Answers
This is the simplified ratio of lengths DE:EF as (2/√(29))√(34) : 1.
What is ratio?A ratio is a relationship between two or more quantities that indicates how many times one quantity is contained in another. It is a way of comparing quantities of the same kind, such as lengths, areas, volumes, or numbers. A ratio is usually expressed as a fraction or a colon (:). Ratios can be simplified by dividing both terms of the ratio by their greatest common factor (GCF). Ratios are used in many fields such as mathematics, finance, science, engineering, and statistics, among others. They are used to compare different quantities, to express proportions or rates, and to solve various mathematical problems.
Here,
We can use the distance formula to find the lengths DE and EF, and then calculate their ratio:
Length DE = √[(xE - xD)² + (yE - yD)²]
= √[(10 - 4)² + (15 - 4)²]
= √(6² + 11²)
= √(136)
= 2√(34)
Length EF = √[(xF - xE)² + (yF - yE)²]
= √[(12 - 10)² + (20 - 15)²]
= √(2² + 5²)
= √(29)
Therefore, the ratio of lengths DE:EF is:
DE:EF = (2√(34)) : (√(29))
We can simplify this ratio by dividing both sides by √(29):
DE:EF = (2√(34))/√(29) : (√(29))/√(29)
= (2/√(29))√(34) : 1
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Related Questions
At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. What is the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item?
0.13
0.14
0.20
0.22
Answers
Let's use conditional probability to solve this problem. We want to find the probability of a customer purchasing a specialty espresso drink and a food item, so we can use the following formula:
P(specialty espresso drink and food) = P(food|specialty espresso drink) * P(specialty espresso drink)
We know that P(specialty espresso drink) = 0.56 and P(food|specialty espresso drink) = 0.35, so we can substitute these values into the formula:
P(specialty espresso drink and food) = 0.35 * 0.56
P(specialty espresso drink and food) = 0.196
Therefore, the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item is 0.196 or approximately 0.20 (rounded to two decimal places).
So, the answer is option C: 0.20.
A parabola is defined as the set of points the same distance from (6,2) and line y=4. Select all points that are on this parabola
Answers
In conclusion there are no points among the given options that are on the parabola.
why it is?
The vertex of the parabola is the midpoint between the point (6, 2) and the line y = 4, which is at (6, 3). Since the focus is below the vertex and the directrix is a horizontal line, the equation of the parabola is of the form:
(x - h)²2 = 4p(y - k)
where (h, k) is the vertex and p is the distance from the vertex to the focus (and from the vertex to the directrix).
Using the vertex and the given point (6, 2), we can find that p = 1. Therefore, the equation of the parabola is:
(x - 6)²2 = 4(y - 3)
Now we can check which of the given points satisfy this equation:
A. (4, 6)
(4 - 6)²2 = 4(6 - 3)
4 = 12 - 12
This point is not on the parabola.
B. (5, 7)
(5 - 6)²2 = 4(7 - 3)
1 = 16
This point is not on the parabola.
C. (6, 5)
(6 - 6)²2 = 4(5 - 3)
0 = 8
This point is not on the parabola.
D. (7, 6)
(7 - 6)²2 = 4(6 - 3)
1 = 12
This point is not on the parabola.
E. (8, 5)
(8 - 6)²2 = 4(5 - 3)
4 = 8
This point is not on the parabola.
Therefore, there are no points among the given options that are on the parabola.
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Complete question:
Which points are on the parabola defined as the set of points the same distance from (6,2) and the line y=4?
would most people take the following gamble? flip a coin, if heads you win $75, if tails you lose $50. explain your answer.
Answers
Answer:
50/50 Chance
Step-by-step explanation:
I'm not sure if you wrote the entire question correctly, but the highest chance you would have of winning would be 100% because the 2 sides * the 50/50 chance they have. So that would make the odds of winning 50%.
suppose s and t are finite sets and there is a function such that f is a k-to-1 correspondence. what can be inferred about the cardinality of s and t?
Answers
The we can infer that the cardinality of s is less than or equal to the cardinality of t multiplied by k.
Given that s and t are finite sets and there is a function f such that f is a k-to-1 correspondence. We need to determine what can be inferred about the cardinality of s and t.
Definition of K to 1 function: A function f is k-to-1 correspondence if the function f maps at most k distinct elements of the domain to a given element of the range.
Let |s| and |t| be the cardinalities of s and t respectively. According to the pigeonhole principle,
|s| <= k |t| This implies that the cardinality of s is less than or equal to the cardinality of t multiplied by k.
Note: We cannot infer anything about the equality of cardinalities of s and t, as the k-to-1 correspondence allows a function to map a single element of the domain to k elements of the range.
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if a watch was sold for RS 1656 after allowing 10% discount on the market price and adding 15% VAT ,find the discount amount
Answers
the discount amount is RS 160.
define discountA discount is a reduction in the price of a product or service that is offered by a seller to a buyer. The discount may be a percentage of the original price or a specific amount of money.
Let the market price of the watch be x.
After allowing a 10% discount, the selling price becomes 0.9x.
Then, adding 15% VAT, the final selling price is:
0.9x + 0.15(0.9x) = 1.035x
We know that the final selling price is RS 1656, so we can set up an equation:
1.035x = 1656
Solving for x, we get:
x = 1600
Therefore, the market price of the watch was RS 1600.
The discount amount is the difference between the market price and the discounted selling price:
Discount amount = Market price - Discounted selling price
= 1600 - 0.9x
= 1600 - 0.9(1600)
= 1600 - 1440
= 160
So the discount amount is RS 160.
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Please help me! This is due at 2:15 PM!!!! WHICH ALREADY PASSED!!! ITS GOING TO BE LATE> A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability? Explain please.
Answers
Answer: O: 252
Step-by-step explanation:
Theoretically, all of the letters would've been drawn 250 times as that is the theoretical possibility. The closest number to the theoretical number in this experiment would be 252 which belongs to O
[9,7] is the difference between 2 vectors with components [3,4] and [-6, b] what is b
Answers
The value of b is -6
We know that the difference between two vectors with components (a1, a2) and (b1, b2) is given by (b1-a1, b2-a2).
So in this case, we have
[b1 - 3, b2 - 4] = [(-6) - 3, b - 4]
Simplifying the right-hand side gives us
[-9, b - 4]
So we can set the components of the left-hand side equal to the corresponding components of the right-hand side
b1 - 3 = -9
b2 - 4 = b - 4
Solving for b in the first equation gives us
b1 = -9 + 3 = -6
Substituting this into the second equation and simplifying gives us
-6 - 4 = b - 4
-10 = b - 4
b = -10 + 4 = -6
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Let x and y both represent rational numbers. Select whether each expression is always, sometimes, or never a
rational number.
x-y
x + y
Always Sometimes Never
Answers
The expressions x - y and x = y are sometimes a rational number.
Classifying the types of the numbers
From the question, we have the following parameters that can be used in our computation:
x and y = rational numbers
The difference of two rational numbers is always a rational number, so x - y is sometimes a rational number.
The sum of two rational numbers is always a rational number, so x + y is sometimes a rational number.
Therefore, both expressions are sometimes a rational number.
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PLEASE HELP ME!!!!!!!!!!!!!!
This figure is a rectangle with a semicircle on the shorter side.
What is the perimeter of this figure?
Use 3.14 for pi.
A. 20.28 ft
B. 30.28 ft
C. 46.28 ft
D. 74.24 ft
Answers
Answer: it should be b
Step-by-step explanation:
10 ft + 4 ft + 10 ft = 24 ft
The perimeter of the semicircle is (1/2)*2*pi*r. The diameter of the circle is 4 ft, so the radius is 2 ft.
(1/2)*2*pi*2 = 6.28 ft
Add the perimeters of the rectangle and semicircle to find the total perimeter of the figure:
24 ft + 6.28 ft = 30.28 ft
Therefore, the answers is 30.28 ft.
GEOMETRY: Find the area of the parallelogram. Be sure to include the correct unit in your answer.
Answers
(700 inches squared)
Break the shape into 1 square and 2 triangles. The area of a triage is
length(width)/2
Amala listed her assets and liabilities.
Credit Card Balance
Car
(Paid in full)
Jewelry
Student Loan
Savings Account
Stocks
$850
$2,200
$125
$2,500
$1,200
$1,500
What is the total of Amala’s liabilities?
Answers
take a picher of that your working on
Answer:
C: 3,350
Step-by-step explanation:
took test 2023
4.
You are given an isosceles trapezoid ABCD with median XY. Complete the following.
AX = 4, CD = __________
Answers
If isosceles trapezoid ABCD has a median XY then CD = 8 .
