True. The sum of squares due to regression (ssr) represents the amount of variation in the dependent variable that is explained by the independent variable(s) in a regression model. On the other hand, the sum of squares total (sst) represents the total variation in the dependent variable.
In fact, the coefficient of determination (R-squared) in a regression model is defined as the ratio of ssr to sst. It represents the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the model. Therefore, R-squared values range from 0 to 1, where 0 indicates that the model explains none of the variations and 1 indicates that the model explains all of the variations.
Understanding the relationship between SSR and sst is important in evaluating the performance of a regression model and determining how well it fits the data. If SSR is small relative to sst, it may indicate that the model is not a good fit for the data and that there are other variables or factors that should be included in the model. On the other hand, if ssr is large relative to sst, it suggests that the model is a good fit and that the independent variable(s) have a strong influence on the dependent variable.
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Sally's balance on her credit card is $75.00 on the first day of august. she makes a payment of $18.00 on august 17 and
a new purchase of $41.00 on august 29. the annual interest rate is 21.25%. what is sally's average daily balance and
finance charge for the month of august?
The average daily balance for the month was $84.21, and the finance charge for the month was $30.13.
AveragesGiven that Sally's balance on her credit card is $75.00 on the first day of August, and she makes a payment of $18.00 on August 17 and a new purchase of $41.00 on August 29, and the annual interest rate is 21.25%, to determine what is Sally's average daily balance and finance charge for the month of August, the following calculation must be made:
75 x ((21.15/12 x 16) / 100) + 75 = A = 86.8957 x ((21.15/12 x 13) / 100) + 57 = B = 70.0698 x ((21.15/12 x 3) / 100) + 98 = C = 103.18(86.89 x 16 + 70.06 x 13 + 103.18 x 3) / 31 = X84.21 = X86.89 + 70.06 + 103.18 - 75 - 57 - 98 = Y30.13 = YTherefore, the average daily balance for the month was $84.21, and the finance charge for the month was $30.13.
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Write an equation to represent the following statement.
51 divided by 3 is k
Solve for k.
Answer:
K = 17
Based on the given conditions, formulate:
51 / 3 = k
Swap the sides : k = 51 / 3
Cross out the common factor: k = 17
Can anyone help me solve this
I need it left in terms of pi and pls show work
Circumference = 10π in, Area = 25π in²
Circumference = 19 π in, Area = 90. 25 π in²
Area = 225 π in²
Circumference = 16π
How to determine the circumference and areaIt is important to note that the formula for area and circumference are;
Area = πr^2
Circumference = 2πr
For the first column, we have
radius = 5in
Substitute the values of the radius into the formula
Circumference = 2 × π × 5
Circumference = 10π in
The area;
Area = π × 5 × 5
Area = 25π in²
For the second column,
radius = 9. 5 in
Substitute the values of the radius into the formula
Circumference = 2 × π × 9. 5
Circumference = 19 π in
Area = π × 9. 5 × 9. 5
Area = 90. 25 π in²
For the third column
radius = 15in
Substitute the values of the radius into the formula
Area = π × 15 × 15
Area = 225 π in²
For the fourth column
radius = 8 in
Substitute the values of the radius into the formula
Circumference = 2 × π × 8
Circumference = 16π
From the solved solution, we can see that the shape is a circle.
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Matthew is flying with his jet pack at 100m/min. A strong wind has blown him 10m east of his intended flight path in 2 minutes. By how many degrees is Matthew off his flight path? Include a diagram.
Mathew's speed of 100 m/min, and the distance of 10 m. east to which he is blown by the wind gives the angle in degrees Mathew is blown off his path as approximately 2.86°.
How can the angle of deflection be found from the given speeds?The given parameters are;
Speed at which Mathew is flying = 100 m/min
Distance and direction in which the strong wind blows him = 10 m. east
Time it takes the wind to deflect Mathew by 10 m. = 2 minutes
Therefore;
Speed and direction of the wind = 10/2 m/min east
Speed and direction of the wind = 5 m/min east
Mathew's flight path can be represented using a vector diagram (please see attached drawing)
Distance Mathew travels in 2 minutes = 100 m/min × 2 minutes = 200 m.
Tangent of the angle by which Mathew is off his flight path, A, can be found as follows;
tan(A) = 10/200 = 1/20
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please answer both asap!!!
A population of protozoa develops with a constant relative growth rate of 0.469 per member per day. On day zero the population consists of five members. Find the population size after eight days.
If the growth rate is 0.469 per member per day and in the beginnning there are 5 members then the population size after eight days is 108.42.
Given growth of population of protozoa 0.469 per member per day and population in beginninng is 5 members.
We have to find the population afte eight days.
First of all we have to find the function or equation showing sum of population after t days.
Because it is given that the rate is 0.469 per member per day it means it is like compounding.
The equation which shows the sum after compounding is P[tex](1+r)^{n}[/tex]
where P is the amount in beginning, r is the rate and n is the number of years.
In this problem the equation will be 5[tex](1+0.469)^{t}[/tex] where t is number of days.
We have to put the value of t=8 to find the population after 8 days=
=5[tex](1.469)^{8}[/tex]
=5*21.68
=108.42
Hence the population of protozoa after 8 days is 108.42.
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prove that if r is a matrix in echelon form, then a basis for row(R) consists of the nonzero rows of R
Let [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex] be the nonzero rows of [tex]$R$[/tex] starting from the 1st row to the [tex]k[/tex]th row.
Step 1: We want to show that
R(R)= span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]
For any vector [tex]v $$\in \mathcal{R}(R)$$[/tex], We may write
v= [tex]$$c_{1} \boldsymbol{r}_{1}+c_{2} \boldsymbol{r}_{2}+\cdots+c_{k} \boldsymbol{r}_{k}+c_{k+1} \mathbf{0}+\cdots+c_{m} \mathbf{0}$$[/tex]
Then v= [tex]$$c_{1} r_{1}+c_{2} r_{2}+\cdots+c_{k} r_{k}$$[/tex]
So [tex]v[/tex] belongs to span{ [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]}
Thus R(R)[tex]\leq[/tex] Span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]
But trivially,
span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]≤ span{[tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex], 0, . . . , 0} = R(R),
span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]=R(R)
Step 2: We want to show that [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]are linearly independent. Suppose otherwise,
then we can write
[tex]$$c_{1} \boldsymbol{r}_{i_{1}}+\cdots+c_{\ell} \boldsymbol{r}_{i_{\ell}}=\mathbf{0}$$[/tex]
From Steps 1 and 2, we have proven that the nonzero rows of R form a basis for the row space.
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How do I put the pairs for the values in the domain
Answer:
Step-by-step explanation: use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded.
Which geometric shape could be used to model the building?
cylinder
pyramid
cone
rectangular prism
Answer:
Rectangular Prism
Step-by-step explanation:
We usually see building shaped as a 3D rectangle. If this is the type of building you are talking about, we use a rectangular prism in order to build the building with correct measurements.
I can't figure out the equivalent fraction. Whoever gets it first gets brainliest, and please do explaination
Factorize the numerator and denominator. You'll see that they both have a factor of 4 that can be canceled. The introduce a factor of 3 to change the denominator to 36.
[tex]\dfrac{28}{48} = \dfrac{4\times7}{4\times12} = \dfrac7{12} = \dfrac{3\times7}{3\times12} = \boxed{\dfrac{21}{36}}[/tex]
The surface area of a rectangular prism that has height of 4 inches, width of 9 inches and length of 3 inches
The surface area of a rectangular prism is found as 150 square inches.
What is rectangular prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces make up a rectangular prism, and each face has a rectangle shape and twelve edges.
Actually, prisms get their name from the way their faces are shaped. Therefore, a rectangular prism is just a prism with rectangular faces. Although it is a closed, three-dimensional object, two rectangles serve as its foundation.
