) where n is the number of stars (12) and k is the number of bars (3).
Using this formula, the number of ways to distribute the 12 computers among the four schools is:
Number of ways = (12 + 3 - 1) choose (3 - 1)
= 14Choosee 2
= 91
Therefore, there are 91 ways to distribute the 12 identical computers among the elementary, middle, high school, and community colleges, ensuring that all 12 computers are given out.
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The table below represents a linear function.
Х y
-1 5
1 9
3 13
5 17
Which function has a greater slope and a greater y-intercept than the linear functon represented
in the table?
UWA
A. y = 2x + 8.5
B. y = 3x + 7.5
C. y = 5x + 6.5
y = 10x + 5.5
Select all the equations that are true when xis -4.
A)-8 = 2x
B) -12 = x.-3
C) -12 = x+x+x
D = -1
Ex+4 = -8
F = -16
Answer:
A,C and D are the correct options.
What angle of rotation maps p onto P'?
At a certain time of day, the angle of elevation is 40°. To the nearest foot, find the height of a tree whose shadow is 31 feet long.
Answer: Height of tree = 26 ft
Make a triangle ABC with 40 degrees angle. The shadow is the base of the triangle equals 31 feet.
Base = AC = 31
Perpendicular = CB = ?
Hypotenuse = AB
Using trigonometric equation
tan 40 (deg) = CB / AC
CB = Tan 40 x AC
CB = 0.83909 x 31
CB = 26.011
Thus the height of the tree = 26 ft
Why didn't some materials Sink in water and some others didn't?
Answer: Materials sink in water depending on how heavy they are. It is about how heavy something is compared to the same amount (volume) of water. This ratio of an object’s mass to its volume is known as density. Density is what really determines whether something will sink or float.
58, 72, 74, 92, 84, 40, 74, 81, 76, 83 What was the mean score on Mr. Shenton’s final exam?
Answer: 73.4
Step-by-step explanation:
To find the mean, you add up all your data value then divide the sum by the # of values in the set.
58 + 72 + 74 + 92 + 84 + 40 + 74 + 81 + 76 + 83
= 734
There are 10 numbers in the set.
734 ÷ 10 = 73.4
The mean score on Mr. Shenton's final exam is 73.4
Which expression is equivalent to
[tex](3 {u}^{3} {v}^{4}) ^{2} [/tex]
A.
[tex]3 {u}^{5} {v}^{6} [/tex]
B.
[tex]3 {u}^{6} {v}^{8} [/tex]
C.
[tex]9 {u}^{6} {v}^{8} [/tex]
D.
[tex]9 {u}^{5} {v}^{6} [/tex]
Answer:
C
Step-by-step explanation:
When 3 is squared, it becomes 9. That means that both A and B are incorrect.
The powers on u and v are doubled not added to become u^6 and v^8 so that makes C the only possible answer.
Calculate the total surface area of the pyramid. Show your work!
Answer: 22.44
Step-by-step explanation:
Base × Height /2 → (3 × 2.24)/2
3.36 · 4 = 13.44
13.44 + 3²
22.44
HELP ME!!!!!!!!!!!!!!!!!!!!!!
Answer:
H
Step-by-step explanation:
If they are similar that means that they are racially the same so just divide 60 by 84 to find the rate and then multiply the rate by 210 to get your answer
The slope of AB of problem 7 is
Answer:
Slope of line is 0 and intercept is 7 Step-by-step explanation:
the same
2. When graphing a system of equations with no solution, the y-intercept of the lines would be?
Answer:
not telling u, imbecil
Step-by-step explanation:
hahhahahahah
A piece of blue yarn is 8 3/10 yards long. A piece of pink yarn is 4 times as long as the blue yarn. What is the total length of the blue and pink yarn
Answer:
41.5 Yards
Step-by-step explanation:8 3/10 * 4 = 33.2,
33.2+8 3/10 = 41.5
If a car travels at 60 MPH, how many seconds does it go per mile?
Answer:
60 seconds
Step-by-step explanation:
Calculate the relative error of approximation On methods. y(t) = 8e²-8 (t+1) y (1) for all of three
The relative error is found by approximating y(1) relative to the exact value 8e²-16.
The relative error of approximation for the given method can be calculated using the formula:
Relative error = |(approximated value - exact value) / exact value| * 100%
In this case, we have the function y(t) = 8e²-8 (t+1) and need to approximate the value of y(1) using three different methods. To calculate the relative error for each method, we substitute t = 1 into the function and compare the approximated value with the exact value.
In the first paragraph,
To calculate the relative error of approximation for the given methods in estimating y(t), we substitute t = 1 into the function y(t) = 8e²-8 (t+1). By comparing the approximated values with the exact value, we can determine the relative error for each method.
In the second paragraph:
Let's evaluate the function at t = 1:
y(1) = 8e²-8 (1+1) = 8e²-8(2) = 8e²-16
Now, let's consider the three methods for approximating y(1) and calculate their respective relative errors:
Method 1: Approximated value = 8e²-8 (1+1) = 8e²-16
Relative error = |(8e²-16 - 8e²-16) / 8e²-16| * 100% = 0%
Method 2: Approximated value = 8e²-8 (1+1) - 8 = 8e²-24
Relative error = |(8e²-24 - 8e²-16) / 8e²-16| * 100% = |8e²-24 - 8e²-16| / |8e²-16| * 100%
Method 3: Approximated value = 8e²-8 (1+1) + 8 = 8e²-8
Relative error = |(8e²-8 - 8e²-16) / 8e²-16| * 100% = |8e²-8 - 8e²-16| / |8e²-16| * 100%
By calculating the relative error using the above formulas, we can determine the accuracy of each method in approximating y(1) relative to the exact value 8e²-16.
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What is the length of AC
A)72
B)8
C)None of these
D)136
E)132
F)96
Suppose a conic section passes through the point (2, - 7). If the conic section has focus ( - 1, -3), directrix 2 = 3, then it is a ellipse parabola hyperbola cannot be determined.
The conic section has focus ( - 1, -3), directrix 2 = 3, then it is a parabola.
How to find if the conic section is a ellipse parabola hyperbola?For a parabola, the focus and directrix play important roles in determining its shape. The distance between a point on the parabola and the focus is equal to the perpendicular distance between that point and the directrix.
Let's calculate the distances and verify if they are equal:
Distance between the point (2, -7) and the focus (-1, -3):
d₁ = √[(2 - (-1))² + (-7 - (-3))²] = √[9 + 16] = √25 = 5
Distance between the point (2, -7) and the directrix 2 = 3:
d₂ = |y - directrix| = |(-7) - 3| = |-10| = 10
Since d₁ ≠ d₂, we can conclude that the conic section cannot be an ellipse.
In an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant. However, in this case, the distances are not equal.
Similarly, for a hyperbola, the difference between the distances from any point on the hyperbola to the two foci is constant. Since the distances are not equal in this case, we can also rule out a hyperbola.
Therefore, based on the given information, the conic section is a parabola.
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