Answer:
(A) The equation for computing Gustin's profit per seminar; given the values of the relevant parameters is:
π = 0.01AC - 3500
Where π = profit per seminar
A = attendance per seminar
C = commission earning per new account opened
(B) A continuous random variable
(C) No
(D) An audience of 71 persons
STEP BY STEP EXPLANATION:
(A) Profit is equal to total revenue minus total cost.
TR = PAC
Where P = probability that an attendee will open a new account
A = number of attendees per seminar
C = commission Gustin gets from each new account opened.
TC = $3,500
Where cost of organizing 1 seminar is constant at $3,500
So the function for profit per seminar is given thus:
π = TR - TC = 0.01AC - 3500
(B) There are 2 types of random variable; discrete random variable and continuous random variable
We say the number of new accounts opened (NNAO) is a continuous random variable because it is not specific. It is a function of both P and A. It depends on both P and A.
From the profit function or equation we have, we can see that you can't derive the exact NNAO per attendee. It is based on probability so if you were to measure it distinctly, you would have a very minimal value.
Discrete random variables occur in specific intervals e.g. 4, 5, 6,... while continuous random variables occur over an interval; e.g. 4.01, 4.02, 4.03,...
(C) Constructing a spreadsheet simulation model to analyze the profitability of Gustin's seminars, I would not recommend that Gustin continue running the seminars!
(D) The question points to A; which is the total attendance per seminar.
So if we calculate profit with the values given in the full question, we see that profit is negative, hence Gustin is running at a loss with 25 people attending one seminar.
π = (0.01 × 25 × 5000) - 3500
π = -$2,250
So, to make a profit greater than zero, we first check how many attendees it takes for TR to equal TC or for Profit to equal 0.
We set pie π to zero.
0 = (0.01 × 5000 × A) - 3500
0 = 50A - 3500
50A = 3500
A = 70 attendees
So Gustin needs an audience of more than 70 persons before a seminars expected profit will be greater than zero.
Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter μ = 0.2. (Round your answers to three decimal places.)
Required:
a. What is the probability that a disk has exactly one missing pulse? (Round to four decimal places)
b. What is the probability that a disk has at least two missing pulses? (Round to four decimal places)
c. If two disks are independently selected, what is the probability that neither contains a missing pulse?(Round to four decimal places)
Answer:
a) 0.164 = 16.4% probability that a disk has exactly one missing pulse
b) 0.017 = 1.7% probability that a disk has at least two missing pulses
c) 0.671 = 67.1% probability that neither contains a missing pulse
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the binomial distribution(for item c).
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!} [/tex]
In which
x is the number of sucesses
[tex] e = 2.71828[/tex] is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Binomial distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Poisson mean:
[tex]\mu = 0.2[/tex]
a. What is the probability that a disk has exactly one missing pulse?
One disk, so Poisson.
This is P(X = 1).
[tex]P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164 [/tex]
0.164 = 16.4% probability that a disk has exactly one missing pulse
b. What is the probability that a disk has at least two missing pulses?
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!} [/tex]
[tex]P(X = 0) = \frac{e^{-0.2}*0.2^{0}}{(0)!} = 0.819[/tex]
[tex]P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164 [/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.819 + 0.164 = 0.983[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.983 = 0.017[/tex]
0.017 = 1.7% probability that a disk has at least two missing pulses
c. If two disks are independently selected, what is the probability that neither contains a missing pulse?
Two disks, so binomial with n = 2.
A disk has a 0.819 probability of containing no missing pulse, and a 1 - 0.819 = 0.181 probability of containing a missing pulse, so [tex]p = 0.181[/tex]
We want to find P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.181)^{0}.(0.819)^{2} = 0.671[/tex]
0.671 = 67.1% probability that neither contains a missing pulse
What is the value of x?
65°, 79° , X
Answer:
x=36 degrees
Step-by-step explanation:
Remember that all angles of a triangle must add up to 180 degrees due to the Angle Addition Postulate. So let's plug it in! x+65+79=180
Now you solve, x=180-79-65
x=36!
x=36 degrees
Answer:
Option B
Step-by-step explanation:
All interior angles of a triangle add up to 180°.
