To determine whether a transformation is one-to-one or onto, one must analyze its behavior and properties, such as passing the horizontal line test for one-to-one or checking if the range equals the codomain for onto.
In mathematical terms, a transformation refers to a function that maps elements from one set, called the domain, to another set, called the range. A transformation is said to be one-to-one if no two distinct elements in the domain are mapped to the same element in the range. This means that each element in the range is associated with a unique element in the domain.
On the other hand, a transformation is onto if every element in the range is mapped to by at least one element in the domain. In other words, for each element in the range, there exists at least one element in the domain that maps to it.
To determine whether a transformation is one-to-one or onto, one can analyze its properties and behavior. For example, a transformation is one-to-one if and only if it passes the horizontal line test. This means that no two points in the domain map to the same point on a horizontal line. To determine if a transformation is onto, one can check if the range of the transformation equals the codomain.
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The given question is incomplete, the complete question is:
How to determine the transformation is one to one and/or onto?
of the following people, who would be included in the survey conducted by the bureau of labor statistics?
The people who are included in the survey conducted by Bureau of Labor Statistics are (a) certain unpaid workers, (b) part-time workers and (c) workers on vacation, the correct option is (d).
The Bureau of Labor Statistics (BLS) is a unit of the US Department of Labor that is responsible for collecting, analyzing, and publishing data on labor market activity, working conditions, and price changes in the economy.
The Bureau of Labor Statistics (BLS) considers individuals to be employed if they meet any of the given criteria:
(i) Worked at least one hour as paid employees
(ii) Worked at least 15 hours as unpaid workers in a family-owned enterprise
(iii) Were temporarily absent from their regular jobs due to illness, vacation, strike, etc.
⇒ This means that certain unpaid workers, such as family members working in a family-owned business, would be considered employed by the BLS.
⇒ Part-time workers, who work less than 35 hours per week but are paid for their work, are also included in the employed category.
⇒ The Workers on vacation are considered employed by the BLS because they are temporarily absent from their job.
Therefore, all the options are correct , which is Option(d).
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The given question is incomplete, the complete question is
Who of the following are included in the Bureau of Labor Statistics "employed" category?
(a) certain unpaid workers
(b) part-time workers
(c) workers on vacation
(d) All of the above are correct.
Select all the expressions that are equivalent to (12 + x)10.5.
It’s multiple choice and these are the answers
10.5(12x)
(10.5 + 12 + x)
10.5(12 + x)
126x
126 + 10.5x
22.5 + x
What is the slope of the line passing through the points (-1, -7) and (-9, -2)?
Answer:
m = -5/8
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-1, -7) (-9, -2)
We see the y increase by 5 and the x decrease by 8, so the slope is
m = -5/8
Letsha wants to produce 80 pages information books for school project. She can have this done at local printing company at R0.35 per page.
Answer:
if u want total price then,
=Rs.35×80=Rs.2800
generally, cold fronts move fast er than warm fronts generally, cold fronts have steeper slopes generally, precipitation cover s a much broader area with a cold front especially in winter, cumuliform clouds are more often associated with cold fronts
Cold fronts generally move faster than warm fronts because cold air is denser and thus, moves more quickly. Precipitation with a cold front typically covers a broader area, especially during the winter.
On the other hand, warm fronts move more slowly as they are characterized by the gradual lifting of warm air over colder air. Cold fronts also typically have steeper slopes than warm fronts. This is because the leading edge of a cold front is more abrupt.
With a steep rise in the cold air mass. In contrast, the leading edge of a warm front has a gentler slope as the warm air gradually rises over the colder air.
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Question 6
One gallon of water weighs 8.34 lb. How much weight is added to a fire truck when its tank is filled
with 750 gal of water?
Question 7
1
Answer
6255 pounds
8.34×750=6255lbs
type the correct words in the blanks. two radicals are said to be radicals if they have the same and the radicand.
Two radicals are said to be radicals if they have the same indices and the radicand.
In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:
3√(pq) → pq is the radicand
√(a+b) → a + b is the radicand
4√15 → 15 is the radicand
A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.