Calculation for the surface area of rectangular prism-
Height of a rectangular prism => H = 4 inches
Width of a rectangular prism => B = 9 inches
Length of a rectangular prism => L = 3 inches
Surface area of a rectangular prism = 2(LB + BH + HL)
= 2(9×3 + 9×4 + 4×3)
= 150
Therefore, the surface area of a rectangular prism is found as 150 square inches.
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Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. x + y = 6 x - y = 0
The solution of the system of equations contains one point
How to determine the number of solutions?The system is given as:
x + y = 6
x - y = 0
Add both equations
2x = 6
Divide by 2
x = 3
Substitute x = 3 in x - y = 0
3 - y = 0
Solve for y
y = 3
So, we have x =3 and y = 3
Hence, the solution of the system of equations contains one point
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Suppose that events E and F are independent, P(E)=0.6, and P(F)=0.7.
What is the P(E and F)?
The probability P(E and F) is
(Type an integer or a decimal.)
Answer:
Step-by-step explanation:
hello :
P(E and F)=0.7×0.6 =0.42
a total of $7000 is invested: part at 6% and the remainder at 10%. How much is invested at each rate if the annual interest is $470?
Answer:
680
Step-by-step explanation:
You work on a surgical unit that receives 87 new patients per week. In your spare time, you are trying to improve pain control across the unit. As you prepare to collect your baseline data before testing your change, you consider your plan to gather this information. Which of the following would be the best data collection plan for this project, and why
Collect data on a representative selection of patients for two weeks.
is the best data collection plan for this project.
According to the statement
we have a given that the surgical unit that receives 87 new patients per week.
and we have to tell the data plan to collect the baseline data before testing your change to control the pain across the unit.
And We know that the Data collection is A representative sample is one technique that can be used for obtaining insights and observations about a targeted population group
So,
Collecting data on a representative portion of your population — that is, sampling — allows you to collect baseline data and start making improvements faster, using fewer resources, than would be possible if you tried to look at every patient. Baseline data is important so that you can see if the changes you are testing are leading to improvement. Collecting data about a non representative sample of your population, such as by looking only at patients with the most severe pain, won't show the broad impact of your project on your unit.
So, Collect data on a representative selection of patients for two weeks.
is the best data collection plan for this project.
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Disclaimer: This question is incomplete. Please read the full content below.
Question:
You work on a surgical unit that receives 87 new patients per week. In your spare time, you are trying to improve pain control across the unit. As you prepare to collect your baseline data before testing your change, you consider your plan to gather this information. Which of the following would be the best data collection plan for this project, and why?
(A) Collect data on the pain level of every patient for at least a year.
(B) Collect data for at least a year, focusing only on patients who have undergone especially painful surgeries.
(C) Collect data on a representative selection of patients for two weeks.
(D) There is no reason to collect baseline data.
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Jagrit is looking at two computer repair stores.
Store 1: Data-Fix
The total cost charged by Data-Fix is represented by the graph
as shown.
a) Write an equation to model the relation of total cost, C, and
number of hours, n as shown in the graph.
b) One of the points on the graph is (3, 60). Explain the
meaning of this point, in the context of this scenario.
Store 2: Comput-Repair
It charges a fixed cost of $10 plus $15 per hour for repair
services.
c) Write an equation to model the relation of total cost, C, and
number of hours, n, in Comput-Repair.
d) On the grid provided, graph the line that describes the fee structure for Compu-Repair.
e) What are the coordinates of the point of intersection?
f) What does it mean in this scenario?
g) Based on the point of intersection, how would you advise Jagrit when trying to choose between the two
computer repair stores? Fully explain your answer supported by the information from the graph.