[tex]79+65+x=180\\144+x=180 \\144-144+x=180-144\\\boxed {x=36}[/tex]
The missing angle is 36°.
Option B should be your correct answer.
Rathaus thinks all the factors of even numbers are even which explains wether Rathan is correct
Answer:
Incorrect
Step-by-step explanation:
It is incorrect because all even numbers have a factor of 1.
That is odd.
Answer:
False
Step-by-step explanation:
even numbers has odd & even factors
6 is an even number
Factors of 6 = 2 , 3
Where 3 is a odd number
Simplify the expression
(8y^2)(-9y^2)
Answer:
-72 y^4
Step-by-step explanation:
(8y^2)(-9y^2)
Multiply the coefficients
8*-9 = -72
Add the exponents since the bases are the same
y^2 * y^2 = y^(2+2) = y^4
(8y^2)(-9y^2) = -72 y^4
Please answer this correctly
Answer:
Area = 2.33 mm²
Explanation:
Perimeter of quarter circle = 14.28
But
Perimeter of quarter circle = 2πr+2r
So
2πr+2r = 14.28
6.3r+2r = 14.28
8.3r = 14.28
r = 14.28/8.3
r = 1.7 mm
Now the Area
Area of quarter circle = 1/4(πr²)
= 1/4(3.14)(1.7)²
= 1/4(3.14)(2.97)
= 1/4(9.34)
= 2.33 mm²
how much is 78ml when you turn it to litres
1000ML = 1 L
78ML ?
78*1/1000 = 0.078 L
Consider triangle ABC. The legs have a length of 5 units each. Triangle A B C is shown. Angle A C B is a right angle. The lengths of sides A C and C B are 5. The length of the hypotenuse c is unknown. What is the length of the hypotenuse of the triangle? 5 units 5 StartRoot 2 EndRoot units 10 units 10 StartRoot 2 EndRoot units
Answer:
Hypotenuse = 5√2 units
Step-by-step explanation:
Triangle ABC:
The legs are 5 units each
Opposite = 5unit
Adjacent = 5unit
Triangle ACB:
lengths of sides A C and C B are 5
The legs are 5 units each
Leg =AC = Opposite = 5unit
Leg = CB = Adjacent = 5unit
The hypotenuse for both ∆ACB is unknown. Since ∆ACB is a right angled triangle, we would apply Pythagoras theorem to find the hypotenuse.
Using Pythagoras theorem:
Hypotenuse ² = opposite ² + adjacent ²
Hypotenuse ² = leg² + leg²
AB = hypotenuse in ∆ACB
AB² = 5² + 5²
AB² = 25+25 = 50
AB = √50 = √(25×2)
AB = 5√2
Hypotenuse = 5√2 units
Answer:
The answer is B! Person above me is right!
Step-by-step explanation:
What’s the correct answer for this?
Answer:
Tangent
Step-by-step explanation:
Tangent intersects a circle at exactly one point
What is the range of the function f(x)= 1/2sin(2x-pi)
The answer is [-1/2-1/2]
The range of the function f(x) is [-1/2, 1/2].
What is the range of a function?The range is the set of possible output values, which are shown on the y-axis. The range of a function, f is the set of all values f(x) , such that x is in the domain of f. Graphically speaking, the range is the set of all y such that (x,y) is a point on the graph of f.
For the given situation,
The function f(x) = 1/2sin(2x-π)
The graph below shows the range of the function f(x) = 1/2sin(2x-π) graphically.
As the range of sinx function is [-1, 1], the range of sin2x is also [-1, 1].
Let us consider [tex]\theta = 2x-\pi[/tex]
⇒ Then, [tex]sin \theta[/tex] lies in the range [tex][-1,1][/tex]
⇒ [tex]-1\leq sin(2x-\pi )\leq 1[/tex]
⇒ [tex](\frac{1}{2} )(-1)\leq sin(2x-\pi )\leq( 1)(\frac{1}{2} )[/tex]
⇒ [tex]\frac{-1}{2} \leq sin(2x-\pi )\leq\frac{1}{2}[/tex]
Hence we can conclude that the range of the function f(x) is [-1/2, 1/2].
Learn more about range of a function here
https://brainly.com/question/3112051
#SPJ3
a bear travel 15km at an angle of 135 degrees from his den. it then travels for 3.7 km at an orientation of 55 degrees. the bear ends his trip walking 12 km at an orientation of 320 degrees. what distance is the bear from his den?
Answer:
30.7
Step-by-step explanation:
add the 15,3.7 ,and the 12
Choose which reasoning process is shown in the following example. Explain your answer.
It can be shown that 1 + 2 + 3 + ... +n=
n(n+1)
2
This formula can be used to conclude that the sum of the first 600 numbers, 1+2+3+...+600, is the following.
600(600 + 1
2
600(601)
= 300(601), or 180,300
2
Choose the correct answer below.
O A. This is inductive reasoning because a specific conclusion is being proved from a general statement.
OB. This is deductive reasoning because a specific conclusion is being proved from a general statement.
OC. This is deductive reasoning because it is an educated guess to say that the formula can be used to calculate the sum of the first 600 numbers.
OD. This is inductive reasoning because it is an educated guess to say that the formula can be used to calculate the sum of the first 600 numbers.
Click to select your answer.
Answer:
OB
Step-by-step explanation:
When you deduct something it means an intelligent reasoning based on given information for prediction.
In the above case we have a given formula from which we can deduct the facts .
We see a general statement is given from there we get a specific value.
By the way the formula given meant n(n+2)/ 2
The correct option is B. This is deductive reasoning because a specific conclusion is being proved from a general statement. This is obtained by checking the requirements of deductive reasoning.
What is deductive reasoning ?Deductive reasoning is a process in which a conclusion is based on multiple assertion that are generally taken to be true. Makes logical assertions based on a conclusion around the assertion.Which reasoning process is shown in the given example?The given question is deductive reasoning by referring to the definition of deductive reasoning.In the question, a specific conclusion, that is, sum of first 600 numbers is being proved from a general statement, that is, sum of n numbers.Hence this is deductive reasoning because a specific conclusion is being proved from a general statement.
Learn more about reasoning process here:
brainly.com/question/14265467
#SPJ2
Billy’s Restaurant ordered 200 flowers for Mother’s Day. They ordered carnations at
$1.50 each, roses at $5.75 each, and daisies at $2.60 each. They ordered mostly
carnations, and 20 fewer roses than daisies. The total order came to $589.50. Write
a system of linear equations that can be used to find c, the number of carnations, r,
the number of roses, and d, the number of daisies.
Answer:
c+r+d= 200
1.50c+5.75r+2.60d= 589.50
r=d-20
Step-by-step explanation:
From the information given you have that Billy's restaurant ordered roses, daisies and carnations that total 200 flowers. The first equation is:
c+r+d= 200
c= number of carnations
r= number of roses
d= number of daisies
Also, you can say that the sum of the results of multiplying the price of each flower for its quantity is equal to $589.50. The second equation is:
1.50c+5.75r+2.60d= 589.50
Besides, from the statement you know there are 20 fewer roses than daisies and from that you can write the third equation:
r= d-20
The system of linear equations that can be used to find c, the number of carnations, r, the number of roses, and d, the number of daisies is:
c+r+d= 200
1.50c+5.75r+2.60d= 589.50
r=d-20
A water tower in New York City has the shape of a cylinder with a cone on top. The cylinder has a diameter of 12 feet and a height of 15 feet. The roof has an inclination angle of 25o . There are 7.48 gallons in a cubic foot. If residents of an apartment building are using the water from the tower at an average rate of 56 gallons per minute, determine how long, to the nearest minute, it will take to drain the entire tower.
Answer:
number of minutes to drain the entire tower = 241 minutes(nearest minutes)
Step-by-step explanation:
The water tower has the shape of a cylinder with a cone on top . The volume of the water tower can be find when you find the sum of the volume of the cylinder and the cone.
Therefore,
volume of the cylinder = πr²h
where
r = 12/2 = 6 ft
h = 15 ft
volume = π × 6² × 15
volume = π × 36 × 15
volume of the cylinder = 540π
Volume of the cone = 1/3πr²h
r = 6 ft
Using tangential ratio we can find the height which is the opposite side of the triangle
tan 25° = opposite/adjacent
tan 25° = h/6
cross multiply
h = 6 tan 25°
h = 6 × 0.46630765815
h = 2.79784594893
h = 2.8 ft
volume of the cone = 1/3πr²h
volume = 1/3 × π × 36 × 2.8
volume = 100.8π/3
volume = 33.6π
Volume of the tower system = 540π + 33.6π = 573.6π
volume of the tower system = 573.6 × 3.14 = 1801.104 ft³
1 cubic ft = 7.48 gallons
1801.104 cubic fit = ? gallons
cross multiply
gallons = 1801.104 × 7.48
gallons = 13472.25792 gallons
The residents drains the water at the rate of 56 gallons per minute. Therefore,
56 gallons = 1 minutes
13472.25792 gallons = ? minutes
number of minutes = 13472.25792 /56
number of minutes = 240.576034286
number of minutes to drain the entire tower = 241 minutes(nearest minutes)
factor 9 - 6a - 24a^2
Answer:
[tex]3(-4a-3)(2a-1)[/tex]
Step-by-step explanation:
[tex]-24a^2-6a+9[/tex]
[tex](-12a-9)(2a-1)[/tex]
[tex]3(-4a-3)(2a-1)[/tex]
Answer:
−3(2a−1)(4a+3)
Step-by-step explanation:
9 - 6a - 24a^2
24a²-6a-9=
−3(2a−1)(4a+3)
We get this because −3(2a−1)(4a+3) equals out to 24a²-6a-9. If you need more explanation, reply to this answer.
What can you conclude from a box plot where the length of the left box and whisker is the same as the length of the right box and whisker?
Answer/Step-by-step explanation:
The length of the boxes and whiskers of a box plot tells us more about the spread the data being represented is and as well as the shape of the spread.
Invariably, if the length of the left box and left whiskers is of the same length as the right box and right whiskers, this implies that the distribution of the data point is close to being symmetric, or approximately symmetrical.
find the equation in standard form of the line passing through the points (2, negative 3) and (4, 2)
A.5x-2y=16
B.2x-3y=9
C.y=5/2x+8
D.5x+2y=16
Answer:
Step-by-step explanation:
(2 + 3)/(4 - 2)= 5/2
y + 3 = 5/2(x - 2)
y + 3 = 5/2x - 5
y = 5/2x - 8
2y = 5x - 16
5x - 2y = 16
What's the present value of $11,000 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?
Select the correct answer.
a. $7,083.20
b. $7,025.60
c. $7,040.00
d. $7,068.80
e. $7,054.4
Answer:
Step-by-step explanation:
A = P[1 + (r/n)]^(nt)
Look the formula up online to find out what each variable represents if needed.
We are solving for P, which is the principal amount 5 years back.
Substitute 11,000 for A (total amount), 4.5% for r(rate), 2 for n(number of times -- in this case, semiannually), and 5 for t(time -- 5 years).
11000 = P[1+(0.045/2)]^(2x5)
11000 = P (1.0225)^10
11000 = P (1.2492) approx.
Divide both sides by 1.2492 to find P.
P = $8805.64 (approx)
I know that the answer I got is not an option listed. However, I feel that my workings may help other people to answer this question or give them inspiration to answer similar questions. Therefore, I will leave this answer up.
Thanks, and sorry I couldn't do much.
A circle is centered on point BBB. Points AAA, CCC and DDD lie on its circumference.
If \blue{\angle ABC}∠ABCstart color #6495ed, angle, A, B, C, end color #6495ed measures 124^\circ124
∘
124, degrees, what does \orange{\angle ADC}∠ADCstart color #ffa500, angle, A, D, C, end color #ffa500 measure?
Answer:
[tex]\angle ADC=62^\circ[/tex]
Step-by-step explanation:
Given the circle centered on point B with points A, C and D on its circumference.
[tex]\angle ABC[/tex] is the angle subtended by arc AC at the centre.
Since D is on the circumference, [tex]\angle ADC[/tex] is the angle subtended by arc AC on the circumference.
Circle Theorem: The measure of the angle subtended by an arc at the center is twice the measure of the angle subtended by same arc at the circumference.
By the theorem stated above:
[tex]\angle ABC = 2 X \angle ADC\\Since \angle ABC=124^\circ\\124^\circ = 2 X \angle ADC\\ \angle ADC=124^\circ \div 2\\\\ \angle ADC=62^\circ[/tex]
Answer:
The real answer is 20 its not that high of a number
Step-by-step explanation:
College Algebra functions?
Answer:
See below.
Step-by-step explanation:
For the first one:
[tex]f(x)=\frac{4x+3}{5x+2}[/tex]
[tex]f(\frac{1}{x})= \frac{4(\frac{1}{x})+3}{5(\frac{1}{x})+2 }[/tex]
First, multiply both top and bottom by [tex]x[/tex].
Thus:
[tex](\frac{4(\frac{1}{x})+3}{5(\frac{1}{x})+2 } )\cdot \frac{x}{x}[/tex][tex]=\frac{4+3x}{5+2x}[/tex]
It cannot be simplified further.
For the second one:
[tex]g(x)=\sqrt{x^2-8x}[/tex]
[tex]g(x-2)=\sqrt{(x-2)^2-8(x-2)}[/tex]
[tex]\sqrt{(x^2-4x+4)-8x+16}[/tex]
[tex]\sqrt{x^2-12x+20}[/tex]
And that cannot be simplified further.
Fahim is 6 feet tall. At noon, he stands with the sun behind him casting a shadow. The distance from the top of Fahim’s head to the furthest tip of the shadow is 13 feet. A right triangle with side length 6 feet, s, and hypotenuse 13 feet. [Not drawn to scale] What is the length of Fahim’s shadow? Round to the nearest tenth of a foot.
Answer:
11.5
Step-by-step explanation:
using Pythagoras theorem
the square of 13 equals the square of 6 and the unknown side
Answer:
11.5 feet
Step-by-step explanation:
I just took the quiz on edge
Does consuming beer attract mosquitoes? A study done in Burkino Faso, Africa, about the spread of malaria investigated the connection between beer consumption and mosquito attraction.1 In the experiment, 25 volunteers consumed a liter of beer while 18 volunteers consumed a liter of water. The volunteers were assigned to the two groups randomly. The attractiveness to mosquitoes of each volunteer was tested twice: before the beer or water and after. Mosquitoes were released and caught in traps as they approached the volunteers. For the beer group, the total number of mosquitoes caught in the traps before consumption was 434 and the total was 590 after consumption. For the water group, the total was 337 before and 345 after. 1Lefvre T, Gouagna L-C, Dabir KR, Elguero E, Fontenille D, et al. 2010 Beer Consumption Increases Human Attractiveness to Malaria Mosquitoes. PLoS ONE 5(3): e9546. doi:10.1371/journal.pone.0009546 (a) State the null and alternative hypotheses for a test to see if, after consumption, the average number of mosquitoes is higher for the volunteers who drank beer. Let group 1 be the people who drank beer and let group 2 be the people who drank water. SHOW HINT (b) Compute the average number of mosquitoes per volunteer before consumption for each group. Round your answers to two decimal places. Beer group: Water group: Are the two sample means different? Do you expect that this difference is just the result of random chance? SHOW HINT (c) Compute the average number of mosquitoes per volunteer after consumption for each group. Round your answers to two decimal places. Beer group: Water group: Are the two sample means different? Do you expect that this difference is just the result of random chance? SHOW HINT (d) If the difference in part (c) is statistically significant, do we have evidence that beer consumption increases mosquito attraction?
Answer:
Take u1 = average number of mosquitoes attracted after drinking beer
u2 = average number of mosquitoes attracted after drinking water
a) The null and alternative hypotheses:
H0 : u1 = u2
H1 : u1 > u2
b) i) The average number of mosquitoes per volunteer before drinking (beer group) :
[tex] x'1 = \frac{x_1}{n} = \frac{434}{25} = 17.36 [/tex]
Sample mean for mosquitoes attracted before consumption for beer group is 17.36
The average number of mosquitoes per volunteer before drinking (water group) :
[tex] x'2 = \frac{x_2}{n} = \frac{337}{18} = 18.72 [/tex]
Sample mean for mosquitoes attracted before consumption for water group is 18.72
The two means are different.
The difference in the two means are as a result of random choice.
c) i) The average number of mosquitoes per volunteer after drinking (beer group) :
[tex] x'1 = \frac{x_1}{n} = \frac{590}{25} = 23.60 [/tex]
Sample mean for mosquitoes attracted after consumption for beer group is 23.60
ii) The average number of mosquitoes per volunteer after drinking (water group) :
[tex] x'2 = \frac{x_2}{n} = \frac{345}{18} = 19.17[/tex]
Sample mean for mosquitoes attracted after consumption for water group is 19.17
The two sample means are different.
This difference here is likely not to be as a result of random choice, because the mean difference here is greater than the mean difference before consumption.
d) A statistically significant difference provides evidence that beer consumption increases mosquito attraction, as the average number of mosquitoes attracted when drinking beer is higher than the mean number of mosquitoes attracted when drinking water.
Evaluate the expression 6•14-(9+8)2
Answer:
50
Step-by-step explanation:
First things first, use PEMDAS.
Parenthesis is first.
(9+8) is in parenthesis. 9+8 is obviously 17.
The equation now looks like this:
6 x 14 - 17 x 2
There is no exponents, but there is multiplication. 6 x 14 is 84 and 17 x 2 is 34. They both are multiplication equations.
The equation now looks like this:
84 - 34
84-34 is 50. 50 is your answer.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
Range : { -3,0,4,6}
Step-by-step explanation:
The range of the function is the output values
Range : { -3,0,4,6}
Answer:
C. {-3, 0 ,4, 6}
Step-by-step explanation:
→The range is the total of y-intercepts/outputs. In this case, looking at the function, you can see that the y-intercepts/outputs are 0, -3, 4, and 6.
→The others numbers are the x-intercepts/inputs, which would be the domain of the function.
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
It is the complement of the circle in the square
Okay,
Let the square be Universal set(U) and the circle be A
So
A complement = A' = U-A So
The shaded area is the complement of the circle
Select the statement that is true. Group of answer choices There are integers s and t such that 2=102⋅s+72⋅t . here are integers s and t such that 8=102⋅s+72⋅t . There are integers s and t such that 1=102⋅s+72⋅t . There are integers s and t such that 6=102⋅s+72⋅t .
Answer:
Step-by-step explanation: true
In the figure below, the polygons are similar. Find the value of x and y. Have a nice day
Answer:
x is 4 and y is 3.
Step-by-step explanation:
The scale factor between the triangles is 2, as you can see. The hypotenuse of the small triangle is 5 while the hypotenuse of the larger one is 10, so the scale factor between the triangles is 2. This means you can divide the other leg lengths of the large triangle by 2 to find the lengths for the corresponding legs of the small one.
Please answer this correctly
Answer:
[tex]11\dfrac{3}{8}\text{cm}[/tex]
Step-by-step explanation:
[tex]1\dfrac{5}{8}+2\dfrac{9}{16}+2\dfrac{9}{16}+4\dfrac{1}{8}=11\dfrac{3}{8}[/tex]
Hope this helps!
A single card is drawn at random from a standard 52 card deck. Work out in its simplest
Answer:
1/52
Step-by-step explanation:
Bromeliads are tropical flowering plants. Many are epiphytes that attach to trees and obtain moisture and nutrients from air and rain. Their leaf bases from cups that collect water and are home to larvae of many insects. As a preliminary to study of changes in the nutrient cycle, Jacqueline Ngai and Diane Srivastava examined the effects of adding nitrogen, phosphorus, or both to the cups. They randomly assigned 8 bromeliads growing in Costa Rica to each of four treatment groups, including an unfertilized control group. A monkey destroyed one of the plants in the control group, leaving 7 bromeliads in that group. Here are the numbers of new leaves on each plant over the seven months following fertilization:
Nitrogen Phosphorus Both Neither
16 14 14 11
15 14 16 13
15 14 15 16
17 11 14 15
17 13 14 15
18 12 13 11
18 15 17 12
13 15 14
(a) Give the degrees of freedom for the F statistic.
numerator degrees of freedom
denominator degrees of freedom
(b) Find the F-statistic. (Round your answer to two decimal places.)
F =
(c) Find the associated P-value. (Round your answer to four decimal places.)
(d) State conclusions. Select the correct answer.We have significant evidence at the 5% level that the means are not all the same.We do not have significant evidence at the 5% level that the means are not all the same..
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
Y: number of new leaves of Bromeliads grown under different types of fertilization.
Factor: Type of fertilizer
Treatments: 1. Nitrogen, 2. Phosphorus, 3. Both, 4. Neither (control group)
To compare these four groups you have to conduct an ANOVA
The hypotheses are:
H₀: μ₁= μ₂= μ₃= μ₄
H₁: At least one population mean is different from the others.
α: 0.05
a)
The degrees of freedom of the F-statistic are:
[tex]F_{I-1;N-I}= F_{4-1;31-4}= F_{3;27}[/tex]
I= number of treatments
N= total number of experimental units (in all groups)
b)
SSTreatments= 39.37
SSError= 72.18
MSTreatments= SStreatments/DfTreatments= 39.37/3= 13.12
MSError=SSError/DfError= 72.18/27= 2.67
[tex]F= \frac{MS_{Treatments}}{MS_{Error}} = \frac{13.12}{2.67} = 4.91[/tex]
c)
This test is one-tailed to the right and so is the p-value:
P(F₃;₂₇≥4.91)= 1 - P(F₃;₂₇<4.91)= 1 - 0.9925= 0.0075
d)
The decision rule using the p-value is:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The p-value is less than α, the test is significant at 5% significance level.
"We have significant evidence at the 5% level that the means are not all the same."
I hope this helps!
What is the center of the circle and the radius
X2+y2-4x+12y-24=0
Answer:
Subtract
31
31
from both sides of the equation.
x
2
+
y
2
−
4
x
−
12
y
=
−
31
x2+y2-4x-12y=-31
Complete the square for
x
2
−
4
x
x2-4x
.
Tap for more steps...
(
x
−
2
)
2
−
4
(x-2)2-4
Substitute
(
x
−
2
)
2
−
4
(x-2)2-4
for
x
2
−
4
x
x2-4x
in the equation
x
2
+
y
2
−
4
x
−
12
y
=
−
31
x2+y2-4x-12y=-31
.
(
x
−
2
)
2
−
4
+
y
2
−
12
y
=
−
31
(x-2)2-4+y2-12y=-31
Move
−
4
-4
to the right side of the equation by adding
4
4
to both sides.
(
x
−
2
)
2
+
y
2
−
12
y
=
−
31
+
4
(x-2)2+y2-12y=-31+4
Complete the square for
y
2
−
12
y
y2-12y
.
Tap for more steps...
(
y
−
6
)
2
−
36
(y-6)2-36
Substitute
(
y
−
6
)
2
−
36
(y-6)2-36
for
y
2
−
12
y
y2-12y
in the equation
x
2
+
y
2
−
4
x
−
12
y
=
−
31
x2+y2-4x-12y=-31
.
(
x
−
2
)
2
+
(
y
−
6
)
2
−
36
=
−
31
+
4
(x-2)2+(y-6)2-36=-31+4
Move
−
36
-36
to the right side of the equation by adding
36
36
to both sides.
(
x
−
2
)
2
+
(
y
−
6
)
2
=
−
31
+
4
+
36
(x-2)2+(y-6)2=-31+4+36
Simplify
−
31
+
4
+
36
-31+4+36
.
(
x
−
2
)
2
+
(
y
−
6
)
2
=
9
(x-2)2+(y-6)2=9
This is the form of a circle. Use this form to determine the center and radius of the circle.
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
(x-h)2+(y-k)2=r2
Match the values in this circle to those of the standard form. The variable
r
r
represents the radius of the circle,
h
h
represents the x-offset from the origin, and
k
k
represents the y-offset from origin.
r
=
3
r=3
h
=
2
h=2
k
=
6
k=6
The center of the circle is found at
(
h
,
k
)
(h,k)
.
Center:
(
2
,
6
)
(2,6)
These values represent the important values for graphing and analyzing a circle.
Center:
(
2
,
6
)
(2,6)
Radius:
3
3
Answer:
center: (2,-6)
radius: 8
Step-by-step explanation:
trust me i checked khan academy