An angle A in standard position has a terminal side which passes through the point (-5,8)Determine the following Sin ACos A Tan ACot A Sec ACsc A
Answers
The points on the terminal side of an angle α can be described as:
\((r\cos(\alpha),r\sin(\alpha))\)Where r is the distance from the origin to the point. Find r for the point (-5,8):
\(r=\sqrt{(-5)^2+(8)^2}=\sqrt{89}\)Then:
\(\begin{gathered} \sqrt{89}\cos(\alpha)=-5\Rightarrow\cos(\alpha)=-\frac{5}{\sqrt{89}} \\ \\ \sqrt{89}\sin(\alpha)=8\Rightarrow\sin(\alpha)=\frac{8}{\sqrt{89}} \end{gathered}\)Recall the definitions of the tangent, cotangent, secant, and cosecant of an angle in terms of its sine and its cosine:
\(\begin{gathered} \tan(\alpha)=\frac{\sin(\alpha)}{\cos(\alpha)} \\ \cot(\alpha)=\frac{\cos(\alpha)}{\sin(\alpha)} \\ \sec(\alpha)=\frac{1}{\cos(\alpha)} \\ \csc(\alpha)=\frac{1}{\sin(\alpha)} \end{gathered}\)Replace the expressions for cos(α) and sin(α) to find the values of tan(α), cot(α), sec(α) and csc(α):
\(\begin{gathered} \tan(\alpha)=\frac{\frac{8}{\sqrt{89}}}{-\frac{5}{\sqrt{89}}}=-\frac{8}{5} \\ \\ \cot(\alpha)=\frac{-\frac{5}{\sqrt{89}}}{\frac{8}{\sqrt{89}}}=-\frac{5}{8} \\ \\ \sec(\alpha)=\frac{1}{-\frac{5}{\sqrt{89}}}=-\frac{\sqrt{89}}{5} \\ \\ \csc(\alpha)=\frac{1}{\frac{8}{\sqrt{89}}}=\frac{\sqrt{89}}{8} \end{gathered}\)Related Questions
g a study based on the association primate ebmarah looked at the average age a baby gorilla leaves it's mother versus the average age a human baby leaves it's mother. naturally they are different, so we don't want a hypothesis test. instead, find an 86% confidence interval for the difference in age to leave mother.
Answers
An 86% confidence interval for the difference in age to leave mother is -3.10091
What is confidence Interval?
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
Given, Gorilla Baby sample
x means x bar here so, \(x_{1}\) = 3.21
\(s_{1}\) = 0.81
\(n_{1}\) = 64
Human Baby sample
x means x bar here so, \(x_{2}\) = 19.1
\(s_{2}\) = 2.16
\(n_{2}\) = 200
Confidence interval needs t score
t score = 1.18
86% confidence interval = \(x_{1}\) - \(x_{2}\) ± tc \(\sqrt{s^{2} {1} / n_{2} + s^{2} {2} / n_{2}\)
= 3.21 - 19.1 ± 1.18 √0.81²/64 +2.16²/200
= 3.21 - 19.1 ± 1.18 √0.033
= -3.10091
An 86% confidence interval for the difference in age to leave mother is -3.10091
The detail question is here,
A study based on the Association primate Ebmarah looked at the average age a baby gorilla leaves it’s mother versus the average age the human baby leaves it’s mother . Naturally they are different , so we don’t want a hypothesis test. Instead, find an 86% confidence interval for the difference in age to leave mother.
Gorilla:
Sampled 64 babies
Stayed with mother on average 3.21 years
Standard deviation: 0.81
Human:
Sampled 200 babies
Stayed with mother on average 19.1 years
Standard deviation: 2.16
Matched pairs standard deviation :0.23
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you dont need to show your work i just need and answer ASAP
Answers
Answer:
y = 2x +4
Step-by-step explanation:
sorry...
round off 10256 to the nearest 1000
Answers
Answer:
Step 1:10256 will fortunately have 17777 nearest
Step-by-step explanation:
Plss answer my Question
The round off 10,256 to the nearest 1,000 is 10,000.
What is rounding off numbers?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. The crucial figures are preserved when numbers are rounded off.
Given to round off 10256 to the nearest 1000,
steps to round off,
Determine the two consecutive multiples of 1000 that bracket 10,256
10,256 is between 10,000 and 11,000
10,500 is the midpoint between 10,000 and 11,000
from the number line, 10,256 is less than the midpoint
Therefore, 10,256 rounded to the nearest 1,000 = 10,000.
Hence the digit is 10,000.
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there are seven teams in a basketball competition, each team must play each of the other team once, how many games will each play?
Answers
Answer:
49 games
Step-by-step explanation:
Help me check my answers for my homework please
Answers
Answer:
17.2 feet
Step-by-step explanation:
Use the pythagorean theorem with 14 and 10 as the legs of the triangle
jenny had 20 makers her sis gave her a few she has 84 now how many did she have befor
Answers
Jenny started with 20 markers
her sister gave her 64
Answer:
64
Step-by-step explanation:
64 because 20 to 84 is 64
64+20=84
84-64=20 so it is 64
÷6=7 what is the answer
Answers
Answer:
42
Step-by-step explanation:
42÷6 = 7
If you want to find out on your own, you can do 6 * 7 and get 42
Simplify the algebraic expression: 4y + 6x + 5x - 2y
Answers
Answer:
11x+2y
Step-by-step explanation:
Change the statement from standard form to slope-intercept form. Identify the slope and y-intercept
4x + 3y = 12
_________ slope(m)
_________ y - intercept
A. -4
B. 4
C. 3
D. -4/3
E. 3/4
F. 4/3
Answers
What is the probability that both events will occur? Two dice are tossed. Event A: the first die is a 5 or 6. Event B: The second die is not a 1
Answers
Answer: The probability that both events A and B will occur is 5/18 or 0.28.
Step-by-step explanation:
To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.
Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.
Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.
To find the probability that both events A and B occur, we multiply the probabilities:
Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.
Triangle ABC is translated to image A′B′C′. In this translation, A(5, 1) maps to A′(6, –2). The coordinates of B′ are
(–1, 0). What are the coordinates of B?
Answers
Answer:
We know that point A(5, 1) maps to A'(6, -2) in the translation. To find the translation vector, we can subtract the coordinates of A from the coordinates of A':
Translation vector = A' - A = (6, -2) - (5, 1) = (1, -3)
This means that every point in the preimage moves 1 unit to the right and 3 units down to reach its corresponding point in the image.
We also know that point B'(−1, 0) is the image of a point B in the preimage. To find the coordinates of point B, we can apply the translation vector to B':
B = B' - Translation vector = (-1, 0) - (1, -3) = (-2, 3)
Therefore, the coordinates of point B in the preimage are (-2, 3).
Find the area and the circumference of a circle with radius 7 m.
Use the value 3.14 for π, and do not round your answers.
Area=?
Circumference=?
Answers
Answer:
\(Area = 153.938040026m^2\)
\(Circumference= 43.9822971503m\)
Step-by-step explanation:
Area
\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)
Circumference
\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)
A.60
B.120
C.240
D.360
Answers
Answer:
b i think brainlest me plz
Step-by-step explanation:
A bag contains 3 red, 5 blue, and 4 white marbles. If a marble is drawn from the bag, not replaced, and another is drawn, what is the probability of selecting a white and then blue marble?
Answers
Answer:
5/33
Step-by-step explanation:
The probability of selecting a white marble is 4/12 = 1/3(because we have 4 white marbles and 12 marbles in total )
The probability of selecting a blue marble is 5/11 (because we have 5 blue marbles and 11 marbles left(1 has been drawn already) )
Probability of selecting a white and then blue marble equals 1/3*5/11 = 5/33
There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
How many people use at least two
facilities?
Answers
Answer:
he total number of people who use at least two facilities is 4 + 45 = 49
Step-by-step explanation:
To find the number of people who use at least two facilities, we can find the number of people who use all three facilities and add the number of people who use only two facilities.
The number of people who use all three facilities is 4, and the number of people who use only two facilities is 27 + 23 + 31 - 3 * 4 = 45.
Therefore, the total number of people who use at least two facilities is 4 + 45 = 49.
You are given that z > 2. Write an inequality for each expression.
a) 2z+ 9
b) 3(z - 4)
c) 4+2z
d) 5(3z-2)
Answers
a) The inequality for the expression 2z + 9 is 2z + 9 > 13.
b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.
c) The inequality for the expression 4 + 2z is 4 + 2z > 8.
d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.
a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:
2z > 2 * 2
2z > 4
Adding 9 to both sides:
2z + 9 > 4 + 9
2z + 9 > 13
Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.
b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:
3z - 3 * 4
3z - 12
Since we are given that z > 2, we can substitute z > 2 into the expression:
3z - 12 > 3 * 2 - 12
3z - 12 > 6 - 12
3z - 12 > -6
Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.
c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:
4 + 2z > 4 + 2 * 2
4 + 2z > 4 + 4
4 + 2z > 8
Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.
d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):
5 * 3z - 5 * 2
15z - 10
Considering the given inequality z > 2, we can substitute z > 2 into the expression:
15z - 10 > 15 * 2 - 10
15z - 10 > 30 - 10
15z - 10 > 20
Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.
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The graph below represents results of a survey in which students stated the numberof minutes they'd spent watching TV the previous day.
Answers
Explanation:
First, we need to find what is the total number of values in the data. So, taking into account the height of the bars, we can calculate the size of the data as follows:
6 + 2 + 3 + 5 + 4 + 4 = 24
Where each number in the sum is the height of each bar.
Then, the position of the median can be calculated using the following equation:
\(\frac{n+1}{2}=\frac{24+1}{2}=\frac{25}{2}=12.5\)Where n is the size of the data.
Finally, the value in position 12.5 is in the interval 90 - 119
Because, there are 6 values in 0- 29, there are
20ft flag pole has a rope tied from to top to the ground. The rope makes a 35° angle with the ground. How long is the rope?
Answers
the length of the rope is approximately 11.9 feet.
What is right angle triangle?
The term "right-angled triangle" refers to any triangle with an internal angle that is either a right angle or 90 degrees in value. The right triangle or the 90-degree triangle are other names for this triangle because of this. Right triangles have "opposite" and "adjacent" sides, which refer to the sides that are across from and next to respective angles, respectively. When a right triangle is formed, the hypotenuse is its longest side.
We can consider the flagpole, the ground, and the rope as forming a right triangle. The angle between the flagpole and the rope is 90 degrees, and the angle between the rope and the ground is 35 degrees. Therefore, the angle between the flagpole and the ground is 90 - 35 = 55 degrees.
Let's call the length of the rope "r". We can use the trigonometric function tangent to find r:
tan(35°) = opposite/adjacent = r/20
Multiplying both sides by 20, we get:
r = 20 tan(35°)
Using a calculator, we get:
r ≈ 11.9 feet
Therefore, the length of the rope is approximately 11.9 feet.
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-b-
Note: Figure is not drawn to scale.
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
OA.
21 m
OB.
32 m
29 m
34 m
OC.
OD.
6 of 10 Answered
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Answers
After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.
The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted measurement regarding the distance around the outside of a two-dimensional shape. In this system the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m
EXERCISE Carlos is jogging at a constant speed. He starts a timer when he is 12 feet from his starting position. After 3 seconds, Carlos is 21 feet from his starting position. Write a linear equation to represent the distance d of Carlos from his starting position t seconds after starting the timer.
Answers
The linear equation that represent the distance d of Carlos from his starting position is d=3t+12 where d denotes the distance and t denotes the time.
What is the meaning of speed?
The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined.
Given that when Carlos is 12 feet from his starting position, starts a timer.
He is 21 feet from his starting position after 3 s.
He covers (21 - 12) = 9 feet in 3 second.
The speed of an object is the distance that covers in unit time.
The Carlos's speed is 9/3 = 3 feet/s.
After t seconds, he covers (3×t) = 3t feet.
The distance of his from his starting position after t seconds is (3t + 12) feet.
The linear equation is d = 3t + 12.
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Graph f(x) = -1/3x + 5 and g(x) + f(x-4). Describe the transformation from the graph of f to the graph of g
Answers
notice that g(x) is a translation of 4 units to the right of the parent function f(x)
Which transformation was used here?Here we have the parent function f(x) and the transformed function g(x), and we want to graph both of them on the same coordinate axis, you can see that in the image below.
Here we have:
f(x) = -1/3x + 5
g(x) = f(x - 4) = -1/3(x - 4) + 5
The blue one is the graph of g(x) and the green one the graph of f(x), notice that g(x) is a translation of 4 units to the right of the parent function f(x).
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Find the value of 3a when a = -4.
(b)- 7
(d) -12
(a) 7
(c) 12
Answers
Answer:
(d) -12
Step-by-step explanation:
3a = _____
a = -4
3(-4) = ___
3(-4) = -12
The answer is (d) -12
in a popular shopping Centre waiting time for an ABC bank ATM machine is found to be uniformly distributed between 1 and 5 minutes what is the probability of waiting between 2 and 4 minutes to use the ATM
Answers
so here we get two outcomes one is 2 and other is 4.
so there is total 2 outcomes.
total no. of possibility is 5
so the probability of waiting between 2 and 4 minutes to use the ATM is 2/5.
Really need help fast!! Will give BRAINLIEST
Answers
Answer: the answer is C.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
AM = MB is dependant, that means that M has to be the midpoint first before those two
PLEASE HELP ME ITS DUE TODAY!!!
Answers
4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.
5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.
How to verify that RSTU is a trapezoid?In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;
RU ║ ST
Slope of side RU = Slope of side ST
Slope of RU = (y₂ - y₁)/(x₂ - x₁)
Slope of RU = (1 + 3)/(5 + 3)
Slope of RU = 4/8
Slope of RU = 0.5.
Slope of RS = (y₂ - y₁)/(x₂ - x₁)
Slope of RS = (-9 + 3)/(-4 + 3)
Slope of RS = -6/-1
Slope of RS = 6.
Slope of ST = (y₂ - y₁)/(x₂ - x₁)
Slope of ST = (-2 - 1)/(10 - 5)
Slope of ST = -3/5
Slope of ST = -0.6.
Slope of UT = (y₂ - y₁)/(x₂ - x₁)
Slope of UT = (-2 + 9)/(10 + 4)
Slope of UT = 7/14
Slope of UT = 0.5.
Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.
Question 5.
In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance RT = √[(-2 + 3)² + (10 + 3)²]
Distance RT = √170 units.
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance US = √[(5 + 4)² + (1 + 9)²]
Distance US = √181 units.
Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.
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Plz someone help me.
Answers
Answer:
825 students
Step-by-step explanation:
multiply the ratio by the amount of students
1000*0.825=825
Which equation can be used to solve for x in the following diagram
Answers
Answer:
10x+10 = 110
Step-by-step explanation:
The two angles are vertical angles and vertical angles are equal
10x+10 = 110
dont know the answer to last question
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line AB.... hmmm wait a second!!!, you found it already, well, we know AB has a slope of -1/3.
so we're really looking for the equation of a line whose slope is -1/3 and that it passes through (0 , -5)
\((\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{0}) \implies y +5= -\cfrac{1}{3} (x -0) \\\\\\ y+5=-\cfrac{1}{3}x\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x-5 \end{array}}\)
What THREE statements are correct with the variation in the random samples?
A-Samples 1, 2, and 4 best represent the data set because the data in these sets have similar results.
B-Sample 5 may not be an accurate sample for hamburgers and other because of the difference in numbers compared to other samples.
C-Samples 1, 2, and 4 best represent the data set because there are different results when comparing these samples.
D-Sample 2 may not be an accurate sample for pizza and hot dogs because of the difference in numbers compared to other samples.
E-Sample 3 may not be an accurate sample for pizza and hot dogs because of the difference in numbers compared to other samples.
Answers
A, B, and E are the consistent with the random samples on preferred school lunches by 100 students.
What is a random sample?A random sample is a subset of a larger population that is selected in such a way that each member of the population has an equal chance of being included in the sample. Random sampling is an important tool in statistics and allows researchers to make inferences about the larger population based on the characteristics of the sample.
Random sampling helps to ensure that the sample is representative of the population and that any statistical analysis done on the sample can be generalized to the larger population.
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Write a quadratic function in standard form whose graph has the given characteristics.
Answers
The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
The standard form of a quadratic equation in vertex form is given as,
y = a(x-h)² + 8
Where (h,k) is the coordinate of the vertex and a is constant.
Given the vertex (h,k) = (-1,8)
Substitute, vertex, and (0,2)
2 = a(0 + 1)² + 8
a = -6
Therefore, the equation converts as,
y = -6(x+1)²+8
Hence "The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8".
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