Stratified sampling is a technique where the sample is split into exclusive groups proportional to the population and then simple random sampling is employed within those groups. So, option B is correct.
This sampling technique involves dividing the population statistics into smaller subgroups on certain given characteristics and then selecting a random sample of solution from each stratum based on the requirement.
This technique is best suitable when the type of population is heterogeneous with respect to characteristics of interest. This sampling uses Proportionate sampling which takes an equal stratum with population size. The output of data is identical to the entire population size.
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it takes carlos 9 minutes to drive from home to work at an average rate of 22 miles per hour. how many minutes will it take carlos to cycle from home to work along the same route at an average rate of 6 miles per hour?
It will take Carlos 33 minutes to cycle from home to work along the same route at an average distance rate of 6 miles per hour.
To find out how many minutes it will take Carlos to cycle from home to work, we'll need to determine the distance of the route first, and then calculate the time it takes to cover that distance at the average cycling speed.
To solve this problem, we can use the formula:
time = distance/speed
1. Find the distance: Since Carlos drives from home to work in 9 minutes at an average rate of 22 miles per hour, we can calculate the distance using the formula: distance = rate × time.
First, convert the time from minutes to hours: 9 minutes ÷ 60 minutes/hour = 0.15 hours.
Now, calculate the distance: distance = 22 miles/hour × 0.15 hours = 3.3 miles.
2. Calculate the cycling time: Now that we know the distance is 3.3 miles, we can find out how long it will take Carlos to cycle at an average rate of 6 miles per hour.
Use the formula: time = distance ÷ rate.
time = 3.3 miles ÷ 6 miles/hour = 0.55 hours.
Now, convert the time back to minutes: 0.55 hours × 60 minutes/hour = 33 minutes.
So, it will take Carlos 33 minutes to cycle from home to work along the same route at an average rate of 6 miles per hour.
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One bag of marbles contains one red, one yellow, one green and two blue marbles.
Another bag contains one marble of each of the same four colors. One marble from each
bag is chosen at the same time. Use the complement to calculate the probability of
selecting two different colors.
The probability of selecting two different colors is P(A) = [_____]
Give answer in simplified fraction form.
The probability of selecting two different colors is 13/15.
What is the probability?The probability of selecting two different colors is determined using the complement rule as follows:
The probability of selecting two different colors from both bags, P(different colors) = 1 - P(same color from bag 1) * P(same color from bag 2)The probability of selecting two marbles of the same color from the first bag is:
P(same color) = P(red and yellow) + P(red and green) + P(red and blue) + P(yellow and green) + P(yellow and blue) + P(green and blue)
P(same color) = 0 + 0 + 0 + 0 + (1/6)(2/5) + (1/6)(2/5)
P(same color) = 2/15
The probability of selecting two marbles of the same color from the second bag is:
P(same color) = P(red and yellow) + P(red and green) + P(red and blue) + P(yellow and green) + P(yellow and blue) + P(green and blue)
P(same color) = 0 + 0 + 0 + 0 + (1/6)(1/3) + (1/6)(1/3)
P(same color) = 1/9
The probability of selecting two different colors from both bags will be:
P(different colors) = 1 - (2/15) * (1/9)
P(different colors) = 13/15
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Two restaurants sell meals for different
prices, as shown below.
Ruby wants to buy 2 meals. What is the
difference between the prices she would
pay at the two restaurants?
Give your answer in pounds (£).
Restaurant A
£19.50 each
Buy one meal,
get another meal
half price
Restaurant B
£18 each
Buy two meals,
get 15% off the
cost of both
Answer:
Step-by-step explanation:
To calculate the price at Restaurant A, we need to find the cost of one meal at full price and the cost of the other meal at half price. One meal at full price would be £19.50, and the other meal at half price would be £19.50/2 = £9.75. So the total cost at Restaurant A would be:
£19.50 + £9.75 = £29.25
To calculate the price at Restaurant B, we need to find the cost of two meals with a 15% discount. The cost of two meals at full price would be £18 x 2 = £36. Then we can calculate the discount:
15% of £36 = £5.40
So the total cost at Restaurant B would be:
£36 - £5.40 = £30.60
The difference between the prices at the two restaurants is:
£29.25 - £30.60 = -£1.35
So Ruby would pay £1.35 less if she bought the meals at Restaurant B.
Answer: Hence the correct answer is difference between price=£1.35
Step-by-step explanation:
Ruby wants to buy two meals at Restaurant A ,price of meal=£19.5 each and get another meal at half price, Price of two meal= 19.5+9.75=£29.25.
At Restaurarant B, Price of meal=£18 each and get 15% Off the cost of both.
The price of two meal= 36-36 x 15/100= £30.6.
Differece between the price =30.6-29.25=£1.35,
Hence the correct answer is difference between price=£1.35
I hoped this helped you!<3!
Which dot plot shows 3 people that sleep for eight hours at night and three people that sleep for six hours at night
Answer:
select me as brainliest
Feeling sleepy? Students in a high school statistics class responded to a survey designed by their teacher. One of the survey questions was “How much sleep did you get last night?” Here are the data
One cube has edges / meters long. Another has edges 37 meters long. What is the ratio of the volume of the first cube to the volume of the
second cube?
OA 1:3
OB. 1:9
OC. 1:27
OD. 1:6
OE. 1:81
The ratio of the volume of the first cube to the volume of the second cube is 1:27. The correct option is (C).
Let's represent the length of the edge of the first cube "n" and the length of the edge of the second cube "3n".
The volume of the first cube is:
V1 = n³
The volume of the second cube is:
V2 = (3n)³ = 27n³
To find the ratio of the volume of the first cube to the volume of the second cube, we divide V1 by V2:
V1/V2 = n³ / (27n³) = 1/27
Therefore, the required ratio is 1:27.
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The correct question is as follows:
One cube has edges n meters long. Another has edges 3n meters long. What is the ratio of the volume of the first cube to the volume of the
second cube?
A 1:3
B. 1:9
C. 1:27
D. 1:6
E. 1:81
In a recent year, 24% of all college students were enrolled part-time. If 8.6 million college students were enrolled part-time that year, what was the total number of college students?
what is the volume for the triangular prism
The volume of the triangular prism whose base = 4.8m , height = 3.2m, length = 9m is 69.12 cubic meters.
To find the volume of a triangular prism, we need to multiply the area of the base by the height and the length of the prism. The formula for the volume of a triangular prism is:
V = 1/2 x b x h x l
where b is the length of the base, h is the height of the base, and l is the length of the prism.
In this case, the base of the triangular prism has a length of 4.8m and a height of 3.2m, so the area of the base is:
A = 1/2 x b x h = 1/2 x 4.8m x 3.2m = 7.68m²
The length of the prism is 9m, as given in the problem.
Therefore, the volume of the triangular prism is:
V = A x l = 7.68m² x 9m = 69.12m³
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find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ).
To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first visualize the graph of the limaçon.
The equation r = 1 2 + cos(θ) represents a curve that resembles a snail shell or a heart shape with a loop inside another loop. To find the area inside the larger loop and outside the smaller loop, we need to set up the integral using the polar coordinates.
The formula for the area enclosed by a polar curve is given by:
A = 1/2 ∫(θ2-θ1) (r2-r1)² dθ, where r2 is the outer curve, r1 is the inner curve, and θ1 and θ2 are the angles where the curves intersect.
In this case, the inner curve is r = 1 - cos(θ), and the outer curve is r = 1/2 + cos(θ). The curves intersect when cos(θ) = 1/2 or θ = π/3 and θ = 5π/3.
So, we need to split the integral into two parts, one for θ = π/3 to θ = 5π/3, and another for θ = 5π/3 to θ = π/3.
This is because the outer curve becomes the inner curve and vice versa when we cross the angle θ = 5π/3. For the area inside the larger loop and outside the smaller loop, we need to subtract the area enclosed by the inner curve from the area enclosed by the outer curve.
Using the formula above and plugging in the values, we get:
A = 1/2 ∫(5π/3-π/3) [(1/2 + cos(θ))² - (1-cos(θ))²] dθ
Simplifying this integral, we get:
A = 1/2 ∫(5π/3-π/3) [5/4 + 2cos(θ)] dθ
A = 5/8 [θ + sin(θ)](5π/3-π/3)
A = 5/8 [4π/3 + sin(4π/3) - (π/3 + sin(π/3))]
A = 5/8 [4π/3 - √3/2]
A = 5π/6 - (5/16)√3
Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is 5π/6 - (5/16)√3.
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To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 + 2cos(θ), use the formula for finding the area enclosed by a polar curve.
Explanation:122π/3∫0(12+cosθ)2dθ, r=(1/2)+cos\u0026#952, , 1, 2, cos, , FindThe general formula is A = (1/2)∫(r^2)dθ, where r is the equation of the curve. In this case, we need to find the area between two curves: the larger loop given by r = 1 + 2cos(θ) and the smaller loop given by r = 1. To find the limits of integration, we need to find the values of θ where the two curves intersect. After finding the values of θ where the curves intersect, we can integrate the difference between the two equations r = 1 + 2cos(θ) and r = 1 with respect to θ.
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Solving a word problem using a two-step linear inequality
Reuben wants to rent a boat and spend at most $52. The boat costs $6 per hour, and Reuben has a discount coupon for $8 off. What are the possible numbers
of hours Reuben could rent the boat?
User for the number of hours.
Write your answer as an inequality solved for t.
Answer:
t is less than or equal to 10
Step-by-step explanation:
At most means less than or equal to. The boat costs 6 an hour, so, 6t. He has a $8 off coupon, so, 6t-8 is less than or equal to 52. Add 8 on both sides and then divide by 6 to isolate t. t is less than or equal to 10 hours.
What is the area of this figure
Thanks for any answer or help :)
Answer:
72
Step-by-step explanation:
3x6=18
8x7=56
18+56=72
Hope this helps :)
How to solve for y=mx on a graph
Answer:
see below
Step-by-step explanation:
y=mx is the start of a line equation. The line equation is:
[tex]y=mx+b[/tex]
with m being the slope and b is the y-intercept.
If you have 2 points, let's say (0,1) and (4,0), the slope would be -1/4.
The slope is [tex]\frac{rise}{run}[/tex]. The rise is the number of units going up or down from one point to another. The run is the number of units going left or right from one point to the other.
In this case, the slope is -1/4 because you go down 1 unit and right 4 units.
The y-intercept is 1 because the y-intercept is when x=0 and is located on the y-axis.
Hope this helps :)
animal conservation counted 15 deer in a circular region with radius of 10 miles.find the number of deer in a 560square mile region
As per the unitary method, there would be approximately 84 deer in a 560 square mile region, based on the assumption that the deer population density is uniform throughout the region.
In this case, we want to find the number of deer in a 560 square mile region, given that there are 15 deer in a circular region with a radius of 10 miles.
The first step is to find the area of the circular region with a radius of 10 miles. We can use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. Substituting the values, we get:
A = π(10)² = 100π
The area of the circular region is 100π square miles.
Next, we can use a unitary method to find the number of deer in one square mile. We know that there are 15 deer in 100π square miles. To find the number of deer in one square mile, we can divide both sides by 100π:
15 deer ÷ 100π square miles = x deer ÷ 1 square mile
Simplifying this equation, we get:
x = (15 ÷ 100π) deer per square mile
Now, we can use this value of x to find the number of deer in a 560 square mile region. We can multiply x by 560 to get:
x deer per square mile × 560 square miles = 560x deer
Substituting the value of x, we get:
560(15 ÷ 100π) deer = 84 deer (rounded to the nearest whole number)
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The blueprint below represents a circular garden. Nicole wants to put a pond in sector ACB as marked on the blueprint. The radius of the garden is 3 meters. What area of the garden will be covered by the pond? Round to the nearest tenth.
Answer:
Step-by-step explanation:
To find the area of the garden covered by the pond, we need to find the area of sector ACB.
First, we need to find the measure of the central angle of sector ACB. The central angle is the same as the angle formed by radii OA and OB.
Since the radius of the garden is 3 meters, we can use the Pythagorean theorem to find the length of the chord AB:
AB² = OA² + OB²
AB² = 3² + 3²
AB² = 18
AB = √18 ≈ 4.24 meters
Now, we can use the formula for the area of a sector:
A = (θ/360)πr²
where θ is the central angle and r is the radius of the circle.
The central angle of sector ACB can be found using the inverse cosine function:
cos(θ/2) = AB/2r
cos(θ/2) = 4.24/(2*3)
cos(θ/2) ≈ 0.707
θ/2 ≈ cos⁻¹(0.707)
θ ≈ 2cos⁻¹(0.707)
θ ≈ 144.1 degrees
Now we can calculate the area of sector ACB:
A = (θ/360)πr²
A = (144.1/360)π(3)²
A ≈ 10.6 square meters
Therefore, the area of the garden covered by the pond is approximately 10.6 square meters.
The graph of f(x) = x³ with three reference points
is shown. Which of the following represents
points from f(x) to a point on
g(x) = 2(x-4)³-3? Select three that apply.
A. (5,3)
B. (5,-1)
C. (3,-5)
D. (4,-3)
☐ E. (2,-5)
Based on the graph of f(x) = x³ with three reference points, the points from f(x) to a point on g(x) = 2(x - 4)³ - 3 include the following:
B. (5, -1)
C. (3, -5)
D. (4, -3)
What is a translation?In Mathematics and Geometry, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.
At the ordered pair (5, -1), the function g(x) = 2(x - 4)³ - 3 would be tested with given points as follows;
g(x) = 2(x - 4)³ - 3
-1 = 2(5 - 4)³ - 3
-1 = 2(1) - 3
-1 = -1 (True).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Please find it quickly
The area of the shade region as shown in the figure below is 50 yd².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the shaded region, we use the formula below.
Formula:
Area of the shaded region = Area of the rectangle-area of the triangleA = LW-bh/2Where:
A = Area of the shaded portionL = Length of the rectangleW = Width of the rectangleb = Base of the triangleh = Height of the triangleFrom the diagram,
Given:
L = 9 ydW = 6 ydb = 4 ydh = 2 ydSubstitute these values into equation 1
A = (9×6)-(4×2/2)A = 54-4A = 50 yd²Hence, the area is 50 yd².
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Jeremiah signed up for a streaming music service that costs $7 per month.
The service allows Jeremiah to listen to unlimited music, but if he wants to
download songs for offline listening, the service charges $1.25 per song. How
much total money would Jeremiah have to pay in a month in which he
downloaded 50 songs? How much would he have to pay if he downloaded s
songs?
Cost with 50 songs:
Cost with s songs:
Jeremiah will have to pay $69.5 in a month in which he downloaded 50 songs. The Total amount Jeremiah will pay for s songs $7 + $1.25 s
We are given that Jeremiah signed up for a streaming music service that costs $7 per month.
Cost per month = $7
Cost of Offline download = $0.50 per song
Total amount Jeremiah will pay = $7 + $1.25(50)
= 7 + 62.5
= $69.5
Jeremiah will have to pay $69.5 in a month in which he downloaded 50 songs.
Therefore, Total amount Jeremiah will pay for s songs = $7 + $1.25* s
= $7 + $1.25 s
Total amount Jeremiah will pay for s songs = $7 + $1.25 s
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hayden wants to place 5 of his 8 trophies on the fireplace. how many ways can he arrange the trophies
Hayden can arrange his 5 trophies on the fireplace in 56 different ways.
The formula for combinations,
which is nCr = n!/r!(n-r)!, where n is the total number of items and r is the number of items being chosen. In this case, n=8 and r=5.
So, we can calculate the number of ways that Hayden can arrange his trophies as follows:
8C5 = 8!/5!(8-5)! = 8!/5!3! = (8x7x6)/(3x2x1) = 56
Therefore, there are 56 ways that Hayden can arrange his 5 trophies on the fireplace.
Hence, Hayden can arrange his 5 trophies on the fireplace in 56 different ways using the formula for combinations.
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2. Calculate the mean absolute deviation of the following data set: (36, 54, 49, 39, 41, 48, 50)
45.3
8.7
5.7
07
To calculate the mean absolute deviation, we first need to calculate the mean of the data set:
Mean = (36 + 54 + 49 + 39 + 41 + 48 + 50) / 7 = 45
Next, we calculate the absolute deviation of each data point from the mean:
|36 - 45| = 9
|54 - 45| = 9
|49 - 45| = 4
|39 - 45| = 6
|41 - 45| = 4
|48 - 45| = 3
|50 - 45| = 5
To calculate the mean absolute deviation, we take the average of these absolute deviations:
Mean Absolute Deviation = (9 + 9 + 4 + 6 + 4 + 3 + 5) / 7 = 5.7
Therefore, the answer is option (c) 5.7.
The growing population of town A can be modeled by the equation P(t)=8t2+2000, where t represents number of years after 2010. The growing population of town B can be modeled by the equation P(t)=100t+3000. In which year will the populations of the towns be approximately equal?
In the year 2040, the populations of the two towns will be approximately equal.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
To find the year when the populations of the towns will be approximately equal, we need to set the two equations equal to each other and solve for t:
8t² + 2000 = 100t + 3000
8t² - 100t - 1000 = 0
We can simplify this equation by dividing both sides by 4:
2t² - 25t - 250 = 0
Now we can solve for t using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = 2, b = -25, and c = -250. Plugging in these values, we get:
t = (25 ± √(25² - 4(2)(-250))) / (2(2))
t = (25 ± √(9375)) / 4
t = (25 ± 97.0) / 4
So t = 30.25 or t = -6.25. We can ignore the negative solution since we're looking for a year after 2010. Therefore, the populations of the two towns will be approximately equal in the year:
2010 + 30.25 = 2040.25
So, in the year 2040, the populations of the two towns will be approximately equal.
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write a funtion whose graph has two vertical asymptotes located at x = -5 and x = 2
The denominator, (x+5)(x-2) + 1, ensures that the function is never zero and avoids any potential holes in the graph. The numerator, (x+5)(x-2), is zero precisely when x=-5 or x=2, which leads to the vertical asymptote
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
One possible function whose graph has two vertical asymptotes located at x = -5 and x = 2 is:
f(x) = (x+5)(x-2) / ((x+5)(x-2) + 1)
The denominator, (x+5)(x-2) + 1, ensures that the function is never zero and avoids any potential holes in the graph. The numerator, (x+5)(x-2), is zero precisely when x=-5 or x=2, which leads to the vertical asymptotes.
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Choose an expression that is equivalent to (-3)^4/(-3)^2.
An expression that is equivalent to (-3)^4/(-3)^2 is(-3)^2
Choosing an expression that is equivalentFrom the question, we have the following parameters that can be used in our computation:
(-3)^4/(-3)^2.
Applying the law of indices, we have
(-3)^4/(-3)^2 = (-3)^(4 - 2)
Evaluate
So, we have
(-3)^4/(-3)^2 = (-3)^2
Hence, the solution is (-3)^2
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Use the graph to answer the question. graph of polygon ABCD with vertices at 1 comma 6, 3 comma 2, 7 comma 2, 5 comma 6 and a second polygon A prime B prime C prime D prime with vertices at negative 5 comma 6, negative 3 comma 2, 1 comma 2, negative 1 comma 6 Determine the translation used to create the image. 6 units to the right 6 units to the left 2 units to the right 2 units to the left
The polygon is translated 6 units to the left
Given data ,
A ( 1 , 6 ) , B ( 3 , 2 ) , C ( 7 , 2 ) , D ( 5 , 6 ) transformed to A' ( -5 , 6 ) , B' ( -3 , 2 ) , C' ( 1 , 2 ) , D' ( -1 , 6 )
The given coordinates represent two sets of points, one for the original polygon ABCD and the other for the transformed polygon A' B' C' D'.
Now , we can observe that the x-coordinates of each vertex have changed, while the y-coordinates remain the same. Specifically, the x-coordinates of the original vertices have been decreased by 6 units to obtain the x-coordinates of the transformed vertices.
This indicates that a translation has been applied to the original polygon, shifting it 6 units to the left along the x-axis
Hence , the function is translated 6 units to the left
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Hi!, I need help with this question:) any help would be wonderful<3
Which expression is equivalent to 1/3 (9- 6x +12)?
A. 2x + 7
B. -2x + 1
C. 2x + 1
D. -2x + 7
Answer:
B
Step-by-step explanation:
1/3(9-6x+12)
3-2x+4
1-2x
help with my homework
rewrite as a single power using laws of exponents
(3²) x 3⁷ ÷ 3⁸
Answer:
3^(2 + 7 - 8) = 3^1 = 3
Write two different quadratic functions that go through the points (5,3) and (8,0). (PLEASE ANSWER CORRECTLY)
Answer:
[tex]y=x^{2} -14x+48[/tex] (when a=1)
[tex]y=2x^{2} -27x+88[/tex] (when a=2)
The general form of the quadratic functions you asked is :
[tex]y=a(x-5)(x-8)-x+8\\(a\neq 0)[/tex]
Here,
-x+8 is a line that passes two given points.
When you put x=5, you get y=3,
which is a coordinate of one of the given points.
When you put x=8, you get y=0,
which is a coordinate of the other one.
-----------------------------------------------------------------------------------------------------
This is the way I got the form above :
Since what we're looking for is a quadratic function, (let's call it "f(x)")
the equation
f(x)=-x+8
can have at most 2 different real solutions.
You can note that the real solution of the equation above
represents the x coordinate of the intersection point of two graphs:
y=f(x) and y=-x+8.
Again, the equation can have at most 2 different solutions.
And we have 2 different real solutions already given -
(It's a requirement ; we want y=f(x) to contain (5,3) and (8,0))
- which are x=5, x=8.
So these are the only two solutions of the equation.
Since the coefficient of a highest order term
hasn't been decided, we can introduce an unknown 'a' for it.
(i.e. Let 'a' be the coefficient of a highest order term.)
To sum up, an equation
f(x)=-x+8
f(x)+x-8=0
has two different real solutions x=5, x=8,
thus it can be written like this;
a(x-5)(x-8)=0
where a is not zero.
Therefore
f(x)+x-8 = a(x-5)(x-8)
(Because two italic-texted equations have the same meaning)
∴ [tex]f(x)=a(x-5)(x-8)-x+8[/tex][tex]\QED[/tex].
Find the GCF:
-60 + 60n2 + 50n3
Step-by-step explanation:
You can factor out a '10' from each of the terms
10 ( -6 + 6n^2 + 5 n^3 )
If you meant - 60 n + 60 n^2 + 50 n^3
you can factor out a 10 n
10n ( -6 + 6n + 5n^2)
The two figures are similar. What is the value of x?
Answer:
Step-by-step explanation:
Create a proportion between the sides of both triangles:
4 corresponds to 8 and 2x+2 corresponds to 12:
So, the proportion will be [tex]\frac{4}{8}=\frac{2x+2}{12}[/tex].
Continue by simplifying the rest:
[tex]\frac{1}{2}=\frac{2x+2}{12}[/tex]
Multiply by 12 on both sides (the 12 will cancel out with itself on the right side):
[tex]12*\frac{1}{2}=2x+2[/tex]
[tex]2x+2=6[/tex]
So, using basic algebra skills, we get that x = 2.
Check:
Is [tex]\frac{4}{8}=\frac{6}{12}[/tex] ?
Yes, it is!
The equation of the axis is y=6, the focus is at (0,6), and p = -3.
The equation of the parabola as (y-6)^2 = 12x
Here, we have to solve:
Given an axis equation of y=6, focus at (0,6), and p=-3, this is a horizontal parabola with its vertex at (0,6).
Since p<0, it opens to the left.
The standard equation of a horizontal parabola with vertex (h,k) and distance p is (y-k)^2 = -4p(x-h)
Plugging in the values (h,k)=(0,6) and p=-3,
we get the equation of the parabola as (y-6)^2 = 12x
Hence, The equation of the parabola as (y-6)^2 = 12x
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the volume of a rectangular prism is represented by 36x^3-28x+8 the height is 3x-1 and the width is 4. write an expression representing the prisms length then use polynomial long division to simply the expression.
The expression for the length of the rectangular prism is L = 9x² + 7x - 2
Given data ,
Let the length of the rectangular prism be L
Let the volume of the rectangular prism be V = 36x³ - 28x + 8
Let the height of the prism be H = 3x - 1
Let the width of the prism be W = 4
And , Volume of Rectangle = Length x Width x Height
On simplifying , we get
36x³ - 28x + 8 = L ( 3x - 1 ) ( 4 )
L ( 12x - 4 ) = 36x³ - 28x + 8
By long division , we get
-----9x² + 7x - 2--------------------------------------
4(3x - 1) | 36x³ - 28x + 8
- (36x - 9x)
-------------------------------------------------
7x - 2
- (7x - 2)
---------------------------------------------
0
Hence , the length of the prism is L = 9x² + 7x - 2
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NEED HELP ASAP PLS ILL MARK YOU BRAINLIEST IF ITS RIGHT
Answer:
The top table shows the sample space for two spins of this spinner.