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Complete question:
Type the correct words in the blanks:
Two radicals are said to be radicals if they have the same and the radicand.
1. A living room measures 4.75 m by 5.2 m. a. What is the area of the living room? 24.7m b. The area of the game room is one and a half times that of the living room. Fi the living room and the game room.
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
What is area?Area is the measure of the two-dimensional space occupied by a figure or an object. It is usually expressed in square units such as cm2, m2, or in2. It is used to measure the size of a figure or object, and can also be used to calculate the amount of material required for a project.
The area of a living room measuring 4.75 m by 5.2 m can be calculated using the formula A = l × w, where A is the area, l is the length and w is the width. In this case, A = 4.75 m × 5.2 m = 24.7 m².
To calculate the area of the game room, we must multiply the area of the living room by 1.5. Therefore, the area of the game room is 1.5 × 24.7 m² = 37.05 m².
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
The area of a room can be used to determine how much furniture can fit in the room or how much floor space is available for activities. Knowing the area of a room is also important for calculating the cost of painting, wallpapering, carpeting, and other flooring materials.
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1 On a map of scale 1:100 000, the distance between Tower Bridge
and Hammersmith Bridge is 12.3 cm.
What is the actual distance in km?
To calculate the actual distance in km, we need to use the scale factor of 1:100 000. This means that 1 cm on the map is equivalent to 100 000 cm in real life.
Therefore, 12.3 cm on the map is equivalent to 12.3 x 100 000 cm in real life.
Now, 1 km is equivalent to 100 000 cm.
Therefore, 12.3 x 100 000 cm is equivalent to 1.23 km.
Hence, the actual distance in km is 1.23 km.
1. (Non-Isomorphic Trees) (a) Think of a by-hand method to give a list of all non-isomorphic trees on exactly (b) Use your results from (a) to give a list of all non-isomorphic trees on exactly six Be sure to explain in detail the method you came up with to acquire your five vertices. Display your results. vertices. Show you're results. lists in (a) and (b).
Method to list all non-isomorphic trees on n vertices is to add edges to a single vertex tree. Using A, B, C, D, E, we list 5 non-isomorphic trees on 6 vertices.
A by-hand method to give a list of all non-isomorphic trees on exactly n vertices is to start with a tree on n vertices and then generate all possible trees by adding edges between vertices that are not already connected.
For example, to find all non-isomorphic trees on 4 vertices, we can start with a single vertex and then add edges to form a tree with 2 vertices, then add edges to form a tree with 3 vertices, and finally add edges to form a tree with 4 vertices. We can then check each tree for isomorphism by comparing their adjacency matrices.
Using the method from (a), we can find all non-isomorphic trees on exactly six vertices by starting with a single vertex and adding edges until we have a tree on six vertices.
To ensure that we generate all possible trees, we can use the following five vertices: A, B, C, D, E. We can then generate all trees by adding edges between vertices that are not already connected, making sure to avoid creating cycles. After generating all trees, we can check for isomorphism by comparing their adjacency matrices.
The resulting list of non-isomorphic trees on six vertices, in alphabetical order, is shown. The tree 1 and tree 2 are the same. Also, trees 3, 4, and 5 are not isomorphic to each other or to trees 1 and 2.
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PLEASE HURRY!!
Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle? Please show your work.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%
What is Conditional probability?
Conditional probability is the probability of an event occurring given that another event has occurred or is known to have occurred. It is denoted by P(A|B), which reads as "the probability of A given B."
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
The total number of Plastic #2 bottles is 8 (correctly placed) + 5 (incorrectly placed) = 13.
The total number of Plastic #4 bottles is 5 (correctly placed) + 2 (incorrectly placed) = 7.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is given by:
(number of Plastic #4 bottles correctly placed) / (total number of bottles)
So the probability is:
5/20 = 1/4 = 0.25
Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%.
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What is the missing value in the equation shown below?
4/10+ ?/100= 7/10
A 1
B 3
C 10
D 30
Answer: D 30
Step-by-step explanation:
4/10 + 30/100
2/5 + 3/10
7/10
NB: LEFT-HAND SIDE IS EQUAL TO THE RIGHT-HAND SIDE
THE FIRST ANSWER GETS BRAINLIEST AND FIVE STARS!
Parallelogram ABCD is a rhombus with measure EBC = 36. What is the measure of DAE?
picture below
Consider two agents, Alice and Bob, who have utility functions 0.3x3 + 0.72A if xa > XB (0.314 +0.72B if XB > XA UA(2A, 2B) = UB(XA, XB) 4X A – 32B if XB > IA -0.32A + 1.3xB if x A > XB If Alice is the dictator in the dictator game with a $10 endowment, then she will offer Bob (A) $0; (B) $5; (C) $2; (D) $10.
The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.
Compare Alice's utility from each option and choose the one that maximizes her utility.
Let us consider each option,
If Alice offers Bob $0, her utility will be,
If XA > XB then
UA (XA , XB )= 0.3x3 + 0.72A
UA(10,0)
= 0.3(10)³ + 0.72(10)
= 307.2
If Alice offers Bob $5, Bob's utility will be,
UB(10,5)
= 0.314 + 0.72(5)
= 0.314 + 3.6
= 3.914
And Alice's utility will be,
UA(5,10)
= -0.32(5) + 1.3(10)
= 11.4
Total utility for both Alice and Bob will be,
UA(5,10) + UB(10,5)
= 11.4 + 3.914
= 15.314
If Alice offers Bob $2, Bob's utility will be,
UB(10,2)
= 0.314 + 0.72(2)
= 1.754
And Alice's utility will be,
UA(2,10)
= -0.32(2) + 1.3(10)
= 12.4
So the total utility for both Alice and Bob will be,
UA(2,10) + UB(10,2)
= 12.4 + 1.754
= 14.154
If Alice offers Bob $10, Bob's utility will be,
UB(10,10)
= 0.314 + 0.72(10)
= 7.514
And Alice's utility will be,
UA(10,10)
= 0.3(10)³ + 0.72(10)
= 307.2
So the total utility for both Alice and Bob will be,
UA(10,10) + UB(10,10)
= 307.2 + 7.514
= 314.714
Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.
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I will mark you brainiest!
Given parallelogram STUV, what is the length of TV?
TW = y2
WV = 2y − 1
A) 2
B) 8
C) 4
The required value of TV is 2 units.
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel edges in Euclidean geometry. A parallelogram's confronting or opposing sides are of equal length, and its opposing angles are of equal size.
According to question:
We have given that;
TW = y²
WV = 2y − 1
We know that in parallelogram
TW = WV
y² = 2y − 1
y² - 2y + 1 = 0
y² - y - y + 1 =0
y(y - 1)-1(y - 1) = 0
(y - 1)(y - 1) = 0
(y - 1)² = 0
y - 1 = 0
y = 1
So;
TV = TW + WV
TV = y² + 2y − 1
TV = 1² + 2(1) - 1
TV = 1 + 2 - 1
TV = 2 units
Thus, required value of TV is 2 units.
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Solve each proportion round to the nearest tenth
Answer:
[tex]v = \frac{7}{2}[/tex]
Step-by-step explanation:
Joann had a vegetable stand where she sold tomatoes. She sold 15 tomatoes the first day. The second day she sold half of what was left. On the third day she sold 12 and sold half of what was left on the fourth day. On the fifth day there were 4 tomatoes left to be sold. How many tomatoes did she have to begin with?
On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.
What is prοbability?Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.
Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.
On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).
On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.
On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.
On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.
Finally, οn the first day, she sοld 15 tοmatοes.
Therefοre, Jοann had 71 tοmatοes tο begin with.
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How do you find the slope of (-4, 8) and (4, 2)
To find the slope of a line that passes through two points, you can use the slope formula. The slope formula is:
Slope = (y2 - y1) / (x2 - x1)
Using the points given in your question, the slope formula to find the slope of the line is:
Slope = (2 - 8) / (4 - (-4))
Using the order of operations, the calculation of the slope formula is as follows:
Slope = -6 / 8
Therefore, the slope of the line passing through (-4, 8) and (4, 2) is -3/4.
There are two types of trees to plant in the yard type A trees are 36 inches tall and grows 8 inches per year type B are 18 inches tall but grow 10 inches per year when will the trees be the same height
As a result, both varieties of trees will be the same height after 9 years. We can change both equations to a = 9 to verify this: Height of the type A tree is 36 + 8(9) or 36 + 72 inches, whereas the height of the type B tree is 18 + 10(9) or 18 + 90 inches.
What function do height and distance serve in everyday life?Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It utilised to compute height of towers, structures, mountains, etc., and distance between any two objects such celestial bodies others. ,sys,s tos.as to .... and.
Let's use "a" to denote the number of years after planting the trees.
A type A tree will reach the following height after "a" years:
Height of type A tree = 36 + 8a
After "a" years, the height of a type B tree will be:
Height of type B tree = 18 + 10a
We must set the two types of trees' heights equal to one another and solve for "a" to determine when they will reach the same height:
36 + 8a = 18 + 10a
Subtracting 8a from both sides, we get:
36 = 18 + 2a
Subtracting 18 from both sides, we get:
18 = 2a
Dividing both sides by 2, we get:
a = 9
Therefore, after 9 years, both types of trees will be the same height.
To check this, we can substitute a = 9 into both equations:
Height of type A tree = 36 + 8(9) = 36 + 72 = 108 inches
Height of type B tree = 18 + 10(9) = 18 + 90 = 108 inches
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Question:
You have two types of trees to plant in your yard: type A trees are 36 inches tall and grow 8 inches per year, while type B trees are 18 inches tall and grow 10 inches per year. At what point in time will the trees be the same height? How tall will the trees be at that time?
-51+((-5+(-4)) all calculation
Answer:
the answer to that is -31
can you help me to solve these two questions?
Case 1: The constant c of the piecewise function is equal to 1 / 7.
Case 2: The value of the constant b of the piecewise function with the greater absolute value is equal to 20.
How to determine the value of a variable such that a piecewise function is continuous
A piecewise function is function formed by two or more functions relative to intervals. A piecewise function is continuous if they do not have any jump on graph. For two functions, we must solve the following equation for the case of a piecewise function formed by two functions:
g(a) = h(a)
Case 1 - g(y) = c · y + 3, h(y) = c · y² - 3, a = 7
c · a + 3 = c · a² - 3
c · (a² - a) = 6
c = 6 / (a² - a)
c = 6 / (7² - 7)
c = 6 / 42
c = 1 / 7
The value of the constant c is equal to 1 / 7.
Case 2 - g(x) = b - 2 · x, h(x) = - 150 / (x - b), a = 5
b - 2 · a = - 150 / (a - b)
(b - 2 · a) · (a - b) = - 150
a · b - b² - 2 · a² + 2 · a · b = - 150
- b² + 3 · a · b - 2 · a² = - 150
b² - 3 · a · b + 2 · a² - 150 = 0
b² - 15 · b - 100 = 0
(b - 20) · (b + 5) = 0
b₁ = 20 or b₂ = - 5
The solution with the greater absolute value is b = 20.
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Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
What is probability?Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.
Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.
Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:
P(accurate order) = 1246 / 1300 = 0.958 for McDonald's
P(accurate order) = 1020 / 1100 = 0.927 Taco Bell
P(accurate order) = 708 / 800 = 0.885 for Burger King
P(accurate order) = 940 / 1000 = 0.94 for Wendy's
P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929
As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
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can anyone help me with this question triangles?
The missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Problem 2 (Vector and Matrix Refresh) Seven data points are arranged as columns of a data matrix X given as follows: 2 1 0 0 -1 0 -2 X = 2 0 1 0 0 -1 -2 a) Draw all data points on a 2D plane by hand. Properly label the two axes. Clearly provide important tick values to facilitate a precise graphical description of the data. b) Consider each point as a vector. Calculate the angle in between (2 27 and the five other points (excluding [0 07), respectively, using the inner/dot product formula that involves the angle. Note that the angle between two vectors can be negative. c) Calculate the matrix outer product for X, namely, R = XXT. Show the intermediate steps of calculating each element of the 2-by-2 matrix R. d) The matrix outer product can also be calculated via R =
a) The drawing of all data points on a 2D plane is illustrated below.
b) The angle in between the five other points is 27
c) The matrix outer product for X is R = XXT.
d) The matrix outer product can also be calculated via R is (2,27)
The data matrix X is a 2-by-7 matrix, where each column represents a data point with two components. We can visualize each data point as a vector in a two-dimensional plane, where the horizontal axis represents the first component and the vertical axis represents the second component.
To draw all data points on a 2D plane, we can plot each column of X as a vector starting from the origin. Proper labeling of the two axes and providing important tick values will facilitate a precise graphical description of the data.
Next, we can use the inner product formula to calculate the angle between the first data point (2, 27) and the other five data points, respectively.
The inner product, also known as the dot product, is a way to measure the similarity between two vectors by multiplying their corresponding components and summing the products.
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any point on the parabola can be labeled (x,y), as shown. a parabola goes through (negative 3, 3)
The correct standard form of the equation of the parabola is:
[tex]y = -x^2 - 1[/tex].
To find the standard form of the equation of the parabola that passes through the given points (-3, 3) and (1, -1), we can use the general form of the equation of a parabola:
[tex]y = ax^2 + bx + c[/tex] ___________(1)
Substituting the coordinates of the two given points into this equation, we get a system of two equations in three unknowns (a, b, and c):
[tex]3 = 9a - 3b + c[/tex]
[tex]-1 = a + b + c[/tex]
To solve for a, b, and c, we can eliminate one of the variables using subtraction or addition. Subtracting the second equation from the first, we get:
[tex]4 = 8a - 4b[/tex]
Simplifying this equation, we get:
[tex]2 = 4a - 2b[/tex]
Dividing both sides by 2, we get:
[tex]1 = 2a - b[/tex]___________(2)
Now we can substitute this expression for b into one of the earlier equations to eliminate b. Using the first equation, we get:
[tex]3 = 9a - 3(2a - 1) + c[/tex]
Simplifying this equation, we get:
[tex]3 = 6a + c + 3[/tex]
Subtracting 3 from both sides, we get:
[tex]0 = 6a + c[/tex]
Solving for c, we get:
c = -6a __________(3)
Substituting this expression for c into the second equation, we get:
[tex]-1 = a + (2a - 1) - 6a[/tex]
Simplifying this equation, we get:
[tex]-1 = -3a - 1[/tex]
Adding 1 to both sides, we get:
[tex]-3a =0[/tex]
Solving for a, we get:
[tex]a = 0[/tex]
Substituting this value of a into the equation(3) for c, we get:
c = 0
Substituting a = 0 into the equation(2) for b that we found earlier, we get:
[tex]1 = 0 - b[/tex]
Solving for b, we get:
[tex]b = -1[/tex]
Putting the values of a, b and c in (1), we get
[tex]y = -x^2 - 1[/tex]
Therefore, the equation of the parabola that passes through the given points (-3, 3) and (1, -1) is:
[tex]y = -x^2 - 1[/tex]
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Complete question:
A parabola goes through (-3, 3) & (1, -1). A point is below the parabola at (-3, 2). A line above the parabola goes through (-3, 4) & (0, 4). A point on the parabola is labeled (x, y).
What is the correct standard form of the equation of the parabola?
The figure is in the image attached below
What is the smallest possible average of five distinct positive even integers?
A. 10
B. 8
C. 6
D. 4
E. 0
Answer:
The smallest possible average of five distinct positive even integers will occur if we choose the five smallest even integers. Since we want the integers to be distinct, we start with 2 and add the next four even integers:
2, 4, 6, 8, 10
The average of these five integers is:
(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
Therefore, the smallest possible average of five distinct positive even integers is 6, which is answer choice C.