PLEASE I DON'T HAVE TIME
See below for the solution of each question
The equation of the modelThe points are given as:
(3,60) and (5, 80)
The equation is calculated as:
[tex]C(n) = \frac{C_2 -C_1}{n_2 -n_1} * (n - n_1) + C_1[/tex]
This gives
[tex]C(n) = \frac{80- 60}{5-3} * (n - 3) + 60[/tex]
Evaluate the quotient
C(n) = 10 * (n - 3) + 60
Expand
C(n) = 10n - 30 + 60
Evaluate
C(n) = 10n + 30
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10n + 30
Explain the points on (3, 60)The point (3, 60) means he paid $60 for 3 hours
The equation of the model for Comput-RepairHere, we have:
Fixed = $10
Hourly rate = $15
The equation is calculated as:
C(n) = Fixed + Rate * Number of hours
This gives
C(n) = 10 + 15n
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10 + 15n
The graph of the fee structure for Compu-RepairThe equation is represented as:
C(n) = 10 + 15n
See attachment for the graph
The coordinates of the point of intersectionThis is the point where the two lines intersect.
From the graph, we have the point of intersection to be:
(n, C(n)) = (4, 70)
The meaning in this scenarioThis means that the charges for Comput-Repair and Data-Fix are the same after 4 hours
Advice JargitBased on the point of intersection, it is best that Jargit uses Compu-Repair because they have a lesser hourly rate
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For the real-valued functions f(x)=2x+3 and g(x)=√x-5, find the composition fog and specify its domain using interval notation.
(fog)(x) =
Domain of fog:
Find fog
fog(x)f(g(x))f(√x-5)2√(x-5)+3For real range the domain
x-5≥0x≥5Domain is [5,oo)
Please HELP!!!!
will give brainliest!!
Answer:
Original equation:
y = a sin(b(θ -c)) + d
a = vertical dilation (stretch) of the amplitude
b = horizontal compression (shrink) of the period
c = horizontal shift (left/right)
d = vertical shift (up/down)
Your function is:
y = 3 sin(3θ + π) - 2
First, put it into the general from by factoring out the three in the argument of the sine:
y = 3 sin(3(θ + π/3)) - 2
a = vertical (amplitude) dilation = 3
b = horizontal (period) compression = 2π/period = 3
c = horizontal shift = π/3 to the left
d = vertical shift = -2
Select the correct answer. Find the solution(s) for x in the equation below. x^2 -25 =0
Answer:
Step-by-step explanation:
Find the roots of x^2-25=0 by solving for x.
Add 25 to both sides
x^2=25
Square root both sides
x=-5
x=5
Answer:
x=5;x=-5
Step-by-step explanation:
It was right for me
The line plot (shown in the attached image) shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
Please help!! show all work
a. The median is 70, the mode is 60, and the mean is 70.8.
b. Mean best captures the data.
c. When there are outliers, the mean might be a deceptive center measure.
Calculating the Mean, Median, and Mode
Mean: Total number of sunglasses / total quantity of pries
Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25
Mean = 70.8
Median is equal to the (n/2 + 1)th term.
The number of sunglasses in this case is n.
(25/2 + 1)th term as the median
Median = 13th term
Median is 70
Mode is the most frequent data
Therefore, mode = 70
Why is mean the most appropriate central measure ?
The mean is often the ideal measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data are normally distributed. So, mean here denotes the typical cost of the sunglasses.
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Answer:
Step-by-step explanation:
Choose the equation that satisfies the data in the table.
Answer:
Option A.
Step-by-step explanation:
Demonstration
[tex]y=\frac{7}{4} x+7[/tex]
for x = -4
[tex]y=\frac{7}{4} (-4)+7=-\frac{28}{4} +7=-7+7=0[/tex]
for x= 0
[tex]y=\frac{7}{4}(0) +7=0+7=7[/tex]
for x= 4
[tex]y=\frac{7}{4} (4)+7=\frac{28}{4} +7=7+7=14[/tex]
Hope this helps
A researcher records the hospital admission rates for coronary heart disease at 10 local hospitals. She finds that 2 different hospitals had the highest overall rates of hospital admissions. Which measure of central tendency did this researcher use to describe these data
The central tendency researcher use to describe these data is "mode".
What is mode?The value that appears most frequently in a data set is called the mode. One mode, several modes, or none at all may be present in a set of data. The mean, or average of a set, and the median, or middle value in a set, are two more common measurements of central tendency.
Calculation of mode is done by-
The number that appears the most frequently in a piece of data is its mode. Put the numbers in ascending order by least to greatest, then count the occurrences of each number to quickly determine the mode. The most frequent number is the mode.Simply counting how many times each number appears in the data set can help you identify the mode, which is the number that appears the most frequently in the data set. The figure with the largest total is the mode.Example: Since it happens most frequently, the mode for the data set [5, 7, 8, 2, 1, 5, 6, 7, 5] is 5.To know more about the mode of the data, here
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solve these linear equation
x + 4y = 16
3x + 5y = 27
Use elimination
x+4y=16--(1)3x+5y=27--(2)(1)×5 and (2)×4
5x+20y=80--(3)12x+20y=108--(4)(3)-(4)
-7x=-28x=4Putting in eq(1)
4y=16-44y=12y=3x + 4y = 16 __(1)
3x + 5y = 27 __(2)
Multiply the 1st equation by 3
3x + 12y = 48 __(3)
Solving (2) and (3)
3x + 12y = 48
3x + 5y = 27
__________
(-) (-) (-)
7y = 21
So, y = 3
By, putting the value of y = 3 in equation 1
x + 4(3) = 16
x + 12 = 16
x = 16 - 12
x = 4
We got -The value of x = 4 and y = 3
Hope it helps you any confusions you may ask!
According to a survey, 15% of city workers take the bus to work. Donatella randomly surveys 10 workers. What is the probability that exactly 6 workers take the bus to work
By using Binomial Distribution the probability that exactly 6 workers take the bus to work is 0.001.
What is Binomial Distribution?When every experiment shares the probability of achieving a given value, the number of trials or observations is summarised using the binomial distribution.
The likelihood of observing a specific percentage of successful occurrences in a specific number of trials is determined by the binomial distribution.
The formula for binomial distribution is-
[tex]P(X=x)={ }^{n} C_{k} p^{k}(1-p)^{n-k}[/tex]
'p' is the probability of success,
(1-p) is probability of failure,
'n' is the number of workers,
'k' is number of given workers.
According to the question,
Calculate the probability of success as;
[tex]p=\frac{15}{100}=0.15[/tex]
The, the probability of the failure becomes;
[tex](1-p)=1-0.15=0.85[/tex]
Put above two value in formula of binomial theorem to get the value.
[tex]{ }^{10} C_{6}(0.15)^{6}(0.85)^{4}=0.001[/tex]
Therefore, the probability that exactly 6 workers take the bus to work is 0.001.
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Vic is standing on the ground at a point directly south of the base of the CN Tower and can see the top when looking at an angle of elevation of 61°. Dan is standing on the ground at a point directly west of the base of the tower and must look up at an angle of elevation of 72° in order to see the top. If the CN Tower is 553.3 m tall,how far apart are Vic and Dan to the nearest meter? Include a well-labeled diagram as part of your solution.
The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.
How can the distance between Vic and Dan be calculated?Location of Vic relative to the tower = South
Vic's sight angle of elevation to the top of the tower = 61°
Dan's location with respect to the tower = West
Dan's angle of elevation in order to see the top of the tower = 72°
Height of the tower = 553.3m
[tex]tan( \theta) = \frac{opposite}{adjacent} [/tex]
[tex]tan( 61 ^{ \circ}) = \frac{553.3}{ Vic' s\: distance \: to \: tower} [/tex]
[tex]distance = \frac{553.3}{tan ( {61}^{ \circ} )} = 306.7[/tex]
Vic's distance from the tower ≈ 306.7 mSimilarly, we have;
[tex] Dan's distance = \frac{553.3}{tan ( {72}^{ \circ} )} = 179.8[/tex]
Dan's distance from the tower ≈ 179.8 mGiven that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan d is found as follows;
d = √(306.7² + 179.8²) ≈ 356Therefore;
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The following two-way table describes student's
after school activities. find the probability that a
randomly selected student either does sports or
works.
grade
sports
music/drama
work
20
7
sophomore
3
junior
20
13
2
25
5
senior
5
p(sports u work) = [?]
round to the nearest hundredth.
lol
P ( work/ senior ) = 0.14
The attached table
required
P ( work/ senior )
This is calculated using:
P ( work/ senior ) = n ( work/ senior )/ n ( senior ).
n ( work/ senior ) = 5
n ( senior ) = 25 + 5 + = 35
So:
P ( work/ senior ) = 5/35
P ( work/ senior ) = 0.14
Add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).
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PLEASE HELP QUICK!!!!
Bernie borrowed b books from his friend Grant's collection of 29 books. What does the expression 29 - b represent?
A compound inequality is shown below.
x ≤ 3 and x ≥ 0
Which graph represents the solution of the inequality?
Answer:
It is the first graph
Step-by-step explanation:
The line under the > and < sign means that it must include the 3 and the 0. The closed circle is showing that the 3 and 0 or included.
What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?
The minimum value of c = 7x + 8y is 42. The minimum value is obtained at point (6, 0).
How to calculate the minimum value?To calculate the minimum value of the given equation w.r.t the given constraints(inequalities), the steps are:
Step 1: Identify the system of inequalities in the given constraints
Step 2: Graph those inequalities
Step 3: Identify the maximum and minimum values of x and y that satisfy the given inequalities
Step 4: Then, with the obtained coordinates solve the given equation to get the minimum value.
Calculation:The given equation is C = 7x + 8y, and the constraints list is
2x + y ≥ 0
x + y ≥ 6
x ≥ 0
y ≥ 0
Graphing these inequalities and shading the region that satisfies the given inequalities.
So, from the graph,
the x-values that satisfy all the given inequalities are [6, ∞]
the y-values that satisfy all the given inequalities are [0, ∞]
So, the required coordinate is (6, 0). By this, we can calculate the minimum value of the given equation C = 7x + 8y
Then,
C = 7(6) + 8(0) = 42 + 0 = 42
Thus, the minimum value of the given equation is 42.
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Disclaimer: The given question is incomplete. Here is the complete question.
Question: What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?
2x + y ≥ 0
x + y ≥ 6
x ≥ 0
y ≥ 0
Help please!!!
will give brainliest
The parameters of the sinusoidal function graphs can be found from the coordinates of the given locations.
First graph;
a. Amplitude = 0.5
b. The period = 2•π
c. The horizontal shift = 1
d. The vertical shift = π/4
Second graph;
a. Amplitude = 2
b. The period = π
c. The horizontal shift = -π/4
d. The vertical shift = -2
Which method can be used to find the graph parameters?First graph;
a. The amplitude is half the distance between the y-value peak point and the y-value of a throw (lowest point) on the graph.
The coordinate of a peak point in the first graph is (0, -1.5)
The coordinate of a throw point is (π/2, -2.5)
Therefore;
Amplitude = (-1.5 - (-2.5)) ÷ 2 = 0.5
b. The period is the number of cycles per second, we have;
Period = 1/ff = FrequencyFrom the graph, we have;
f = 1 cycle per πTherefore;
The frequency = 1/π cycle per unit length
Period = 1/(1/π) = πc. The horizontal shift is the distance from the closet intersection of the midline and the rising region of the graph and the y-axis.
Therefore;
The horizontal shift = (-π/2)/2 = -π/4
d. The vertical shift is the distance from the horizontal axis to the midline of the graph.
By observation, the midline is y = -2
Therefore;
The vertical shift = -2Second Graph;
For the second graph, we have;
a. Amplitude = (3 - (-1))/2 = 2
b. Frequency = 1/(2×(5•π/4 - π/4)) = 1/(2•π)
Therefore;
Period = 1/(1/(2•π)) = 2•πc. Horizontal shift = Distance between x-coordinate of the intersection of the midline and the graph and the x-coordinate of the closest peak.
Therefore;
Horizontal shift = π/4 - 0 = π/4d. Vertical shift = (3 + (-1))/2 = 1
Learn more about the graphs of sinusoidal functions here:
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