apply the half-angle identities for sine and cosine to rewrite or evaluate the following expression.
\(tan(\frac{11\pi}{12} )\)
Answers
Answer: We can use the halfangle formula for the tangent to answer this question. Using this formula we get that \($\tan\left(\frac{11\pi}{12}\right) = \sqrt{3} - 2\).
Step by Step Explanation: The half angle formula for tangent is \($\tan\left(\frac{A}{2}\right) = \frac{\sin(A)}{1+\cos(A)}\) . So
\($\tan\left(\frac{11\pi}{12}\right)\)
\($= \frac{\sin(\frac{11\pi}{6})}{1+\cos(\frac{11\pi}{6})}\)
\($= \frac{\sin(2\pi - \frac{\pi}{6})}{1+\cos(2\pi - \frac{\pi}{6})}\)
\($ = \frac{-\sin(\frac{\pi}{6})}{1+\cos(\frac{\pi}{6})}\)
\($= \frac{-1/2}{1 + \sqrt{3}/2}\)
\($= -\frac{1}{2+\sqrt{3}}\)
\($= - \frac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}\)
\(= - \frac{2 -\sqrt{3}}{4-3}}\)
\(= \sqrt{3} -2\)
What are the half angle identitiesThese are some of the common halfangle identities:
\(\cos(A/2) = \sqrt{\frac{1+\cos(A)}{2}\)
\(\sin(A/2) = \sqrt{\frac{1-\cos(A)}{2}\)
\(\tan(A/2) = \frac{\sin(A)}{1+\cos(A)} = \frac{1 - \cos(A)}{\sin(A)}\)
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Related Questions
LESSON 18 SESSION 4
7 Tell whether each statement is True or False.
a. 80% of 90 is the same as of 90.
b. 45% of 60 is 27.
c. 20% of 90 is the same as
as
d. 25 is 35% of 80.
of 90.
of
True False
о
O
о
O
L
Answers
a. 80% of 90 is the same as of 90 - False
b. 45% of 60 is 27 - True
c. 20% of 90 is the same as as of 90- True
d. 25 is 35% of 80 -False
What are the statement about?a. 80% of 90 is not the same as 90. To find 80% of 90, we multiply 90 by 0.8, which gives us 72. Therefore, the statement is false.
b. To find 45% of 60, we multiply 60 by 0.45, which gives us 27. Therefore, the statement is true.
c. 20% of 90 is the same as of 90. To find 20% of 90, we multiply 90 by 0.2, which gives us 18. Therefore, the statement is true.
Lastly, for question d. 25 is not 35% of 80. To find 35% of 80, we multiply 80 by 0.35, which gives us 28. Therefore, the statement is false.
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A company charges a shipping fee that is 4.5% of the purchase price for all items it ships. What is the fee to ship an item costs $56?
Answers
Answer: $2.52
Step-by-step explanation:
Since 4.5% = 0.045 we can just take that and multiply by the item cost, $56, and get $2.52. Therefore that is the fee.
an important goal of inferential statistical analysis is to:
Answers
A important goal of inferential statistical analysis is to generalize results from the study to the target population (option c).
An important goal of inferential statistical analysis is to generalize the findings and results obtained from a study or sample to the larger target population. Inferential statistics involves making inferences, drawing conclusions, and making predictions about a population based on the analysis of a sample.
When conducting a study, it is often impractical or impossible to collect data from the entire population of interest. Instead, a sample is typically selected and studied. Inferential statistics helps researchers make inferences about the population based on the sample data.
By analyzing the sample data using inferential statistical techniques, researchers can estimate population parameters, test hypotheses, determine the significance of findings, and make predictions about the larger population. This allows for generalization of the findings and helps in making informed decisions and drawing conclusions that extend beyond the specific sample studied.
Options A, B, and D are also important goals in statistical analysis, but they are not specific to inferential statistics. Analyzing and describing data (option A) is a goal of descriptive statistics. Determining the validity of theoretical constructs (option B) and measuring the reliability and validity of measurement tools (option D) are goals related to assessing the quality and soundness of research instruments and constructs, but they do not specifically address the goal of generalizing results to a larger population. The correct option is c.
The complete question is:
An important goal of inferential statistical analysis is to:
A. analyze and describe data collected during a study.
B. determine whether theoretical constructs are valid.
C. generalize results from the study to the target population
D. measure the reliability and validity of measurement tools
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Can someone prove 1+cosx/1+secx=cosx
with all the steps included?
Please and thank you.
Answers
Answer:
Proved , since LHS= RHS
Step-by-step explanation:
We need to prove the given expression ,
=> 1 + cos x / 1 + sec x = cos x
Simplifying LHS.=> 1 + cos (x) / 1 + sec (x)
=> 1 + cos (x) / 1 + 1/cos (x)
=> 1 + cos (x) ÷ 1 + cos(x) / cos (x)
=> 1 + cos (x) × cos(x) / { 1 + cos (x) }
1 + cos (x) gets cancelled . So we are finally left out with ,=> cos (x)
= RHS
Hence proved !what are the first six digits of the mathematical sign pi?
Answers
The first six digits of the mathematical sign PI are 3.14159.
Pi is a mathematical constant that is commonly used in geometry and trigonometry. The number is defined as the ratio of a circle's circumference to its diameter, and it is approximately 3.14159.
The value of PI has been computed to millions of decimal places, but the first six digits, which are 3.14159, are the most often used in computations.
The first six digits of the mathematical sign PI are 3.14159. These digits are frequently used to calculate the value of a circle's circumference or area. Pi is irrational, which means it can't be expressed as a fraction of two integers, and it goes on indefinitely without repeating.
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Show that if A and B are sets with A ⊆ B, then a. A ∪ B = B b. A ∩ B = A
Answers
If A and B are sets with A⊆B the a) A ∪B = B, b) A∩B = A.
a) Let A⊆B
Let x ∈ A∪B
Then x ∈ A or x ∈ B .....(i)
By definition of union we have
x ∈ A ⇒ x ∈ B .....(ii)
Using (i) and (ii), if x ∈ A, then x ∈ b. If x ∈ B, then clearly x ∈ B.
Thus given A⊆ B, then A∪B = B.
b) First assume A∩B which implies that x ∈ A and x ∈ B.
Hence we can implies the
A∩ B ⊆ A (we started with the element in A∩B and concluded that it is in A) ------(i)
Now, let x ∈ A which implies x ∈ B ( as A⊆ B)
Hence, x ∈ A∩B, which in turn imply
A ⊆ A∩B -----(ii)
From (i) and (ii) we get
A∩B = A
Therefore if A and B are sets with A⊆B, then A ∩B = B and A∩B = A.
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please help me for this
Answers
The factor of x?
What are the excluded values of x for x^2-9x/ x^2 -7x-18
?
O x = -9, x = 2
O x = -9, x = 0
Ox= -2, x = 9
O x=0, x= 9
Answers
Answer:
3rd option
Step-by-step explanation:
the denominator cannot be zero as this would make the expression undefined.
equating the denominator to zero and solving gives the values that x cannot be.
x² - 7x - 18 = 0 ← in standard form
(x - 9)(x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x - 9 = 0 ⇒ x = 9
x + 2 = 0 ⇒ x = - 2
then
x = - 2, x = 9 ← are the excluded values
an oak tree is planted when it is 550 centimeters tall . what is the height in meters
Answers
Answer:
5.5 meters
Step-by-step explanation:
Hope this helps ^^
Have a great day and enjoy your assignment!
:p
~sunny~
An arrow is fired into the air with an initial upward velocity of 64 feet per second from the top of a building 80 feet high.
The equation that gives the hight of the arrow at any time t is h = 80 +64t-16t^2 Find the times at which the arrow
will be 128 feet in the air?
Answers
Answer:
128 = 80 + 64 t - 16 t^2
8 = 5 + 4 t - t^2
3 = t (4 - t)
Inspection shows the equation is solved if
t = 1 and t = 3
Plug into original equation to check
What is the chance you'll roll this FNC (fair # cube) and it will land on a number less than 5?
A. 4 in 6 chance
B. 3 in 6 chance
C. 1 in 6 chance
D. 5 in 6 chance
Answers
calculate the taylor polynomials and centered at of the function for the given value of .f(x) = sinx, a = 0 f(x) =, a = 0 f(x) =, a = 1 f(x) = tanx, a = 0
Answers
These are the general formulas for the Taylor polynomials of the given functions centered at the specified values of "a". To obtain specific values, you can substitute the desired values of "x" into the respective polynomial equations.
To find the Taylor polynomials centered at the given value of "a" for the respective functions, we can use the Taylor series expansion. Here are the Taylor polynomials for the given functions:
f(x) = sin(x), centered at a = 0:
The Taylor polynomial of degree n for f(x) = sin(x) centered at a = 0 is given by:
Pn(x) = x - (x^3 / 3!) + (x^5 / 5!) - (x^7 / 7!) + ... + (-1)^n * (x^(2n+1) / (2n+1)!)
f(x) = e^x, centered at a = 0:
The Taylor polynomial of degree n for f(x) = e^x centered at a = 0 is given by:
Pn(x) = 1 + x + (x^2 / 2!) + (x^3 / 3!) + ... + (x^n / n!)
f(x) = ln(x), centered at a = 1:
The Taylor polynomial of degree n for f(x) = ln(x) centered at a = 1 is given by:
Pn(x) = (x - 1) - ((x - 1)^2 / 2) + ((x - 1)^3 / 3) - ... + (-1)^(n-1) * ((x - 1)^n / n)
f(x) = tan(x), centered at a = 0:
The Taylor polynomial of degree n for f(x) = tan(x) centered at a = 0 is given by:
Pn(x) = x + (x^3 / 3) + (2x^5 / 15) + ... + (2^(n-1) * Bn * x^(2n-1) / (2n - 1)!)
where Bn are the Bernoulli numbers.
These are the general formulas for the Taylor polynomials of the given functions centered at the specified values of "a". To obtain specific values, you can substitute the desired values of "x" into the respective polynomial equations.
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if f(x) = x^2 - x^3
what is the value of f(-2) ?
Answers
Answer:
\(f(x) = {x}^{2} - {x}^{3} \\ f( - 2) = {( - 2)}^{2} - {( - 2)}^{3} \\ = 4 - ( - 8)\\ f( - 2) =4 + 8 = 12\)
Triangle ABC is similar to triangle DEF. Solve for r.
Answers
Answer:
9
Step-by-step explanation:
since they're similair then similair sides will be proportional
CB is similair to EF
\(\frac{6}{8}\)= \(\frac{3}{4}\)
same thing if you try with the hypotenuse AB similair to DE
\(\frac{13.5}{18}\)= \(\frac{3}{4}\)
So, if you multiply r (DF) by 3/4 you will get the similair side AC
rx 3/4=12
r= 12÷ 3/4
r=16
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Three identical uniform meter sticks are placed on the floor. The first stick lies along the y-axis from y = 0.470 m to y = 1.47 m. The second stick lies along the x-axis from x = 0.320 m to x = 1.32 m. The third stick is positioned so that one end is on the x-axis at x = 0.690 m, and the other end is on the y-axis at y = 0.724 m. Calculate the location of the center of mass of the meter sticks
Answers
The x position of center of mass is = 0.389 m , the y position of center of mass is = 0.444 m .
In the question ,
it is given that , first stick lies along y-axis from y = 0.470 m to y = 1.47 m.
So , coordinate of first stick is (x1 , y1) = (0 , (0.47+1.47)/2) = (0 , 0.97)
the second stick lies along x-axis from x = 0.320 m to x = 1.32 m ,
So , the coordinate of second stick is (x2 , y2) = ((0.32+1.32)/2 , 0) = (0.82 , 0)
the third stick is positioned so that one end is on x-axis at x = 0.690 m, and the other end is on the y-axis at y = 0.724 m .
the coordinate of third stick is (x3 , y3) = (0.690/2 , 0.724/2) = (0.345 , 0.362)
So , x position of center of mass is x = (0 + 0.82 + 0.345)/3
= 0.389 m
So , y position of center of mass is y = (0.97 + 0 + 0.362)/3
= 0.444 m
Therefore , The x position of the center of mass is = 0.389 m , the y position of center of mass is = 0.444 m .
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for all equations, writ the value(s) of the bariable that makes the denominator 0. Solve the equations
2/X +3 = 2/ 3x +28/9= 3/x-2+2=11/X-2 4/x
=4 + 5/x-2 =30/(x+4)(x-2)
Answers
In summary, for equations 1, 5, and 6, the denominators do not have any values that make them zero. For equations 2, 3, 4, and 7, the denominators cannot be zero, so we need to exclude the values x = 0, 2, -4 from the solution set.
To find the values of the variable that make the denominator zero, we need to set each denominator equal to zero and solve for x.
2/X + 3 = 0
The denominator X cannot be zero.
2/(3x) + 28/9 = 0
The denominator 3x cannot be zero. Solve for x:
3x ≠ 0
3/(x-2) + 2 = 0
The denominator (x-2) cannot be zero. Solve for x:
x - 2 ≠ 0
x ≠ 2
11/(X-2) + 2 = 0
The denominator (X-2) cannot be zero. Solve for x:
X - 2 ≠ 0
X ≠ 2
4/x = 0
The denominator x cannot be zero.
4 + 5/(x-2) = 0
The denominator (x-2) cannot be zero. Solve for x:
x - 2 ≠ 0
x ≠ 2
30/((x+4)(x-2)) = 0
The denominator (x+4)(x-2) cannot be zero. Solve for x:
(x+4)(x-2) ≠ 0
x ≠ -4, 2
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What is the best approximation for the circumference of a circle with a radius of 18 ft? use 3.14 to approximate pi. responses 21.1 ft 21.1 ft 36 ft 36 ft, 56.5 ft 56.5 ft 113.04 ft
Answers
The circumference of a circle with a radius of 18 feet is 113.04 ft.
The distance around the circle's edge is referred to as the circumference. It is a basic characteristic of a circle and is incorporated into a number of geometric and trigonometric calculations.
C = 2πr, where C is the circumference, is a mathematical constant, and r is the circle's radius, is the formula for calculating a circle's circumference. An irrational number is one that contains an endless number of decimal places and cannot be stated as a ratio of integers. However, the value of is roughly 3.14 for the majority of practical purposes.
The circle's radius in the provided situation is 18 feet. We can use pi = 3.14 to determine the closest approximation for the circumference of this circle.
C = 2πr = 23.1418 = 113.04 feet.
So ,the circumference of circle is 113.04 feet.
Therefore, 113.04 feet is a circle's circumference with a radius of 18 feet.
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Can anyone help with this?
Answers
Step-by-step explanation:
(a): √8 = √4√2 = 2√2. => k = 2
(b): √50 = √25√2 = 5√2. => k = 5
(c): √98 = √49√2 = 7√2. => k = 7
(d): √12 = √4√3 = 2√3. => k = 2
(e): √300 = √100√3 = 10√3. => k = 10
(f): √45 = √9√5 = 3√5. => k = 3
(g): √125 = √25√5 = 5√5. => k = 5
(h): √28 = √4√7 = 2√7. => k = 2
(PLEASE HELP!!) Which is the equation of the line in slope-intercept form?
Answers
Answer:
its a
Step-by-step explanation:
4.
Cheyene is doing archery practice using a target that has three colored zones. The
results of her most recent session are shown in the table.
# of hits
Color
Gold
9
Red
15
Blue
11
a. If this trend continues, what is the probability that Cheyene's next shot will be in the
gold?
b. Assuming the trend continues, what is the probability that her next shot will not be
in the blue?
Answers
Total shots = 9 + 15 + 11 = 35
a. Probability of getting gold = number of gold / total shots
Probability = 9/35
b. Probability of not being in blue = gold + red / total shots
gold + red = 9+15 = 24
Probability = 24 /35
David bought 4.75 pounds of chicken for $11.40.
How much did he pay per pound?
HURRYYYY
Answers
Answer:
2.4 so B
Step-by-step explanation:
you will divide 11.40 by 4.75
2.4 so B
Step-by-step explanation
you will divide 11.40 by 4.75
Complete the table below using the given function
Answers
The complete table of the function is:
x | 7 8 9 10 11
y | -55 -63 -71 -79 -87
How to Complete a Table Using a Function?To complete the given table above, we have to plug in each value of x into the function, y = -8x + 1.
For x = 7, we have:
y = -8(7) + 1
y = -56 + 1
y = -55
For x = 8, we have:
y = -8(8) + 1
y = -64 + 1
y = -63
For x = 9, we have:
y = -8(9) + 1
y = -72 + 1
y = -71
For x = 10, we have:
y = -8(10) + 1
y = -80 + 1
y = -79
For x = 11, we have:
y = -8(11) + 1
y = -88 + 1
y = -87
Therefore, the complete table is:
x | 7 8 9 10 11
y | -55 -63 -71 -79 -87
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The residents of a city voted on whether to raise property taxes. The ratios of yes votes to no votes was 5 to 7. If there were 10,740 total votes, how many no votes were there?
Answers
Answer:
6,265 votes
Step-by-step explanation:
The residents of a city voted on whether to raise property taxes. The ratios of yes votes to no votes was 5 to 7. If there were 10,740 total votes, how many no votes were there?
Given that :
Ratio of yes votes to no votes = 5 to 7
Yes votes : no votes = 5 : 7
Total votes = 10,740
The actual number of yes votes and no votes can be obtained thus :
Sum of ratio = (5 + 7) = 12
(ratio of vote / sum of ratio) * total votes
Number of no votes :
(Ratio of no votes / total ratio) * total votes
(7 / 12) * 10,740
0.5833333 * 10,740
= 6,265 votes
Number of no votes = 6,265 votes.
7y - 14 factor please
Answers
Answer:
7(y - 2)
Step-by-step explanation:
7y - 14 ← factor out 7 from each term
= 7(y - 2)
Answer:
7(y -2)
Step-by-step explanation:
Factorize:
Find the GCF.
7y= 7 * y
14 = 7 * 2
GCF = 7
7y - 14 = 7*y - 7*2
= 7*(y - 2)
The frequency table represents the job status of a number of high school students. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for job with entries 12, 38, 50. The third column is labeled not looking for a job with entries 28, 72, 100. The fourth column is labeled total with entries 40, 110, 150. Which shows the conditional relative frequency table by column? A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for a job with entries 0.3, nearly equal to 0.33, 1.0. The third column is labeled not looking for job with entries 0.7, nearly equal to 0.65, 1.0. the fourth column is labeled total with entries nearly equal to 0.27, nearly equal to 0.73, 1.0. A 4-column table with 3 rows titled job status. The first column is blank with entries currently employed, not currently employed, total. The second column is labeled Looking for a job with entries 0.12, 0.38, 050. The third column is labeled not looking for a job with entries 0.28, 0.72, 1.00. The fourth column is labeled total with entries 0.4, 1.1, 1.5. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for a job with entries 0.24, 0.76, 1.0. The third column is labeled not looking for a job with entries 0.28, 0.72, 1.0. The fourth column is labeled total with entries nearly equal to 0.27, nearly equal to 0.73, 1.0. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for job with entries 0.08, nearly equal to 0.25, nearly equal to 0.33. The third column is labeled not looking for a job with entries nearly equal to 0.19, 0.48, nearly equal to 0.67. The f
Answers
Answer:
\(\begin{array}{cccc}{} & {Looking\ for\ job} & {Not\ looking} & {Total} & {Employed} & {0.24} & {0.28} & {0.27} & {Not\ Employed} & {0.76} & {0.72} & {0.73}& {Total} & {1} & {1} & {1} \ \end{array}\)
Step-by-step explanation:
The question is not properly formatted (see attachment for the frequency table and the options)
Required
The conditional relative frequency table by column
We have:
\(\begin{array}{cccc}{} & {Looking\ for\ job} & {Not\ looking} & {Total} & {Employed} & {12} & {28} & {40} & {Not\ Employed} & {38} & {72} & {110}& {Total} & {50} & {100} & {150} \ \end{array}\)
To get the conditional frequency by column, we simply divide each cell by the corresponding total value (on the last row)
So, we have:
\(\begin{array}{cccc}{} & {Looking\ for\ job} & {Not\ looking} & {Total} & {Employed} & {12/50} & {28/100} & {40/150} & {Not\ Employed} & {38/50} & {72/100} & {110/150}& {Total} & {50/50} & {100/100} & {150/150} \ \end{array}\)
\(\begin{array}{cccc}{} & {Looking\ for\ job} & {Not\ looking} & {Total} & {Employed} & {0.24} & {0.28} & {0.27} & {Not\ Employed} & {0.76} & {0.72} & {0.73}& {Total} & {1} & {1} & {1} \ \end{array}\)
Solve for x. Trapezoids
Answers
Answer:
I think x=3.9
Step-by-step explanation:
I think the midline is the bottom value divided by 2 so that means 61/2=30.5. then 30.5-11=19.5. then 19.5/5=3.9
What is the solution to the linear equation? 2.8y 6 0.2y = 5y – 14 y = –10 y = –1 y = 1 y = 10
Answers
The solution of the linear equation 2.8y+6+0.2y=5y-14 is y=10.
Given linear equation 2.8y+6+0.2y=5y-14 and we have to find the solution of the equation.
An equation is relationship between two or more variables which is expressed in equal to form. It is solved in order to find the values of variables. Equation of two variables look like ax+ by=x.
The given linear equation is 2.8y+6+0.2y=5y-14 which can be solved as under:
2.8y+6+0.2y=5y-14
We have to add the coefficients of same variables. Coefficients are the numbers which are present with the variable.
3y+6=5y-14
We have to take same variables at one side.
3y-5y=-14-6
-2y=-20
y=-20/-2
y=10
Hence the solution of the linear equation 2.8y+6+0.2y=5y-14 is y=10.
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Pls help meeeee and thank you so so much i don’t know how to do this
Answers
Answer:
The new coordinate after translating the figure are : (- 1 , -2)
Step-by-step explanation:
By using the following a translation mapping rule for this problem:
( x,y) → (x -2, y - 5)
the major difference between simple random samples and systematic samples is that the latter are not selected randomly. select one: true false
Answers
Its true that major difference simple random samples and systematic samples is that the latter are not selected randomly.
Simple random samples are those samples which are selected from the population totally randomly
here , each data point have equal probability of being chosen.
The data point are independent to each other. This sampling technique requires the reach throughout the total scope of the population.
That's why for sample random sample population size should be small for effective result
whereas , Systematic samples are those samples which are selected in a proper systematic order .
Here , only the starting point is being selected randomly and then next data points are selected as pre-defined order.
So , The major difference between simple random samples and systematic samples is that the latter are not selected randomly.
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Consider the segment AB on the graph.
...What is the vertical component of the distance from A to B
Answers
Answer:
2 units.
Step-by-step explanation:
Point A's coordinates are (2,1) and Point B's coordinates are (3, 3). The vertical distance between these points can be found by taking the absolute value of the y-values. The absolute value of 3-1 = 2. Therefore, the vertical component of the distance from A to B is 2 units.
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