Answer:
A. how much of the students time is spent on social media during school hours.
B. By using some kind of selection technique Like Having students draw number from a hat, who ever have the specific numbers will take her survey.
C. The population for Sofies research would be a rate of 5/2. For every 5 people who take the survey only 2 turned it in.
D. She would conclude that 1 out of every 2 or 50 percent of students use social media while doing school work.
Step-by-step explanation:
The percent of all high school students who use social media while doing schoolwork, if Sofie uses only the completed surveys, is 50%.
What is random sample?Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.
For a research project, students are asked to study how often students at an online high school look at social media while doing schoolwork.
A) Example of a question she could ask on her survey-Sofie can use the question as, how many times a student look at social media while doing schoolwork?
B) The way, Sofie select a simple random sample of students to take her survey-Sofie can use a simple random sampling technique to select a simple random sample of students to take her survey.
C) Sample and population for Sofie's research-
As Sofie gives out 80 surveys but receives only 32 completed surveys. Thus, the sample is data of 32 completed surveys and the population is total 80 surveys.
D) Percent of all high school students who use social media while doing schoolwork-Of the 32 students who completed surveys, 16 said they use social media while doing schoolwork. Thus, the percentage is,
[tex]P=\dfrac{16}{32}\times100\\P=50\%[/tex]
Hence, the percent of all high school students who use social media while doing schoolwork if Sofie uses only the completed surveys, is 50%.
Learn more about the random sample here;
https://brainly.com/question/17831271
Please help ill give brainlist
Answer:
N⊥M
Step-by-step explanation:
If N║ P and P⊥M then N⊥M
Jan typically earns $575 per week. She has $172.50 withheld from her paycheck each week. What percent is being withheld from her paycheck? Type your answer as a percentage using the % symbol.
Answer:
30%
Step-by-step explanation:
What your problem is asking basically is how many percent is the withholding of her earnings each week. We just divide what is withheld by the earnings.
[tex]\dfrac{172.50}{575}=0.3[/tex]
Because we need it in percentage, we then multiply it by 100%.
0.30 x 100% = 30%
Answer:
30%
Step-by-step explanation:
Jenny bought a new car for $25,995. The value of the car depreciates by 16 percent each year. Which type of function could model the value of the car? A. Exponential B. Can't be determined C. Linear D. Quadratic
Answer:
an exponential function
Step-by-step explanation:
Use a function of the same form as the compound amount formula:
A = P(1+r)^5, where r is the appreciation or depreciation rate and P is the initial value. This is definitely an exponential function.
The given function could model the value of the car as an exponential function.
We have given that,
Jenny bought a new car for $25,995. The value of the car depreciates by 16 percent each year.
We have to determine which type of function could model the value of the car.
Use a function of the same form as the compound amount formula
A = P(1+r)^5,
where r is the appreciation or depreciation rate and P is the initial value. This is definitely an exponential function.
Therefore the given function could model the value of the car as an exponential function.
Therefore the option A is correct
To learn more about the exponential function visit:
https://brainly.com/question/12940982
#SPJ2
What is the distance between the center and edge of a circle called
Answer: The radius
Step-by-step explanation:
The radius is the distance between the center point of the circle and a edge, it is half of the diameter which is the straight line passing through the center point.
Yvonne is a salesperson who earns a fixed amount of $1,850 per month. She also earns a commission of 4% on the amount of goods that she sells. If she wants to earn more than $2,300 in one month, how many dollars (x) in goods must she sell?
Answer:
$11,250
Step-by-step explanation:
Yvonne earns a fixed amount of $1,850 per month and want to earn $2,300. The difference is
[tex]\$2,300-\$1,850=\$450.[/tex]
This difference is her commission. If she earns the commission of 4% on the amount of goods that she sells, then
$x - 100%
$450 - 4%
Make a proportion:
[tex]\dfrac{x}{450}=\dfrac{100}{4}\Rightarrow 4x=45,000\\ \\x=\dfrac{45,000}{4}\\ \\x=\$11,250[/tex]
Yvonne must sell $11,250
Planes S and R both intersect plane T .
