An
Step-by-step explon:
A telescope contains both a parabolic mirror and a hyperbolic mirror. They share focus , which is 46feet above the vertex of the parabola. The hyperbola's second focus is 6 ft above the parabola's vertex. The vertex of the hyperbolic mirror is 3 ft below . Find the equation of the hyperbola if the center is at the origin of a coordinate system and the foci are on the y-axis. Complete the equation.
the center is at the origin of a coordinate system and the foci are on the y-axis, then the foci are symmetric about the origin.
The hyperbola focus F1 is 46 feet above the vertex of the parabola and the hyperbola focus F2 is 6 ft above the parabola's vertex. Then the distance F1F2 is 46-6=40 ft.
In terms of hyperbola, F1F2=2c, c=20.
The vertex of the hyperba is 2 ft below focus F1, then in terms of hyperbola c-a=2 and a=c-2=18 ft.
Use formula c^2=a^2+b^2c
2
=a
2
+b
2
to find b:
\begin{gathered} (20)^2=(18)^2+b^2,\\ b^2=400-324=76 \end{gathered}
(20)
2
=(18)
2
+b
2
,
b
2
=400−324=76
.
The branches of hyperbola go in y-direction, so the equation of hyperbola is
\dfrac{y^2}{b^2}- \dfrac{x^2}{a^2}=1
b
2
y
2
−
a
2
x
2
=1 .
Substitute a and b:
\dfrac{y^2}{76}- \dfrac{x^2}{324}=1
76
y
2
−
324
x
2
=1 .
It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.
(a) On average, how many young adults do not own a landline in a random sample of 100?
(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?
(c) What is the proportion of young adults who do not own a landline?
(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?
(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?
(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?
(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?
Answer:
a) 75
b) 4.33
c) 0.75
d) [tex]3.2 \times 10^{-13}[/tex] probability that no one in a simple random sample of 100 young adults owns a landline
e) [tex]6.2 \times 10^{-61}[/tex] probability that everyone in a simple random sample of 100 young adults owns a landline.
f) Binomial, with [tex]n = 100, p = 0.75[/tex]
g) [tex]4.5 \times 10^{-8}[/tex] probability that exactly half the young adults in a simple random sample of 100 do not own a landline.
Step-by-step explanation:
For each young adult, there are only two possible outcomes. Either they do not own a landline, or they do. The probability of an young adult not having a landline is independent of any other adult, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.
This means that [tex]p = 0.75[/tex]
(a) On average, how many young adults do not own a landline in a random sample of 100?
Sample of 100, so [tex]n = 100[/tex]
[tex]E(X) = np = 100(0.75) = 75[/tex]
(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100(0.75)(0.25)} = 4.33[/tex]
(c) What is the proportion of young adults who do not own a landline?
The estimation, of 75% = 0.75.
(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?
This is P(X = 100), that is, all do not own. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 100) = C_{100,100}.(0.75)^{100}.(0.25)^{0} = 3.2 \times 10^{-13}[/tex]
[tex]3.2 \times 10^{-13}[/tex] probability that no one in a simple random sample of 100 young adults owns a landline.
(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?
This is P(X = 0), that is, all own. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.75)^{0}.(0.25)^{100} = 6.2 \times 10^{-61}[/tex]
[tex]6.2 \times 10^{-61}[/tex] probability that everyone in a simple random sample of 100 young adults owns a landline.
(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?
Binomial, with [tex]n = 100, p = 0.75[/tex]
(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?
This is P(X = 50). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 50) = C_{100,50}.(0.75)^{50}.(0.25)^{50} = 4.5 \times 10^{-8}[/tex]
[tex]4.5 \times 10^{-8}[/tex] probability that exactly half the young adults in a simple random sample of 100 do not own a landline.
sketch the graph of y=x(x-6)^
Answer:
i have attached pic of the graph
i hope this helps you
Can u please help I got 1 minnnn lefttttt
Answer:
26 cm
Step-by-step explanation:
P = 2a + 2b
a = side
b = base
Answer:
The area=base×height
=10×4
=40cm^2
perimeter=2(length+breadth)
I think to find the height Dc you use the pythagoras theorem of
Dc^2=de^2+ce^2
=√16+9
=5
therefore the perimeter will be
p=2(5+10)
=20cm
I hope this helps and sorry if it's wrong
Stuck on this one!!
Shelly believes the honor roll students at her school have an unfair advantage in being assigned to the math class they request. She asked 500 students at her school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are shown in the table below:
Honor roll Not on honor roll Total
Received math class requested 125 215 340
Did not get math class requested 80 80 160
Total 205 295 500
Help Shelly determine if all students at her school have an equal opportunity to get into the math class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.
Answer: No, there isn't equal opportunity
======================================================
Explanation:
Let's define the two events
A = person is on the honor rollB = person got the math class they requestedFrom the table, we see that
P(B) = 340/500 = 0.68
meaning that there's a 68% chance of picking someone who got the class they wanted (i.e. 68% of the people got the class they wanted)
------------
Now let's assume that the person is on the honor roll. This means we only focus on the "honor roll" column. There are 125 people here that got the class they wanted out of 205 honor roll students total.
So,
P(B given A) = 125/205 = 0.609756
which rounds to 0.61
This says that if a person is on the honor roll, then they have roughly a 61% chance of getting the class they want.
The chances have gone down from 68% to 61% roughly.
------------
It appears that being on the honor roll does affect your chances of getting into the class you want.
Therefore, all students do not have the same equal opportunity.
We would need to have P(B) and P(A given B) to be the same exact value for true equal opportunity to happen.
All students do not have equal opportunity.
From the table, we have the following parameters:
205 people are on honor roll call340 people got the math class requested500 people were surveyedThe above means that:
The probability that a person is on honor roll call is:
p1 = 205/500
p1 = 0.41
The probability that a person got the math class requested
p2 = 340/500
p2 = 0.68
Both probabilities are not equal.
Hence, it is true that all students do not have equal opportunity.
Read more about probability at:
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Please answer this and show the work/explain for me
2/7m - 1/7 = 3/14
help please! I need the answer quickly! thank you!
Answer:
B) 1 unit to the left
Step-by-step explanation:
Cho A=( căn x -4x /1-4x -1) : (1+2x/1-4x -2căn x/ 2căn x -1 -1)
Answer:
0.85714285714286 x 100 = 85.7143%.
Step-by-step explanation:
The sum of three numbers is 124
The first number is 10 more than the third.
The second number is 4 times the third. What are the numbers?
Answer:
182/3,3 8/3, 152/3
Step-by-step explanation:
a+b+c=124
a trừ c= 10
4b=c
Answer:
a=29,b=79,c=19
Step-by-step explanation:
a=c+10
b=4c
=> a+b+c=c+10+4c+c=124
=> c=19
=> a= 29, b=79
(b) If 124n= 232 five, find n.
Answer:[tex]n=\frac{58}{31}[/tex]
Step-by-step explanation:
[tex]124n=232\\\frac{124n}{124}=\frac{232}{124}\\n=\frac{232}{124}=\frac{58}{31}[/tex]
The value of n is 18.75. To find the value of n, we need to solve the equation: 124n = 232 five
Let's first convert "232 five" into a numerical value:
"232 five" means 2325 (since five is in the units place).
Now, the equation becomes:
124n = 2325
To solve for n, divide both sides of the equation by 124:
n = 2325 / 124
Now, perform the division:
n = 18.75
So, the value of n is 18.75.
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[tex] \frac{3x - 2}{7} - \frac{5x - 8}{4} = \frac{1}{14} [/tex]
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
[tex]\frac{3x-2}{7}-\frac{5x-8}{4}=\frac{1}{14}[/tex]
In order to factor an integer, we need to divide it by the ascending sequence of primes 2, 3, 5.
The number of times that each prime divides the original integer becomes its exponent in the final result.
