Answer:
=91.5384615385
Step-by-step explanation:
(59.5/65)x100= 91.5384615385
See a picture, please
Due to length restrictions, we kindly invite to check the explanation herein for further details of the hyperbola.
How to analyze an hyperbola
Herein we have an hyperbola whose axis of symmetry is parallel to the y-axis and the major semiaxis length is in the y-direction. By analytical geometry, we know that eccentricities of hyperbolae are greater than 1.
a) The formula for eccentricity is:
e = √(a² + b²) / a (1)
Where:
a - Major semiaxis lengthb - Minor semiaxis lengthIf we know that a = 4 and b = 3, then the eccentricity of the hyperbola is:
e = √(4² + 3²) / 4
e = 5 / 4
b) The coordinates of the two vertices of the hyperbola are:
V(x, y) = (h, k ± a) (2)
Where (h, k) are the coordinates of the center of the hyperbola.
V₁ (x, y) = (0, 4), V₂ (x, y) = (0, - 4)
The coordinates of the foci of the hyperbola are:
F(x, y) = (h, k ± c), where c = √(a² + b²). (3)
c = √(4² + 3²)
c = 5
F₁ (x, y) = (0, 5), F₂ (x, y) = (0, - 5)
The equations of the asymptotes of the hyperbola are:
y = ± (a / b) · x
y = ± (4 / 3) · x (4)
And the equations of the directrices of the hyperbola are:
y = k ± (2 · a - c)
y = 0 ± (8 - 5)
y = ± 3 (5)
The graph is presented in the image attached below.
c) The parametric equations for the hyperbola are the following formulae:
y = ± a · cosh t → y = ± 4 · cosh t (6)
x = b · sinh t → x = 3 · sinh t (7)
d) First, we determine the slopes of the two tangent lines by implicit differentiation:
m = (16 · x) / (9 · y)
m = (16 · 2.3) / [9 · (± 4.807)]
m = ± 0.851
Second, we find the intercept of each tangent line:
(x, y) = (2, 4.807)
b = 4.807 - 0.851 · 2
b = 3.105
y = 0.851 · x + 3.105 (8)
(x, y) = (2, - 4.807)
b = - 4.807 - (- 0.851) · 2
b = - 3.105
y = - 0.851 · x - 3.105 (9)
e) The definite integral of the arc length of the hyperbola is presented below:
[tex]s = \int\limits^{2}_{1} {\sqrt{\left(\frac{dx}{dt} \right)^{2}+\left(\frac{dy}{dt} \right)^{2}}} \, dt[/tex]
If we know that dx / dt = a² · sinh² t and dy / dt = b² · cosh² t, then the definite integral for the arc length is:
[tex]s = \int\limits^2_1 {\sqrt{a^{2}\cdot \sinh ^{2}t +b^{2}\cdot \cosh^{2}t}} \, dt[/tex] (10)
f) We apply the following substitutions on (1): x = r · cos θ, y = r · sin θ. Then, we have the polar form by algebraic handling:
r(θ) = (a · b) / (b² · sin² θ - a² · cos² θ) (11)
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The Lao Construction Company recognizes revenue over time according to percentage of completion for its long-term construction contracts. In 2024, Lao began work on a construction contract. Information on this contract at the end of 2024 is as follows: Cost incurred during the year = $ 1,500,000 Estimated additional cost to complete = $6,000,000 & Gross profit recognized in 2024 = $250,000. What is the contract price (total revenue) on this contract?
The contract price is $8,750,000
What is contract price?
Contract price means the amount Lao Construction Company charged the customer for total contract's execution.
We need to ascertain the percentage completion of the project first and foremost, which is the total costs incurred to date divided by the contract's total costs.
cost incurred to date=$ 1,500,000
total contract's cost=cost incurred to date+ expected future costs
total contract's cost=$1,500,000+$6,000,000
total contract's cost=$7,500,000
% completion=$1,500,000/$7,500,000
% completion=20%
gross profit recognized=(contract price*% completion)-costs incurred till date
gross profit recognized=$250,000
contract price=unknown(assume it is X)
% completion=20%
cost incurred to date=$ 1,500,000
$250,000=(20%*X)-$1,500,000
$250,000+$1,500,000=0.20X
$1,750,000=0.20X
X=$1,750,000/0.20
X=$8,750,000
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If a number is tripled & the result is increased by 5, we get 50. Find the number.
Solution:
Let x be the number
Triple the number=3x
According to the question,
3x+5=50
⇒3x+5−5=50−5 [Subtract 5 from both sides]
⇒3x=45
⇒ x = 45/3
[Divide 3 from both sides]
⇒x=15
∴15 is the required number. When it is tripled and increased by 5, we get 50.