What is trapezoid?
A trapezοid is alsο knοwn as a trapezium is a fοur-sided pοlygοn οr a quadrilateral. It has οne set οf οppοsite sides which are parallel and a set οf nοn-parallel sides. The parallel sides are knοwn as the bases and the nοn-parallel sides are knοwn as the legs οf the trapezοid. A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
Given AX = 4
Now, AX = BX as XY is the meridian
i.e.
AB = 2AX
AB = 2(4)
AB = 8
We have given that the trapezoid is an isosceles trapezoid, which means
AB = CD
i.e.
CD = 8
Thus, If isosceles trapezoid ABCD has a median XY then CD = 8.
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Simplify the expression-4(-3x - 8) - 34
Answers
Answer:
12x-2
Step-by-step explanation:
-4(-3x-8)-34
12x+32-34
12x-2
A hamster runs in its wheel whose radius is 3 inches. The wheel completes 9.2 revolutions in 8 seconds.
What is the linear velocity of the hamster's wheel?
Answers
On solving the provided question we can say that As a result, the radius hamster's wheel has a linear velocity of 3.45 inches per second.
what is radius?In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The phrase was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's perimeter. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.
The circumference of the wheel is equal to 2r, where r is its radius. Thus the hamster's wheel's circumference is:
C = 2(3 inches) = 6 in.
Because the hamster does 9.2 revolutions in 8 seconds, its angular velocity is:
/ (8 seconds) = 1.15 rotations per second
The hamster's wheel has a linear velocity equal to the product of its angular velocity and radius. So:
3.45 inches per second = v = r = (1.15 rotations per second) * (3 inches)
As a result, the hamster's wheel has a linear velocity of 3.45 inches per second.
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Please help me! This is due at 2:15 PM!!!! WHICH ALREADY PASSED!!! ITS GOING TO BE LATE> A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability? Explain please.
Answers
The experimental probability for the letter B is closest to its theoretical probability.
What is probability?A number between 0 and 1 can be used tο represent prοbability, which is the likelihοοd that a given event will οccur. A prοbability οf 0 denοtes an impοssibility, while a prοbability οf 1 denοtes a certainty that the event will οccur.
By dividing the number οf balls that cοrrespοnd tο that letter by the tοtal number οf balls, οne can determine the theοretical prοbability οf drawing a letter in a single draw:
P(B) = 15/75 = 0.2
P(l) = 15/75 = 0.2
P(N) = 15/75 = 0.2
P(G) = 15/75 = 0.2
P(O) = 15/75 = 0.2
The experimental probability of drawing a letter is calculated by dividing the number of times that letter was drawn by the total number of draws:
P(B) = 247/1250 = 0.1976
P(I) = 272/1250 = 0.2176
P(N) = 238/1250 = 0.1904
P(G) = 241/1250 = 0.1928
P(Ο) = 252/1250 = 0.2016
To determine which letter's experimental probability is closest to its theoretical probability, we can calculate the difference between the two probabilities for each letter:
|P(B) - 0.2| = |0.1976 - 0.2| = 0.0024
|P(I) - 0.2| = |0.2176 - 0.2| = 0.0176
|P(N) - 0.2| = |0.1904 - 0.2| = 0.0096
|P(G) - 0.2| = |0.1928 - 0.2| = 0.0072
|P(O) - 0.2| = |0.2016 - 0.2| = 0.0016
The letter with the smallest difference is B, with a difference of 0.0024. Therefore, the experimental probability for the letter B is closest to its theoretical probability.
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AE and CD intersect at point B. Find m
Answers
The measure of angle ABC is 36°
What are vertical opposite angles?When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.
Therefore we can say that angle DBE = angle ABC. This is because this two angles are vertically opposite.
Therefore, < ABC = < DBE = 36°( vertically opposite angles are equal).
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Kevin has $500 in his savings account and he deposits $25 each week. Janet has $250 in her savings account and she deposits $50 each week.
(a) Write a system of equations that represents the scenario
(b) Solve the system to determine after how many weeks Kevin and Janet will have the same amount of savings. What will that amount be?
Answers
Answer:
(a) Let x be the number of weeks and let y be the total amount in their savings accounts. Then, the system of equations that represents the scenario is:
Kevin: y = 25x + 500
Janet: y = 50x + 250
(b) To determine after how many weeks Kevin and Janet will have the same amount of savings, we need to solve the system of equations by setting them equal to each other:
25x + 500 = 50x + 250
Subtracting 25x and 250 from both sides, we get:
250 = 25x
Dividing both sides by 25, we get:
x = 10
Therefore, Kevin and Janet will have the same amount of savings after 10 weeks. To find out what that amount is, we can substitute x = 10 into either equation:
y = 25x + 500
y = 25(10) + 500
y = 750
So after 10 weeks, both Kevin and Janet will have $750 in their savings accounts.
Step-by-step explanation: explained it in the answer
HELP SOLVE PLEASEEE ENOUGH POINTSSS
Answers
Step-by-step explanation:
$ 540 / 12 mos = $ 45 per month for all of the services
SO H + D + N = 45 and N = 2D
So H + D + 2D = 45
and H+ D = 300/12 = $25 / month
so (H+D) + 2D = 45
25 + 2D = 45
D = 10 dollars per month
then H = 15 dollars per month ( because H+D = 25)
and N = 20 dollars per month ( because N = 2D)
Work,
Set up 3 equations
H - cost of Hulu per month
N - cost of Netflix per month
D - cost of Disney per month
1) 12H + 12N + 12D = 540
2) 12H + 12D = 300
3) N = 2D
Now, I’m going to substitute 2D = N for N in the first equation to get the equation…
1) 12H + 12(2D) + 12D = 540. -> substitute 2D in for N
1) 12H + 36D = 540. -> add like terms
For the second equation, I’m going to solve it to make the equation equal H…
2) 12H = 300 - 12D. -> subtracted 12D from both sides
2) H = 25 - D. -> divided the entire equation by 12
Since we have H singled out, we can now substitute this equation in for H in the first equation,
1) 12(25 - D) + 36D = 540. -> you didn’t have to divide by 12 in the second equation but I did it because I wanted you know what to do in any other situation and it also helps in the end.
1) 300 - 12D + 36D = 540. -> distribute the 12
1) 300 + 24D = 540. -> add like terms
1) 24D = 240. -> subtract 300 on both sides
1) D = 10. -> divide by 24
So the Disney subscription is 10 dollars per month. Using that we can find the value of H and N…
2) H = 25 - 10. -> substitute the value of D into the equation
2) H = 15. -> solve
3) N = 2(10). -> substitute
3) N = 20. -> solve
So the cost of the Disney plus subscription is $10, Netflix is $20, and Hulu is $15 per month.
I hope this helps and you understand how I got my answer! If you have any questions about the explanation you can comment it and I can to help you! :)
The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel.
Create a linear model that represents the amount of fuel on the plane, in gallons, as a function of the flight time, in hours. Show all of your work.
Answers
Answer: To create a linear model that represents the amount of fuel on the plane as a function of flight time, we need to use the given information to calculate the fuel burn rate of the airplane in gallons per hour.
Fuel burn rate = Fuel capacity ÷ Range
Fuel burn rate = 63,500 gallons ÷ 14,430 km = 4.4 gallons per km
We need to convert km to miles, as flight time is usually measured in hours and miles. We can use the conversion factor 1 km = 0.621371 miles to convert kilometers to miles.
Range in miles = Range in km ÷ 0.621371
Range in miles = 14,430 km ÷ 0.621371 = 23,594 miles
Fuel burn rate = Fuel capacity ÷ Range in miles
Fuel burn rate = 63,500 gallons ÷ 23,594 miles = 2.69 gallons per mile
Therefore, the linear model that represents the amount of fuel on the plane as a function of flight time, in hours, is:
Fuel on plane (in gallons) = Fuel capacity - Fuel burn rate x Flight time (in hours)
F(t) = 63,500 - 2.69t
where F(t) is the amount of fuel on the plane (in gallons) after flying for t hours.
Step-by-step explanation:
Reasoning with similarity geometry please help. 40 points
Answers
Answer:
ABC and CEF are right triangles | definition of right triangle
ABC and CEF are 30-60-90 triangles | definition of 30-60-90 triangle
ABC is similar to CEF | Angle-Angle-Angle similarity theorem
I NEED HELP ON THIS ASAPPP!
Answers
Answer:
i thinks its scalene
Step-by-step explanation:
scalene is under 90 degrees
equal is 90 exact
and obtuse is over 90 but under 180
A rectangle and triangle are shown below.
The area of the rectangle is equal to the perimeter of the triangle.
Solve for x.
If your answer is a decimal, convert it to 1 d.p.
Answers
Answer:
5
Step-by-step explanation:
We know that the area of the rectangle is equal to the perimeter of the triangle
S (rectangle) = (x + 8) × (2x - 1)
P (triangle) = (5x - 1) + (6x + 8) + (8x + 15)
Now we can form an equation:
(x + 8) × (2x - 1) = (5x - 1) + (6x + 8) + (8x + 15)
[tex] {2x}^{2} - x + 16x - 8 = 5x - 1 + 6x + 8 + 8x + 15[/tex]
[tex]2 {x}^{2} - 4x - 30 = 0[/tex]
[tex]d = {b}^{2} - 4 \times a \times c = ({ - 4})^{2} - 4 \times 2 \times ( - 30) = 16 + 240 = 256 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2 \times a} = \frac{4 - 16}{4} = \frac{ - 12}{4} = - 3[/tex]
-3 is a negative number and we cannot use it, since x must be a natural number
[tex]x2 = \frac{ - b + \sqrt{d} }{2 \times a} = \frac{4 + 16}{4} = \frac{20}{4} = 5[/tex]
Use a trigonometric ratio to solve for a. found to two decimal places as necessary cas22shapping to whoever gets it right
Answers
Answer: a = 16.62
Step-by-step explanation:
sin(37) = 10/a
a = sin(37) / 10
a = 16.62
Answer:
a ≈ 16.62
Step-by-step explanation:
using the sine ratio in the right triangle
sin37° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{10}{a}[/tex] ( multiply both sides by a )
a × sin37° = 10 ( divide both sides by sin37° )
a = [tex]\frac{10}{sin37}[/tex] ≈ 16.62 ( to 2 decimal places )
three-fourths of the chocolates in a box are dark chocolate. three-eighths of the dark chocolates are filled with caramel. what fraction of the chocolates in the box are dark chocolate and filled with caramel?
Answers
Fraction of the chocolates in the box that are dark chocolate and filled with caramel is 3/32.
To solve this problem, we need to determine what fraction of chocolates in the box are both dark chocolate and filled with caramel. We are given that:
Three-fourths of the chocolates in a box are dark chocolate. Three-eighths of the dark chocolates are filled with caramel. We need to find out the fraction of chocolates that are dark chocolate and filled with caramel. To find out the fraction of chocolates in the box that are dark chocolate, we divide the number of dark chocolates by the total number of chocolates.
This is given by:
3/4 (dark chocolates)
To find the fraction of dark chocolates that are filled with caramel, we multiply the fraction of dark chocolates by the fraction of dark chocolates filled with caramel. This is given by:
3/4 × 3/8 = 9/32
Therefore, the fraction of chocolates in the box that are dark chocolate and filled with caramel is 9/32.
To simplify the fraction 9/32, we can divide the numerator and denominator by their greatest common factor, which is 1:9/32 = 9 ÷ 1 / 32 ÷ 1 = 9/32.
Hence, the answer is 3/32.
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WHAT EVEN IS THIS! PLEASE HELP
Answers
Step-by-step explanation:
It is a trapezoid with bases 9 and 12 ft and height ( dashed line) found using Pythagorean theorem = 4 ft
area = height * average of bases = 4 * (9+12)/2 = 24 ft^2
IK THE PIC IS DARK BUT PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answers
Step-by-step explanation:
For x
From -6 to 2 is 8 units from -6 to -1 is 5/8ths of this
to verify:
for y from 5 to -3 is 8 units 0 is 5/8 of this
5:8
Draw triangle LMN with vertices L(2,-2), M(6,-4) and(5,4). Find the coordinates of the vertices after 90degrees rotation about the origin and about each of the point of L,M,and N
Answers
The coordinates of the vertices after rotation depend on the point around which rotation is done.
Rotation of a shape around the origin (0,0) means that each point in the shape has to be moved around the origin by a certain angle. This is done by using the equation x'=xcosθ-ysinθ and y'=xsinθ+ycosθ, where x and y are the coordinates of the point before rotation and x' and y' are the coordinates of the point after rotation. In this case, the angle of rotation is 90 degrees. When we rotate triangle LMN by 90 degrees around the origin, the coordinates of the vertices become L'(2,2), M'(-4,6) and N'(4,-5).When we rotate the triangle around any of the points of L, M, or N, the coordinates of the vertices will change accordingly. For example, if we rotate the triangle around point L, the coordinates of the vertices become L'(2,-2), M'(-2,4) and N'(-6,0). Similarly, if we rotate the triangle around point M, the coordinates of the vertices become L'(2,-2), M'(6,-4) and N'(0,6). Lastly, if we rotate the triangle around point N, the coordinates of the vertices become L'(2,-2), M'(4,5) and N'(5,4).
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do seagulls show a preference for where they land? to answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of 56% sand, 29% mud, and 15% rocks. the biologists chose 200 seagulls at random. each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. in all, 128 seagulls landed on the sand, 61 landed in the mud, and 11 landed on the rocks. carry out a chi-square goodness-of-fit test. what do you conclude?
Answers
Based οn the results οf the chi-square gοοdness-οf-fit test, we can cοnclude that seagulls shοw a preference fοr where they land οn the shοre.
What is statistics?Statistics is the branch οf mathematics dealing with data cοllectiοn, οrganizatiοn, analysis, interpretatiοn and presentatiοn.
Tο determine whether seagulls shοw a preference fοr where they land, we can cοnduct a chi-square gοοdness-οf-fit test.
First, we need tο state the null and alternative hypοtheses.
Null hypοthesis (H0): Seagulls have nο preference fοr where they land οn the shοre; the prοpοrtiοns οf seagulls landing οn sand, mud, and rοcks are equal tο the prοpοrtiοns οf sand, mud, and rοcks in the area.
Alternative hypοthesis (Ha): Seagulls have a preference fοr where they land οn the shοre; the prοpοrtiοns οf seagulls landing οn sand, mud, and rοcks are nοt equal tο the prοpοrtiοns οf sand, mud, and rοcks in the area.
We can use the fοllοwing fοrmula tο calculate the chi-square statistic:
χ² = Σ (O − E)2 / E
where χ² is the chi-square statistic, O is the οbserved frequency, E is the expected frequency, and Σ is the sum οf all cells.
The expected frequencies can be calculated as fοllοws:
Expected frequency οf sand = Tοtal number οf seagulls released x Prοpοrtiοn οf sand in the area = 200 * 0.56 = 112Expected frequency οf mud = Tοtal number οf seagulls released x Prοpοrtiοn οf mud in the area = 200 * 0.29 = 58Expected frequency οf rοcks = Tοtal number οf seagulls released x Prοpοrtiοn οf rοcks in the area = 200 * 0.15 = 30We can nοw calculate the chi-square statistic:
χ² = [(128 - 112)2 / 112] + [(61 - 58)2 / 58] + [(11 - 30)2 / 30] = 8.89
Tο determine the degrees οf freedοm fοr the test, we need tο subtract 1 frοm the number οf categοries (3) tο accοunt fοr the fact that the frequencies are nοt independent. Therefοre, the degrees οf freedοm is 2.
Using a chi-square distributiοn table with 2 degrees οf freedοm and a significance level οf 0.05, we find the critical value tο be 5.99.
Since οur calculated chi-square value οf 8.89 is greater than the critical value οf 5.99, we reject the null hypοthesis. This means that seagulls dο nοt land οn the different types οf surfaces in equal prοpοrtiοns.
In cοnclusiοn, based οn the results οf the chi-square gοοdness-οf-fit test, we can cοnclude that seagulls shοw a preference fοr where they land οn the shοre.
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i need this answer asap with explanation
Answers
Answer:
1 , 1.01 , 1.02 , 1.03 , 1.04
Step-by-step explanation:
a sequence with steps of constant size is an arithmetic sequence.
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d has to be found
given a₅ = 1.04 , then
1 + 4d = 1.04 ( subtract 1 from both sides )
4d = 0.04 ( divide both sides by 4 )
d = 0.01
then sequence is
1 , 1.01 , 1.02 , 1.03 , 1.04
what ratio is commonly used as an alternative to 3.14?
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The ratio commonly used as an alternative to 3.14 is 22/7 whichj commonly represents the mathematical expression of pi.
This ratio is often used as an approximation for pi (π) which is the mathematical constant representing the ratio of the circumference of a circle to its diameter. While pi is an irrational number and has an infinite number of decimal places, 22/7 is a rational number and can be easily computed.
The value of 22/7 is approximately equal to 3.1428571, which is a fairly accurate approximation for most practical applications. It is often used in situations where a quick estimate is required or where a more accurate value of pi is not necessary.
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