Answer:
Table B
Step-by-step explanation:
we are given 4 tables and we want to find the table that represents a function.
well recall, The conditions of a relation to be a function
A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the following two properties:
For every element x in A, there is an element y in B such that (x, y) ∈ F. For all elements x in A and y and z in B if (x, y) ∈ F and (x,z) ∈ F, then y = z.more precisely,if F is a function from a set A to a set B, then given any element x in A, property (1) from the function definition guarantees that there is at least one element
of B that is related to x by F and property (2) guarantees that there is at most one such
element.
at first rewrite the input and output of Table A,B ,C and D as ordered pairs
\(A = \{(5,3),(5,2),(4,1) \}\)
\(B= \{(1,2),(3,2),(5,3) \}\)
\(C = \{(0,0),(1,2),(1,3) \}\)
\(D= \{(4,2),(4,3),(4,4) \}\)
Table A,C & D:Table A, C and D does not represent a function because it does not satisfy property (2). The ordered pairs (5, 3) and (5, 2) in A, (1,2) and (1,3) in C and (4,2),(4,3),(4,4) have the same first element but different second elements.
Table B:Table B represents a function: Each inputs {1, 3, 5} is related to some outputs {2, 2, 3} and no inputs {1, 3, 5} is related to more than one outputs {2, 2, 5}.
hence, it's our answer
Input is noted as domain.
Output is noted as range .
How to spot out relation and function?
Functions have unique range for each domains .Where as relation haven't .Now
#Table A
5 is repeated in domain .
So it's relation#Table B
2 is repeated is range but it's unique for each domain
It's a function#Table C
1 is repeated in domain
So it's a relation#Table D
There is only 4 in domain
Clearly it's a relationTable B is correct
Evan's mom drops him off at Entertainment Zone for 3 hours and buys him 11 tickets. Evan
can spend his tickets driving go karts or playing mini golf which each cost 1 ticket. Driving the go
kart track takes 10 minutes and a game of mini golf lasts 45 minutes. How many of each activity
can Evan participate in before his mom comes back to pick him up?
Evan can play 2 games of mini golf and 9 games of kart track.
Given that Evan's mom gave him 11 tickets and left in game zone for 3 hours,
He can spend 1 ticket on one game, and he spend 10 minutes in kart track and a game of mini golf lasts 45 minutes.
We need to find how many games he played of both the games,
So, let he played x games of kart track and y games of mini golf,
So,
x + y = 11
x = 11 - y.............(i)
10x + 45y = 180...........(ii) [ ∵ 3 hours = 180 minutes]
Use the equation i in ii,
So,
10(11-y) + 45y = 180
110 - 10y + 45y = 180
35y = 70
y = 2
Put y = 2 in equation 1,
x = 11-2
x = 9
Hence he played 2 games of mini golf and 9 games of kart track.
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How does the quantity of shares you own impact your dollar gains and losses?
how does the length of time you hold the shares impact your rate of return?
How does the quantity of shares you own impact your rate of return?
The quantity of shares you own can impact your dollar gains and losses, but not your rate of return. The length of time you hold the shares can have a significant impact on your rate of return, with longer holding periods generally leading to higher returns.
Investing in stocks can be a great way to earn money, but it's important to understand how your investments can impact your gains and losses. Two key factors that can impact your returns are the quantity of shares you own and the length of time you hold the shares. In this article, we'll explore how these factors can affect your rate of return.
Impact of Quantity of Shares:The quantity of shares you own can have a direct impact on your dollar gains and losses. When the stock price goes up, the value of your shares also increases. Similarly, when the stock price goes down, the value of your shares also decreases. If you own more shares, the dollar amount of your gains and losses will be greater.
But, how does the quantity of shares impact your rate of return? Rate of return is the percentage change in the value of your investment over a certain period of time. It takes into account the gains and losses as well as the length of time you held the investment.
Impact of Length of Time:The length of time you hold the shares can have a significant impact on your rate of return. Generally, the longer you hold the shares, the higher your rate of return will be. This is because the stock market tends to go up over time, and the longer you hold the shares, the more time you have to benefit from this growth.
Impact of Quantity and Time on Rate of Return:So, how does the quantity of shares you own impact your rate of return? As we mentioned earlier, the rate of return is only impacted by the percentage change in the stock price, not the quantity of shares. However, owning more shares can provide you with a higher dollar amount of gains, which can lead to a higher rate of return.
Additionally, the longer you hold the shares, the higher your rate of return will be. This means that if you own more shares and hold them for a longer period of time, you can potentially earn a higher rate of return.