The table shows the cost of birdseed at the Feed n Seed store. What is the constant of proportionality between the cost and the number of pounds?
A table titled Feed n Seed Bird Seed. The table has 2 columns, Pounds and Cost. Row 1 says 5, 2 dollars and ninety-five cents. Row 2 says ten, five dollars and ninety cents. Row 3 says fifteen, 8 dollars and eighty-five cents.
A
0.59
B
0.60
C
1.18
D
2.95
The constant of proportionality between the cost and the number of pounds is: A. 0.59.
What is Constant of Proportionality?The constant of proportionality of a relationship between two variables X and Y can be defined as the ratio between of X and Y at a constant value. This means that the ratio or product of X and Y will give us a constant if both are in a proportional relationship.
Thus, the constant of proportionality for the relationship between two variables X and Y would be calculated as:
Constant of proportionality (k) = Y/X. [this is the proportional between the two quantities, X and Y].
Given the table of values, using a pair of points on the table, say, (5, 2.95), we can calculate the constant of proportionality as:
X = 5
Y = 2.95
Constant of proportionality (k) = Y/X = 2.95/5
Constant of proportionality (k) = 0.59 pounds per dollar.
Therefore, the constant of proportionality between the cost and the number of pounds is: A. 0.59.
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Solve the system. 9=4x-2y 2x+6=y
Step-by-step explanation:
4x-2y = 9 ...1
2x-y = -6 ...2
if ...2 × 2
4x-2y = -12
9 is not equal to -12
17. What is the probability that the student will play football and baseball? (a) 28 /33 (b) 35 /66 (c) 4 /33 (d) 8 /11
How to solve these questions?
(with work)
The angles and length of the triangle area as follows:
∠CBD = 61°∠A = 35°AD = 32.77 unitsBD = 22.94 unitsBC = 11.12 unitsCD = 9.73 unitsHow to find the sides and angle of a triangle?The sum of angles in a triangle is 180 degree.
Therefore,
∠DBC = 180 - 29 - 90 = 61°
Hence,
∠A = 180 - 29 - 61 - 55 = 35°
∠CBD = 61°
Using trigonometric ratios,
sin 55 = opposite / hypotenuse
sin 55 = AD / 40
AD = 40 sin 55
AD = 32.7660817716
AD = 32.77 units
cos 55 = adjacent / hypotenuse
cos 55 = BD / 40
BD = 40 cos 55
BD = 22.943057454
BD = 22.94 units
sin 29 = 22.94 / BC
BC = 22.94 sin 29
BC = 11.1215326885
BC = 11.12 units
cos 29 = CD / 11.12
CD = 11.12 cos 29
CD = 9.72577114339
CD = 9.73 units
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10005²³ x + cos x = 11 sin²x = 9
Middler Corporation, a manufacturer of electronics and communications systems, uses a service department charge system to charge profit centers with Computing and Communications Services (CCS) service department costs. The following table identifies an abbreviated list of service categories and activity bases used by the CCS department. The table also includes some assumed cost and activity base quantity information for each service for October.
CCS Service
Category
Activity Base
Budgeted Cost Budgeted Activity
Base Quantity
Help desk Number of calls $160,000 3,200
Network center Number of devices monitored 735,000 9,800
Electronic mail Number of user accounts 100,000 10,000
Smartphone support Number of smartphones issued 124,600 8,900
One of the profit centers for Middler Corporation is the Communication Systems (COMM) sector. Assume the following information for the COMM sector:
• The sector has 5,200 employees, of whom 25% are office employees.
• All the office employees have been issued a smartphone, and 96% of them have a computer on the network.
• One hundred percent of the employees with a computer also have an e-mail account.
• The average number of help desk calls for October was 1.5 calls per individual with a computer.
• There are 600 additional printers, servers, and peripherals on the network beyond the personal computers.
a. Determine the service charge rate for the four CCS service categories for October.
CCS Service Category Service Charge Rate
Help desk $fill in the blank 1
Per call
Network center $fill in the blank 3
Per device monitored
Electronic mail $fill in the blank 5
Per user or e-mail account
Smartphone support $fill in the blank 7
Per smartphone issued
The answers to the service charge rate are:
50751014How to determine the service charge rate for the month of OctoberThis is the number of calls for the help desk
160000/3200 = 50per call
For the network center
735000/9800
= 75 per device that was monitored
For the Electronic mail
100000/10000 =
10 for the mail account
For local voice support
124600/8900
= 14 per phone extension
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Find the equation of the line that passes through point (6,1) with the x-intercept of 2.
Answer:
y=1/4x-1/2
Step-by-step explanation:
2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000
Answer:12002/9987
Step-by-step explanation:
INDUSTRIES IS CONSIDERING PURCHASING A CERTAIN STOCK. AFTER
CONSIDERABLE RESEARCH, THE BOARD MEMBERS DETERMINE THAT THERE IS A 60% CHANCE OF MAKING $8000, A 10% CHANCE OF BREAKING EVEN, AND A 30% CHANCE
OF LOSING $6200. FIND THE EXPECTATION OF THIS PURCHASE
Which of the following is the equation of the line that passes through the points (-3,4) and (6,7)?
The equation of the line that passes through the given points is
y = 1/3x + 5.
What is the formula for calculating the equation of a line passing through two points?The formula for the equation of a line passing through two points (x1, y1) and (x2, y2) is
[tex](y-y1) = \frac{(y2-y1)}{(x2-x1)} (x-x1)[/tex]
Where the fraction (y2 - y1)/(x2 - x1) is the slope of the line denoted by 'm'.
Calculation:It is given that, a line passes through the points (-3,4) and (6,7).
So, the equation of the line is
[tex](y-y1) = \frac{(y2-y1)}{(x2-x1)} (x-x1)[/tex]
On substituting x1 = -3, y1 = 4, x2 = 6, and y2 = 7
(y - 4) = [(7 - 4)/(6 + 3)](x + 3)
⇒ (y - 4) = (3/9)(x + 3)
⇒ (y - 4) = 1/3(x + 3)
⇒ y- 4 = 1/3x + 1
⇒ y = 1/3x + 1 + 4
∴ y = 1/3x + 5
Thus, the equation of the line passing through the points (-3,4) and (6,7) is y = 1/3x + 5. Where the slope m = 1/3.
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8 ABC please trig assignment
Using equivalent angles, the solutions are given as follows:
a) [tex]x = \frac{15\pi}{23}[/tex].
b) [tex]x = \frac{9\pi}{62}, x = \frac{53\pi}{62}[/tex].
c) [tex]x = \frac{3\pi}{8}, \frac{11\pi}{8}[/tex]
What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
For item a, we have to find the equivalent angle on the 2nd quadrant, where the sine is also positive.
Hence:
[tex]\pi - \frac{8\pi}{23} = \frac{23\pi}{23} - \frac{8\pi}{23} = \frac{15\pi}{23}[/tex]
Hence [tex]x = \frac{15\pi}{23}[/tex].
For item b, if two angles are complementary, the sine of one is the cosine of the other.
Complementary angles add to 90º = 0.5pi, hence:
[tex]x + \frac{11\pi}{31} = \frac{\pi}{2}[/tex]
[tex]x = \frac{31\pi}{62} - \frac{22\pi}{62}[/tex]
[tex]x = \frac{9\pi}{62}[/tex]
The equivalent angle on the second quadrant is:
[tex]\pi - \frac{9\pi}{62} = \frac{62\pi}{62} - \frac{9\pi}{62} = \frac{53\pi}{62}[/tex]
Hence the solutions are:
[tex]x = \frac{9\pi}{62}, x = \frac{53\pi}{62}[/tex]
For item c, the angles are also complementary, hence:
[tex]x + \frac{\pi}{8} = \frac{\pi}{2}[/tex]
[tex]x = \frac{4\pi}{8} - \frac{\pi}{8}[/tex]
[tex]x = \frac{3\pi}{8}[/tex]
The tangent is also positive on the third quadrant, hence the equivalent angle is:
[tex]x = \pi + \frac{3\pi}{8} = \frac{8\pi}{8} + \frac{3\pi}{8} = \frac{11\pi}{8}[/tex]
Hence the solutions are:
[tex]x = \frac{3\pi}{8}, \frac{11\pi}{8}[/tex]
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4 Which of the following is the solution to 8√3+7√3?
O 15√9
O 15√6
O 15/3
O 56√3
Answer:
15√3
Step-by-step explanation:
after grouping and adding them to get 15√9
then you apply Surds
If s(x) = 2 - x and t(x) = 3x, which value is equivalent to (s•f)(-7)?
Answer:
Step-by-step explanation:
t(-7)= 3(-7)= -21
s(-21)= 2-(-21)= 2 + 21= 23
Jeff decided to purchase a house, his mortage is a 30-year loan at 4.1 % compounded monthly. The final purchase price was $150,000.00 Jeff put down 2808.00 at closing. Find Jeffs monthly payment
Answer:
$711.23
Step-by-step explanation:
We assume the entire closing cost went to reducing the principal of the loan. Then the amount borrowed was $147,192.
Monthly paymentThe amortization formula tells you the monthly payment.
A = P(r/12)/(1 -(1 +r/12)^(-12t))
P is the principal, r is the annual rate, and t is the number of years.
The monthly payment is ...
A = $147,192(0.041/12)/(1 -(1 +0.041/12)^-360) ≈ $711.23
Jeff's monthly payment is $711.23.
A rectangle is 6x-4 feet long and 2x + 3 feet wide. What is the perimeter of the rectangle?
Answer:
Perimeter o the rectangle = 16x - 2
Step-by-step explanation:
Perimeter of a rectangle = 2(long+ wide)
Then:
Perimeter = 2((6x-4)+(2x+3))
Perimeter = 2(6x+ 2x + 3 - 4)
Perimeter = 2(8x - 1)
Perimeter = 2*8x + 2*-1
Perimeter = 16x - 2
After finishing the prep work, Gilberta and María start removing wallpaper at the same time. Gilberta removes the paper at a constant rate of
4.3
m
2
4.3m
2
4, point, 3, start text, m, end text, squared per hour, while María removes
3.4
m
2
3.4m
2
3, point, 4, start text, m, end text, squared of paper per hour. Gilberta's room starts with
35
m
2
35m
2
35, start text, m, end text, squared of paper, and María's room starts with
30.5
m
2
30.5m
2
30, point, 5, start text, m, end text, squared of paper.
Let
t
tt represent the time, in hours, since Gilberta and María start removing the wallpaper.
Complete the inequality to represent the times when Gilberta has more wallpaper left in her room than María has in hers.
t
tt
select inequality symbol
hours
Show Calculator
Using linear functions, the inequality that represents when Gilberta has more wallpaper left in her room than María has in hers is: t < 5.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we consider:
The initial amount as the y-intercept.The rate as the slope.Hence the amounts Gilberta and Maria have left after t hours are given by:
G(t) = 35 - 4.3t.M(t) = 30.5 - 3.4t.Gilberta has more papers when:
G(t) > M(t).
Hence:
35 - 4.3t > 30.5 - 3.4t
-0.9t < -4.5
Multiplying by -1:
0.9t < 4.5
t < 4.5/0.9
t < 5.
Hence the inequality is:
t < 5.
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Answer:
t < 5
Step-by-step explanation:
Other dude is right but here's the version without explanation
Una página de plástico diseñada para guardar cromos puede contener hasta 9 cartas. ¿Cuántas páginas se necesitarán para almacenar 517 tarjetas? Dé una respuesta numérica adecuada a la pregunta. (Encuentre el número contable mínimo que funcionará).
Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.´
¿Cuántas páginas se necesitarán para almacenar 517 tarjetas?Sabemos que cada página puede almacenar hasta 9 cartas.
Entonces queremos ver cuantos grupos de 9 cartas hay en el conjunto de 517, para ver esto tomamos el cociente entre 517 y 9.
N = 517/9 = 57.44
Y no podemos tener un numero racional, así que debemos redondear al proximo número entero, que es 58.
Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.
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How to make 3 dimensional object to 4 dimensional object
In order to make 3 dimensional object to 4 dimensional object, it's important to draw the 4 dimensional shape in a way that gives the illusion of the 3 dimensional object.
How to illustrate the information?It should be noted that shapes play an important part in geometry.
Here, to make make 3 dimensional object to 4 dimensional object, it's important to draw the 4 dimensional shape in a way that gives the illusion of the 3 dimensional object.
Also, it should be noted that a 4D tesseract can be used to project the image.
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Find the missing number
1 4 6 2 5 7 8 9 7 15 41 ?
Answer:
43
Step-by-step explanation:
I would see a pattern like this
1 4 6 2 5 7 8 9 7 15 41 ?
------------------- ---------
start pattern key
then
15 = 8 × 2 - 1
a10 = a7 × a4 - a1
41 = 9 × 5 - 4
a11 = a8 × a5 - a2
? = 7 × 7 - 6 = 43
a12 = a9 × a6 - a3
Which choice shows 40 + 30+ 10 rewritten correctly using the commutative property and then simplified correctly?
