The equation of a parabola with a focus at (0,-5) and a directrix at y=-3 is derived by equating the distances of any point (x, y) in the parabola from the focus and the directrix respectively. Simplifying these expressions leads to the equation y = (1/8)x² - 1.
Explanation:The equation for a parabola can be derived from its definition. A parabola is defined as the set of all points (x, y) in a plane which are equidistant from a fixed point, the focus (given here as (0,-5)) and a fixed line, the directrix (given as y=-3).
Let's calculate the distance between the focus (0, -5) and any point in the parabola (x, y). We get the equation:
√[(x-0)² + (y-(-5))²].
And the distance between the point (x, y) and the directrix (y=-3) is |y - (-3)| = y + 3.
Since we know that the two distances are equal, we can equate the two expressions:
√[(x-0)² + (y-(-5))²] = y + 3.
Solving it further, squaring both sides, and simplifying, we get:
y = (1/8)x² - 1.
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You are planning to buy one of two brands of sofas, which you hope to use over the next twenty years. Brand J costs $975 and lasts for about twenty years. Brand K costs $265 and lasts for about five years, so you will need to buy four Brand K sofas to equal one Brand J sofa. In either case, you plan to pay for your sofa using your credit card, which has an interest rate of 14.55%, compounded monthly. You can pay off a Brand J sofa with eight years of monthly payments, and you can pay off a Brand K sofa with three years of monthly payments. Assuming that you make no other purchases on your credit card, over twenty years, which brand will be cheaper, and how much cheaper will it be? (Round all dollar values to the nearest cent.) a. Brand J will be $591.36 cheaper than Brand K. b. Brand J will be $85.00 cheaper than Brand K. c. Brand K will be $1,132.23 cheaper than Brand J. d. Brand K will be $340.32 cheaper than Brand J.
The loan amount is calculated by amortization and Brand K will be $340.32 cheaper than Brand J
What is Amortization?Loan amortisation is the practise of making recurrent payments over time to completely pay off the principal and interest on a loan.
Mortgage amortisation is a word used in finance to describe the process of paying down your mortgage. The mortgage lender establishes a payment plan for you when you take out a mortgage. This uncomplicated plan, which includes equal payments over the course of your loan if you have a fixed-rate mortgage, is easy to understand.
The amount is calculated using the amortization formula:
P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}
where:
P is monthly payment
a is credit amount
r is the interest rate
t is the time in years
n is number of times the interest is compounded
Given data ,
Let the total loan amount for the brand J be represented as J
a = $975
r = 14.55% = 0.1455
t = 8 years
n = 12
Now , the amortization formula is
P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}
P = 975 ÷ {{[(1 + 0.1455/12)^12×8] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×8]}
P = $17.24
Total amount paid J = $17.24 × 96 = $1655.04
Let the total loan amount for the brand K be represented as K
a = $265
r = 14.55% = 0.1455
t = 3 years
n = 12
Now , the amortization formula is
P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}
P = 265 ÷ {{[(1 + 0.1455/12)^12×3] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×3]}
P = $9.13
Total amount paid K = $9.13 × 12 × 3 × 4 = $1314.72
The difference of amount of sofa j and sofa k = D
D = J - K
D = $1 655.04 - $ 1314.72 = $ 340.32
Hence , Brand K will be cheaper than Brand J by $340.32
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In Zoe's class, 4 /5 of the students have pets. Of the students who have pets, 1/8 have rodents. What fraction of the students in Zoe's class have rodents? Enter the answer in simplest form. The fraction of students in Zoe's class who have rodents is
Answer:
The fraction of students in Zoe's class who have rodents is [tex]\frac{1}{10}[/tex].
Step-by-step explanation:
In Zoe's class, 4 /5 of the students have pets.
Of the students who have pets, 1/8 have rodents.
This means [tex]\frac{1}{8} of \frac{4}{5}[/tex] have rodents.
So,fraction of students who have rodents = [tex]\frac{1}{8}\times\frac{4}{5}[/tex]
= [tex]\frac{1}{10}[/tex]
The fraction of students in Zoe's class who have rodents is [tex]\frac{1}{10}[/tex].