Find any critical numbers of the function.
Answer:
(1, 2) and (-1, -2). or. (±1, ±2)
Step-by-step explanation:
[tex]{ \sf{f(x) = \frac{4x}{ {x}^{2} + 1 } }} \\ [/tex]
- Simply, a critical number or critical point is gotten by differentiating the function.
From Quotient rule;
[tex]{ \sf{ {f}^{l}(x) = \frac{4( {x}^{2} + 1) - (2x)(4x)}{ {( {x}^{2} + 1)}^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{ {4x}^{2} + 4 - {8x}^{2} }{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{4(1 - {x}^{2}) }{ {( {x}^{2 } + 1) }^{2} } }}[/tex]
Then equate this derivative to zero;
[tex]{ \sf{0 = \frac{4(1 - {x}^{2} )}{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{4(1 - {x}^{2} ) = 0}} \\ \\ { \sf{4 - {4x}^{2} = 0}} \\ \\ { \sf{4 {x}^{2} = 4}} \\ \\ { \sf{x = \sqrt{1} }} \\ \\ { \sf{ \underline{ \: x = \pm 1 \: }}}[/tex]
Substitute for x in f(x)
For x = 1
[tex]{ \sf{f(1) = \frac{4(1)}{ {(1)}^{2} + 1} = \frac{4}{2} = 2 }} \\ [/tex]
For x = -1
[tex]{ \sf{f( - 1) = \frac{4( - 1)}{ {( - 1)}^{2} + 1 } = \frac{ - 4}{2} = - 2 }} \\ [/tex]
Therefore points are;
(1, 2) and (-1, -2)
Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. He made a $4,330 partial payment at 2 months and another partial payment of $2,600 at 6 months. How much is due at maturity?
If Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. Andres Michael owes $18806.6 at maturity.
How to find the amount?To calculate how much is due at maturity, we first need to determine how much of the loan remains after the two partial payments.
To do this, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest
P = Principal (original loan amount)
r = Annual interest rate
t = Time (in years)
The interest for the first two months can be calculated as:
I1 = P * r * t1
= 24420 * 0.035 * (2/12)
= 142.45
So after the first two months, the amount owing on the loan is:
P1 = P + I1 - 4330
= 24420 +142.45 - 4330
= 20,232.45
The interest for the next four months can be calculated as:
I2 = P1 * r * t2
= 20,232.45 * 0.035 * (4/12)
= 236.05
So after six months, the amount owing on the loan is:
P2 = P1 + I2 - 2600
= 20,232.45 + 236.05- 2600
= 17868.50
Now we can calculate the interest for the remaining 18 months:
I3 = P2 * r * t3
= 17868.50* 0.035 * (18/12)
= 938.10
So the total amount owing at maturity (after 2 years) is:
Total amount owing = P2 + I3
= 17868.50 + 938.10
= 18806.6
Therefore, Andres Michael owes $18806.6 at maturity.
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I need help with this
Answer:
D.
Step-by-step explanation:
In an effort to figure out why application rates are slipping, your college decides to set up an experiment to determine why students who are interested in the college decide to enroll or not. The college decides to send out a questionnaire to everyone who submitted an application to the college in 2017. What's the population for this study, and what's the sample?
A. The population is all college students everywhere, and the sample is all college students interested in your school.
B. The population is all college students everywhere, and the sample is the individuals who responded to the survey.
C. The population is all students who applied to your college, and the sample is the individuals who responded to the survey.
D. The population is all college students interested in your school, and the sample is everyone who decided to enroll.
The population of interest is the group of students who submitted an application to the college in 2017.
What is sample?A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.
According to question:The correct answer is C.
The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.
Option A is incorrect because the population is not all college students everywhere, only those who applied to the college in question.Option B is incorrect because the sample is not just the individuals who responded to the survey, but rather all students who submitted an application in 2017.Option D is incorrect because the sample is not just everyone who decided to enroll, but rather all students who submitted an application, regardless of whether they enrolled or not.To know more about sample visit:
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