Identify how the graph is transformed from that of the parent function.
y = cot(x/5)
>
DONE
y=1/4tan(x)
DONE
Answers
The graph is transformed from that of the parent function by using the trigonometric relationship between tangent and cotangent function, dilation of the independent variable and vertical dilation.
How to comparent a parent function with a child functionLet be [tex]f(x) = \cot \frac{x}{5}[/tex] the parent function and [tex]g(x) = \frac{1}{4}\cdot \tan x[/tex] the child function. We can obtain the child function by applying the following three steps:
Relationship between tangent and cotangent functions: [tex]f'(x) = \frac{1}{f(x)} = \frac{1}{\cot \frac{x}{5} } = \tan \frac{x}{5}[/tex]Dilation of the independent variable by 5: [tex]f''(x) = f(5\cdot x) = \tan x[/tex]Vertical dilation by [tex]\frac{1}{4}[/tex]: [tex]g(x) = \frac{1}{4}\cdot f''(x) = \frac{1}{4}\cdot \tan x[/tex]In consequence, the graph is transformed from that of the parent function by using the trigonometric relationship between tangent and cotangent function, dilation of the independent variable and vertical dilation. [tex]\blacksquare[/tex]
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Answer: first is stretched horizontally, second is compressed vertically
Step-by-step explanation:
Related Questions
please help meeeeeeeeeee
Answers
Answer:
area of trapezoid is [tex]\mathbf{Area=(\frac{4+8}{2})\times 6}[/tex]
Step-by-step explanation:
We have
a = 4 cm
b = 8cm
h = 6cm
We need to find area of trapezoid
The formula used is: [tex]Area=\frac{a+b}{2}\:h[/tex]
Putting values and finding expression:
We will not be solving the expression as question required just to find the expression by putting respective values.
[tex]Area=\frac{a+b}{2}\:h\\Area=(\frac{4+8}{2})\:\times 6[/tex]
So, area of trapezoid is [tex]\mathbf{Area=(\frac{4+8}{2})\times 6}[/tex]
Installation of a certain hardware takes a random amount of time with a standard deviation of 5 minutes. A computer technician installs this hardware on 64 different computers, with the average installation time of 42 minutes. Compute a 95% confidence interval for the mean installation time. Explain your interval in context.
Answers
Answer:
The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{5}{\sqrt{64}} = 1.225[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.225 = 40.775 minutes
The upper end of the interval is the sample mean added to M. So it is 42 + 1.225 = 43.225 minutes
The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.
The 95% confidence interval for the mean installation time is (40.775, 43.225) and this can be determined by using the formula of margin of error.
Given :
Standard deviation is 5 minutes. Sample size is 64.Mean is 42 minutes.95% confidence interval.The following steps can be used in order to determine the 95% confidence interval for the mean installation time:
Step 1 - The formula of margin of error can be used in order to determine the 95% confidence interval.
[tex]M = z \times \dfrac{\sigma}{\sqrt{n} }[/tex]
where z is the z-score, [tex]\sigma[/tex] is the standard deviation, and the sample size is n.
Step 2 - Now, substitute the values of z, [tex]\sigma[/tex], and n in the above formula.
[tex]M = 1.96 \times \dfrac{5}{\sqrt{64} }[/tex]
[tex]M = 1.225[/tex]
Step 3 - So, the 95% confidence interval is given by (M - [tex]\mu[/tex], M + [tex]\mu[/tex]) that is (40.775, 43.225).
The 95% confidence interval for the mean installation time is (40.775, 43.225).
For more information, refer to the link given below:
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find
the value of :
sin 0° + cos 0° + tan 45°
Answers
Answer:
this is easy
Step-by-step explanation:
sin 0 is 0
cos 0 is 1
tan 45 is 1
so ...
0+1+1 is 2
There are 7 girls and 10 boys taking lifeguard lessons. Write the ratio that compares the number of girls taking lifeguard lessons to the total number of students taking lifeguard lessons
Answers
Answer:
7 to 10 or 70%
Step-by-step explanation:
Graphs that represent situations that may not have numerical values are Called?
Answers
42 % of what number is .21
Answers
Answer:
0.5
Step-by-step explanation:
0.21=42%
0.21/42=1%
0.005=1%
0.005 x 100 = 100%
0.5=100%
0.5
After four rounds, 74 teams are eliminated from a robotics competition. There are 18 teams remaining. Write and solve an equation to find the number of teams t that started the competition.
Answers
WILL MARK BRAINLIEST! THANK YOUUUU
An equilateral triangle has a side length of 40.
Another side of the same triangle measures 3x + y.
The third side of the same triangle measures 4x - 2y.
What are the values of x and y that would keep the triangle equilateral?
Answers
Answer:
x=12, y=4
Step-by-step explanation:
All the sides are the same length.
3x+y = 40
4x-2y = 40
Eliminate y terms: divide second equation by 2 and add to first equation
2x-y = 20
3x+y = 40
---------------
5x = 60
x = 12
y = 40-3x = 4
Answer:
We know that all sides of the equilateral triangle is equal.
Given :---
An equilateral triangle has a side length of 40.
Another side of the same triangle measures
3x + y.
The third side of the same triangle measures
4x - 2y.
According to the above problem, the equation are
3x+y=40........(i) and 4x-2y=40.........(ii)
Divide the equation (ii) by 2, we get
2x-y=20..........(iii)
Now solving for x and y we get,
3x+y=40.......(i)
2x-y=20........(iii)
5x =60
x=60/5
x=12
Putting the value of x in equation in equation (iii) we get
24-y=20
y=24-20
y=4
The values of x and y that would keep the triangle equilateral are 12 and 4 respectively.
Hence, the value of x is 12 and y is 4.Scottie is testing to see if people who go to a lot of movies do better than average on the Verbal SAT (which has a mean of 500 and a standard deviation of 100 and is normally distributed). She has a sample of six people. What kind of hypothesis testing do we use
Answers
Answer:
The kind of hypothesis testing we can use is z-test for means
Step-by-step explanation:
Given that;
sample mean x" = 500
standard deviation σ = 100
sample size n = 6
What kind of hypothesis testing do we use?
There are two cases where z-test can be use;
first, when we know the population standard deviation or variance
and secondly, when the population size is more than 30.
So from the question, the population standard deviation was given, which is 100.
Since we know the S.D, it meets the first condition.
Therefore, The kind of hypothesis testing we can use is z-test for means
3 ÷ 1/8 show your work on paper! :D
Answers
Answer:
24
Step-by-step explanation:
3 : 1/8 = 3/1 · 8/1 = 3 · 8/1 · 1 = 24/1 = 24
Hope this helped!
Can someone help me please
Answers
Answer:
38 degrees
Step-by-step explanation:
just know
The sum of nineteen and four times a number equals 39. Suppose x represents the unknown number. Translate this problem into a mathematical statement.
Answers
Answer:
19 + 4x = 39
Step-by-step explanation:
mams buy 3 large sandwiches to serve at a picnic. 9 people come to the picnic. Show 3 different ways to cut the sandwich so that each person gets an equal share.
Answers
Cut each sandwich into thirds.
Hopefully, your friends aren't very hungry
#1
Ben and Irene shared an apple. Ben ate 3/4of the apple
and Irene ate 1/4
of the apple.
How much of the apple did Ben and Irene eat?
Answers
Answer:
all of it. because he ate 3/4 and she ate 1/4
Answer:4/4 of the apple
Step-by-step explanation: Ben ate 3/4 of the apple and Irene ate 1/4 parts of the apple what is 1 + 3 =4 and there are 4 part of the apple so 4 is how much they ate and 4 is how much there is to eat so it would be 4/4
(sorry if this does'nt help)
ACTIVITY 1
Directions: Find the unknown principal P, rate r, time t, and simple
interest Is by completing the table. Use separate sheet/s of paper for your
answer.
Principal (P)
Rate (T)
Time (t)
8%
15
2%
5
Simple Interest
(Is)
(1)
10,000
3,600
175,500
10,000
(2)
360,000
500,000
2
(3)
10.5%
Activity 2
Directions: Find the unknown principal P, maturity value, and
compound interest Ic by completing the table. Use separate sheet/s of paper
for your answer.
Maturity Value
Principal (P) Rate(r) Time(t)
Compound
Interest (Ic)
(1)
10,000
(3)
8%
2%
15
5
(2)
50,000
Answers
Answer:
500,000
2
(3)
10.5%
Activity 2
Directions: Find the unknown principal P, maturity
Find the perimeter of a triangle with side lengths: (y + 5) ft, (3y + 5) ft, and (4y - 3) ft.
Answers
Answer:
8y + 7
Step-by-step explanation:
add them: y + 5 + 3y + 5 + 4y - 3 = 8y + 7
3. Mandy obtains a $155,000 20/6 balloon mortgage with a rate of 4.25%. What will her monthly payments be? (2 points)
O $959.81
O $1044.46
O $1110.47
$1225.74
Answers
Answer:
$279.98
Step-by-step explanation:
A 20/6 balloon payment means loan amortization is for 20 years and constant payments is for 6 years after which balloon payment is due.
The formula to calculate her constant payments based on a 15 year amortization plan is
A= P × r × r(1+r)^n/(1+r)^n-1
Where A = constant monthly payments for the 6 year period
r= interest rate
P= mortgage value loan
n= number of months =20×12=240 payments
Substitute values in the formula:
A= $155000× 0.0425×0.0425(1+0.0425)^240/(1+0.0425)^240-1
A= $279.98
To calculate what she would pay before balloon payment is due, we simply multiply her monthly payments $279.98 by number of payments 240
Which type of transformation is described by (x, y)
->
+ (x + 3, y — 2)?
Answers
Answer:
(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.
Step-by-step explanation:
Given the rule of transformation:
(x, y) → (x+3, y-2)
If we move horizontally 3 units to the right, 3 is added to the x-coordinate of any given point, and then 2 units down.
In other words,
(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.
For example,
Let say if we have the point A(4, 5)
Using the translation rule:
(x, y) → (x+3, y-2)
A(4, 5) → A'(4 + 3, 5 - 2) → A'(7, 3)
Therefore, the new position of A(4, 5) after translating 3 units left and 2 units down would be: A'(7, 3)
A club’s first meeting was attended by 72 people. Nine times as many people went to the first meeting than the second meeting. How many people attended the second meeting?
Answers
Answer:
8 people attended the second meeting.
Step-by-step explanation:
Given that:
Number of people who attended the first meeting = 72
Let,
x be the number of people who attended second meeting.
9 times people of second meeting = Number of people who attended first meeting
9x = 72
Dividing both sides by 9
[tex]\frac{9x}{9}=\frac{72}{9}\\x=8[/tex]
Hence,
8 people attended the second meeting.
sarah spent a total of 10 on oranges and apples at the supet marke
t. if she spent 3 dollars less for oranges than she did on apples how much did sarah spend on oranges
Answers
apples = x+3 dollars
An equation is
Oranges + Apples = 10 dollars, or
x + (x+3) = 10
2x = 10-3
2x = 7
x = 7/2 = 3.5
ANSWER. Sara spent $3.50 for oranges.
Is this good ?
Need this turned in by tonight. Solving for x. My brain is fried, I have been doing math for the last 4 hour.Help!!!!!
Answers
Answer:
18. x = 24.519. x = 421. x = 10Step-by-step explanation:
Corresponding sides have same ratio
Q18
7/6 = x / (27- 6)6x = 7*21x = 147/6x = 24.5Q19
(x + 5)/15 = (5x + 1)/35(x + 5)/3 = (5x + 1)/77(x + 5) = 3(5x + 1)7x + 35 = 15x + 315x - 7x = 35 - 38x = 32x = 4Q21
(x + 6)/24 = (2x - 2)/27(x + 6)/8 = (2x - 2)/98(2x - 2) = 9(x + 6)16x - 16 = 9x + 5416x - 9x = 54 + 167x = 70x = 10Which of the following can a seismograph not show scientists?
Answers
A line with a positive slope will go up and to the right on the graph. True false
Answers
Answer:
True
Step-by-step explanation:
Let's say the slope of an equation is 3/2. You move the point by moving it up by three and moving it to the right by two or moving it down by 3 and moving it to the left by two.
If the equation was - 3/2. You would move the point by moving it up by three and moving it to the left by two or moving it down by three and moving it the right by two.
Which statement has a false converse?
A If a quadrilateral is a rectangle, then the diagonals of the quadrilateral are
congruent.
B If a quadrilateral has diagonals that bisect each other, then the quadrilateral is a
parallelogram
C if a quadrilateral is a rectangle, then all angles of the quadrilateral are right angles.
D If a quadrilateral is a parallelogram, then both pairs of opposite sides of the
quadrilateral are congruent.
Answers
Answer:
B If a quadrilateral has diagonals that bisect each other, then the quadrilateral is a parallelogram
Explanation:
A rectangle just like a square has diagonals that bisect each other and they are congruent( two lines are congruent if they are equal). A parallelogram is a quadrilateral with parallel sides and when its diagonals intersect, they are congruent too. Therefore a rectangle with diagonals that bisect each other is not necessarily a parallelogram.
Helpp
(Show ur work please)
This is law of cosine
Answers
Answer:
13.3
Step-by-step explanation:
[tex] a^2 = b^2 + c^2 - 2bc \cos A [/tex]
[tex] a^2 = 8^2 + 18^2 - 2(8)(18) \cos 43^\circ [/tex]
[tex] a^2 = 64 + 324 - 288(0.73135) [/tex]
[tex] a^2 = 388 - 210.6299 [/tex]
[tex] a^2 = 177.370 [/tex]
[tex] a = \sqrt{177.370} [/tex]
[tex] a = 13.318 [/tex]
Answer: 13.3
Ssssssssssssssssssssssssssssssssssssssssssssssssss
Answers
help please i’ll try to give brainliest:)
Answers
9514 1404 393
Answer:
108
Step-by-step explanation:
The circumference of a circle is given by ...
C = 2πr
The circle shown has a radius of 9 in, so the circumference is ...
C = 2π(9 in) = 18π in
__
When the circle is dilated by a factor of 6, the circumference is multiplied by 6. It becomes ...
dilated C = 6(18π in) = 108π in
The multiplier of π inches is n = 108.
Quadrilateral ABCD is a rhombus.
AD = 13 cm & BD = 24 cm,
find AC
Answers
Answer:
64
Step-by-step explanation:
What is the constant proportionally of the graph
Help me
Answers
Answer:
The constant proportionally of the graph is:
k = 8Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get the equation
y ∝ x
y = kx
k = y/x
here 'k' is called the constant of proportionality.
From the graph, it is clear that:
at x = 0.5, the value of y = 4
so substituting x = 0.5 and y = 4 in the equation
k = y/x
k = 4/0.5
k = 8
at x = 1, the value of y = 8
so substituting x = 1 and y = 8 in the equation
k = y/x
k = 8/1
k = 8
Therefore, the constant proportionally of the graph is:
k = 8A triangle has sides measuring 2 inches and 7 inches. If x represents the
length in inches of the third side, which inequality gives the range of possible
values for x?
A. 25x37
B. 5 sxs 9
C. 2
D. 5< x < 9
Answers
Answer:
its d.
Step-by-step explanation:
the other guy is wrong
Using sides of a triangle rule, the inequality gives the range of possible values for x is 5 < x < 9.
What is sides of a triangle rule?
The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.
Given that two sides of triangle are 2 and 7 inches.
Let the third side be x inches.
x < 2+7 ⇒ x < 9
7 < 2 + x ⇒ x > 5
2 < 7 + x, which is true for any positive value of x.
Thus, 5 < x < 9.
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