According to the Journal of the American Medical Association (JAMA), hospitals that routinely staff with 1:8 nurse-to-patient ratios experience five additional deaths per 1,000 patients than those staffing with 1:4 ratios (2002). If the local hospital has decided to follow the 1:4 nurse-to-patient ratio, how many patients can they treat if they have 120 nurses?
Final answer:
The local hospital can treat a maximum of 480 patients if they follow the 1:4 nurse-to-patient ratio and have 120 nurses.
Explanation:
The local hospital can treat a maximum of 480 patients if they follow the 1:4 nurse-to-patient ratio and have 120 nurses.
To calculate the maximum number of patients the hospital can treat, we divide the number of nurses by the nurse-to-patient ratio. In this case, the ratio is 1:4, so for every 1 nurse, there are 4 patients. Therefore, each nurse can handle 4 patients.
To find the maximum number of patients, we multiply the number of nurses by the number of patients each nurse can handle. In this case, 120 nurses multiplied by 4 patients per nurse equals 480 patients.
Jean-Marc used a scale factor of 5 to make this scale drawing of a moth.
In the drawing, the wingspan of the moth measures 3 centimeters. What was the actual wingspan, in millimeters, of the moth Jean-Marc observed?
The formula for glue says to add 50ml of hardener to each container of resin. How much hardener should be added to 15 containers of resin?
Answer:
0.75
Step-by-step explanation:
PLZ HURRY!!!
A line passes through the points (6,5) and (2,2) . Select all that describe this line.
1. y − 5 = 3/4 (x − 6)
2. y − 5 = −4/3 (x − 2)
3. y − 2 = −3/4 (x − 6)
4. y − 2 = 3/4 (x − 2)
logan made a treasure hunt map.the treasure is 25cm away from his location.if each 1cm on the scale drawing equals 5 meters, then how far he is from treasure?
Logan's treasure is represented as 25 cm away on his map; using the scale of 1 cm to 5 meters, it can be calculated that he is 125 meters away from the treasure by multiplying the map distance by the scale factor.
Logan has created a treasure hunt map where the scale indicates that 1 cm on the map corresponds to an actual distance of 5 meters. To determine the actual distance Logan is from the treasure, we first note that the treasure is shown as 25 cm away from his location on the map. Since the scale factor is 1 cm to 5 meters, we can set up a simple multiplication to find the actual distance.
The calculation would be as follows:
Scale factor: 1 cm = 5 meters
Map distance: 25 cm
Actual distance: 25 cm x 5 meters/cm
By multiplying the map distance by the scale factor, we get:
Actual distance = 25 x 5 = 125 meters
Therefore, Logan is 125 meters away from the treasure.
write 3.25 x 10^4 as an ordinary number
could you please show your working out it would be helpful
Numbers that are used to represent the rank or position of an object or a person are known as ordinal numbers.
The ordinary number for 3.25 x [tex]10^{4}[/tex] is 32500.
What is an ordinary number?Numbers that are used to represent the rank or position of an object or a person are known as ordinal numbers.
We have,
3.25 x [tex]10^{4}[/tex]
We need to remove the decimal point and the exponents 4.
Let us find in two parts:
3.25 can be written as 325/100 ______(1)
[tex]10^{4}[/tex] can be written as 10 x 10 x 10 x 10 = 10000 ______(2)
Now,
From (1) and (2)
= 3.25 x [tex]10^{4}[/tex]
= (325 / 100) x 10000
= (325/100) x 100 x 100
100 can be canceled.
= 325 x 100
= 32500
Thus the ordinary number for 3.25 x [tex]10^{4}[/tex] is 32500.
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600,000 to the nearest hundred thousand is
Bank of america customers select their own three-digit personal identification number (pin) for use at atms.(b) if zero can be the first digit and the numbers can be repeated, what is the probability mr. jones and mrs. smith select the same pin?
A package of 10 cans of soup costs $14. An individual can costs $2. You need at least 25 cans. Find You decide to buy 3 packages of 10 cans. How much do you pay for each can?the price of each combination of items.You decide to buy 3 packages of 10 cans. How much do you pay for each can?
To find the cost per can when buying 3 packages of cans, multiply the cost of a single package by 3 to get the total cost, then divide the total cost by the total number of cans to find the cost per can.