In here, Prime number 2 to the power of 2 equals 4.
[tex]\frac{3x-2}{7}-\frac{5x-8}{2^{2} }=\frac{1}{14}[/tex]
First, We need to add fractions-
Rule:-
[tex]\frac{A}{B} +\frac{C}{D} =\frac{\frac{LCD}{B}+\frac{LCD}{D}C }{LCD}[/tex]
LCD = [tex]7 \cdot 2^{2}[/tex]
[tex]\frac{4(3x-2)+7(-(5x-8))}{7*2^{2} } =\frac{1}{14}[/tex]
[tex]x=2[/tex]
OAmalOHopeO
Plzzz I’m giving a away 25 points
Answer:
sin ß = opposite / hypotenuse
sin45° = x / 4√2
Cross multiply
x = sin 45° × 4√2
x = √2/2 × 4√2
x = 4 × √2 ×√2 / 2
x = 4 × 2 / 2
x = 8 / 2
x = 4
a principal of $1500 is invested at 5.5 interest compounded annually. how much will the investment be worth after 7 years
Answer:
Step-by-step explanation:
1500(1.055)^7= 2182.02
Given the following coordinates complete the glide reflection transformation.
9514 1404 393
Answer:
A"(-1, -2)B"(4, 0)C"(6, -3)Step-by-step explanation:
The reflection over the x-axis is ...
(x, y) ⇒ (x, -y)
The shift left 3 units is ...
(x, y) ⇒ (x -3, y)
So, the two transformations together will be ...
(x, y) ⇒ (x -3, -y)
A(4, 2) ⇒ A"(1, -2)
B(7,0) ⇒ B"(4, 0)
C(9, 3) ⇒ C"(6, -3)
A 12 ounce bag of rice costs $4.08. A 16-ounce bag of the same rice costs $5.76. Which bag is the better by
and by how much
Answer:
16 once is the better one.
Answer: 12-ounce bag is better by $0.02 per ounce
Concept:
When coming across questions that ask for a comparison between prices, we should make the final unit [price per object].
In finding [price per object], simply do [Total price / number of objects].
Solve:
A 12-ounce bag of rice costs $4.08
Total price / number of objects = 4.08 / 12 = $0.34 per ounce
A 16-ounce bag of rice costs $5.76
Total price / number of objects = 5.76 / 16 = $0.36 per ounce
$0.36 - $0.34 = $0.02
$0.34 < $0.36, therefore, 12-ounce bag is better by $0.02 per ounce.
Hope this helps!! :)
Please let me know if you have any questions
The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approximately normally distributed with mean $440 and standard deviation $20. How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.1
Answer:
$465.6 should be budgeted.
Step-by-step explanation:
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.
Normally distributed with mean $440 and standard deviation $20.
This means that [tex]\mu = 440, \sigma = 20[/tex]
How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.1?
The 100 - 10 = 90th percentile should be budgeted, which is X when Z has a p-value of 0.9, so X when Z = 1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 440}{20}[/tex]
[tex]X - 440 = 1.28*20[/tex]
[tex]X = 465.6[/tex]
$465.6 should be budgeted.
lyng
whose zeros and
Zeros: - 4, 4, 8; degree: 3
Need this in polynomial form
on the same graph draw line 2y-x=10 and y=3x
Answer:
Step-by-step explanation:
A 100.0 m long polymer cable of uniform circular cross section and of diameter 0.4cm has a mass of 1885.0 gm. What is the mass density, of the polymer in kg/m3?
The mass density in kg/m3 will be - 15 x [tex]10^{-2}[/tex] Kg/m3.
We have a 100.0 m long polymer cable of uniform circular cross section and of diameter 0.4cm has a mass of 1885.0 gm.
We have to determine its mass density in kg/m3.
What is Mass density ?The amount of mass per unit volume present in the body is called its mass density.
According to question, we have -
Length of polymer cable = 100.0 m
diameter of polymer cable = 0.4 cm = 0.004 m
Therefore, its radius = 0.002 m
The mass density of the wire will be -
[tex]\rho =\frac{m}{\pi r^{2} l}[/tex]
[tex]\rho[/tex] = [tex]\frac{1885}{3.14 \times0.002 \times 0.002 \times 100 }[/tex]
[tex]\rho = \frac{1885}{0.001256}[/tex] = 1500796.1 g/m3
1 Kg = 1000g
1g = 1/1000kg
1500796.1g = 1500.7 Kg = 15 x [tex]10^{-2}[/tex] Kg
Therefore, mass density = 15 x [tex]10^{-2}[/tex] Kg/m3
Hence, the mass density in kg/m3 will be - 15 x [tex]10^{-2}[/tex] Kg/m3.
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find the missing side length in the image below
Let missing side be x
Using basic proportionality theorem
[tex]\\ \sf\longmapsto \dfrac{18}{14}=\dfrac{27}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{27}{x}[/tex]
[tex]\\ \sf\longmapsto 9x=7(27)[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{7(27)}{9}[/tex]
[tex]\\ \sf\longmapsto x=21[/tex]
Team A scored 30 points less than four times the number of points that Team B scored. Team C scored 61 points more than half of the number of points that Team B scored. If Team A and Team C shared in the victory, having earned the same number of points, how many more points did each team have than Team B?
Answer:
team a and team c scored 74 points which is 48 points more than team b, scoring 26 points.
Step-by-step explanation:
Each side of a regular polygon is 3.2 cm in length. The perimeter of the polygon is 19.2 cm. How many sides does the polygon have? What is the name of the polygon?
Answer:
The polygon consists of 6 sides and the given polygon is a regular hexagon.
Step-by-step explanation:
The definition of perimeter is the total measure of the side lengths of a polygon. If the polygon said is regular, it means the polygon has equal sides and equal angles.
So the perimeter of a regular polygon is given by the formula:
P = (length of one side) x (number of sides)
In this case, the perimeter of the polygon is 19.2 cm and one side is equal to 3.2 cm.
DIVIDE (use the formula but in division to maintain a proportonal relationship):
19.2 ÷ 3.2 = 6
You could alsk check if its correct using the formula:
19.2 = 3.2 x 6 (TRUE)
A 6 sided regular polygon is known as a HEXAGON.
Hope this helps!
For the right angle, find the missing quantity indicated below the figure.
Answer:
The Answer is 28.........
give that 1/x+2/y=1/2, express y in terms of x and 2
9514 1404 393
Answer:
y = 4x/(x -2)
Step-by-step explanation:
Subtract 1/x
2/y = 1/2 -1/x
Combine terms
2/y = (x-2)/(2x)
Cross multiply
4x = y(x -2)
Divide by the coefficient of y
y = 4x/(x -2) . . . . simplest
y = 2^2/(x -2) . . . . in terms of x and 2
help pls! I need the answer quickly and pls explain. thank you!
Answer:
h = 6[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The given is the special right triangle with angle measures : 90-60-30
and the side lengths for the given angles are represented by :
2a-a[tex]\sqrt{3}[/tex]-a
the side length that sees 60 degrees is represented by a[tex]\sqrt{3}[/tex] (h in this case)
the area of a triangle is calculated by multiplying height and base and that is divided by 2
a[tex]\sqrt{3}[/tex]*a/2 = 18[tex]\sqrt{3}[/tex] multiply both sides by 2
a^2[tex]\sqrt{3}[/tex] = 36[tex]\sqrt{3}[/tex] divide both sides by [tex]\sqrt{3}[/tex]
a^2 = 36 find the roots for both sides
a = 6
since h sees angle measure 60 and is represented by a[tex]\sqrt{3}[/tex]
h = 6[tex]\sqrt{3}[/tex]
Suppose y varies inversely with x, and y = 32 when x = 4. What is the value of y when x = 8?
a. 1/8
b. 64
c. 16
d. 8
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Answer:
16
Step-by-step explanation:
Inverse variation is of the form
xy = k where k is a constant
x=4 and y = 32
4*32 = k
128 = k
xy = 128
Let x = 8
8y = 128
Divide each side by 8
8y/8 = 128/8
y =16
Use AABC to find the value of sin B.
Answer:
35/37
Step-by-step explanation:
sin(B)=(AC)/(AB) = 35/37
PLS HELP
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (g o f) (-5)
–6
3
–59
26
Answer:
1st option
Step-by-step explanation:
Evaluate f(- 5) then substitute the value obtained into g(x)
f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then
g(3) = - 4(3) + 6 = - 12 + 6 = - 6
Find the value of a.
A. 58
B. 130
C. 86
D. 65
Answer:
[tex]C. \ \ \ 86[/tex]°
Step-by-step explanation:
1. Approach
In order to solve this problem, one must first find a relationship between arc (a) and arc (c). This can be done using the congruent arcs cut congruent segments theorem. After doing so, one can then use the secants interior angle to find the precise measurement of arc (a).
2. Arc (a) and arc (c)
A secant is a line or line segment that intersects a circle in two places. The congruent segments cut congruent arcs theorem states that when two secants are congruent, meaning the part of the secant that is within the circle is congruent to another part of a secant that is within that same circle, the arcs surrounding the congruent secants are congruent. Applying this theorem to the given situation, one can state the following:
[tex]a = c[/tex]
3. Finding the degree measure of arc (a),
The secants interior angle theorem states that when two secants intersect inside of a circle, the measure of any of the angles formed is equal to half of the sum of the arcs surrounding the angles. One can apply this here by stating the following:
[tex]86=\frac{a+c}{2}[/tex]
Substitute,
[tex]86=\frac{a+c}{2}[/tex]
[tex]86=\frac{a+a}{2}[/tex]
Simplify,
[tex]86=\frac{a+a}{2}[/tex]
[tex]86=\frac{2a}{2}[/tex]
[tex]86=a[/tex]
In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty-four gearboxes are in stock, 6 with improperly drilled holes. Five gearboxes must be selected from the 24 that are available for installation in the next five robots. (Round your answers to four decimal places.) (a) Find the probability that all 5 gearboxes will fit properly. (b) Find the mean, variance, and standard deviation of the time it takes to install these 5 gearboxes.
Answer:
The right answer is:
(a) 0.1456
(b) 18.125, 69.1202, 8.3139
Step-by-step explanation:
Given:
N = 24
n = 5
r = 7
The improperly drilled gearboxes "X".
then,
⇒ [tex]P(X) = \frac{\binom{7}{x} \binom {17}{5-x}}{\binom{24}{5}}[/tex]
(a)
P (all gearboxes fit properly) = [tex]P(x=0)[/tex]
= [tex]\frac{\binom{7}{0} \binom{17}{5}}{\binom{24}{5}}[/tex]
= [tex]0.1456[/tex]
(b)
According to the question,
[tex]X = 91+5[/tex]
Mean will be:
⇒ [tex]\mu = E(x)[/tex]
[tex]=E(91+5)[/tex]
[tex]=9E(1)+5[/tex]
[tex]=9.\frac{nr}{N}+5[/tex]
[tex]=9.\frac{5.7}{24} +5[/tex]
[tex]=18.125[/tex]
Variance will be:
⇒ [tex]\sigma^2=Var(X)[/tex]
[tex]=V(9Y+5)[/tex]
[tex]=81.V(Y)[/tex]
[tex]=81.n.\frac{r}{N}.\frac{N-r}{N}.\frac{N-n}{N-1}[/tex]
[tex]=81.5.\frac{7}{24}.\frac{24-7}{24}.\frac{24-5}{24-1}[/tex]
[tex]=69.1202[/tex]
Standard deviation will be:
⇒ [tex]\sigma = \sqrt{69.1202}[/tex]
[tex]=8.3139[/tex]