The equation of parabola is ( x + 5 )² = 16 ( y - 6 )
What is a Parabola?
A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k - p
Given data ,
The vertex of the parabola is ( -5 , 6 )
The directrix of the parabola y = 2
From the equations of parabola , we know that
The vertex ( h , k ) = ( -5 , 6 )
h = -5
k = 6
y = k - p
y = 2
k - p = 2
Substituting the value k in the equation , we get
6 - p = 2
On Simplifying , we get
p = 4
So , now we have the values of h , k , and p
The equation of the parabola is
( x - h )² = 4p ( y - k )
Substituting the values , we get
( x - (-5) )² = 4 x 4 ( y - 6 )
( x + 5 )² = 16 ( y - 6 )
x² + 25 + 10x = 16y - 96
x² + 10x - 16y = -121
Hence , the equation of parabola is ( x + 5 )² = 16 ( y - 6 )
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The 9th grade class was surveyed about their plans after high school graduation. The table describes the results.
Plans to live at home Plans to live on their own Row Totals
Plans to attend college 55%. 10% 65%
Plans not to attend college 20% 15% 35%
Column Totals 75% 25% 100%
Part A: Find the conditional relative frequency of a student who does not plan to attend college, given that they plan to live at home. (3 points)
Part B: Is there an association between not attending college and living on their own? (3 points)
a) The conditional relative frequency of a student who does not plan to attend college, given that they plan to live at home is of: 0.5714 = 57.14%.
b) There is a negative association between not attending college and living on their own.
How to obtain a relative frequency?The relative frequency of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For the conditional relative frequency of a student who does not plan to attend college, given that they plan to live at home, in item a, the outcomes are given as follows:
Desired outcomes: 20% that plans to live at home and not attend college.Total outcomes: 35% that plan to live at home.Hence the relative frequency is of:
p = 0.2/0.35 = 0.5714 = 57.14%.
Among people who plan to live on their own, the relative frequency of people who plan to attend college is of:
0.55/0.65 = 0.846 = 84.6%.
Hence there is a negative association between not attending college and living on their own, as people who live on their own are significantly more likely to attend college then people who do not live on their own.
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there are 7 students on a team. if they must elect a president, a vice president, and a treasurer, how many different arrangements of candidates are possible
Different arrangements of candidates are possible is 210.
Given:
There are 7 students on a team. if they must elect a president, a vice president, and a treasurer.
Number of arrangements = [tex]7_p_{3}[/tex]
= 7!/(7-3)!
= 7!/4!
= 7*6*5*4! / 4!
= 7*6*5*1
= 42*5*1
= 42*5
= 210
Therefore Different arrangements of candidates are possible is 210.
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9a-b-2a-10b simplify this expression
A. -7a+11b
B. 11a+9b
C. -11a-9b
D. 7a-11b
please solve with explanation Q^Q
Step-by-step explanation:
answer is D
if u like it mrk me as brainliest
Answer: d) 7a-11b
Step-by-step explanation:
First collect all like terms
9a - 2a - 10b - b
= 9a - 2a = 7a
= -10b - b = -11b
Therefore the answer is 7a - 11b (D)
18) The profit that the vendor makes per day by selling x pretzels is given by the function
P(x) = -0.004x2 + 2.8x - 100. Find the number of pretzels that must be sold to maximize profit.
A) 390 pretzels
B) 350 pretzels
C) 700 pretzels
D) 1.4 pretzels
Answer:
B) 350 pretzels=====================
GivenFunction P(x) = - 0.004x² + 2.8x - 100To findThe value of x, which makes the P(x) maximumSolutionThis is a quadratic function and it can get maximum at vertex.
The x-coordinate of the vertex is determined by x = - b/(2a).
We have:
a = - 0.004 and b = 2.8Find the value of x:
x = - 2.8 / (2* (-0.004)) = 350Correct choice is B.
Value of (64/25)^-1/2
final answer:
Hence, the simplest form of (64/25) -1/2 is 5/8
which is greater? 0.056 or 0.546?
Answer:
0.546 is greater than 0.056
What is the next three terms in the sequence: -21, -17, -13, -9, -5,
Answer:
-1, 3, 7
Step-by-step explanation:
this is adding 4 every time
hopes this helps please mark brainliest
Answer: -1, 3, 7
Explanation: The pattern in this sequence, is that you add 4 for every new number in the sequence. So -5+4 is -1. Then the next one would be -1+4 is 3. And then finally, the next one would be 3+4, which is 7.
If n is a positive integer, the symbol n! (read ’n factorial’) represents the product of the integers from 1 to n. For example, 4! = (1)(2)(3)(4) = 24. If x and y are integers 30!/36x+25y is equal to an integer, what is the maximum possible value of x + y?
(A)10 (B)47 (C)17 (D)26 (E) 13
Answer:c
Step-by-step explanation:
Juan paga por un saco S/ 224, después de que le han
hecho dos descuentos sucesivos del 30% y 20%, sobre
el precio de lista. ¿Cuál fue dicho precio?
El saco tiene un precio original de 400 soles.
¿Cómo determinar el precio inicial de un saco comprado con descuento?
En este problema tenemos el caso de un precio de compra (P'), en soles, que es resultado de aplicar dos descuentos consecutivos al precio original del saco (P), en soles. El precio es el resultado de multiplicar el precio original por los dos factores de porcentaje, descrito por la siguiente fórmula:
P' = P · (1 - r₁ / 100) · (1 - r₂ / 100), 0 ≤ r₁, r₂ ≤ 100.
Donde:
r₁ - Porcentaje del primer descuento.r₂ - Porcentaje del segundo descuento.Si sabemos que P' = 224, r₁ = 30 y r₂ = 20, entonces el precio original del saco es:
224 = (1 - 30 / 100) · (1 - 20 / 100) · P
224 = 0.7 · 0.8 · P
P = 224 /(0.7 · 0.8)
P = 400
El precio original del saco es de 400 soles.
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lee said that the multiplication fact 5 x 5 can be used to check 10 ÷ 5
is lee correct? Explain how you know if he is right or wrong
Answer: no he is not correct because 5x5 is 25 and 10/5 is 2
Step-by-step explanation:
Rosa's friend jake claims that he can read minds. To test jake's abilities, rosa chooses 333 different numbers from 111 to 101010. Rosa then asks jake to identify which 333 of the 101010 numbers she chose in the correct order. Assume that jake has no special abilities and is randomly guessing the numbers. What is the probability that jake correctly identifies all 333 numbers in the correct order?.
By using the concept of Probability, the result obtained is -
Probability of guessing the correct order = [tex]\frac{1}{720}[/tex]
What is Probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probality of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
There are 10 numbers from 1 to 10
Number of favourable outcomes = 10 [tex]\times[/tex] 9 [tex]\times[/tex] 8
= 720
There is only one correct order
So probability of guessing the correct order = [tex]\frac{1}{720}[/tex]
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Correct Question
To test Jake's abilities, Rosa chooses 3 different numbers
from 1 to 10. Rosa then asks Jake to identify which 3 of the 10 numbers she chose in the correct order.
Assume that Jake has no special abilities and is randomly guessing the numbers. What is the probability that Jake correctly identifies all 3 numbers in the correct order?.
Complete this statement: 500 students is to 25 classes as 120 students is to ___ classes
Answer:
6 Classes
Step-by-step explanation:
500 Students =25 Class
1 class= 500/25
=20
120 students = 120/20
=6
Hope it helps you
Answer:
6
Step-by-step explanation: i think its right
NEED HELP PLS
Barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes. The function g(x) represents the number of gallons of ice cream Barrett makes per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 2x2 + 4
g of x equals the square root of the quantity 3 x cubed
Answer:
Step-by-step explanation:
f(g(x)) = 6x^3 + 4 dollars/hour
In triangle ABC, m∠A = 36°, m∠B = 84°, and m∠C = 60°. The side lengths, in order from greatest to least, are , , .
In the triangle ABC, the side lengths, in order from the greatest to the least, are : AC > AB > BC.
We are given a triangle. The vertices of the triangle are A, B, and C. The measures of the angles ∠A, ∠B, and ∠C are 36°, 84°, and 60°, respectively. We need to arrange the side lengths in order from the greatest to the least.
The side lengths are proportional to their opposing angles in a triangle. It means that the side opposite the largest angle is the largest side, and vice versa. The angles arranged in descending order are : 84° > 60° > 36°. The angles arranged in descending order according to the vertices are : B > C > A. The order of the lengths of the opposite sides must be the same.
Hence, the side lengths, in order from the greatest to the least, are : AC > AB > BC.
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Sylvie is going on vacation. She has already driven 60 miles in one hour. If she then travels for 7 hours at an average speed of 57 miles per hour, what is the total distance that sylvie will have driven?.
The total distance that Sylvie will have driven is, 459 miles.
What is distance?
The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors.
Let, Sylvie is going on vacation. She has already driven 60 miles in one hour. She then travels for 7 hours at an average speed of 57 miles per hour.
In 7 hours Sylvie travel 7 x 57 = 399 miles.
So, the total distance is,
399 + 60 = 459 miles
Hence, the total distance that Sylvie will have driven is, 459 miles.
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PLEASE HELP
2. Given AKMN APRT, then answer the following questions. Show all work.
a.
The congruence statement:
ΔNKM ≅ ΔTPR.
since given ΔKMN ≅ ΔPRT.
KM = PR
MN = RT
KN = TP.
b.
The side is congruent to TR is MN.
TR = MN.
c.
TR = MN
4x - 3 = 25
4x = 25 + 3
4x = 28
divide by 4 on both sides
4x/4 = 28/4
x = 7.
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Write equations for lines a, b, c, d, and e.
PLEASE HURRY! I'll give you brainiest pleaseee.
The equations of lines are given below.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The equation for line a is,
x=-5.
The equation for line b is,
x=5.
The equation for line c is,
y=5.
The equation for line d is,
y=-2.
The equation for line e is
x+y=1
The equations of lines are given above.
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905789 x 9417???
THANK YOU FOR ALL YOUR HELP BRAINLIEST TO WHOEVER CORRECTLY ANSWERS FIRST TYSM TYSM TYSM
Answer:
905789 x 9417 = 8529815013
Step-by-step explanation:
I hope this helps, friend :)
assume that each of 2000 frogss living near a nuclear power plant is exposed to particles of a certain kind of radiation at an average rate of one per week. suppose that each hit by a particle is harmless with probability 1 - 10-5 , and produces a tumor with probability 10-5 . find the approximate distribution of
distribution of the total number of tumors produced in the whole population over a one-year period by this kind of radiation is 0, 1, 2, ..................104000.
let, x denote the total number of hits,
y denotes the number of hits by a particle in a year or an individual,
one per week ⇒ 52 per year
therefore, rate = 52 per year
since it is very rare to hit all individuals, we can use Poisson distribution.
therefore by using the formula p (x = x) = (e^(-rate) × rateˣ) ÷ x! ; x = 0, 1, 2, ............( 2000 × 52)
p (x = 2) = (e⁻⁵² × 52ˣ) ÷ x! ; x = 0, 1, 2, ............104000
now each hit has a harm of probability 10⁻⁵.
so p(total no. of tumors produced over a one year period)
= {e⁻⁵² × 52ˣ} ÷ x! × 10⁻⁵ ; x = 0, 1, 2, ............104000
therefore total no. of tumors = 2000 × (e⁻⁵² × [tex]52^{x.10^{-5} }[/tex] ) ÷ x! × xⁿ ; x = 0, 1, 2, ............104000
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(complete question)
Assume that each of the 2000 individuals living near a nuclear power plant is exposed to particles of a certain kind of radiation at an average rate of one per week. Suppose that each hit by a particle is harmless with a probability of 1 - 10⁻⁵, and produces a tumor with a probability of 10⁻⁵. Find the approximate distribution of the total number of tumors produced in the whole population over a one-year period by this kind of radiation.
Find an expression for d so the line that passes through (a, b) and (c, d) has a slope of 1/2
Answer:
Step-by-step explanation:
In the book, they gave you the values of 'a', 'b', and 'c', and you're supposed to find the value of 'd'.
If you have two points on the line, then the slope of the line is
(the change in 'y') divided by (the change in 'x') .
If the two points are (a, b) and (c, d), then the slope of the line is
(d - b) divided by (c - a),
and you have to find the value of 'd' that makes that whole expression
equal to 1/2.
(d - b) / (c - a) = 1/2
Multiply each side by (c - a): (d - b) = 1/2(c - a)
Add 'b' to each side: d = 1/2(c - a) + b
If you know the values of 'a', 'b', and 'c', you can find the value of 'd'.
PLS HELP
1) What is the value of x?5(4x+8)=85+5x
2) What is the value of x?x+3x+2x+3(x+1)=30
3)What is the value of x?
3/2-7/4= -9/8
what is 4 1/10 plus -2 3/10
If cos x = -2/5, what is the value of cos 2x?
The value of cos 2x = -21/25.
Given:
cos x = -2/5
we know that,
cos 2x = [tex]2cos^{2}x -1[/tex]
= 1([tex](-2/5)^{2}[/tex] - 1
= 1[tex](2/5)^{2}[/tex] - 1
= 1*4/25 - 1
= 4/25 - 1
= 4 - 25 / 25
= -21/25.
Therefore the value of cos 2x = -21/25.
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A spherical tennis ball has a volume
of 200 cm³. Calculate the radius
of the ball. Give your answer
correct to 3 significant figures
Answer:
Step-by-step explanation:
V = (4/3) πR³
R = ³√(3V/(4π))
R = ³√(3*200/(4π)) = ³√(150/π) см
is m=-6 a solution to the inequality m less than or equal to -12
Answer:
No
Step-by-step explanation:
1) Write out the inequality to get a better understanding
m ≤ -12
From this we can see that m can be any number less than -12!
2) Find out possible solutions
As -12 is a negative number, any number less than it would have a larger absolute value.
Some examples of numbers less than -12 would be -15, -13, -36 ect.
HINTS:
It may be easy to confuse which number is greater or smaller than a negative number.
To make sure that we don't make a mistake, we can always put the numbers on a number line!
Any number to the left of it, is smaller, and any number to the right, is larger!
Hope this helps, have a great day!
Vineeth alary wa r 25000 per month due to the pandemic her alary wa reduced by 40 percentage what i her new alary
By using the concept of Percentage, it is obtained that
New Salary of Vineeth = Rs. 15000
What is Percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example 2% means 2 is expressed as a fraction of 100.
Here, the concept of percentage has been used.
Original salary of Vineeth = Rs. 25000
Percentage decrease in salary = 40%
Decrease in salary = [tex]\frac{40}{100}\times 25000\\[/tex]
= Rs. 10000
New Salary of Vineeth = Rs.(25000 - 10000)
= Rs. 15000
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Lorenzo uses 2 1/2 cups of vinegar in his salad dressing recipe. How much vinegar would Lorenzo use to make 4 2/5 recipes?
11 cups of vinegar would Lorenzo use to make [tex]4\frac{2}{5}[/tex] recipes.
Given that, Lorenzo uses [tex]2\frac{1}{2}[/tex] cups of vinegar in his salad dressing recipe.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Lorenzo use to make [tex]4\frac{2}{5}[/tex] recipes
Here, [tex]2\frac{1}{2}=\frac{5}{2}[/tex] and [tex]4\frac{2}{5}=\frac{22}{5}[/tex]
Now, 5/2 × 22/5
= 11
Hence, 11 cups of vinegar would Lorenzo use to make [tex]4\frac{2}{5}[/tex] recipes.
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Jackson's city took a telephone poll about a plan to build a new hotel downtown. 1,000 people took the poll. 440 of them were in favor of the new hotel. What percentage of the people polled were in favor of the hotel?
The percentage of the people polled who were in favor of the hotel is 44%.
What is the percentage?From the information, Jackson's city took a telephone poll about a plan to build a new hotel downtown and 1,000 people took the poll whike.440 of them were in favor of the new hotel.
The percentage for those that were in favor will be:
= People in favor / Total survey × 100
= 440/1000 × 100
= 44%
The percent is 44%.
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Use the order of operations to evaluate 14+13(10 − 1).
Answer:
131
Step-by-step explanation:
14+13(10-1)
14+13(9)
14+117
131
Answer:
The solution is 131
Step-by-step explanation:
I think we must prioritize multiplication
14+13(10-1)
= 14+13(9)
= 14+117
= 131
Electronics Company assembles 240 iPads every day. How many iPads are assembled in one year?
Answer:
87,600 iPad are assembled in a year.
Step-by-step explanation:
You take the number of iPads assembled every day (240) and multiply it by the number of days in a year (365). 240 multiplied by 365 is 87,600.