To find the cost per can when buying 3 packages of 10 cans each:
Cost of 1 package with 10 cans = $14Cost of 3 packages = 3 x $14 = $42Number of cans = 3 packages x 10 cans per package = 30 cansCost per can = Total cost / Number of cans = $42 / 30 cans = $1.40Solve: 3x - 2x + 4 = 5x - 4x - 8
f(x)=x g(x)=1 what is the domain of (g/f)(x)
[tex]\left(\dfrac{g}{f}\right)(x)=\dfrac{g(x)}{f(x)}\\\\\text{We have}\ f(x)=x\ \text{and}\ g(x)=1.\ \text{Substitute}\\\\\left(\dfrac{g}{f}\right)(x)=\dfrac{1}{x}\\\\\text{The domain}:\ x\neq0\\\\Answer:\ \boxed{\text{All real numbers except 0}\to x\in\mathbb{R}-\{0\}}[/tex]
The domain of the function is a real number except 0 because the function is not defined at x = 0.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The functions are given below.
f(x) = x
g(x) = 1
Then the domain of the function (g/f)(x) will be
(g/f)(x) = 1 / x
Then the graph of the function is given below.
The domain of the function is a real number except 0 because the function is not defined at x = 0.
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How to find the general solution to y"'+2y"-4y'-8y=0?
How to factorise and appear a commun facteur
I need the answer please
TIMMY and JEROD are eating cupcakes if they each can eat 2 cupcakes in 3 minutes how long will it take them to eat 18 cupcakes?
A) what value represents the 40th percentile of these returns?
Jeremy is shopping online for skating equipment. He buys a longboard complete with trucks and wheels for $146.25. At checkout, Jeremy gets a discount of $21 on his purchase. The final amount that Jeremy will be billed is $ 42.00 104.25 125.25 167.25
Answer:
Option C. $125.25
Step-by-step explanation:
Jeremy is shopping online for skating equipment.
The price of long board with trucks and wheels = $146.25
Jeremy gets a discount on his purchase = $21.00
the final amount that Jeremy would be billed.
We subtract the discount from the price of item.
= $146.25 - $21.00 = $125.25
The final amount that Jeremy would be billed is $125.25.
Karl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute
A minute is 6 times as long as 10 seconds, so we expect Karl will ride 6 times as far.
[tex]\dfrac{120\,ft}{10\,s}=\dfrac{120\,ft}{10\,s}\cdot\dfrac{60\,s}{1\,min}=\dfrac{720\,ft}{1\,min}[/tex]
Karl rides 720 ft in 1 minute.
Answer:
720
Step-by-step explanation:
120/10 to find his feet per second which is 12 feet per second
12*60
since there are 60 seconds in a minute
= 720
Solve x2 – 8x = 20 by completing the square. Which is the solution set of the equation? {–22, 14} {–14, 22} {–10, 2} {–2, 10}
Answer: D is the right answer. The solution set of the given equation={-2,10}.
Explanation:
Given equation: [tex]x^2-8x=20[/tex]
The standard perfect square trinomial equation is [tex]x^2+2ax+a^2=(x+a)^2[/tex]
On comparing this with the left side of the given equation ,we get 2a=-8
⇒a= -4 and [tex]a^2=16[/tex]
Now to make given equation perfect square add 16 on the both sides, we get [tex]x^2-8x+16=20+16\\\Rightarrow(x-4)^2=36[/tex]
Taking square root on both the sides we get,
[tex]x-4=-6\ or\ x-4=6[/tex]
add 4 on both sides, we get
⇒x= -6+4 or x=6+4
⇒x=-2 or x=10
Therefore, the solution set of the given equation={-2,10}.
Thus D is the right answer.
Fred wants to find 48+34 using compensation.He says you can take 2 from 34 and give it to 48 to make 50.What is the sum?Explain why compensation can work to find the sum.
the figure below will be translated 4 units up and 3 units to the right. Which of the following represents the coordinates of the transformed figure?
A. A'(6, 9), B'(9, 14), C'(12, 11)
B. A'(8, 10), B'(11, 15), C'(15, 12)
C. A'(9, 9), B'(12, 14), C'(16, 11)
D. A'(9, 10), B'(12, 15), C'(16, 12)
Name the triangle with the following characteristics. Sides: 5 cm, 5 cm, 7 cm.
Answer:
Isosceles triangle.
Step-by-step explanation:
A triangle has been given in this question with the sides 5 cm, 5 cm, 7 cm.
As per definition of the triangle if two sides are equal then opposite angles of these corresponding sides will be equal.
More than this if two sides of a triangle are equal then the triangle is called as isosceles triangle.
Therefore the given triangle with the equal sides 5 cm, 5 cm will be the isosceles triangle.
A superhero recently asked his nemesis how many cats she has. She answered with a riddle:two-thirds of my cats plus two
how many cats does she have
The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. suppose the number of tickets written per day follows a poisson distribution with a mean of 6.5 tickets per day. interpret the value of the mean.question 3 options:
The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website, January 5, 2015). Assume that GMAT scores are bell-shaped with a standard deviation of 100.
. What percentage of GMAT scores are 647 or higher?
15.8
b. What percentage of GMAT scores are 747 or higher (to 1 decimal)?
2.9
c. What percentage of GMAT scores are between 447 and 547 ?
25
d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)?
Answer:
16%; 2.5%; 34%; 81.5%
Step-by-step explanation:
Using the empirical rule, we know that 68% of data falls within one standard deviation of the mean; 95% of data falls within two standard deviations of the mean; and 99.7% of data falls within 3 standard deviations of the mean.
This means from the mean to 1 standard deviation (σ) above is 34% of data; from the mean to 1 σ below is 34% of data; from 1 σ to 2σ above is 13.5% of data; from 1σ to 2σ below is 13.5% of data; from 2σ to 3σ above is 2.35% of data; from 2σ to 3σ below is 2.35% of data; more than 3σ above is 0.15% of data; and more than 3σ below is 0.15% of data.
647 is 1 σ above the mean. This means that we go from here above;
13.5+2.35+0.15 = 16%
747 is 2σ above the mean. This means that we go from here above:
2.35+0.15 = 2.5%
447 is 1σ below the mean and 547 is the mean. This means that we have 34%.
347 is 2σ below the mean and 647 is 1 above the mean. This means we go from:
13.5+34+34 = 81.5%
To find the percentage of GMAT scores between 347 and 647, find the z-scores and use a z-table to calculate the cumulative area.
Explanation:To find the percentage of GMAT scores between 347 and 647, we need to find the area under the bell curve between these two scores. First, we need to find the z-scores for both scores using the formula z = (x - μ) / σ. For 347, the z-score is (-200) / 100 = -2, and for 647, the z-score is 100 / 100 = 1.
Next, we need to find the percentage of data between these z-scores. We can use a z-table to find the cumulative area. The cumulative area for -2 is 0.0228 and for 1 is 0.8413.
To find the percentage between these two z-scores, we subtract the cumulative area for -2 from the cumulative area for 1: 0.8413 - 0.0228 = 0.8185.
Therefore, the percentage of GMAT scores between 347 and 647 is 81.85%.
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Solve for 10 - 6x - 9x^2 = -9x10−6x−9x 2 =−9x
x = (1 ±√41)/6 is the correct answer.
To solve the equation 10 - 6x - 9x^2 = -9x, we'll use the quadratic formula. The solutions for x are (3 + √369)/18 and (3 - √369)/18.
Explanation:To solve the equation 10 - 6x - 9x2 = -9x, we'll start by bringing all the terms to one side of the equation to set it equal to zero. Rearranging the equation, we get 9x2 - 3x - 10 = 0. We can then use factoring, the quadratic formula, or completing the square to solve for x. In this case, let's use the quadratic formula.
The quadratic formula states:
x = (-b ± √(b2 - 4ac))/(2a)
Using the values from our equation, we have:
x = (-(-3) ± √((-3)2 - 4(9)(-10)))/(2(9))
Simplifying further, we have:
x = (3 ± √(9 + 360))/18
x = (3 ± √369)/18
Therefore, the solutions for x are:
x = (3 + √369)/18
x = (3 - √369)/18
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kelly puts $350 in a savings account. The savings account accrues interest at a flat rate of 1.05% a month. How much will it count be worth in 7 months?
Which fraction shows 2.8 as the quotient of two integers?
14/5
12/5
9/4
9/2
Answer:14/5 is the correct answer, just took test
Step-by-step explanation: