Answers
From our circle we can infer that [tex]sin\frac{5 \pi }{3}= \frac{- \sqrt{3} }{2} [/tex] and [tex]cos\frac{5 \pi }{3}= \frac{1}{2} [/tex].
Since [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex], [tex]tan\frac{5 \pi }{3}= \frac{\frac{- \sqrt{3} }{2}}{\frac{1}{2} } [/tex]
[tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex]
We can conclude that [tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex].
Related Questions
Tom bought 7 books. He has space only for 3 books in his bookshelf. In how many ways can he arrange the 3 books?
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The required, Tom can arrange the 3 books in the combination of 35 different ways on his bookshelf.
The number of ways to choose a subset of 3 books from a set of 7 books can be calculated using the combination formula:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of items and k is the number of items we want to choose.
In this case, Tom wants to arrange 3 books out of a set of 7 books. Using the combination formula, we have:
C(7, 3) = 7! / (3!(7-3)!)
= 7! / (3!4!)
Calculating the factorials:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
3! = 3 * 2 * 1 = 6
4! = 4 * 3 * 2 * 1 = 24
Substituting these values into the formula:
C(7, 3) = 5040 / (6 * 24)
= 5040 / 144
= 35
Therefore, Tom can arrange the 3 books in 35 different ways on his bookshelf.
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Eight car dealerships reported the number of cars they sold last month. Car Dealership Number of Cars Sold GMC 84 Chevrolet 81 Nissan 92 Toyota 92 Ford 95 Honda 94 Hyundai 80 Acura 72 What is the interquartile range of this set of data?
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We first find the median. To do this, order the data from least to greatest and find the middle value:
72, 80, 81, 84, 92, 92, 94, 95
There are 8 data values. The median is between 84 and 92:
(84+92)/2 = 176/2 = 88
The median splits the data into two halves. The lower quartile is the median of the lower half; this is between 80 and 81:
(80+81)/2 = 161/2 = 80.5
The upper quartile is the median of the upper half; this is between 92 and 94:
(92+94)/2 = 186/2 = 93
The interquartile range is found by subtracting these:
93-80.5 = 12.5
Answer:
upper quartile is 93
lower quartile is 80.5
Step-by-step explanation:
I got a 100 on quiz
For f(x)=3x+1 and g(x)=x²-6, find (f o g)(4)
Answers
so, we can simply first find g(4), and then plug that in f(x),
[tex]\bf \begin{cases} f(x)&=3x+1\\ g(x)&=x^2-6\\ (f\circ g)(4)&=f(~~g(4)~~) \end{cases} \\\\\\ g(4)=(4)^2-6\implies g(4)=16-6\implies g(4)=10 \\\\\\ f(~~g(4)~~)\implies f(~~10~~)=3(10)+1\implies f(~~10~~)=31[/tex]
Explain why the graph of quadratic function could not contain both a minimum vertex and a maximum vertex at the same time.
Your explanation should be 3-4 sentences and include at least 6 of the following words/phrase.
-parabola
- u-shaped graph
- vertex
- minimum
- maximum
- y-value of the vertex
- x-value of the vertex
- quadratic function
Answers
If you prove that ∆WXZ is congruent to ∆YZX, which general statement best describes what you have proved?
A.Diagonals of a parallelogram bisect each other.
B. Diagonals of a parallelogram are congruent.
C. Opposite sides of a parallelogram are congruent.
D. The diagonal of a parallelogram connects two non-consecutive vertices.
Answers
Proving that ΔWXZ is congruent to ΔYZX does not directly prove any of the provided statements about a parallelogram without additional context. Likely, it could imply that diagonals of a parallelogram bisect each other, but more information is needed.
Explanation:If you prove that ΔWXZ is congruent to ΔYZX, you have demonstrated the congruence of triangles within a geometric figure, likely referencing elements of a parallelogram. However, the specific elements such as sides or diagonals are not indicated in the proof of congruence between the triangles in question.
From the options you have provided and general geometric principles, proving congruent triangles within a figure doesn't necessarily directly prove any of those statements without additional context. If we assume ΔWXZ and ΔYZX are created by a diagonal of a parallelogram, congruent triangles might imply that diagonals of a parallelogram bisect each other (Option A). However, it could also relate to the congruence of opposite sides depending on the specifics of the figure, not the diagonals being congruent (Option B), because congruence of triangles does not guarantee equal length of diagonals, just segments within the triangles.
Using the following set of data, calculate the lower quartile, the upper quartile, and the interquartile range. 20, 22, 25, 28, 29, 30, 32, 33, 34.
Be sure to show your work for finding:
The lower quartile
The upper quartile
The interquartile range
PLs help
Answers
1st find the median, which would be the middle of the data set. Since there are 9 numbers the median would be the middle number of the set, this would give you the same amount of numbers on each side of it. The numbers to the left would be the lower and the numbers on the right would be the upper
so in the given data set the median is 29
the lower quartile is the median of the lower numbers, in this case the numbers below 29 are 20, 22 , 25, 28
since there is an even amount of numbers you need to add the 2 middle numbers together and divide by 2 to find the lower quartile so 22 +25 = 47, 47 / 2 = 23.5 this is the lower quartile
the upper quartile is found the same way, but using the upper numbers so in this case using 30, 32, 33 , 34
add the 2 middle numbers 32 +33 = 65 divide by 2 = 65/ 2 = 32.5 this is the upper quartile
the inter quartile range is subtracting the lower quartile from the upper quartile: 32.5 - 23.5 = 9
9 is the inter quartile range
According to the information we can infer that the Lower Quartile is 23.5, the upper quartile is 32,5, and the interquartile range is 9.
How to calculate these information?Arrange the data in ascending order: 20, 22, 25, 28, 29, 30, 32, 33, 34.
Calculate the position of the lower quartile using the formula: (n + 1) / 4, where n is the number of data points.
(9 + 1) / 4 = 10 / 4 = 2.5Since 2.5 falls between the 2nd and 3rd data points, you need to find the average of these two values:
(22 + 25) / 2 = 47 / 2 = 23.5Upper Quartile (Q3):
Calculate the position of the upper quartile using the formula: 3 * (n + 1) / 4.
3 * (9 + 1) / 4 = 30 / 4 = 7.5Since 7.5 falls between the 7th and 8th data points, find the average of these two values:
(32 + 33) / 2 = 65 / 2 = 32.5Interquartile Range (IQR):
Calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 32.5 - 23.5 = 9.So, the lower quartile (Q1) is 23.5, the upper quartile (Q3) is 32.5, and the interquartile range (IQR) is 9.
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Hugo is 6 feet 4 inches tall, weighs 225 pounds, and very muscular. if you think hugo is more likely to be a professional football player rather than a professional ballroom dancer, you are using:
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An inductive argument is intended to show that its conclusion is probably or likely true, though not certainly true, if its premises all are true. The author of an inductive argument (if sincere) only aims to establish the intended conclusion with a high degree of probability although not with complete certainty.
Words such as “probably,” “likely,” and “it is reasonable to conclude” suggest that you intend your argument to show that the conclusion is probably, but not certainly, true. The statement above use the words "more likely", then this word tell us that this is, in fact, an inductive argument.
Answer:
I think it is the option "representative heuristic"
Step-by-step explanation:
Heuristics are kind of like "mental shortcuts" that we use to make assumptions quickly. They are based off of our category prototypes and what we believe are typical examples of a certain object or group. The reason why it would be representative heuristic is because when you use this, you are comparing the new situation to an already existing image of the object. In this case, you are comparing Hugo to the "typical" image of a football player.
Hope this helps you :)
The GRE is an entrance exam that many students are required to take in order to apply to graduate school. In 2014, the combined scores for the Verbal and Quantitative sections were approximately normally distributed with a mean of 310 and a standard deviation of 12.
What is the probability that a randomly selected score is greater than 334? Write your answer as a decimal.
Answers
The probability that a randomly selected score is greater than 334 is 0.0228
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have [tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
For this case, we're given that:
Combined scores were approximately normally distributed with mean of 310 and a standard deviation of 12.If we take:
X = a randomly selected score obtained in the GRE exam.
Then, by the given data, we have:
[tex]X \sim N(\mu = 310, \sigma = 12)[/tex]
And therefore, we can write:
Probability that a randomly selected score is greater than 334 = P(X > 334)
Converting X to standard normal distribution:
[tex]Z = \dfrac{X - \mu}{\sigma} = \dfrac{X - 310}{12}[/tex]
The probability we need can be calculated as:
[tex]P(X > 334) = 1 - P(X \leq 334)\\P(X > 334) = 1 - P(Z \leq \dfrac{334 - 310}{12})\\\\P(X > 334) = 1 - P(Z \leq 2)[/tex]
From the z-tables, the p-value for Z = 2 is 0.9772
Thus, we get [tex]P(Z \leq 2) = 0.9772[/tex], and therefore,
[tex]P(X > 334) = 1 - P(Z \leq 2) = 1- 0.9772 = 0.0228[/tex]
Thus, the probability that a randomly selected score is greater than 334 is 0.0228
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In the equation 2x - y = 4, the x-intercept is 2 and the y-intercept is -4.
Answers
Triangle RST was dilated by a scale factor of 1/2. The image, triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units. What is the length of a leg of the pre-image, triangle RST?
Answers
Triangle RST was dilated by a scale factor of 1/2
Given: triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units.
Pre-image: measure of pre-image * scale factor = measure of resulting image
measure of pre-image = measure of resulting image / scale factor
measure of pre-image = 8 / 1/2measure of pre-image = 8 * 2/1
measure of pre-image = 16 units.
Answer:
16 units
Step-by-step explanation:
RST was dilated by a scale factor of 1/2. This means R'S'T' has sides that are 1/2 the length of the sides of RST.
Since the legs of R'S'T' are 8 units, this gives us the equation
8 = 1/2x
Divide both sides by 1/2:
8÷1/2 = x
8 × 2/1 = x
16 = x
Each leg in RST is 16 units.
The quotient of two numbers is negative. It must be true that _____.
Answers
Bobby is testing the effectiveness of a new cough medication. There are 100 with a cough in the study. Seventy patients received the cough medication, and 30 other patients did not receive treatment. Thirty-four of the patients who received the medication reported no cough at the end of the study. Twenty of the patients who did not receive medication reported no cough at the end of the study. What is the probability that a patiebt chosen at random from this study took the medication, given that they reported no cough?
A. 63%
B. 53%
C. 38%
D. 43%
Answers
[tex]=\frac{34}{54}=63\%[/tex]
The probability that a patient chosen at random from this study took the medication, given that they reported no cough is 63%.
Answer:
The answer to this question is 63%
Find the exact value. tan240°
Answers
[tex] \sqrt{3} [/tex]
The exact value of tan 240° is found by recognizing that 240° is in the third quadrant with a reference angle of 60°. The sine and cosine values are both negative in this quadrant. Therefore, tan 240° simplifies to √3.
To find the exact value of tan 240°, we need to consider its position on the unit circle. The angle 240° is in the third quadrant, where both sine and cosine are negative.
First, recognize that 240° is 60° beyond 180°, making its reference angle 60°.The sine and cosine of 60° are given by sin 60° = √3/2 and cos 60° = 1/2, but since 240° is in the third quadrant, these values will be negative.Thus, sin 240° = -√3/2 and cos 240° = -1/2.Tangent is the ratio of sine to cosine: tan 240° = (sin 240°) / (cos 240°) = (-√3/2) / (-1/2).Simplifying this, we get tan 240° = √3.Therefore, the exact value of tan 240° is √3.
An archway is modeled by the equation y = -2x^2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B?
A. 8 units
B. 6 units
C. 5 units
D. 3 units
Answers
1. You have that the the archway is modeled by the equation y=-2x^2+8x and the angle mentioned in the problem is defined by the equation x−2.23y+10.34=0.
2. Therefore, you must susbtitute y=-2x^2+8x into x−2.23y+10.34=0, as below:
x−2.23(-2x^2+8x)+10.34=0
3. When you apply the distributive property, you obtain:
x−2.23(-2x^2+8x)+10.34=0
x+4.46x^2-17.84x+10.34=0
4.46x^2-16.84x+10.34=0
4. When you solve the quadratic equation, you obtain:
x=3 units
Therefore, the answer is the option D: D. 3 units.
Answer
The answer is 6
Step-by-step explanation:
Which expression is equivalent to 18x + 45
Answers
not sure what you're looking for
9*2X=18X
9*5=45
18X+45=18X+45
simplify the expression 36^1/2
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[tex] {36}^{ \frac{1}{2} } \\ = \sqrt{36} \\ = 6[/tex]
Answer is 6.
Hope this helps. - M
The _____ is a measure of variability that is simply the difference between the highest score and the lowest score. variance standard deviation median range
Answers
The answer to this is range! Because when you are figuring out the range, you subtract the lowest score from the highest score. Good luck on your test!
The range is a measure of variability that is simply the difference between the highest score and the lowest score. which is the correct answer would be option (D).
What is the range of the data?The range of the data is defined as the difference between the maximum number of data to the minimum number of data.
The range of given data = maximum number - minimum number
The range is the correct answer to this because you subtract the lowest score from the highest score to determine the range.
Therefore, the range is a measure of variability that is simply the difference between the highest score and the lowest score.
Hence, the correct answer would be an option (D).
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Need this geometry answer
Answers
so according to this
7x+x-4 = 180
8x = 184
x= 23
therefore angle DBC 23-4 = 19
SO 19 IS THE ANSWER
Using the following diagram, solve for x.
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Answer:
[tex]x=10.5[/tex]
Step-by-step explanation:
Use Thales' Theorem which says: If two lines, not necessarily parallel, are cut by a system of parallel lines, then the segments that result on one of the two lines are proportional to the corresponding segments obtained on the other.
Take a look at the picture I attached you, from it, It is true that:
[tex]\frac{AB}{A'B'} =\frac{BC}{B'C'}[/tex]
Hence:
[tex]\frac{12}{6} =\frac{21}{x}[/tex]
Solving for x:
[tex]x=\frac{21}{2} =10.5[/tex]
Uppose it costs $10 to roll a pair of dice. you get paid the sum of the numbers in dollars that appear on the dice. what is the expected value of this game?
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A circle has a circumference of 324\pi324π324, pi. what is the radius of the circle?
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C = 2πr
=> 324π = 2πR
=> R = ( 324 / 2 ) = 162 units
Would someone Please answer this question please will be thanked and also will pick brainly!! (please be honest)
Answers
d=√[(x-x1)²+(y-y1)²]
given the points: (-3,-8) and (10,-8)
thus:
d=√[(10-(-3))²+(-8-(-8))²]
d=√[(10+3)²+(8-8)²]
d=√(13²+0)
d=13 units
What are the lengths?
Answers
Two sides of the right angled triangles are given and we are to find the Third side. This can be done using the Pythagoras Theorem, which states:
Hypotenuse² = Base² + Perpendicular²
For 1st figure, we have
Base = 21
Perpendicular = 20
So,
Hypotenuse² = 20² + 21² = 841
⇒
Hypotenuse = 29 (1st option is correct)
For 2nd Image, we have
Base= 6
Hypotenuse = 10
So, we can write:
10² = 6² + Perpendicular²
Perpendicular² = 64
⇒
Perpendicular = 8 (Option Fourth)
You are required to choose two topics from a list of six to write about on your science test. How many different pairings are possible?
10
15
20
12
Answers
The answer is 12 :)
The cost of printing the football roster for games was 25 for 4.00 what is the cost per copy
Answers
STEPS:
Divide 4 by 25
= $0.16
CHECK YOUR ANSWER:
Each copy costs $0.16. You decided to get 25 copies.
25 * $0.16
= $4.00
Stella divides 12/8 on her calculator and gets 1.5. Assuming that Stella has not adjusted the calculator's settings, what do the displayed digits tell you about the answer?
A) Stella made an error.
B) The answer is exactly 1.5.
C) The calculator rounded the answer.
D) The calculator truncated the answer.
Answers
Stella divided 12/8.
If we divide 12 by 8, we get exactly 1.5.
Let us check given options one by one .
A) Stella made an error : Stella didn't made an error because it's just division of two numbers.
B) The answer is exactly 1.5. : On dividing 12 by 8, we get exactly 1.5, so this option is correct.
C) The calculator rounded the answer. : On dividing 12 by 8, we get exactly 1.5. So, no rounding is required.
D) The calculator truncated the answer. : On dividing 12 by 8, we get exactly 1.5. So, no truncation in the answer.
Therefore, correct option is B) The answer is exactly 1.5.
Square root of -1 divided by (3+8i)-(2+5i)
Answers
Used:[tex](a+b)(a-b)=a^2-b^2[/tex]
Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth. a rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.
a. substitute the values into the vertical motion formula h = −16t2 + vt +
c. let h = 0.
b. use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. round to the nearest tenth of a second.
Answers
a] substitutng the values into the vertical motion formula h = −16t2 + vt +c
we shall have:
v=116 ft/s
c=101
thus
h(t)=-16t^2+116t+101
b] The time taken for the rocket to hit the ground will be evaluated as follows:
let h=0
thus
h(t)=-16t^2+116t+101
0=-16t^2+116t+101
solving the quadratic equation using quadratic formula we obtain:
t=29/8+/-sqrt(1245)/8
thus
t=8.04 sec or -0.79
but since there is no negative time, we shall take t=8.04 seconds
Thus the rocket hit the ground after 8.04 sec
which polynomial is a quadratic factor of 27x^3+64
Answers
I notice that 27x^3+64 factors into (3x+4)(9x^2-12x+16). The 2nd factor is the quadratic factor that you wanted.
In general, a^3+b^3 = (a+b)(a^2-ab+b^2).
The solution is that 27x^3+64 factors into (3x+4)(9x^2-12x+16).
The 2nd factor is the quadratic factor that you wanted.
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
3x+2x-5, for example, is a polynomial.
here, we have,
we know that,
In general, a^3+b^3 = (a+b)(a^2-ab+b^2).
given that,
27x^3+64
now, we have to factorize the given expression.
using the above formula, we get,
27x^3+64
= (3x+4)(9x^2-12x+16)
Hence, The solution is that 27x^3+64 factors into (3x+4)(9x^2-12x+16).
The 2nd factor is the quadratic factor that you wanted.
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Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. write the formula for this sequence in the form an = a1 ⋅ rn−1. explain how you arrived at your answer.
Answers
a ⇒⇒⇒ the first term
r ⇒⇒⇒ common ratio
Given: the fourth term (a4) = 121.5 and the common ratio = 3 and n = 4
∴ [tex]121.5 = a* 3^{4-1} [/tex]
∴ a = 121.5/3³ = 121.5/27 = 4.5
So, The formula for this sequence will be [tex]4.5 * 3^{n-1} [/tex]
Answer:
First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.