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The perimeter of the rectangle is 28 units.
What is the value of w?
5 units
7 units
14 units
15 units
Answer:
5 units
Step-by-step explanation:
P= 2 (l + w) = 2 x (9 + 5) = 28
how do you know that 4/11 is a reapeating decimal
Answer:
Because 4 divided by 11 does not have an exact answer, it just keeps going on.
Step-by-step explanation:
Which graph shows a solution to the following system?
{ x -y ≥ -1
{ x+y ≤ 0
Answer:
That's the answer attached, whatever answer matches up with it is correct.
Step-by-step explanation:
HELP ASAP!! Click the picture to make it bigger
:)
thanks
Answer:
the answer is C.
Step-by-step explanation:
Carry a book bag: Female is 57
Use polar coordinates to find the volume of the given solid. Inside the sphere x^2 + y^2 + z^2 = 36 and outside the cylinder x^2 + y^2 = 1.
The required volume of the given solid is (√16 - r²) -(-√16 - r²).
What is volume?The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.
Volume and the notion of length are connected.
Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.
The cubic meter (m3), a derived unit, is the SI unit of volume.
So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.
We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.
The solid's volume is (√16 - r²) -(-√16 - r²).
Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).
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Correct question:
Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
can someone help me with this?
Answer:
8
Step-by-step explanation:
This problem uses the pythagorean theorem. 15 squared plus 8 squared equals 17 squared.
Consider the following point and line. Point Line (4,1) 9x - 3y = 4
(a) Write the equation for the line through the given point and parallel to the given line. (b) Write the equation for the line through the given point and perpendicular to the given line. Submit Assignment Save Assign
The equation for the line through the given point (4, 1) and parallel to the given line 9x - 3y = 4 is y = -x + 5
a) The given line is 9x - 3y = 4. It can be rewritten as y = 3x/(-3) + 4/(-3) or y = -3x/3 - 4/3 or y = -x + 4/3. This line has a slope of -1. Any line parallel to this line will have the same slope, which is -1.
Therefore, the equation for the line through the given point (4, 1) and parallel to the given line 9x - 3y = 4 will have the form y = -x + b. To find b, we use the fact that the line passes through (4, 1):1 = -4 + b ⇒ b = 5.
Therefore, the equation for the line through the given point (4, 1) and parallel to the given line 9x - 3y = 4 is y = -x + 5.
b) The given line is 9x - 3y = 4. It can be rewritten as y = 3x/(-3) + 4/(-3) or y = -3x/3 - 4/3 or y = -x + 4/3. This line has a slope of -1. Any line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line. The negative reciprocal of -1 is 1. Therefore, the equation for the line through the given point (4, 1) and perpendicular to the given line 9x - 3y = 4 will have the form y = x + b. To find b, we use the fact that the line passes through (4, 1):1 = 4 + b ⇒ b = -3.
Therefore, the equation for the line through the given point (4, 1) and perpendicular to the given line 9x - 3y = 4 is y = x - 3.
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9x = -36
i wasn't given instructions for this question and i got all the other ones right but im having issues with this one for some reason.
any answers will be greatly appreciated.
Answer:
The answer is -4
so x= negative 4
Analyze the responses of Franklin D. Roosevelt's administration to the problems of the Great Depression. How effective were the responses? How did they change the role of the federal government?
Franklin D. Roosevelt's administration responded to the problems of the Great Depression through a series of measures known as the New Deal.
The New Deal included programs such as the Civilian Conservation Corps, the Works Progress Administration, and the Social Security Act, which aimed to create jobs, stimulate economic growth, and provide social welfare benefits to those in need.
Overall, the New Deal was effective in providing immediate relief to millions of Americans suffering from the economic downturn. It also helped to stabilize the banking system and regulate the stock market through the creation of institutions such as the Federal Deposit Insurance Corporation and the Securities and Exchange Commission.
However, the New Deal did not completely end the Great Depression and it took the country's entry into World War II to fully revive the economy.
The New Deal also changed the role of the federal government by greatly expanding its authority and responsibilities. The government became more involved in providing social welfare benefits and regulating the economy. This shift in the government's role has continued to shape American politics and policy to this day.
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A local SPCA has three different colour kittens up for adoption. 31% of the kittens are black, 44% of the kittens are white, and the rest are yellow. Of the kittens who are black, 59% are male, of the kittens who are white, 34% are male & of the kittens who are yellow, 60% are male.
a) Draw a Tree Diagram for this situation
b) What percentage of the kittens are female?
c) Given that the kitten is male, what is the probability that it is white?