Answer:
40 + 10 + 30 = 50 + 30 = 80
Step-by-step explanation:
40 + 10 + 30 = 50 + 30 = 80
Answer:
10(4+3+1)
Step-by-step explanation:
Expand 40+30+10 by the distributive property:: 10(4+3+1)
The Department of Motor Vehicles reports that the proportion of all vehicles registered in
California that are imports is 0.22.
ords
1. Is the number 0.22?
a population proportion.
a.
b. a sample proportion.
2. Which of the following use of notation is correct?
a. p=0.22
b. p=0.22
The number 0.22 represents the population proportion and the correct way to represent it is p = 0.22.
What are statistics?Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.
It is given that:
It is given that:
The Department of Motor Vehicles reports that the proportion of all vehicles registered in California that are imported is 0.22.
The number 0.22 represent the population proportion.
The population proportion can be represented by the letter p:
p = 0.22
Thus, the number 0.22 represents the population proportion, and the correct way to represent it is p = 0.22.
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Given right triangle JKL, what is the value of cos(L)?
Five-thirteenths
Five-twelfths
Twelve-thirteenths
Twelve-fifths
Pls help!!
The value of cos(L) in the triangle is Five-thirteenths
What are right triangles?Right triangles are triangles whose one of its angle has a measure of 90 degrees
How to determine the value of cos(L)?The value of a cosine function is calculated as:
cos(L) = Adjacent/Hypotenuse
The hypotenuse is calculated as
Hypotenuse^2 = Opposite^2 + Adjacent^2
So, we have:
Hypotenuse^2 = 12^2 + 5^2
Evaluate
Hypotenuse^2 = 169
Take the square root of both sides
Hypotenuse = 13
So, we have
Adjacent = 5
Hypotenuse = 13
Recall that
cos(L) = Adjacent/Hypotenuse
This gives
cos(L) = 5/13
Hence, the value of cos(L) in the triangle is Five-thirteenths
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Two jets leave an air base at the same time and travel in opposite directions. One jet travels 80 mi/h faster than the other. If the two jets are 11392 miles apart after 8 hours, what is the rate of each jet?
Jet 1 moves with a speed of 672 mi/h, while jet 2 moves with a speed of 672 mi/h + 80mi = 752 mi/h.
How to get the rate of each jet?
Let's say that the rate (or speed) of the slower jet is R, then the rate of the faster jet is:
R + 80mi/h
Now, if we step on any of the two jets (such that we view it as if it doesn't move) the other jet will move with a speed equal to:
S = R + R + 80mi/h
We know that after 8 hours, the to jets are 11,392 mi apart, then we know that:
(R + R + 80mi/h)*8h = 11,392 mi
Now we can solve that for R:
2*R + 80mi/h = 11,392 mi/8h = 1,424 mi/h
R = 1,424 mi/h - 80mi/h)/2 = 672 mi/h
So Jet 1 moves with a speed of 672 mi/h, while jet 2 moves with a speed of 672 mi/h + 80mi = 752 mi/h.
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Please help! I don't understand how to solve this problem
Using the z-distribution, a sample of 142,282 should be taken, which is not practical as it is too large of a sample.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.Assuming an uniform distribution, the standard deviation is given by:
[tex]S = \sqrt{\frac{(4 - 0)^2}{12}} = 1.1547[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The sample size is found solving for n when the margin of error is of M = 0.006, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.006 = 1.96\frac{1.1547}{\sqrt{n}}[/tex]
[tex]0.006\sqrt{n} = 1.96 \times 1.1547[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 1.1547}{0.006}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 1.1547}{0.006}\right)^2[/tex]
n = 142,282.
A sample of 142,282 should be taken, which is not practical as it is too large of a sample.
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HELP
If 10% of x is 20, what is 23% of x?
Answer:
46
Step-by-step explanation:
Answer:
46
According to question,
10% × x = 20
x = 20 ÷ 10%
x = 20 ÷ 0.1
x = 200
Now find 23% of x
23% × 200
0.23 × 200
46
The legs of a 45-45-90 triangle has lengths of 21. What is the length of the hypotenuse?
Answer:
[tex]21 \sqrt{2} [/tex]
Step-by-step explanation:
See attached image.
Which function represents g(x), a reflection of f(x) = 1/2(3)^x across the y-axis?
The equation for the reflected function is:
g(x) = (1/2)*(3)^(-x)
How to get the reflected function?
Here we know that function g(x) is a reflection of f(x) across the y-axis.
Remember that the reflection is written as:
g(x) = f(-x)
Here we know that:
f(x) = (1/2)*(3)^x
Then, replacing that in the equation for g(x), we get:
g(x) = f(-x) = (1/2)*(3)^(-x)
g(x) = (1/2)*(3)^(-x)
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