A past survey of 1, 068,000 students taking a standardized test revealed that 8.9% of the students were planning on studying engineering in college.
In a recent survey of 1, 476,000 students taking the SAT. 9.2% of the students were planning to study engineering.
Construct a 95% confidence interval for the difference between proportions ^p1−^p2 by using the following inequality. Assume the samples are random and independent.
(^p1−^p2)−zc√^p1^q1n1+^p2^q2n2
The confidence interval is _____
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The interval is [tex]-0.0037 < p_1-p_2<-0.0023[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n _1 = 1068000[/tex]
The first sample proportion is [tex]\r p_1 = 0.089[/tex]
The second sample size is [tex]n_2 = 1476000[/tex]
The second sample proportion is [tex]\r p_2 = 0.092[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = (100 - 95 )\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is
[tex]Z_{\frac{\alpha }{2} } =z_c= 1.96[/tex]
Generally the 95% confidence interval is mathematically represented as
[tex](\r p_1 - \r p_2 ) -z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}} < (p_1 - p_2 ) < (\r p_1 - \r p_2 ) +z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}}[/tex]
Here [tex]\r q_1[/tex] is mathematically evaluated as [tex]\r q_1 = (1 - \r p_1)= 1-0.089 =0.911[/tex]
and [tex]\r q_2[/tex] is mathematically evaluated as [tex]\r q_2 = (1 - \r p_2) = 1- 0.092 = 0.908[/tex]
So
[tex](0.089 - 0.092 ) -1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}} < (p_1 - p_2 ) < (0.089 - 0.092 ) +1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}}[/tex]
[tex]-0.0037 < p_1-p_2<-0.0023[/tex]
Related Questions
y- (-3y) combine the like terms to create an equivalent expression
Answers
Answer:
4y
Step-by-step explanation:
[tex]y- (-3y)\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=y+3y\\\\=4y[/tex]
Hello there! :D
I love showing people how to use this concept, so lets get right to it! If you have trouble with negative (-) signs and how they interact with each other, I suggest you watch some Khan academy videos, it could realy help you in the future! :)
Alright, so here's the general rule: (multiplication and division)
-,-= +
-,+ = -
+,+=+
So, with this rule, I think we can solve!
Firstly, remember PEMDAS.
Let's look at the signs first. Two negatives equal a positive. Make the 3y in the parenthesis positive. Think of the negative sign as a -1 that is being multiplied by the (-3y) and the y.
That would look like this:
(y) (-1) (-3y)
Now we have:
y*(3y)
So when multiplying a variable by a variable, it becomes squared.
So, we would have 3y^2 or [tex]3y^{2}[/tex]
If you have any questions about this problem feel free to comment on this answer.
I hope this helped you and you have a wonderful day,
Kai xx
PLEASE HELP! A) 7 B) 5.7 C) 4.7 D) 8.2
Answers
Answer:
[tex]\Large \boxed{\mathrm{A) \ 7}}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions to solve the problem.
tan(θ) = opp/adj
tan(35) = x/10
Multiply both sides by 10.
10 tan(35) = x
x = 7.00207538...
ANSWER. 7
Express as a trinomal (2x-9) (3x+4)
Answers
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]\begin{aligned} (2x-9)(3x+4)=\ &2(3x+4)\\&-9(3x+4)\\\\ =\ & 6x+8\\&-27x-36\\\\=\ &(6-27)x+8-36\\\\=\ &-21x-28\end{aligned}[/tex]
Thank you.
a Find the amount compounded annually on Rs 25,000 for 2 years if the rates of
interest for two years ore 10 % and 12 % respectively,
Answers
Answer:
Rs 30800
Step-by-step explanation:
The formula for compound interest is
A = P[1 + (r/100)]^t, where
A = amount of compounded interest
P = principal amount
r = interest rate
Applying this to our question, we have
A = 25000 [1 + (10/100)] [1 + (12/100)]
A = 25000 (1 + 0.1) (1 + 0.12)
A = 25000 * 1.1 * 1.12
A = 25000 * 1.232
A = 30800
Linear function g is shown in the graph. Write the slope-intercept form of the equation representing this function.
Answers
Answer:
y = -2x + 1
Step-by-step explanation:
First, find the slope with rise/run (y2 - y1) / (x2 - x1)
We can use the points (-1, 3) and (0, 1)
Plug in the points:
(1 - 3) / (0 + 1)
-2/1
= -2
The y-intercept is (0, 1) because that is the point where the line intercepts the y axis. So, we can plug in the slope and y-intercept into the equation:
y = mx + b
y = -2x + 1
Find the ratio of the area inside the square but outside the circle to the area of the square in the picture
Answers
Answer:
0.2146
Step-by-step explanation:
From the picture:
The radius of the circle = r. This means that the area of the circle = πr²
Also For the square, the length of the square = 2r, Therefore the area of the square = Length × length = 2r × 2r = 4r²
The area inside the square but outside the circle = Area of square - Area of circle = 4r² - πr² = r²(4 - π) = 0.8584r²
The ratio of the area inside the square but outside the circle to the area of the square = r²(4 - π) / 4r² = (4 - π) / 4 = 1 - π/4 = 0.2146
The amount of time adults spend watching television is closely monitored by firms becayse this helps to determine advertising pricing for commercials. Compete parts (a) through (d).
a) Do you think the variable "weekly time spent watching television" would be normally distributed? Yes or No.
If not, what shape would you expect the variable to have? Skewed Left, Skewed Right, Uniform or Symmetric?
b) According to a certain survey, adults spend 2.35 hours per day watching television on a weekday. Assume that the standard deviation for "time spent watching TV on a weekday" is 1.93 hours. If a random sample of 40 adults is obtained, describe the sampling distribution of x-bar, the mean amount of time spent watching TV on a weekday.
Mean =
A) 2.35
B) 1.89
C) 2.25
SD = (round to six decimal places as needed)
c) Determine the probability that a random sample of 40 adults results in a mean time watching television on a weekday of between 2 and 3 hours.
The probability is ____ .
d) One consequence of the popularity of the Internet is that it is thought to reduce TV watching. Suppose that a random sample of 35 people who consider themselves avid Internet users results in a mean time of 1.89 hours watching TV on a weekday. Determine the likelihood of obtaining a sample mean of 1.89 hours or less from a population who mean is presumed to be 2.35 hours.
The likelihood is ____ .
Based on the result obtained, do Internet users watch less TV? Yes or No.
Answers
Answer:
Yes based on the result 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5
Step-by-step explanation:
a)The variable "weekly time spent watching television" is normally distributed and is skewed right.
b) Mean = x` 2.35 hours
Standard deviation = s/√n = 1.93/√40=1.93/6.3245553= 0.3051598
c) P(2<X<3) = P (2-2.35/ 0.3051598< Z< 3 -2.35/ 0.3051598)
= P ( -1.14694 < Z <2.13003)
= 0.3729 + 0.4830
=0.8559
So the probability is 0.8559
(0.8559 we check the value of 2.13 from the normal distribution tables and add with the value of 1.14 to get the in between value -1.14694 < Z <2.13003)
d) Here n = 35 , s= 1.93 , mean = 2.35 and x= 1.89
So Putting the values
P (X ≤ 1.89) = P (Z ≤ 1.89- 2.35/ 1.93 / √35)
= P ( Z ≤ -0.238341/ 5.9160797)
= P ( Z ≤ -0.04028)
= 0.5 - 0.0159
= 0.4841
Similarly again subtracting from 0.5 the value from normal distribution table to get less than or equal to value.
Yes based on the result 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5
The mean value is 2.35, SD is 1.93 with an SD error of 0.3051597 and the probability is 0.8559, and yes 0.4841 internet users watch less TV.
It is given that the amount of time adults spend watching television is closely monitored by firms because this helps to determine advertising pricing for commercials.
It is required to find the standard deviation and probability.
What is a confidence interval for population standard deviation?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
We know the formula for standard error:
[tex]\rm SE = \frac{s}{\sqrt{n} }[/tex]
Where 's' is the standard error
and n is the sample size.
In the question the value of s = 1.93 hours
and sample size n = 40
[tex]\rm SE = \frac{1.93}{\sqrt{40} }\\[/tex]
SE = 0.3051597
For the probability between 2 and 3 hours.