A local SPCA has three different colour kittens up for adoption. 31% of the kittens are black, 44% of the kittens are white, and the rest are yellow. Of the kittens who are black, 59% are male, of the kittens who are white, 34% are male & of the kittens who are yellow, 60% are male.
Tree Diagram:
________ Kittens ________
/ \
_______ Black _______ _______ White _______
/ \ / \
Male (59%) Female Male (34%) Female
/ \ / \
(31% of 59%) (69% of 59%) (44% of 34%)
/ \ \
Black Black Black
(18.29% of total) (42.71% of total) (14.96% of total)
b) To calculate the percentage of kittens that are female, we need to sum up the percentages of female kittens in each color category:
Female kittens: 69% of black kittens + 56% of white kittens + 66% of yellow kittens
Female kittens = (69% * 31%) + (56% * 44%) + (66% * 25%)
Female kittens ≈ 21.39% + 24.64% + 16.5%
Female kittens ≈ 62.53%
Therefore, approximately 62.53% of the kittens are female.
c) To find the probability that a kitten is white, given that it is male, we need to consider the proportion of male kittens that are white compared to the total number of male kittens:
Probability of being white given male = (34% * 44%) / (59% * 31% + 34% * 44% + 60% * 25%)
Probability of being white given male ≈ (0.34 * 0.44) / (0.59 * 0.31 + 0.34 * 0.44 + 0.60 * 0.25)
Probability of being white given male ≈ 0.1496 / (0.1829 + 0.1496 + 0.15)
Probability of being white given male ≈ 0.1496 / 0.4829
Probability of being white given male ≈ 0.3096
Therefore, the probability that a kitten is white, given that it is male, is approximately 30.96%.
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HELP ITS TIMED
Which is true given the linear equation below?
3x + 4y = 4
A. It has a positive slope.
B. The x-intercept is 3.
C. The y-intercept is 1.
D. It passes through the point (-1,2)
Answer:
D. it passes through the point (-12)
A rectangle initially has dimensions 6cm×8cm. All sides begin increasing in length at a rate of 5cm/s. At what rate is the area of the rectangle increasing after 24s? Let A,b, and h be the area, base, and height of a rectangle, respectively. Write an equation relating A,b, and h.
1. The area of the rectangle is increasing at a rate of 1926 \(cm^2/s\) after 24 seconds.
2The equation relating the area, base, and height of a rectangle is:
A = b * h
where A is the area of the rectangle, b is the base (width), and h is the height (length).
To find the rate at which the area of the rectangle is increasing, we first need to find the equation for the area of the rectangle as a function of time.
Let x(t) be the length of one of the sides of the rectangle at time t.
Since all sides of the rectangle are increasing at the same rate of 5 cm/s, we have:
x(t) = 6 + 5t (for the width)
and
y(t) = 8 + 5t (for the length)
The area of the rectangle is given by:
A(t) = x(t) * y(t)
Substituting the expressions for x(t) and y(t), we get:
A(t) = (6 + 5t) * (8 + 5t) = 40t^2 + 86t + 48
To find the rate at which the area is increasing at t = 24 s, we take the derivative of A(t) with respect to t:
dA/dt = 80t + 86
At t = 24 s, we have:
dA/dt = 80(24) + 86 = 1926 cm^2/s
Therefore, the area of the rectangle is increasing at a rate of 1926 cm^2/s after 24 seconds.
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Please help!!! Urgent for homework
Answer: 7 and 8
Step-by-step explanation:
Square root and squared cancel out
Answer:
a=7
b=32
Step-by-step explanation:
The first one (a) is 7 because if you square a square root, you get the number inside the root. Also, technically a square root has an exponent of (1/2) so when you have a power-to-a-power (power rule of exponents) you multiply the exponents. So (\(7^{1/2}\))^2 is 7.
For (b) you have to take it in two parts. Square the square root and you get 2. Square the 4 in front, you get 16. Multiply those two numbers (16 and 2) together and you get 32.
Edit: Check on your calculator, you get the same answers I got! :)
the grades on the last science exam had a mean of 89%. assume the population of grades on science exams is known to be distributed normally, with a standard deviation of 14%. approximately what percent of students earn a score between 75% and 89%? (6 points) 38.5% 15.7% 50% 34.1%
Approximately 34.1% of students earn a score between 75% and 89%.
the correct answer is 34.1%.
Approximately what percent of students earn a score between 75% and 89%?
To solve this problem, we need to calculate the area under the normal distribution curve between 75% and 89%.
