What is the exact vale of a trigonometric function of a given angle?
Select True or False for each statement .
sin (5π/6) = - 1/2
tan (27π) = 0
sec (- 11π/3) = - 2√3/3
Answers
Answer:
1) False
2) True
3) False
Step-by-step explanation:
From inspection of the attached unit circle, we can see that:
\(\boxed{\sin\left(\dfrac{5\pi}{6}\right)=\dfrac{1}{2}}\)
Therefore, the first statement is false.
\(\hrulefill\)
The tangent function is periodic with a period of π, meaning that for any integer n:
\(\tan(a)=\tan(a+\pi n)\)
\(\tan(n\pi)=\tan \pi\)
Therefore:
\(\tan(27\pi)=\tan \pi\)
From the unit circle we can see that:
\(\tan \pi=\dfrac{\sin \pi}{\cos \pi}=\dfrac{0}{-1}=0\)
Therefore,
\(\boxed{\tan(27\pi)=0}\)
Therefore, the second statement is true.
\(\hrulefill\)
\(\textsf{Using the trigonometric identity\; $\sec x=\dfrac{1}{\cos x}$}:\)
\(\sec \left(-\dfrac{11\pi}{3}\right)=\dfrac{1}{\cos \left(-\dfrac{11\pi}{3}\right)}\)
The cosine function is periodic with a period of 2π, meaning that for any integer n:
\(\cos (a)=\cos (a + 2\pi n)\)
Therefore:
\(\cos \left(-\dfrac{11\pi}{3}\right)=\cos \left(-\dfrac{11\pi}{3}+4\pi\right)=\cos \left(\dfrac{\pi}{3}\right)\)
From the unit circle we can see that:
\(\cos \left(\dfrac{\pi}{3}\right)=\dfrac{1}{2}\)
Therefore:
\(\sec \left(-\dfrac{11\pi}{3}\right)=\dfrac{1}{\cos \left(-\dfrac{11\pi}{3}\right)}=\dfrac{1}{\cos \left(\dfrac{\pi}{3}\right)}=\dfrac{1}{\frac{1}{2}}=2\)
Therefore, the third statement is false.
Related Questions
In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
Determine the value of `w(25)`.
What does this value say about the wolf population?
Answers
Answer:
w(25) = 96
There are 96 wolves in the year 2020
Step-by-step explanation:
Given:
\(w(x)=14\cdot 1.08^{x}\)
w(25) =
\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)
Number of years : 1995 + 25 = 2020
In 2020, there are 96 wolves
someone please answer this its confusing me
Answers
the line AB will be congruent to line DC so 8t + 7 = 9t - 2 which gives you t = 9
line AD will also be congruent to line BC so 4s + 1 = 2s + 25 which gives you s = 12
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Jada and Mackenzie are hosting events that are catered by the same company. Jada plans to have 78 adults and 78 children attend, so the total projected cost of her meals is $3,354. Mackenzie has 58 adults and 76 children on her guest list, so she will pay the caterer $2,800. How much does the caterer charge for each meal?
Every adult's meal costs $____, and every child's meal costs $____.
Answers
Every adult's meal costs $26, and every child's meal costs $17.
How to write system of equation?Let
cost of adults = x
Cost of child = y
78x + 78y = $3,354
58x + 76y = $2,800
From (1)
Divide through by 78
x + y = 43
x = 43 - y
Substitute into (2)
58x + 76y = $2,800
58(43 - y) + 76y = 2800
2494 - 58y + 76y = 2800
- 58y + 76y = 2800 - 2494
18y = 306
y = 306/18
y = 17
Substitute the value of y into
x = 43 - y
x = 43 - 17
x = 26
Therefore, the cost of adults meal is $26 and child's meal is $17
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(b) In a lab, a substance was heated by 6 °C each hour for 24 hours. What was the total change
in temperature?
l
Answers
Answer:
144
Step-by-step explanation:
12. It takes Daphne 25 minutes to assemble a model plane. During her work
minutes for lunch and one 15 minute break. Which inequality could Daphne use to determine the number
of model planes, p, she can assemble in her 8 hour work day?
A. 25p – 45 > 8
B. 25p + 45 2 8
C. 25p – 45 < 480
D. 25p + 45 < 480
Answers
Answer:
25p+45 < 480
Step-by-step explanation:
How many commutes are exactly 68 minutes
Answers
Answer:
three
Step-by-step explanation:
stem. is the tens place and the leaf is the. ones place
so you want to find 68 so you look in the stem column and look for six
in the row there are 6 numbers which mean:
60, 61, 67, 68, 68, 68
as you can see there is three 68 there for the answer ths 3
Select the correct answer.
Which number line shows the solution to this compound inequality?
0<2x + 6 < 16
OA. HE
-10 -8
-6 -4 -2 0 2 4
6
8
10 12 14
B. +++
- 10 -8
-6 -4
-2
0
2
4
6
8
10 12 14
Oc. + +
-10 -8
++
10 12 14
-6 -4 -2
0
2
4
6
8
OD.
httot
-10 -8 -6 -4 -2 0
2
4
6
8
10 12 14
Answers
Answer:
C.
Step-by-step explanation:
pa brnlst hehehheeh
thx m ltr
The pentagons ABCDE and JKLMN are similar.
Find the length x of JK.
Answers
The value of x in the pentagon JKLMN is 7.2.
What is Polygon?A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
The pentagons ABCDE and JKLMN are similar.
when two figures have the same shape but their sizes are different, then such figures are called similar figures.
We need to find the value of x.
1/1.8=4/x
Apply cross multiplication
x=4×1.8
x=7.2
Hence, the value of x in the pentagon JKLMN is 7.2.
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what is negative 2/7 + 1/4 =
Answers
Answer:
-0.03571428571
Step-by-step explanation:
The following statement has been proven true: AABC=AHJK. What is the corresponding side tosegment HK?O segment KHsegment BCO segment ACO segment HJ
Answers
Remember that
If two figures are congruent, then their corresponding sides are congruent
so
In this problem
triangle ABC is congruent with triangle HJK
that means
side HK and side AC are corresponding sides
therefore
The answer is segment AC3x - 10x + 5 = 5x + 1
What is X?
Answers
Answer:
x=1/2
Step-by-step explanation:
the binomial expansion of (x-2y)^3 is__
PLEASE HELP
A) x^3+3x^2y+3xy^2+y^3
B) x^3-3x^2y+3xy^2-y^3
C) 2^2(x^3-3x^2y+3xy^2-y^3)
D) x^3-6x^2y+12xy^2-8y^2
Answers
The answer is D) x^3-6x^2y+12xy^2-8y^2
The length of a rectangle is 4 yards less than 2 times the width. If the perimeter is 34 yards, find the length and the width of the rectangle.
Answers
Answer:
21 yards
Step-by-step explanation:
Let (1=1,2,3, 4, 5, 6, 7, 8, 9, 10
Answers
The list of elements in the sets are as follows:
A. A ∩ B = {2, 9}
B. B ∩ C = {2, 3}
C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D. B ∪ C = {2, 3, 5, 7, 9, 10}
How to find the elements in a set?Set are defined as the collection of objects whose elements are fixed and can not be changed.
Therefore,
universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 7, 8, 9}
B = {2, 3, 5, 9}
C = {2, 3, 7, 10}
Therefore,
A.
A ∩ B = {2, 9}
B.
B ∩ C = {2, 3}
C.
A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D.
B ∪ C = {2, 3, 5, 7, 9, 10}
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Consider the following data on x = weight (pounds) and y = price ($) for 10 road-racing bikes.
Brand Weight Price ($)
A 17.8 2,100
B 16.1 6,250
C 14.9 8,370
D 15.9 6,200
E 17.2 4,000
F 13.1 8,500
G 16.2 6,000
H 17.1 2,580
I 17.6 3,500
J 14.1 8,000
Required:
Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level.
Answers
Answer:
There is a significant relation between weight and price
Step-by-step explanation:
Brand Weight(x) Price ($) (y)
A 17.8 2100
B 16.1 6,250
C 14.9 8,370
D 15.9 6,200
E 17.2 4,000
F 13.1 8,500
G 16.2 6,000
H 17.1 2,580
I 17.6 3,500
J 14.1 8,000
Null Hypothesis : \(H_0: \mu =0\)
Alternate Hypothesis : \(H_a: \mu \neq 0\)
Given : SST=51956800 SSE= 7312286.84 n = 10
SSR = SST-SSE
SSR=51956800-7312286.84
SSR=44644513.16
Level of significance =\(\alpha = 0.05\)
\(F=\frac{\frac{SSR}{m}}{\frac{SSE}{n-k}}\)
Where m = no. of restrictions
k = No. of independent variables
\(F=\frac{\frac{44644513.16}{1}}{\frac{ 7312286.84}{10-2}}\)
F=48.843
Degree of freedom 1 = 1
Degree of freedom 2 = 10-2=8
Using calculator
p-value is .000114.
p value < α
So, we reject the null hypothesis .
Hence There is a significant relation between weight and price
What is the slope of the line shown below?
(1,6) (-5,-7)
A. 13/6
B. -13/6
C. -6/13
D. 6/13
Answers
\((\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{1}}} \implies \cfrac{ -13 }{ -6 } \implies \cfrac{13 }{ 6 }\)
Hi can any one teach me this constant difference
Answers
The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).
How do you find the constant difference in a sequence of numbers?In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.
Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.
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Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = ? (x − μ) σ μ = σ = The original pulse rates are
Answers
Answer:
So we need to find the P (Z< 1.0776) which is equal to 0.86 from z- tables.
Step-by-step explanation:
Given that mean = 77.5 beats per minute
Standard deviation= s= 11.6 beats per minute
We need to find the pulse rate of randomly selected women.
Suppose randomly selected women X= 90
The test statistic used here is
z = (x − μ) /σ
Putting the values we get
z= 90- 77.5/ 11.6
z= 1.0776
So we need to find the P (Z< 1.0776) which is equal to 0.86
This is a supposed values of randomly selected women. Any other value can be solved in the same way.
What’s
1.7a + 0.3a = 0.8
Please explain step by step to get picked brainliest!
Answers
1.7a+0.3a=0.8
2a=0.8
a=0.4
5 pts 1 Details
The drug Lipitor is meant to reduce total cholesterol. In clinical trials, 213 out of 333 patients taking 10mg
of Lipitor daily complained of flu-like symptoms. A patient advocacy group claims that the proportion of
patients taking Lipitor who experience flu-like symptoms is at least 70%. Use a 0.05 significance level to
test the claim.
Claim: Select an answer which corresponds to [Select an answer
Opposite: Select an answer which corresponds to [Select an answer
stion 3
The test is: Select an answer
The test statistic is:
(to 2 decimals)
The p-value is:
(to 4 decimals)
Based on this we: Fail to reject the null hypothesis
Conclusion There does
appear to be enough evidence to support the claim that the
proportion of patients taking Lipitor who experience flu-like symptoms is at least 70%.
Answers
The claim can be said that the proportion of patients taking Lipitor who experience flu-like symptoms is at least 70%.
Opposite: The proportion of patients taking Lipitor who experience flu-like symptoms is less than 0.7.
The test can be said that the one-tailed z-test for proportions that has a significance level of 0.05.
The test statistic is z =- -1.96
The p-value is: 0.0406.
Based on this we: reject the null hypothesis.
Conclusion: we can say that there is not enough evidence to support the claim that the proportion of patients taking Lipitor who experience flu-like symptoms is at least 70%.
Describe some flu-like symptoms?The flu-like symptoms includes fever, chills, headache, muscle or body aches, cough, sore throat, runny nose, and diarrhea.
We can test the statistic using the formula:
z = (/p - p) / √(p x (1-p) / n)
where /p = sample proportion = 213/333 = 0.639
p = hypothesized proportion under the null hypothesis = 0.7
n = sample size = 333
z = (0.639 - 0.7) / √(0.7 * (1-0.7) / 333)
z = -1.96
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i am a cube that has a lenght, width, and hight of 1 unit
Answers
Answer: The volume of the cube is 1.
Step-by-step explanation:
To find the volume for a cube, multiply all of the units for the sides together.
1 x 1 x 1 = 1Explain how to graph the given piecewise-defined
function. Be sure to specify the type of endpoint each
piece of the function will have and why.
f(x)
X + 3, x < 2
3,
2 ≤ x < 4
4 - 2x,
X 2 4
Answers
The Piecewise -Defined function and how it is graphed is given below..
What is the explanation of how the Piecewise -Defined function is graphed?
Given the function in the attached image,
The Graph of f(x) = -x + 3 is drawn for x less than 2 because x is bounded.The Graph of f(x) = 3 is draw for x greater than and equal to 2 and less than 4 because x is bounded.The Graph of f(x) = 4 - 2x is draw for x greater than equal to 4 because x is bounded.See the attached Graph for better understanding.
f(x) = -x + 3 is coded purple.f(x) = 3 is coded orange.f(x) = 4 - 2x is coded green.Learn more about Piecewise -Defined function:
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Match the following. Match the items in the left column to the items in the right column. 1. domain the first element of a relation or function; also known as the input value. 2. output a relation in which every input value has exactly one output value. 3. input the x-value of a function. 4. relation any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane. 5. function the y-value of a function. 6. range the second element of a relation or function; also known as the output value.
Answers
The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.
What is the appropriate matching of the following items?1. Domain - the first element of a relation or function; also known as the input value.
3. Input - the x-value of a function.
6. Range - the second element of a relation or function; also known as the output value.
4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.
2. Output - a relation in which every input value has exactly one output value.
5. Function - the y-value of a function.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Fill in the banks if you had this question before!!
Answers
An equation for the total cars and trucks for dealership A is: x + y = 164.
An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.
The number of cars that dealership A sold is: 98 cars.
The number of trucks that dealership B sold is: 66 trucks.
How to write a system of equations to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of cars sold.Let the variable y represent the number of trucks sold.Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;
x + y = 164.
Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;
2x + 0.5y = 229.
By solving the systems of linear equations simultaneously, we have:
2x + 0.5(164 - x) = 229
1.5x + 82 = 229
x = 98 cars.
For the y-value, we have;
2(98) + 0.5y = 229
0.5y = 229 - 196
y = 33/0.5
y = 66 trucks.
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PLEASE HURRY
Carson bought 50 pounds of rice for his restaurant. He cooked the rice and wanted to evenly divide it into 9 containers to be served later. How many pounds of rice should Carson put in each container?
Answers
Answer:
5.5 pounds for each container
Step-by-step explanation:
Divide 50/9 and you would (hopefully) get 5.5 with a remainder
I need help with this??
Answers
Select both the 2nd and 4th options!
A piece of wood is in the shape of a rectangular prism with a length of 10 inches, a width of 4 inches, and a height of 5 inches. You cut the wood in half to form two pieces of wood, each with a length of 5 inches. What is the percent increase in the total surface area? Round your answer to the nearest hundredth, if necessary. %
Answers
Answer: 18.18%
Step-by-step explanation:
First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:
\($$SA = 2lw + 2lh + 2wh$$\)
where \(\(l\)\) is the length, \(\(l\)\) is the width, and \(\(h\)\) is the height. For the original piece of wood, \(\(l = 10\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\).
After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood, \(\(l = 5\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\). The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.
The percent increase in the total surface area is given by the formula:
\($$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} \times 100\%$$\)
Let's calculate these values.
The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.
worms are used to break down food waste and create a soil conditioning compost. Some worm populations double every 3 months. Suppose the formula y=2(2^x/3) represent the pounds of worms in a population after x months. If there are initially 2 pounds of worms, how many pounds of worms will there be in 1 year? If 2 pounds is approximately 2,000 worms, how many worms will there be after 1 yesr?
Answers
8,000 each three months the population is doubled so i figured that each three months there are 2000 more worms i multiplied 3 by 4 Because 3 x 4 is 12 and a year is 12 months, and got 8,000 by multiplying 2,000 by 4. Hope this helps
A percent is a specific type of (what) that compares one value to the number___?
Answers
A percent is a specific type of ratio that compares one value to the number 100.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The percentage is the ratio that compares a number with the total value of 100.
Thus,
Percent compares one value to the number 100.
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pls help second questoin
Answers
Answer:
b
Step-by-step explanation:
Answer:
b
Step-by-step explanation: