The percentages are given as follows:
20,240 skateboards or fewer: 15.87%.20,420 skateboards or fewer: 97.72%.20,480 skateboards or more: 0.13%.How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 20300, \sigma = 60[/tex]
The proportion of 20,240 of fewer is the p-value of Z when X = 20240, hence:
Z = (20240 - 20300)/60
Z = -1
Z = -1 has a p-value of 0.1587.
The proportion of 20,420 of fewer is the p-value of Z when X = 20420, hence:
Z = (20420 - 20300)/60
Z = 2
Z = 2 has a p-value of 0.9772.
The proportion of 20480 or more is one subtracted by the p-value of Z when X = 20480, hence:
Z = (20480 - 20300)/60
Z = 3
Z = 3 has a p-value of 0.9987.
1 - 0.9987 = 0.0013.
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in exercises 29 to 40, find the area of the given triangle. Round each area to the same number of significant digits given for each of the given sides.
The area of a triangle with base of 4cm and height of 9cm will be 18cm².
How to calculate the areaThe area of a triangle can be found using the following formula:
Area = (base * height) / 2
where base is the length of any one side of the triangle and height is the perpendicular distance from that side to the opposite vertex.
You can use this formula to find the area of a triangle given its base and height or given its three sides using Heron's formula.
The area of a triangle with base of 4cm and height of 9cm will be:
= 1/2 × base × height
= 1/2 × 4 × 9
= 18cm²
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Complete question
Find the area of a triangle with a base of 4cm and height of 9cm.
suppose you look out the window of a skyscraper and see someone throw a tomato downward from above your window. your window is at a height of 450 feet above the ground. the tomato passes your window after 2 seconds and hits the ground 5 seconds after it was thrown. neglect air resistance, and give units in your answers.
Height from window = 450ft the tomato passes your window after 2 seconds and hits the ground 5 seconds after it was thrown. neglect air resistance
Time taken to get from window to ground = 2 secs
V0, initial speed of tomato from drop point = 0 ft/s
Acceleration due to gravity = 32.2 ft/s
When the tomato gets to the observer at the window, its initial speed is no longer 0ft/s but an unknown value, u.
We can apply one of the equations of linear motion to then find this initial velocity at the window using the other parameters given i.e.
s = ut + [tex]\frac{1}{2}[/tex] [tex]at^{2}[/tex]
= 450ft
t = 2 secs
a = g = 32.2ft/sec
=> 450 = (u*2) + (1/2 * 32.2 * 2^2)
450 = 2u + 64.4
2u = 450 – 64.4
2u = 385.6
=> u = 192.8ft/s
Now that we know this initial velocity, we can use another equation of linear motion to find the height distance between the drop point and the window for the resistance
[tex]v^{2}[/tex] - [tex]u^{2}[/tex] = 2gs
where s = distance between drop point and window
v = 192.8ft/s
u = 0ft/s;
=> [tex]192.8^{2}[/tex] - 0^2 = 2*32.2*s
37171.84 = 64.4s
=> s = 37171.84/64.4
s = 577.20ft
Hence, distance from drop point to the ground, H, will be the addition of s and the height from the window to the ground:
=>H = 577.20 + 450
H = 1027.2ft
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Find j.
j
9 ft
10 ft
5 ft
O
N
M
L
K
Write your answer as a whole number or a decimal. Do not round.
j =
feet
The value of j in the triangle is 8.66 feet
How to determine the value of jThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The right triangle
The value of j can be calculated using the following
tan(60) = j/5
So, we have the following representation
j = 5 * tan(60)
Evaluate
j = 5√3
This gives
j = 8.66
Hence, the value is 8.66 feet
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please help me with this question
Answer:
A flood is mainly caused by rapid water flowing through a certain area and drought is when there is little to no water.
I hope this helped:)
Kimberly scored a total of 35.08 points
in four events for her gymnastic
competition. If she scored the same
number of points in each event, how
many points did she score in each? Write
an equation to show your work.
Answer:
4p = 35.088.77 points in each eventStep-by-step explanation:
You want an equation and its solution for the scenario in which Kimberly scored 35.08 points in four gymnastic events, the same number in each event. You want to know her score in each event.
EquationIf p represents the number of points that Kimberly scored in each event, her point total is ...
4p = 35.08
SolutionDividing by the coefficient of p gives the solution:
p = 35.08/4 = 8.77
Kimberly scored 8.77 points in each event.
Details
A student divided the rational expressions as follows:
Describe the errors made
I need help
Answer:
see below
Step-by-step explanation:
when you divide a fraction, it's better to use multiplication of its reversed fraction = flip the y fraction upside down & multiply the first one
then you'll cancel the y & x and result in
y/x
In the expansion of (2+3x)^n, the coefficients of x^3 and x^4 are in the ratio of 8:15. FIn the expansion of (2+3x)^n, the coefficients of x^3 and x^4 are in the ratio of 8:15. Find the value of n.ind the value of n.
The value of n is 8.
What is Binomial Theorem?Binomial theorem is the method of expanding an expression consisting of two terms raised to any power.
Using the expansion of Binomial theorem, we can write,
(2 + 3x)ⁿ = ⁿC₀ (2)ⁿ (3x)⁰ + ⁿC₁ (2)ⁿ⁻¹ (3x)¹ + ⁿC₂ (2)ⁿ⁻² (3x)² + ⁿC₃ (2)ⁿ⁻³ (3x)³ + ⁿC₄ (2)ⁿ⁻⁴ (3x)⁴ + .............
Coefficient of x³ is ⁿC₃ (2)ⁿ⁻³ (3)³ and the coefficient of x⁴ is ⁿC₄ (2)ⁿ⁻⁴ (3)⁴.
Ratio of these coefficients is 8 : 15.
[ⁿC₃ (2)ⁿ⁻³ (3)³] / [ⁿC₄ (2)ⁿ⁻⁴ (3)⁴] = 8 / 15
Simplifying,
(4 × 2) / [(n - 3) 3] = 8/15
8 / 3n - 9 = 8 /15
Equating, we have,
3n - 9 = 15
3n = 24
n = 8
Hence the value of n is 8.
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use the following building blocks to assemble a proof that if m and n are integers, and mn is even, then m is even or n is even. not all blocks belong in the proof. before you start, you might want to write out such a proof on paper, and carefully consider whether a direct proof, a proof by contraposition or a proof by contradiction is the most appropriate.
Proof: If mn is even, then either m = 2k/n or n = 2k/m for an integer k, meaning either m or n must be even.
The following is a direct proof:
Assume m and n are integers.If mn is even, then n must be even or m must be even.We will show that if mn is even, then either m is even or n is even.Suppose mn is even.Then, there exists an integer k such that mn = 2k.This can be written as m = 2k/n or n = 2k/m.Since k is an integer, it follows that either m or n must be even.Thus, if mn is even, then either m is even or n is even.This completes the proof.The proof shows that if m and n are integers and mn is even, then either m must be even or n must be even. The proof starts by assuming that m and n are integers and that mn is even. It then proceeds to show that one of the factors, either m or n, must also be even.
The proof uses the definition of an even number, which is a number that is divisible by 2, to conclude that if mn is even, then there must be an integer k such that mn = 2k. From this equation, the proof derives the expressions m = 2k/n or n = 2k/m. Since k is an integer, it follows that either m or n must be even, since the result of dividing an integer by another integer is also an integer.
The proof concludes by stating that if mn is even, then either m must be even or n must be even, based on the logical reasoning provided in the proof.
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Solve the following equation algebraically: 3 x squared = 48
Answer:
x=16/squared
Step-by-step explanation:
divide each term in 3xsquared = 48 by 3squared and simplify.
Answer:
If squaring a number means multiplying it by itself, according to this rule, you multiply 3 by "x" and then multiply "x" by itself to get 48. In this scenario, you divide 3 by blank squared to get blank. In this case, you set up this problem with division, so we are dividing 3 times blank squared by 3. Whatever the blank value is, we know this equation equals 48, so you must create a mirrored equation of 48 divided by 3. Now that you've divided 48 by 3, that is 16, right? So 16 will be the equivalent of blank squared, or "x" squared. For blank squared, since we are dealing with algebra, the next step is to use square roots using what we know. We know that 16 is composed of 4 squared, right? So turn 4 squared into a radical of √4². This radical is equal to 4, because "radical" = "number" as long as that number is more than or equal to 0. So, in conclusion, x is 4.
Hope this helps!
will give brainliest need help, confused.
The inverse matrix is (b) [tex]\left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]
How to determine the inverse matrixFrom the question, we have the following parameters that can be used in our computation:
x + 2y + 5z = 14
3x + 5y + 9z = -1
x + y - 2z = 6
When represented as a matrix, we have
[tex]\left[\begin{array}{ccc}1&2&5\\3&5&9\\1&1&-2\end{array}\right][/tex]
The determinant is calculated as
D = 1 * (5 * -2 - 9 * 1) - 2 * (3 * -2 - 9 * 1) + 5 * (3 * 1 - 5 * 1)
Evaluate
D = 1
This means that the matrix is invertible
Next, we calculate the cofactor elements
5 * -2 - 9 * 1 = -19
3 * -2 - 9 * 1 = -15
3 * 1 - 5 * 1 = -2
2 * -2 - 5 * 1 = -9
1 * -2 - 5 * 1 = -7
1 * 1 - 2 * 1 = -1
2 * 9 - 5 * 5 = -7
1 * 9 - 5 * 3 = -6
1 * 5 - 2 * 3 = -1
So, we have
[tex]\left[\begin{array}{ccc}-19&-15&-2\\-9&-7&-1\\-7&-6&-1\end{array}\right][/tex]
Next, create the adjoint or the adjugated matrix
[tex]A = \left[\begin{array}{ccc}-19&15&-2\\9&-7&1\\-7&6&-1\end{array}\right][/tex]
Transpose the adjoint
[tex]A^T = \left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]
Divide by the determinant
[tex]A^T = \left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]
Hence, the inverse is (b) [tex]\left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]
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given a 14 , use the law of sines to solve the triangle (if possible) for the value of c. if two solutions exist, find both. round answer to two decimal places.
The values of the solution for the triangle is A = 55°, a = 10. 1, b = 12. 3, B = 86.01°, c = 7.68 and C = 39°
The sine rule is used to show the relationship between the sides and angles of a triangle. It is given as:
a/sinA = b/sinB = c/sinC
Where A, B, and C are the angles and a,b, and c are the opposite sides to the angles.
1)
A = 55°, a = 10. 1, b = 12. 3
10 / sin(55) = 12.3 / sinB
B = 86.01°
A + B + C = 180° (angle in triangle)
55 + C + 86 = 180
C = 39
10 / sin(55) = c / sin(39)
c = 7.68
The values of the solution for the triangle is A = 55°, a = 10. 1, b = 12. 3, B = 86.01°, c = 7.68 and C = 39°
The complete question is-
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank. ) A = 55°, a = 10. 1, b = 12. 3
Case 1
B
C
c
Case 2
B
C
c
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4 difference than the sum of g and 5
The expression for 4 difference than the sum of g and 5 is 4- (g+ 5).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
4 difference than the sum of g and 5
writing the mathematical expression for the above we get
sum of g and 5
= g+ 5
and, 4 difference than the sum of g and 5
= 4- (g+ 5)
= 4- g- 5
= -g- 1
Hence, the expression is (-g-1).
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Find the sum of (-0.3s - 2) + (5-3.4s) + (5r + 2)
The sum of the expression is 5r - 3.7s + 5.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator)
Given the expression,
(-0.3s - 2) + (5 - 3.4s) + (5r + 2)
-0.3s -2 + 5 - 3.4s + 5r + 2
arranging the variables and constants,
(-0.3s - 3.4s) + 5r + (- 2 + 5 + 2)
apply operations,
-3.7s + 5r + 5
5r - 3.7s + 5
Hence the simplified expression is 5r - 3.7s + 5.
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Which si NOT a disadvantage of buying??
Financial risks
Limited mobility
Higher living costs
Possible economic gain
Possible economic gain is not a disadvantage of buying.
What Is Financial Risk?Financial risk refers to the likelihood of losing money on a business or investment decision. Risks associated with finances can result in capital losses for individuals and businesses. There are several financial risks, such as credit, liquidity, and operational risks.
Given here: Disadvantages of buying
The different types of risks are categorized in several different ways. Risks are classified into some categories, including market risk, credit risk, operational risk, strategic risk, liquidity risk, and event risk.
Clearly Financial risk, limited mobility, Higher living costs are all disadvantages of buying but possible economic gains is not a disadvantage.
Thus Possible economic gain is the odd one out of the options.
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a = (2n)² n how is this neither arithmaric or geometric
The sequence is neither arithmetic nor geometric because it does not have a common difference or a common ratio
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
a = (2n)² n
For a sequence to be an arithmetic sequence, the sequence must have a common difference
For a sequence to be a geometric sequence, the sequence must have a common ratio
Using the above as a guide, we have the following:
The sequence is neither because it does not have a common difference or a common ratio
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a national opinion poll found that 44% of all american adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. the result was based on a small sample.
A national opinion poll found that 44% of all American adults agree that parents should be given vouchers good for education at any public or private school of their choice.
The result is based on a small sample, and it is important to note that opinions can change quickly as more people become aware of the issue and as more information becomes available.
While the poll results are encouraging for proponents of school choice and educational vouchers, it is important to recognize that opinions can be subject to change. As the debate over school choice continues, more individuals may become aware of the issue and may form different opinions as they learn more about the issue.
Furthermore, more information and details about the issue may become available which could lead to individuals changing their opinions based on the new information. Additionally, opinions may also differ based on geographical location, as different areas may have different opinions on the issue. All of these factors should be taken into account when assessing the current opinion on educational vouchers.
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true/false. in practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but large.
it is true in practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but large.
The continuous category of random variables refers to those whose spaces are unions of intervals or intervals rather than a countable number of points. When the sample size is too big to treat each individual event discretely or when a variable does not occur in discrete intervals, continuous distributions are employed as probability models (please see Discrete Distributions for more details on discrete distributions). The main distinction between continuous and discrete distributions is that, while discrete distributions deal with smaller sample populations and cannot be treated as if their random variable values are on a continuum (from negative infinity to positive infinity), continuous distributions deal with a sample size so large that its random variable values are treated on a continuum (from negative infinity to positive infinity).
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please help!!!!!!!!!!
Answer:
Step-by-step explanation:
25 because when you take 2x times 3x +1
Machines at a bottling plant are set to fill bottles to 12 ounces. The quality control officer at the plant periodically tests the machines to be sure that the bottles are filled to an appropriate amount. The null hypothesis of the test is that the mean is at least 12 ounces. The alternative hypothesis is that the mean is less than 12 ounces. Which of the following describes a Type I error that could result from the test? A. The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces. B. The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is less than 12 ounces. C. The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is 12 ounces. The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces. E. The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is 11 ounces.
A Type I error that could result from the test is "The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces."
A Type I error occurs when the null hypothesis is rejected when it is actually true. In this case, the null hypothesis is that the mean is at least 12 ounces, and the alternative hypothesis is that the mean is less than 12 ounces. If the test provides convincing evidence that the mean is less than 12 ounces when the actual mean is at least 12 ounces, this is a Type I error. The answer is: The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces. If the test provides convincing evidence that the mean is less than 12 ounces when the actual mean is at least 12 ounces, this is a Type I error.
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1+1+1+1+1+1+1+1+1 x 2 x 2
Answer:
12
Step-by-step explanation:
1+1+1+1+1+1+1+1+1 x 2 x 2= 12
Answer:
12
Step-by-step explanation:
pls tell me if wrong have a good day/night<3
Solve each of the linear systems in Problems 13 through 20 to determine whether the critical point (0, 0) is stable, asymptotically stable, or unstable. Use a computer system or graphing calculator to construct a phase portrait and direction field for the given system. Thereby ascertain the stability or instability of each critical point, and identify it visually as a node, a saddle point, a center, or a spiral point. dx/dt = -2x, dy/dt = -2y
Solve linear system: dx/dt = -2x, dy/dt = -2y. Analyze stability using phase portrait & direction field, identify type of critical point.
The given linear system is:
dx/dt = -2x
dy/dt = -2y
To find the stability or instability of the critical point (0, 0), we need to analyze the behavior of the solutions near that point. To do so, we can linearize the system around (0,0), which means we approximate the system with its tangent line at (0,0). The linearized system is given by:
dx/dt = -2x
dy/dt = -2y
The eigen values of the linearized system are -2 and -2. Since both eigenvalues are negative, the critical point (0,0) is a stable node, which means that any solution that starts close to (0,0) will converge to (0,0) as t approaches infinity. The phase portrait of the system is a set of arrows pointing towards the origin, indicating that all solutions converge to (0,0) as time goes on.
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A rectangle has a width of 7.9 ft and a perimeter of 27.2 ft.
Enter the length of the rectangle, in decimal form, in the box.
Th length of the rectangle, in decimal form, would be = 14.05ft
What is a perimeter?A perimeter of defined as the total area of all the edges that surrounds an object such as a rectangle.
The perimeter of a rectangle = P = 2(length+width)
The perimeter = 27.2ft
The width = 7.9 ft
Therefore the length = ?
That is,
27.2 = 2( L + 7.9)
27.2 = 2L + 55.3
2L = 55.3-27.2
2L = 28.1
L = 28.1/2
L = 14.05ft
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joshua worked five hours,katleho worked for three hours and pevashnee worked for four hours if they paid R288 divide money between the three
The hourly rate that they are paid is $24 per hour
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
Let us assume that all of them are paid the same amount of money per hour.
Let x represent the amount of money each is paid per hour.
Joshua worked five hours, Katleho worked for three hours and Pevashnee worked for four hours if they paid R288. Hence:
5x + 3x + 4x = 288
12x = 288
x = 24
Their hourly rate is $24 per hour
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Not sure how to do this help
The mid-point of segment AB is X. Ray XY is perpendicular to segment AB. Point L is on ray XY. By congruence of triangle, statements (C) point L is equidistant from point A and B.
What is the congruence of triangle?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.
Given that, The mid-point of segment AB is X. Ray XY is perpendicular to segment AB. Point L is on ray XY.
Draw the line segment AL and BL.
In Δ AXL and Δ BXL
AX is equal to BX
XL is common in both Δ
∠AXL is equal to ∠BXL because both are right angle.
So, Δ AXL ≅ Δ BXL
So AL = BL
So we say that point L is equidistant from point A and B.
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Converting the raw data into a '_____' distribution is often a first step in making the data more manageable and easier to assess.
Converting the raw data into a 'frequency' distribution is often a first step in making the data more manageable and easier to assess.
A scatterplot is the most helpful graph for demonstrating the connection between two quantitative variables.
Data are listed in rising or decreasing numerical order in a raw data listing. The stem-and-leaf presentation gives more depth than the frequency distribution since it may explain individual data values as well as indicate how many are in each group, or stem.
Bins should have the same width and be mutually exclusive and exhaustive.
A scattergram is a graphical representation of the linkages or correlations that exist between two numerical variables (or covariables), which are shown as points (or dots) for each pair of scores. A scattergraph depicts the intensity and direction of the covariables' connection.
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this question is for the southern hemisphere. for each direction (n, s, e, or w), pick the drawing that best describes how the stars appear to move above that point on the horizon.
The drawings that best describe the way the stars appear to move in the Southern Hemisphere on the horizon is:
North - DSouth - A East - E West - F What direction do the stars appear to move ?When in the Southern Hemisphere, the drawings would appear to move upwards when moving North. The stars would also appear to move down when moving to the South as shown in A.
The East would show drawings moving towards the right as shown in E and the West would show stars appearing to move to the left which is shown with Drawing F.
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Using the two data points from Exercises 1 and 2, write a linear equation that shows how the wind power would need to grow to make this goal. Use years for the independent variable and terawatt hours for the dependent variable. Let year 0 represent year 2012.
The linear equation that shows how the wind power would need to grow to make this goal is y = 25x + 15
How to determine the equation of the wind powerFrom the question, we have the following parameters that can be used in our computation:
(x, y) = (0, 15) and (5, 90)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 15
Using the other point, we have
5m + 15 = 90
So, we have
5m = 75
Divide by 5
m = 25
So, the equation becomes
y = 25x + 15
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Complete question
Using the two data points from Exercises 1 and 2, write a linear equation that shows how the wind power would need to grow to make this goal. Use years for the independent variable and terawatt hours for the dependent variable. Let year 0 represent year 2012, (0, 15) and (5, 90)
a sample of size n will be selected from a population with population proportion p . which of the following must be true for the sampling distribution of the sample proportion to be approximately normal?
The sampling distribution of the sample proportion is approximately normal when the sample size (n) is large and the population proportion (p) is close to 0.5.
This can be mathematically expressed as follows:
[tex]n*p > 10 and n*(1-p) > 10[/tex]
To illustrate, let's say we are sampling from a population with a proportion of 0.3. For the sampling distribution to be approximately normal, the sample size (n) must be larger than 33.3 (n > 33.3). This is because [tex]33.3*0.3 = 10 and 33.3*0.7 = 23.3[/tex].
In other words, the sample size (n) must be large enough so that the product of the sample size (n) and the population proportion (p) is greater than 10 and the product of the sample size (n) and the population proportion (1-p) is also greater than 10. This ensures that the sampling distribution of the sample proportion is approximately normal.
To sum up, the sampling distribution of the sample proportion is approximately normal when the sample size (n) is large and the population proportion (p) is close to 0.5.
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f(x) = |x|
g(x) = x + 2 + 4
We can think of g as a translated (shifted) version of f.
Complete the description of the transformation.
Use nonnegative numbers.
The description of the translation is given as follows:
To get the function g, shift f up by 4 units and to the left by 2 units.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.Hence the changes to the function in this problem are described as follows:
x -> x + 2: shift left 2 units.y -> y + 4: shift up 4 units.More can be learned about translations at brainly.com/question/28174785
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1. In which quadrant does the following point lie? (-2,1/2)
The required point (-2, 1/2) lies in the second quadrant of the coordinate plane.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
The point (-2, 1/2) lies in the second quadrant of the coordinate plane.
In the second quadrant, the x-coordinates are negative and the y-coordinates are positive. Since the x-coordinate of the point (-2, 1/2) is negative and the y-coordinate is positive, it lies in the second quadrant.
Thus, the point (-2, 1/2) lies in the second quadrant of the coordinate plane.
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