= P(2<X<3)
[tex]\\\rm =P(\frac{2-x)}{s} < Z < \frac{3-x)}{s})\\\\\rm = P(\frac{(2-2.35)}{0.3051598} < Z < \frac{(3-x)}{0.3051598})\\\\[/tex] (because the mean value x is 2.35)
=P(-1.14694 <Z < 2.13003)
=0.3729+ 0.4830 ( values get from Z table for -1.14 and 2.13 )
=0.8559
For P(X≤1.89)
[tex]\rm P(Z\leq \frac{(x'-x)}{\frac{s}{\sqrt[]{n} } } )\\\\\rm P(Z\leq \frac{(1.89-2.35)}{\frac{1.89}{\sqrt[]{35} } } )[/tex]
= P(Z ≤ -0.04028)
= 0.5 - 0.0159
=0.4841
Based on the result of 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5.
Thus, the mean value is 2.35, SD is 1.93 with an SD error of 0.3051597 and the probability is 0.8559, and yes internet users watch less TV.
Learn more about the standard deviation here:
https://brainly.com/question/12402189
Find the measure of ∠ 1 in O.
Answers
Answer:
10°
Step-by-step explanation:
The angle subtended at the circumference is half the angle subtended at the centre of the circle i.e. 20°÷2=10°
Find the value of x.
Answers
Answer:
[tex]\sqrt{205}[/tex]
Step-by-step explanation:
Using the pythagorean theorem, [tex]x^{2} +18^{2} =23^{2} \\[/tex] so that means [tex]x^{2} = 23^{2} -18^{2} =205[/tex] so x = [tex]\sqrt{205}[/tex]
A fitness center is interested in the average amount of time a client exercises in the center each week. Match the vocabulary word with its corresponding example.
Answers
Answer:
Step-by-step explanation:
A. Data of the study: All 45 exercise times there were recorded from the participants in the study
B. Parameter of the study: The average amount of time that all clients exercise in one week.
C. Variable of the study: The amount of time that any given client from the fitness center exercises.
D. Population for the study: All clients at the fitness center.
E. Sample of this study: The 45 client from the fitness center who participated in the study.
F. Statistics of the study: The average amount of time that a sample of clients exercises in one week
Stavros is 1.6m tall. His sister is 95cm tall. How many centimeters taller is Stavros than his sister?
Answers
HELPP !! A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of
7% of sales. Write a linear equation for the salesperson's monthly wage W in terms of monthly sales S
Answers
Answer:
w=5000+0.7s
Step-by-step explanation:
please give 5 star I need it
ASAP: “Use a number line to order the numbers from least to greatest.” 1/5, -0.5, 0, 0.4, 1 1/2, -1.
Answers
Answer:
-1, -0.5, 0, 0.4, 1/5, 11/2
Step-by-step explanation:
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y + z2)j + (z + x2)k, C is the triangle with vertices (5, 0, 0), (0, 5, 0), and (0, 0, 5).
Answers
Answer:
[tex]\mathbf{\int_C F*dr= -125}[/tex]
Step-by-step explanation:
Given that:
[tex]F(x,y,z) = ( x+ y^2) i + (y +z ^2) j+(z + x^2)k[/tex] , where C is the triangle with vertices (5, 0, 0), (0, 5, 0), and (0, 0, 5).