First, we need to convert the scores into z-scores using the formula:
z = (x - mean) / standard deviation
For 75%, the z-score is (75 - 89) / 14 = -1
For 89%, the z-score is (89 - 89) / 14 = 0
Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-scores.
The area between -1 and 0 is approximately 0.3413, which is equivalent to 34.1%.
Therefore, approximately 34.1% of students earn a score between 75% and 89%.
So the correct answer is 34.1%.
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What is equivalent to - 1/4y - 2 1/4y + 1/2 (4 - 2y)
Answer:
-6y+2
Step-by-step explanation:
Trust
Solve for x. (1 point)
-3x + 2b > 8
O -2b +8
x <
-3
Ox<
2b-8
-3
O
O
-2b-8
X>
3
28
-2b +8
-3
-3x + 2b > 8
---Subtract 2b from both sides
-3x > -2b + 8
---Divide both sides by -3. Remember that when multiplying or dividing by a negative in inequalities, we flip the inequality sign.
x < (-2b + 8) / -3
(Option 1)
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I got this wrong on a test and I can't figure out why
Two observers at point A and B, 150 km apart, sight a balloon between them at angles of elevation 42° and 76° respectively.
How far is the observer A from the balloon? Round answer to the nearest tenth
Please show step by step
Two balloons A and B apart 150km with given angle of elevation represents observer A is at a distance of 122.5 km approximately from balloon.
Number of observers = 2
Distance between two observers A and B = 150km
Angles of elevation are 42° and 76°.
Let us consider 'h' be the height of the balloon
Let the distance from observer A to the balloon x.
Use trigonometry to find the value of x.
From observer A, the angle of elevation to the balloon is 42°.
This means that the height of the balloon above observer A is ,
h = x × tan(42°)
From observer B,
The angle of elevation to the balloon is 76°.
This means that the height of the balloon above observer B is ,
h = (150 - x) × tan(76°)
Since both expressions give the same value for h, set them equal to each other,
⇒ x × tan(42°) = (150 - x) × tan(76°)
Simplifying this equation, we get,
⇒ x × (0.9004 ) = (150 - x) × 4.0107
⇒ 0.9004x = 601.605 - 4.0107x
⇒ 4.9111x = 601.605
⇒ x ≈ 122.5 km
Therefore, the distance from observer A to the balloon as per given angle of elevation is approximately 98.3 km.
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A company has 440,000 shares outstanding that sell for $98.48 per share. The company plans a 6-for-1 stock split. Assuming no market imperfections or tax effects, what will the stock price be after the split?
After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.
A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.
To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:
$98.48 / 6 = $16.41
Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.
It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.
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Determine the function f satisfying the given conditions.
f ' (x) = sin(x) cos(x)
f (2p) = 10
f (x) = A sinB(x) cosC(x) + D, where A > 0.
A= ?
B=?
C=?
D=?
The function f satisfying the given conditions is
f(x) = (1/2) sin(x) cos(0) + 10 = (1/2) sin(x) + 10
How to determine the function f?
To determine the function f satisfying the given conditions f ' (x) = sin(x) cos(x), f (2p) = 10, and f (x) = A sinB(x) cosC(x) + D, where A > 0, we need to follow these steps:
1. Integrate f ' (x) to find f (x).
∫(sin(x) cos(x)) dx = (1/2) * sin^2(x) + C
2. Apply the given condition f (2p) = 10.
(1/2) * sin^2(2p) + C = 10
Since sin(2p) = 0, the equation becomes:
C = 10
3. Now, we have f(x) = (1/2) * sin^2(x) + 10. We need to express this function in the form of A sinB(x) cosC(x) + D.
We can rewrite the given function as:
f(x) = A sin(2x/2) cos(0) + D
Comparing this with f(x) = (1/2) * sin^2(x) + 10, we get:
A = 1/2
B = 2/2 = 1
C = 0
D = 10
So, the function f satisfying the given conditions is:
f(x) = (1/2) sin(x) cos(0) + 10 = (1/2) sin(x) + 10
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given the following find dy/dx in each of the following (a)y=3x
The value of dy/dx is 3.
In maths, there is a branch to study and that is calculus. The differentiation is one such part of the calculus that can be defined as the technique of locating the derivatives of a particular function. It is denoted by dy/dx, and the rate of change of variable x with respect to variable y is designated as dy/dx. Differentiation follows a certain list of formulas for its execution.
Finding the value of dy/dx.
∴y=3x [given above]
⇒y=3x
Now, differentiating both sides, we have
dy/dx= 3 x^0 [∵ for y, differentiation of the rate of change of variable x with respect to y]
[formula used in right-hand side is d/dx=nx^(n-1), n is an integer]
⇒dy/dx=3 x^0
⇒dy/dx=3 [∵x^0=1(law of indices)]
⇒dy/dx=3
Thus, the value of dy/dx is 6(x-1).
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gement System Grade 0.00 out of 10.00 (0%) Plainfield Electronics is a New Jersey-based company that manufactures industrial control panels. The equation gives the firm's production function Q=-L³+15
The equation Q = -L³ + 15 represents the production function of Plainfield Electronics, where Q is the quantity of industrial control panels produced and L is the level of labor input.
In this production function, the term -L³ indicates that there is diminishing returns to labor. As the level of labor input increases, the additional output produced decreases at an increasing rate. The term 15 represents the level of output that would be produced with zero labor input, indicating that there is some fixed component of output. To maximize production, the firm would need to determine the optimal level of labor input that maximizes the quantity of industrial control panels produced. This can be done by taking the derivative of the production function with respect to labor (dQ/dL) and setting it equal to zero to find the critical points. dQ/dL = -3L². Setting -3L² = 0, we find that L = 0.
Therefore, the critical point occurs at L = 0, which means that the firm would need to employ no labor to maximize production according to this production function. However, this result seems unlikely and may not be practically feasible. It's important to note that this analysis is based solely on the provided production function equation and assumes that there are no other factors or constraints affecting the production process. In practice, other factors such as capital, technology, and input availability would also play a significant role in determining the optimal level of production.
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Use technology to find points and then graph the function y=√x - 4 following the instructions below.
Plot at least four points with integer coordinates that fit on the axes below. Click a point to delete it.
Answer:
See below
Step-by-step explanation:
Which sets of vectors are orthogonal? Check all that apply.
a = 〈–1, 0〉 and b = 〈1, 0〉
c = 〈1, 0〉 and d = 〈0, –1〉
e = 〈–4, –6〉 and f = 〈12, 8〉
g = 〈4, –6〉 and h = 〈12, 8〉
v = 〈10, –5〉 and w = 〈–10, –20〉
x = 〈10, –5〉 and y = 〈–10, –2〉
Answer:
B, D, and E
Step-by-step explanation:
Edge 2020
The sets of vectors are orthogonal and will be c-d,g-h, and v-w.
What exactly is a vector?A vector is a quantity with a magnitude, and direction that follows the law of vector addition.
Fo the orthogonal vector their dot product is equal to zero.
The dot product for the set are as follows;
a.b)〈–1, 0〉〈1, 0〉 = -1
c.d)〈1, 0〉 〈0, –1〉=0
e.f) 〈–4, –6〉 〈12, 8〉=-96
g.h)〈4, –6〉〈12, 8〉=0
v.w) 〈10, –5〉〈–10, –20〉=0
x.y)〈10, –5〉 〈–10, –2〉=-90
The sets of vectors are orthogonal are;
c-d ,g-h,v-w
Sets B, D, and E of vectors are orthogonal.
Hence the sets of vectors are orthogonal and will be c-d,g-h, and v-w.
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Solve the proportion! Please show work on how to do it
Answer:
You will use \(\frac{1}{4}\) cup of sugar.
Step-by-step explanation:
Given that:
A recipe calls for 3/4 cup of sugar and 1/2 cup of brown sugar.
Ratio of sugar to brown sugar = 3/4 : 1/2
Amount of brown sugar used = 1/6
Amount of sugar used = x
Ratio of sugar to brown sugar = x : 1/6
As the relationship is proportional;
\(\frac{3}{4}:\frac{1}{2}::x:\frac{1}{6}\)
Product of mean = Product of extreme
\(\frac{1}{2}x=\frac{3}{4}*\frac{1}{6}\\\\\frac{1}{2}x = \frac{1}{8}\\\\x = \frac{1}{8}*2\\\\x=\frac{1}{4}\)
Hence,
You will use \(\frac{1}{4}\) cup of sugar.
Question 2
help pls its hard i forgt how to do it
Answer: 52
Step-by-step explanation:
a^2+b^2=c^2
x is the hypotenuse (c). You can find the hypotenuse by finding the opposite of the right angle
48^2+20^2=2304+400=2704
√2704=52
x=52
HELP PLEASE!!
Solve for b.
B/2 - 8 = 3
B = [ ? ]
sum and product of two irrational numbers is irrational give examples. please answer me fast i am waiting
Answer:
π+π/∞+∞/√∞+∛∞
Step-by-step explanation: