If θ is an angle in standard position whose terminal side lies in quadrant III and sin θ=-√3/2, find the exact value of the tan θ
Answers
Answer:
C) √3
tanθ = √3
Step-by-step explanation:
Step:-1
Given that θ be an angle in standard position whose terminal side
Given that the angle
sinθ = [tex]\frac{-\sqrt{3} }{2}[/tex]
Given that the Opposite side AB = [tex]\sqrt{3}[/tex]
Hypotensue AC = 2
Step(ii):-
By using Pythagoras theorem
AC² = AB² +BC²
BC² = AC² - AB²
BC² = 4 - (√3)²
= 4-3
BC = 1
Adjacent side(BC) = 1
Step(iiI):-
Given that 'θ' lies in the third quadrant so tanθ is positive
tanθ = [tex]\frac{AB}{BC} = \frac{\sqrt{3} }{1}[/tex]
Answer:
b. -1/2
Step-by-step explanation:
:)
Related Questions
please answer quickly
noah has $14 more then his brother jared. jared has $51. how much money does noah have?
Answers
Answer:
$65
Step-by-step explanation:
$51 + $14
$65
Answer:
$65
Step-by-step explanation:
14+51=61
What is the area of a rectangle with a length of 7 feet and a width of 3 ¾ feet?
Answers
Answer:
105/4 ft^2
Step-by-step explanation:
Multiply length and width: 7*15/4 = 105/4 ft^2
Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 32 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9370 with a standard deviation of 0.0090, within what interval will 99 percent of the sample means fall
Answers
Answer:
99% of the sample means will fall between 0.93288 and 0.94112.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The true mean is .9370 with a standard deviation of 0.0090
This means that [tex]\mu = 0.9370, \sigma = 0.0090[/tex]
Sample of 32:
This means that [tex]n = 32, s = \frac{0.009}{32} = 0.0016[/tex]
Within what interval will 99 percent of the sample means fall?
Between the 50 - (99/2) = 0.5th percentile and the 50 + (99/2) = 99.5th percentile.
0.5th percentile:
X when Z has a pvalue of 0.005. So X when Z = -2.575.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.575 = \frac{X - 0.9370}{0.0016}[/tex]
[tex]X - 0.9370 = -2.575*0.0016[/tex]
[tex]X = 0.93288[/tex]
99.5th percentile:
X when Z has a pvalue of 0.995. So X when Z = 2.575.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.575 = \frac{X - 0.9370}{0.0016}[/tex]
[tex]X - 0.9370 = 2.575*0.0016[/tex]
[tex]X = 0.94112[/tex]
99% of the sample means will fall between 0.93288 and 0.94112.
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Answers
Answer:
A = 254.34
Step-by-step explanation:
Area of a circle formula:
A = πr²
r = d/2 = 9
A = 3.14(9²)
A = 3.14(81)
A = 254.34
Answer:
254.34
Step-by-step explanation:
Good luck!
Select the correct answer. What is the fractional form of 0.02 ? A. 2/99 B. 1/11 C. 2/100 D. 1/12
Answers
Answer:
C) 2/100
Step-by-step explanation:
0.02 = 2/100
Answer:
It Is C
Step-by-step explanation:
Need help ASAP question 12
Answers
Answer:
Parallelogram
Step-by-step explanation:
Opposite sides are parallel
A rectangle has vertices at P (16,16), Q(16,-16), R(-16,-16) and S(-16,16). The origin is the center of dilation and the rule of a dilation is (x,y)→(1/4x, 1/4y) What is P' of the dilated image, PQ’R’S’?
Answers
Answer:
(4, 4)
Step-by-step explanation:
So you're trying to find what P' is, and P' would be the dilation of P. This means that you apply the rule (x, y) --> (1/4x, 1/4y) with the coordinate point (16, 16). This would be:
(16, 16) --> (1/4 * 16, 1/4 * 16) = (4, 4)
A surgeon has found that she can model the number of surgeries done per week with a Poisson distribution
in which y = 24.5.
How many surgeries would be expected in a year? assume no vacation or time off.
Round to one decimal if needed.
Answers
Answer:
94.5
Step-by-step explanation:
can someone help me understand this problem?
Answers
Hello!
a. 10
b. 1
c. -11
To evaluate f(x) at a certain x, you simply substitute that value of x into the equation for x.
For example:
a. f(x) = 2x, find f(5)
Plug in 5 for x into f(x):
f(5) = 2(5) = 10.
b. f(x) = 4x + 5, find f(-1)
f(-1) = 4(-1) + 5 = 1
c. f(x) = -3x - 5, find f(2)
f(2) = -3(2) - 5 = -11
Suppose lightning strikes at an average of 1.4 strikes per minute during a particular storm. You play the following game: if the next strike occurs within the next minute, you win 3 dollars, if the next strike occurs between 1 minute and 2 minutes from now, you win 5 dollars, and if the next strike occurs more than 2 minutes from now, you win 1 dollar. How much should someone be charged to play this game, to make it a "fair game?"
Answers
Answer:
$3.25
Step-by-step explanation:
Given that:
Mean, λ = 1.4
Strike within next minute = $3 won
Strike between one and 2 minutes = $5
Strike more than 2 minutes = $1
Probability that next strike occurs within the next minute :
Using poisson :
P(x < 1) = 1 - e^-(λx) ;
P(x < 1) = 1 - e^-(1.4*1) = 1 - e^-1.4
P(x < 1) = 1 - 0.2465969
P(x < 1) = 0.7534030
Next strike occurs between 1 and 2 minutes :
(1 < x < 2) :
P(x < 2) - P(x < 1)
P(x < 2) = 1 - e^-(λx) ;
P(x < 2) = 1 - e^-(1.4*2) = 1 - e^-2.8
P(x < 2) = 1 - 0.0608100
P(x < 2) = 0.9391899
P(x < 2) - P(x < 1)
0.9391899 - 0.7534030 = 0.1857869
P(striking after 2 minutes)
P(x > 2) = e^-(λx) ;
P(x > 2) = e^-(1.4*2) = e^-2.8
P(x > 2) = 0.0608100
Amount charged :
(0.7534030 * 3) + (0.1857869 * 5) + (0.06081 * 1)
= 3.2499
= $3.25
question is above in the picture
Answers
Answer:
Known
Step-by-step explanation:
I hope this helps :)
Answer:
Known. The other answers are absurd.
Step-by-step explanation:
In geometry, often times you must have at least one angle to problem solve and find the rest. So having a known angle to build off of is important. Vertical Angles and Supplementary Angles are examples of things that require a known angle to find the rest. Why?
Say you only know one angle and the other is congruent to that angle, but across from it...Due to the theory of vertical angles, you now know the other side has to be the same/congruent. For supplementary angles, say you're dealing with a shape like the one I've attached. Once you have a or b, you can determine c. You have to know at least one of those angles to determine it's other unknown angles.
Helppppppppppp AND NO LINKS
Answers
Will give brainlest, find the area
Answers
A student bought a truck with a down payment of $4,000 and monthly payments of
$250 for four years. What was the total cost of the truck?
Answers
what is the greatest decimal in hundredths that can be rounded to 14.5? What is the least
Answers
Answer:
14.45 and 14.54Step-by-step explanation:
Rule for rounding:
Round up if number is between 5 and 9Round down if number is between 0 and 4What numbers in hundredths can be rounded to 14.5?
14.45 to 14.49and
14.50 to 14.54From above we see that:
The greatest decimal is 14.54The least decimal is 14.45Xander had $24, he spent 3/4 of it how much money does he have left?
Answers
Answer:
6.25
Step-by-step explanation:
Lin went hiking on five different weekends. The table shows the
elevation changes in feet for each of her five hikes. Fill in the
missing numbers
Initial Elevation
Elevation Change Final Elevation
hike
768
1
-96
672
hike
2
82
20
hike
62
3
- 100
hike
354
4
129
hike
-20
-40
-60
5
Explain what each of the numbers-20, -40, and -60 tells you about
hike 5. What does it mean for the numbers to be negative in this
situation?
Answers
Answer:
Hike 1 : 768, -96, 672
Hike 2: -62, 82, 20
Hike 3: 62, -100, -38
Hike 4: 354, -225, 129
Hike 5: -20, -40, -60
The -20 is at what surface level Lin began Hike 5 at. From there, they continued to go in this situation lower by - 40, and arrive at the surface region of -60.
Negative numbers in the present circumstance mean under 0. (Underneath surface region)
A town has a population of 5000 and grows at 3.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 7300?
Answers
Answer:
Step-by-step explanation:
This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is
where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then
a = 5000
If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So
b = 1.035
Our function is
where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.
and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.
Begin by dividing both sides by 5000 to get
and take the natural log of both sides:
The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:
To solve for x, we now divide both sides by ln(1.035):
Do that division on your calculator and get that
x = 11.0 years.
That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)
A company offers a flood insurance policy that costs a homeowner $200 per year, and the company will make a payout of $100,000 to the homeowner if they have a flood in that year. The company set this price based on the probability of a flood in the area being 0.001. The table below displays the probability distribution of X=X= the company's profit from one of these policies.
No flood Flood
X=profit $200 -$99,800
P(X) 0.999 0.001
Given that μX=$100, calculate σX.
You may round your answer to the nearest dollar.
Answers
Answer:
σX = 3161
Step-by-step explanation:
The standard deviation is the square root of the multiplication of each probability multiplied by the squared difference between the values and the mean.
In this question:
[tex]\sigma X = \sqrt{0.999*(200-100)^2 + 0.001*(-99800-100)^2} = 3160.7[/tex]
Rounding to the nearest dollar, σX = 3161
分
타
Sin Of = f (m + You
3
Answers
Answer:
what do you mean by your question I didn't understand it
Select ALL the correct answers.
A pitcher for a professional baseball team allows runs in the first nine games he starts this season. Let A be the set of the number of
runs allowed by the pitcher in his first nine starts.
A = {1, 4, 2, 2, 3, 1, 1, 2, 1}
In the tenth game he starts, he allows 9 runs. Let B represent the set of the number of runs allowed in all ten games he has started.
Select the true statements.
The median of Bis 1 run more than the median of A.
The interquartile range of B is greater than the interquartile range of A.
The interquartile range of A is 1 less than the interquartile range of B.
The median of A is the same as the median of B.
Including the runs allowed in the tenth game does not cause the spread of the data to
change
Answers
Answer:
The median of A is the same as the median of B.
The interquartile range of B is greater than the interquartile range of A.
Step-by-step explanation:
Given that:
A = number of runs allowed in first 9 games
A = {1, 4, 2, 2, 3, 1, 1, 2, 1}
Rearranging A : 1, 1, 1, 1, 2, 2, 2, 3, 4
Median A = 1/2(n + 1) th term
Median A = 1/2(10) = 5th term = 2
Q1 of A = 1/4(10) = 2.5th term = (1 + 1)/ 2 = 1
Q3 of A = 3/4(10) = 7.5th term = (2+3)/2 = 2.5
Interquartile range = Q3 - Q1 = 2.5 - 1 = 1.5
Number of runs allowed in 10th game = 9
B = {1, 4, 2, 2, 3, 1, 1, 2, 1, 9}
Rearranging B = 1, 1, 1, 1, 2, 2, 2, 3, 4, 9
Median A = 1/2(n + 1) th term
Median A = 1/2(11) = 5.5th term = (2+2)/2 = 2
Q1 of A = 1/4(11) = 2.75th tetm = (1 + 1)/ 2 = 1
Q3 of A = 3/4(11) = 8.25th term = (3+4)/2 = 3.5
Interquartile range = Q3 - Q1 = 3.5 - 1 = 2.5
Median A = 2 ; median B = 2
IQR B = 2.5 ; IQR A = 1.5 ; IQR B > IQR A
Answer it. -10 x -2 =
Answers
Answer: 20
Step-by-step explanation: it is 20 because 2 negative numbers multiplied by each other will always be positive
Complete the following to describe how to draw to diagram to represent the answer 3÷3/5
Answers
Answer:
you can do a diagram representing this product by drawing a box with six squares and then putting three lines for each box and divide 3÷3 and you will get 5
In this rectangular box, EF = 6, FD = 5, and DB = 8. Find A F . A. V61 B. V89 C. 10 D. 5V5
Answers
Answer:
Step-by-step explanation: Got it right on E D G E N U I T Y
Answer:
D
Step-by-step explanation:
The height of one cylinder is 8 cm, and the radius of its base is 5 cm. The height of a second cylinder is 24 cm, and the radius of its base is 5 cm. How many times the volume of the first cylinder is the volume of the second cylinder?
Answers
Answer:
Step-by-step explanation:
volume₁ = π5²·8 = 200π cm³
volume₂ = π5²·24 = 600π cm³
volume₂ = 3×volume₁
Answer:
It is 3, hopefully you got a good score! :D
Step-by-step explanation:
Find the product of 5/3 with quotient of 2/11 and 4/11
Answers
Answer:
5/6
Step-by-step explanation:
quotient of 2/11 and 4/11 is 22/44 or 1/2
5/3 · 1/2 = 5/6
The variable z varies jointly with x and y. Also, z = -75 when x = 3 and y = -5.
What equation describes this variation?
x = kyz
y = kxz
z = kxy
k = xyz
Answers
What equation describes this variation?
z = kxy
What is the constant of variation?
k = 5
When x = 1 and y = –2, z =
-10
Step by Step Explanation:
With the equation z = kxy and the values for z, x, and y, we can find k.
z = kxy
-75 = (k) (3) (-5)
-75 = (k) (-15)
5 = k
k = 5 (final answer).
To check our work, we just enter all of the values and make sure it adds up.
z = kxy
-75 = (5)(3)(-5)
-75 = 15(-5)
-75 = -75
correct!
Do the same to find the answer for the next part to get -10.
Further proof in the file attached.
Answer:
C.
5
-10
NEXT SLIDE:
3/8
3/40
NEXT SLIDE:
A.
7
42
NEXT SLIDE:
D.
6
NEXT SLIDE:
B.
10
LAST SLIDE:
A.
D.
Step-by-step explanation:
100% Edge 2021
I did the Assignment.
Good luck catching up in Edge before the end date fam!
true or false: a well-designed sample survey, the sample percentage is very likely to equal the population percentage. explain.
Answers
Answer:
false
Step-by-step explanation:
There's going to be some variabilty between the sample and population percentages, cus the sample only contains part of of the population. Even if it is a well designed survey, it doesn't affect this, because no matter how good the sample is, there will always be variability between the two (unless the sample includes the whole population). I hope this helps :)
please help me on this question. I forgot how to do it
Answers
Answer:
141
Step-by-step explanation:
Area of triangle = 24
Area of Trapezoid= 117
117+24
141
Order the angles in each triangle from smallest to largest.
Answers
9514 1404 393
Answer:
B: L, M, N
Step-by-step explanation:
The sides are listed from shortest to longest. The angles opposite these sides will be in order smallest to largest. The name of the opposite angle is the vertex whose name is missing from the side's name.
MN is opposite angle L, the smallest
LN is opposite angle M, the middle-size
LM is opposite angle N, the largest.
Smallest to largest, the angles are ∠L, ∠M, ∠N.