The objective is to use Stokes' Theorem to evaluate CF. dr
Stokes Theorem : [tex]\int_c F .dr = \iint _s \ curl \ F. dS[/tex]
To estimate curl F , we need to find the partial derivatives:
So;
[tex]P = x+y^2[/tex]
partial derivative is:
[tex]\dfrac{\partial P }{\partial y }= 2y[/tex]
[tex]\dfrac{\partial P }{\partial z }= 0[/tex]
[tex]Q = y + z^2[/tex]
partial derivative is:
[tex]\dfrac{\partial Q }{\partial x }= 0[/tex]
[tex]\dfrac{\partial Q }{\partial z }= 2z[/tex]
[tex]R = z +x^2[/tex]
partial derivative is:
[tex]\dfrac{\partial R }{\partial x }= 2x[/tex]
[tex]\dfrac{\partial R }{\partial y }= 0[/tex]
These resulted into
curl F = (0 - 2z)i + ( 0 -2x) j + ( 0 - 2y) k
= ( -2z, -2x, -2y )
The normal vector and the equation of the plane can be expressed as follows:
If a = (0,5,0 - ( 5,0,0)
a = ( -5,5,0 )
Also ,
b = (0, 0,5) - (5,0,0)
b = (-5. 0,5)
However,
[tex]a \times b = \begin {vmatrix} \begin{array} {ccc} i &j&k \\-5&5&0 \\-5&0&5 \\ \end {array} \end {vmatrix}[/tex]
a × b = (25 - 0)i - (-25-0)j+ (0+25)k
a × b = 25i +25j +25k
∴ the normal vector can be n = (1,1,1)
If we assume x to be x = (x,y,z)
and [tex]x_0 = (5,0,0)[/tex]
Then
[tex]n*(x-x_0) =0[/tex]
[tex](1,1,1)*(x-5,y-0,z-0) =0[/tex]
[tex]x-5+y+z =0[/tex]
collecting like terms
x +y +z = 5
now, it is vivid that from the equation , the plane of the normal vector =(1,1,1)
Similarly, x+y+z = 5 is the projection of surface on the xy - plane such that the line x +y = 5
Thus; the domain D = {(x,y) | 0 ≤ x ≤ 5, 0 ≤ y ≤ 5 - x}
To evaluate the line integral using Stokes' Theorem
[tex]\iint_S \ curl \ F .dS= \iint _S (-2z,-2y,-2x) *(1,1,1) \ dS[/tex]
[tex]\iint_S \ curl \ F .dS= \iint _S -2z-2y-2x \ dS[/tex]
[tex]\iint_S \ curl \ F .dS= \iint _S -2(5-x-y)-2y-2x \ dS[/tex]
[tex]\iint_S \ curl \ F .dS= \iint _S -(10) \ dS[/tex]
[tex]\int_C F*dr= \int ^5_0 \ \int ^{5-x}_0 -10 \ dy \ dx[/tex]
[tex]\int_C F*dr= -10 \int^5_0 (5-x) \ dx[/tex]
[tex]\int_C F*dr= -10 \begin {bmatrix} 5x - \dfrac{x^2}{2} \end {bmatrix}^5_0[/tex]
[tex]\int_C F*dr= -10 \begin {bmatrix} 25 - \dfrac{25}{2} \end {bmatrix}[/tex]
[tex]\int_C F*dr= -10 \begin {bmatrix} \dfrac{25}{2} \end {bmatrix}[/tex]
[tex]\mathbf{\int_C F*dr= -125}[/tex]
which expression is equivalent to 2(x-3) + 4
Answers
Answer:
2x - 2
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Distribute parenthesis
2x - 6 + 4
Step 2: Combine like terms
2x - 2
And we have our answer!
Answer:
[tex]2( x -3) + 4 \\ 2x - 6 + 4 \\ [/tex]
Adam was curious if quadrilaterals ABCDABCDA, B, C, D and GFEHGFEHG, F, E, H were congruent, so he tried to map one figure onto the other using transformations:
Adam concluded:
"It's not possible to map ABCDABCDA, B, C, D onto GFEHGFEHG, F, E, H using a sequence of rigid transformations, so the quadrilaterals are not congruent."
What error did Adam make in his conclusion?
Answers
Answers reflection (b)
Step-by-step explanation:
it’s right on 8th grade khan ywwww
So he tried to reflect(b) map one figure onto the other using transformations.
Are quadrilaterals congruent?If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Are two quadrilaterals congruent?Both the theorems are proved now which states that quadrilaterals are congruent to one another. Note: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles and the opposite sides of a parallelogram are congruent.
Learn more about the quadrilaterals are not congruent at
https://brainly.com/question/20429
#SPJ2
#12 will mark as brainliest
Answers
Answer:
-i
Step-by-step explanation:
[tex]\sqrt{-1}[/tex] * [tex]\sqrt{-1}[/tex] * [tex]\sqrt{-1}[/tex] = -i
Trigonometry!! NEED HELP!!
Answers
=============================================
Explanation:
If angle x is the reference angle, then the side 9 is the adjacent side (it is the closer leg to angle x). The hypotenuse is 17 as it is opposite the largest angle. The largest side is always opposite the largest angle in a triangle.
-----------------
cos(angle) = adjacent/hypotenuse
cos(x) = 9/17
x = arccos(9/17)
x = 58.034281249203
x = 58
Arccosine is the same as inverse cosine, written as [tex]\cos^{-1}[/tex]
Make sure your calculator is in degree mode.
-------------
Edit:
After finding x, we can find y
x+y = 90
58+y = 90
y = 90-58
y = 32
how many numbers are there from 75 to 586 that are divisible by 12 and 30
Answers
Answer:
8
Step-by-step explanation:
Numbers divisible by 12 and 30:
12= 2*630= 5*6LCM(12,30) = 2*5*6= 60So, numbers should be divisible by 60
To find the greatest one divide 586 by 60 and take whole part of quotient, which is 9, so there are 9 multiples of 60 smaller than 586.
Excluding 60 which is less than 75.
So required number is 9 - 1 = 8.
POINTS!!!!!!
If an object is dropped from a height of h meters and it’s the ground in t seconds, then t = *square root* h/4.9. Suppose that an object is dropped from the top of a building that is 290.57 meters tall. How long does it take to hit the ground?
Round your answer to the nearest tenth....
?????? Seconds
Please state how many seconds first...
Answers
Answer:
7.7 seconds
Step-by-step explanation:
Put the given height into the formula and do the arithmetic.
t = √(290.57/4.9) = √59.3 ≈ 7.7 . . . seconds
The object will take 7.7 seconds to hit the ground.
PLEASE HELP IM CONFUSED
If angle ACB is 1 degree 25 minutes (1°25’) what is angle ACD. Please give your answer as degrees and minutes.
Answers
Answer:
178° 35'
Step-by-step explanation:
∠ACB and ∠ACD are supplementary, so they add up to 180°.
First, convert to degrees (there are 60 minutes in a degree).
∠ACB = 1°25' = 1° + (25/60)° = 1.4167°
Now find the supplementary:
∠ACD = 180° − 1.4167°
∠ACD = 178.5833°
∠ACD = 178° 35'
f the perimeter of the adult pinball machine is 167 inches, what is the length, in inches of Segment line G prime A prime ? Type the numeric answer only in the box below
Answers
Answer:
8 inches
Step-by-step explanation:
The computation of the length, in inches of Segment line G prime A prime is shown below:-
Data provided
In two quadrilateral GAME and G'A'M'E',
ME = 35 inches
AM = GE = 56 inches
M'E' = 14 inches
Also, the perimeter of quadrilateral GAME = 167 inches
GA + AM + ME + GE = 167
Now we will put the values into the above equation
GA + 56 + 35 + 56 = 167
GA + 147 = 167
So,
GA = 20 inch
Therefore
GAME is closely related to G'A'M'E'
Now,
By the property of similar figures,
[tex]\frac{M E}{M' E'} = \frac{GA}{G'A'}[/tex]
[tex]G'A' = \frac{M'E'\times GA}{ME} \\\\ = \frac{14\times 20}{35}[/tex]
= 8 inches
what is 826 x 3,569 equal to
Answers
Answer:
826×3569=2947994 ans
Can someone help ! Please !!!! I don’t understand!
Answers
Answer:
(A∩B')∪(A'∩B)(A∩B)'Step-by-step explanation:
Here, we'll use an apostrophe to signify the complement of a set.
__
(a) The shaded portion is two disjoint (non-overlapping) sections, so must be the union of something. The shaded space on the left is that part of A that is not in B, so it is A∩B'. Similarly, the shaded space on the right is that part of set B that is not in set A: A'∩B. Then the shaded area altogether is the union of these sets:
(A∩B')∪(A'∩B)
__
(b) For this one, it might be easier to identify the unshaded area. That is where the sets A and B overlap, so it is A∩B. Then the area that is not that area is the complement of this:
(A∩B)'
Reed wants to have a square garden plot in his backyard. He has covered enough compost to cover an area of 214 square feet.To the nearest tenth of a foot how long can a side of his garden be?
Answers
Answer:
o the nearest tenth of ft
Length of one of the side= 14.6 ft
Step-by-step explanation:
Reed wants to have a square garden plot in his backyard. He has covered enough compost to cover an area of 214 square feet.
His square garden is a square one, and the area of a square is the square of one of it's sides .
So if the area= 214 ft²
Length of one of the side = √(214 ft²)
Length of one of the side= 14.6287 ft
To the nearest tenth of ft
Length of one of the side= 14.6 ft
Find the inverse of the function f(x)= 6x^3-8
Answers
Hello, please consider the following.
[tex](\forall x \in \mathbb{R}) \\ \\ x=(f^{-1}of)(x)\\\\=(fof^{-1})(x)\\\\=f(f^{-1}(x))\\\\=6\left( f^{-1}(x) \right) ^3-8 = x\\\\\text{We need to express }f^{-1}(x) \text{ in function of x.}\\\\\text{Let's do it!}[/tex]
[tex]6\left( f^{-1}(x) \right) ^3-8 = x\\\\\left( f^{-1}(x) \right) ^3 =\dfrac{x+8}{6}\\\\\Large \boxed{\sf \bf \ \ f^{-1}(x)=\sqrt[3]{\dfrac{x+8}{6}}\ \ }[/tex]
Thank you
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8
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6
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6
-38 - 7y = 2 - 7(y + 6)
Answers
Answer:
No solution
Step-by-step explanation:
[tex]-38 - 7y = 2 - 7(y + 6)\\\\\mathrm{Expand\:}2-7\left(y+6\right):\quad -7y-40\\-38-7y=-7y-40\\\\\mathrm{Add\:}38\mathrm{\:to\:both\:sides}\\-38-7y+38=-7y-40+38\\\\Simplify\\-7y=-7y-2\\\\\mathrm{Add\:}7y\mathrm{\:to\:both\:sides}\\-7y+7y=-7y-2+7y\\\\Simplify\\\\0=-2\\\mathrm{The\:sides\:are\:not\:equal}\\No\: solution[/tex]
Answer:
No solution
Step-by-step explanation:
First do distribute property
-38-7y=2-7y-42
then combine like terms the 2 and the -42
-38-7y=-40-7y add 7y from both sides
-38+y=-40 add 38 to -40 you get -2
0=-2 no solution
Milo receives a commission of 8% on all sales. If his commission on a sale was $97.84 find the cost of the item he sold
Answers
Answer:
Cost of the item sold= $1,223
Step-by-step explanation:
Let
x= cost of the item sold
$97.84=commission on the item
Percentage of the commission=8%
To find the cost of the item sold
Commission=8% of cost of the item
97.84=0.08 * x
97.84=0.08x
Divide both sides by 0.08
97.84 / 0.08 = 0.08x / 0.08
1,223=x
x=$1,223
Therefore, cost of the item sold= $1,223
consider the set of A={0,3,5,8}
Answers
Find the eccentricity, b. identify the conic, c. give an equation of the directrix, and d. sketch the conic.
r=12/3--10 Cosθ
Answers
Answer:
a) 10/3
b) hyperbola
c) x = ± 6/5
Step-by-step explanation:
a) A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:
[tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]
Given the conic equation: [tex]r=\frac{12}{3-10cos\theta}[/tex]
We have to make it to be in the form [tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]:
[tex]r=\frac{12}{3-10cos\theta}\\\\multiply\ both\ sides\ by\ \frac{1}{3} \\\\r=\frac{12*\frac{1}{3}}{(3-10cos\theta)*\frac{1}{3}}\\\\r=\frac{12*\frac{1}{3}}{3*\frac{1}{3}-10cos\theta*\frac{1}{3}}\\\\r=\frac{4}{1-\frac{10}{3}cos\theta } \\\\r=\frac{\frac{10}{3}(\frac{6}{5} ) }{1-\frac{10}{3}cos\theta }[/tex]
Comparing with [tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]
e = 10/3 = 3.3333, p = 6/5
b) since the eccentricity = 3.33 > 1, it is a hyperbola
c) The equation of the directrix is x = ±p = ± 6/5