Which statements are true based on the diagram? Check all that apply.
[A] Plane S contains points B and E.
[B] The line containing points A and B lies entirely in plane T.
[C] Line v intersects lines x and y at the same point.
[D] Line z intersects plane S at point C.
[E] Planes R and T intersect at line y.
False
As indicated in Figure A below, Plane S contains only point B (remarked in red). Point E (remarked in blue) lies on plane R.
[B] The line containing points A and B lies entirely in plane T.True
As indicated in Figure B below, the line containing points A and B lies entirely in plane T. That line has been remarked in red and it is obvious that lies on plane T.
[C] Line v intersects lines x and y at the same point.False
As indicated in Figure C below, line v intersects lines x and y, but line x in intersected at point B while line y (remarked in red) is intersected at point A (remarked in blue), and they are two different points, not the same.
[D] Line z intersects plane S at point C.True
As indicated in Figure D below, line z that has been remarked in yellow, intersects plane S at point C that has been remarked in blue.
[E] Planes R and T intersect at line y.True
As indicated in Figure E below, planes R and T intersect at line y. The line of intersection has been remarked in red.
Which of the following is an infinite series?
A. 4 + 8 + 16 + 32
B. 2 − 6 + 18 − 54 + . . .
C. 3, 13, 23, 33, . . .
D. 3, –6, 12, –24, 48
Given the recursive formula below, what are the first 4 terms of the sequence?
A. 17, –6, –3, 0
B. 17, 22, 39, 56
C. 17, 39, 105, 303
D. 17, 63, 201, 615
Answer:
for the first question it would be A. 4+8+16+32 because infinite series are such as :
9,18,36,72,144,288
10,20,40,80,160,
so basically its multiplying *2
I cant do #2 without seeing the formula
For what value of x does (the equation is in the picture)
1
3
12
no solution
the answer is.... no solution
An equation is formed of two equal expressions. For the given equation 64³ˣ=512²ˣ⁺¹² no solution for x exists.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The above equation 64³ˣ=512²ˣ⁺¹² can be solved in the following manner as stated below,
64³ˣ = 512²ˣ⁺¹²
(8²)³ˣ=(8³)²ˣ⁺¹²
8⁶ˣ = 8⁽⁶ˣ⁺³⁶⁾
6x = 6x +36
6x - 6x = 36
0 = 36
As the value of x can not be defined, it can be concluded that the equation has no solution.
Hence, for the given equation no solution for x exists.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ2
Find cscx if sinx+cotx cosx= sqrt3
Answer:
The answer is (d) ⇒ cscx = √3
Step-by-step explanation:
∵ sinx + (cotx)(cosx) = √3
∵ sinx + (cosx/sinx)(cosx) = √3
∴ sinx + cos²x/sinx = √3
∵ cos²x = 1 - sin²x
∴ sinx + (1 - sin²x)/sinx = √3 ⇒ make L.C.M
∴ (sin²x + 1 - sin²x)/sinx = √3
∴ 1/sinx = √3
∵ 1/sinx = cscx
∴ cscx = √3
Answer:
d. [tex]\sqrt{3}[/tex]
Step-by-step explanation:
see attachment, it's correct :))
The length of a rectangle is 6 1/2 inches and the width is 3 3/4 inches. What is the ratio, using whole numbers, of the length to the width?
Answer:The length is 13/2, while the width is 15/4, after combination. Ratio of length to width is then (13/2)/(15/4) = 26/15.
Jenna's packing company uses a machine to fill boxes of raisins. Due to a defect in the machine, the actual weight of the raisins packed differs by a maximum of 5 ounces from the desired weight of 15 ounces.
Select the correct inequality and number line that model the situation above.
Graphs in this order: B, C, D, E, A
Answer:
your answer is a
Step-by-step explanation:
The correct inequality and number line that model the situation above is:
10 ≤ weight of boxes ≤ 20
and the correct graph is: Graph A
Step-by-step explanation:The desired weight of raisins is: 15 ounces.
As the weight of the raisins packed differs by a maximum of 5 ounces.
This means that the weight of the raisins packed could either be less by 5 ounces or more by 5 ounces.
i.e. Weight of raisins could be minimum= 15-5=10 ounces.
and weight of raisins could be maximum= 15+5=20 ounces.
Hence, the inequality that will hold true is:
10 ≤ weight of boxes ≤ 20
and the graph that describe this situation is attached to the answer.
Dr.Potter Provides vaccinations against polio and measles. Each polio vaccination multi-dose vial consist of 44 individual doses, and each measles vaccination multidose vial’s consist of 22 individual doses period last year, Dr.Potter used a total of 60 multi-dose vial’s that consisted of a total of 2024 individual doses. How many individual polio and measles vaccinations did Dr.potter give, respectively?
Write an equation of a line in slope-intercept form that is perpendicular to the line 2x -3y = 12 and passes through the point (2, 6).
For this case we have by definition, that the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We have the following line:
[tex]2x-3y = 12\\2x-12 = 3y\\y = \frac {2} {3} x-4[/tex]
If the line we wish to find is perpendicular to the one given, then its slope is given by:
[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {\frac {2} {3}}\\m_ {2} = - \frac {3} {2}[/tex]
Then the line is:
[tex]y = - \frac {3} {2} x + b[/tex]
We substitute the point:
[tex]6 = - \frac {3} {2} (2) + b\\6 = -3 + b\\b = 6 + 3\\b = 9[/tex]
Finally, the equation is:
[tex]y = - \frac {3} {2} x + 9[/tex]
Answer:
[tex]y = - \frac {3} {2} x + 9[/tex]
Please dont ignore, Need help!!! Use the law of sines/cosines to find..
Answer:
16. Angle C is approximately 13.0 degrees.
17. The length of segment BC is approximately 45.0.
18. Angle B is approximately 26.0 degrees.
15. The length of segment DF "e" is approximately 12.9.
Step-by-step explanation:
16By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.
For triangle ABC:
[tex]\sin{A} = \sin{103\textdegree{}}[/tex],The opposite side of angle A [tex]a = BC = 26[/tex], The angle C is to be found, andThe length of the side opposite to angle C [tex]c = AB = 6[/tex].[tex]\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}[/tex].
[tex]\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}[/tex].
[tex]\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}[/tex].
Note that the inverse sine function here [tex]\sin^{-1}()[/tex] is also known as arcsin.
17By the law of cosine,
[tex]c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}[/tex],
where
[tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are the lengths of sides of triangle ABC, and[tex]\cos{C}[/tex] is the cosine of angle C.For triangle ABC:
[tex]b = 21[/tex],[tex]c = 30[/tex], The length of [tex]a[/tex] (segment BC) is to be found, andThe cosine of angle A is [tex]\cos{123\textdegree}[/tex].Therefore, replace C in the equation with A, and the law of cosine will become:
[tex]a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}[/tex].
[tex]\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}[/tex].
18For triangle ABC:
[tex]a = 14[/tex],[tex]b = 9[/tex], [tex]c = 6[/tex], andAngle B is to be found.Start by finding the cosine of angle B. Apply the law of cosine.
[tex]b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}[/tex].
[tex]\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}[/tex].
[tex]\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree[/tex].
15For triangle DEF:
The length of segment DF is to be found, The length of segment EF is 9, The sine of angle E is [tex]\sin{64\textdegree}}[/tex], andThe sine of angle D is [tex]\sin{39\textdegree}[/tex].Apply the law of sine:
[tex]\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}[/tex]
[tex]\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9[/tex].
How would adding a score of 0 to this data affect the mean and median game scores - i ready lesson ......Choice of measures of center or variability
Answer:
I need to know the data to answer the question
Step-by-step explanation:
Adding a score of 0 to your data will lower both the mean and median, and could potentially increase the standard deviation and affect the percentile rankings.
Explanation:Adding a score of 0 to your data set will affect both the mean (average) and the median (middle value) of the scores. Thus, adding a zero will decrease the mean. The median is the middle score when all the scores are arranged in order. If you add a score that is lower than the current median score, the median will either stay the same or decrease, depending on the number of scores. If the number of scores is odd, the median will remain the same, if the number is even, the median will decrease.
The standard deviation is a measure of the variability or dispersion of a set of scores. If all values are the same, the standard deviation is zero. The standard deviation is small when the scores are close to the mean and larger when the scores vary more from the mean. Adding a score of zero could increase the standard deviation, depending on the other scores.
The percentiles in your data represent the value below which a given percent of data falls. Adding a score of 0 could potentially affect the percentile rankings of the other scores.
Learn more about Statistics here:https://brainly.com/question/31538429
#SPJ3
Please help me with this
Answer:
Step-by-step explanation:
The formula for this is
x° = [tex]\frac{1}{2}[/tex](major arc - minor arc)
The measure around the outside of a circle is 360°. We have the minor arc as 120°. So the major arc is 360 - 120 = 240. Fitting that into the formula:
x° = [tex]\frac{1}{2}[/tex](240 - 120)
x° = [tex]\frac{1}{2}[/tex](120)
x° = 60
Someone please help??
Answer:
2
Step-by-step explanation:
It is not 7, although that looks possible. The 7 is a coefficient (in my day we called it a numerical coefficient).
The constant is not d either. That is a variable.
The constant is the 2
Please Help!!!!!!!Carmela is planning a season-themed event for the residents of a town. She would like to conduct a survey of a sample of residents to determine whether people prefer summer or winter.What is the best way that the she could select the sample? A. Randomly select from residents who own a vacation home at the beach B. Randomly select from residents who skiC. Randomly select from all of the town residentsD. Randomly select from residents who own pools
C. randomly select from all residents.
Answer:
Sorry if i'm late but i think the answer is C. Randomly select from all of the town residents
im 97% sure
a) Using your equation from step 2d, estimate the GPA of a student who studies for 15 hours a week. Justify your answer. The equation is y=0.149x+0.89
Answer:
The predicted GPA is then y = 0.149(15) + 0.89 = 3.125
Step-by-step explanation:
Although you don't specifically say so, the equation you provide here is probably a "best fit" equation based upon data: GPA versus number of hours of study per week.
Here, y = 0.149x + 0.89 and the number of study hours of interest is 15.
The predicted GPA is then y = 0.149(15) + 0.89 = 3.125
The GPA is 3.125 who studies for 15 hours a week if the line of the best fit is y=0.149x+0.89
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have a line of best fit:
y = 0.149x + 0.89
Plug x = 15 hours
y = 0.149(15) + 0.89
y = 3.125
Thus, the GPA is 3.125 who studies for 15 hours a week if the line of the best fit is y=0.149x+0.89
Learn more about the line of best fit here:
brainly.com/question/14279419
#SPJ2
A square pyramid has a height h h and a base with side length b b . The side lengths of the base increase by 50%. Write a simplified expression that represents the volume of the new pyramid in terms of b b and h h . An expression is .
Answer:
the new pyramid in terms of b and h.
Step-by-step explanation:
the new pyramid
Anna and Tamara have four suitcases. Anna's suitcases' weights are represented by x + 4 and 4x - 5. Tamara's suitcases' weights are represented by -3x + 2 and 2x + 4. Write an algebraic expression that represents the total weight of all the suitcases.
Answer:
4x + 5
Step-by-step explanation:
x + 4 + 4x - 5 - 3x + 2 + 2x + 4
= 4x + 5
The algebraic expression that represents the total weight of all the suitcases (Anna's and Tamara's) is 6x + 5.
To find the total weight of all the suitcases, we need to add the weights of Anna's four suitcases and Tamara's four suitcases.
Anna's suitcases' weights: x + 4 and 4x - 5
Tamara's suitcases' weights: -3x + 2 and 2x + 4
The total weight can be represented by the algebraic expression:
Total weight = (x + 4) + (4x - 5) + (-3x + 2) + (2x + 4)
Now, let's simplify the expression:
Total weight = x + 4x - 3x + 2x + 4 - 5 + 2 + 4
Total weight = 6x + 5
So, the algebraic expression that represents the total weight of all the suitcases is 6x + 5.
To know more about algebraic expression, refer here:
https://brainly.com/question/34192827
#SPJ2
Determine the fourth term of the sequence defined by the formula:
t1=2a
t2=3a−1
Tn = 2tn−1−3tn−2+1,n ≥ 3
1
−9a+2
-1
−5a+4
Answer:
B. -9a+2
Step-by-step explanation:
You are given the sequence
[tex]t_1=2a,\\ \\t_2=3a-1,\dots\\ \\t_n=2t_{n-1}-3t_{n-2}+1,\ n\ge 3[/tex]
According to the given rule, find [tex]t_3,\ n=3[/tex]
[tex]t_3=2t_2-3t_1+1=2\cdot (3a-1)-3\cdot 2a+1=6a-2-6a+1=-1[/tex]
and [tex]t_4,\ n=4[/tex]
[tex]t_4=2t_3-3t_2+1=2\cdot (-1)-3(3a-1)+1=-2-9a+3+1=-9a+2[/tex]
Find the value of x.
Answer:
x = 5
Step-by-step explanation:
The sum of the side lengths shown is ...
(2x) + (3x +2) + (4x +1) = 9x +3
That is the perimeter of the inscribed triangle. That triangle is similar to triangle ABC by a scale factor of 1:2, so the perimeter of ΔABC is ...
2(9x +3) = 96 = 18x +6
90 = 18x . . . . subtract 6
90/18 = x = 5 . . . . . divide by the coefficient of x
If C is the midpoint of KN what is KC?
A. 18
B. 4.5
C. 19
D. 9
Answer:
19
Step-by-step explanation:
If C is the midpoint of KN, then KC = CN
So we can equate the expressions
[tex]KC= 2x+10[/tex]
[tex]CN= 4x+1[/tex]
KC = CN
[tex]2x+10=4x+1[/tex]
Subtract 2x on both sides
[tex]2x-2x+10=4x-2x+1[/tex]
[tex]10=2x+1[/tex]
Subtract 1 on both sides
[tex]9=2x[/tex]
Divide both sides by 2
[tex]x=4.5[/tex]
Now we find out KC
[tex]KC= 2x+10[/tex]
[tex]KC= 2(4.5)+10[/tex]
[tex]KC= 19[/tex]
Trig help
Solve these triangles
Any or all please
Answer:
see below
Step-by-step explanation:
21) The law of sines can be used, since you have a side and its opposite angle.
sin(F)/DE = sin(D)/EF
F = arcsin(DE/EF·sin(D)) = arcsin(20/31·sin(95°)) ≈ 39.994°
E = 180° -95° -39.994° ≈ 45.006°
DF = sin(45.006°)/sin(95°)·31 ≈ 22.006
__
22) The remaining two problems can be solved using the law of cosines:
c^2 = a^2 + b^2 - 2ab·cos(C)
Of course, c is the square root of the expression on the right.
EF = √(19^2 +35^2 -2(19)(35)cos(61°)) ≈ √(941.203) ≈ 30.679
Then an angle can be found using the law of sines
E ≈ arcsin(35/30.679·sin(61°)) ≈ 86.203°
F ≈ 180° -61° -86.203° ≈ 32.797°
__
23) As in 22 …
RS = √(20^2 +28^2 -2(20)(28)cos(91°)) ≈ √(1203.547) ≈ 34.692
R ≈ arcsin(20/34.692·sin(91°)) ≈ 35.199°
S ≈ 180° -91° -35.199° ≈ 53.801°
(30 points! I just need someone to correctly answer this, please.)
Graph the system of equations on graph paper to answer the question.
{y=1/3x−2 y=−3x−12
What is the solution for this system of equations?
Step-by-step explanation:
y = ⅓x − 2
y = -3x − 12
The first line has a y-intercept of -2 and a slope of ⅓.
The second line has a y-intercept of -12 and a slope of -3.
The graph looks like this: desmos.com/calculator/raouxrikbg
From the graph, we see they intersect at (-3, -3).
The probability of drawing two red candies without replacement is 1335 , and the probability of drawing one red candy is 25 . What is the probability of drawing a second red candy, given that the first candy is red?
The probability would be 50 because 25+25=50
A cat is watching a bird in a tree nearby the tree is approximately 20 feet from the cat ground distance if the cats line of sight makes a 25 degrees with the ground when he has his eye on the bird how high up is bird in the tree
Answer:
X=20Tan(25)
Step-by-step explanation:
So because the cat is looking at the tree it is a strait line making a right triangle with the tree. The cat spots the bird 25 degrees up in the tree making a triangle. Then use SohCahToa, and because u have the adjacent side use Tangent because you are missing the opposite side of the angle. There are a few other ways to find it but that is the simplest way to perform this, GOOD LUCK!
Identify the equation of the circle B with center B(4,−6) and radius 7. HELP ASAP!!
Answer:
(x − 4)2 + ( y + 6)2 = 49
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is (x − h)2 + (y − k)2 = r2.
Define h, k and r using the given values. So, h = 4, k = −6 and r = 7.
Substitute the values into the equation of a circle:
(x − 4)2 + (y − (−6))2 =72
Simplify.
(x − 4)2 + (y + 6)2 = 49
Therefore, the equation of the circle B with center B(4, -6) and radius 7 is (x − 4)2 + (y + 6)2 = 49.
The equation of the circle B with center B(4,−6) and radius 7 is[tex]\rm (x-4)^2+(y+6)^2=49[/tex], the corrcet option is B.
What is the equation of the circle?A circle can be represented as;
[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]
Where h and k are the centers of the circle and r is the radius of the circle.
The equation of circle B with center B(4,−6) and radius 7.
Substitute all the values in the equation
[tex]\rm (x-h)^2+(y-k)^2=r^2\\\\\rm (x-4)^2+(y-(-6))^2=7^2\\\\\rm (x-4)^2+(y+6)^2=49[/tex]
Hence the equation of circle B with center B(4,−6) and radius 7 is[tex]\rm (x-4)^2+(y+6)^2=49[/tex], the correct option is B.
Learn more about circle here;
https://brainly.com/question/11833983
#SPJ2
The graph of y=cosx is transformed to y=a cos (x−c)+d by a vertical compression by a factor of 1/3 and a translation 2 units down. The new equation is:
y=3cosx+2
y=1/3cos(x−2)
y=1/3cosx−2
y=1/3cosx+2
ANSWER
[tex]y = \frac{1}{3} \cos(x) - 2[/tex]
EXPLANATION
If the graph of y=cosx is transformed to y=a cos (x−c)+d by a vertical compression by a factor of 1/3 and a translation 2 units down,
then
a=1/3
and d=-2.
The 'c' is a phase shift since it is not given, it means it is zero.
Therefore the new equation is:
y=1/3cos(x-0)−2
This simplifies to:
y=1/3cosx−2
The correct option is C.
Answer:
The new equation is y = 1/3 cos(x) - 2 ⇒ 3rd answer
Step-by-step explanation:
* Lets revise the trigonometry transformation
- If the equation is y = a cos(x - c) + d
# a is the scale factor of a vertical stretch or compression
# c is the phase shift (negative is to the right, positive is to the left)
# d is the vertical shift
- If y = cos(x)
∴ a = 1 , c = 0 , d = 0
* Now lets solve the problem
∵ There is a vertical compression by a factor of 1/3
∴ a = 1/3
∵ There is a translation 2 units down (vertical translation)
∴ d = -2
∵ There is now phase shift (horizontal translation)
∴ c = 0
* Now lets write the new equation
∴ y = 1/3 cos(x) - 2
* For more understand look to the attached color graph
- The red is y = cos(x)
- The blue is y = 1/3 cos(x) - 2