Final answer:
The median is a more accurate indicator of the average student's SAT score at Groveland High School in a right-skewed distribution because it is not affected by outliers, unlike the mean.
Explanation:
The question addresses why the median is a more accurate indicator of the SAT score of the average student at Groveland High School rather than the mean when the data is strongly skewed to the right. This is because the median is the middle value that divides the number set into two equal halves, and it is not affected by outliers or extremely high scores that are present in a right-skewed distribution. In contrast, the mean is the average of all values and can be significantly influenced by outliers, leading to a value that may not accurately represent the 'central' tendency of the data. Thus, for a right-skewed data set, the median provides a better measure of center for what can be considered a typical score because it is not skewed by unusually high values.
Calculate the area of the sector
Answer:
Step-by-step explanation:
1/2 3
Answer: Area of sector = 11.8 square meters
Step-by-step explanation:
The formula for determining the area of a sector is expressed as
Area of sector = θ/360 × πr²
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Radius, r = 3 m
θ = 150 degrees
Therefore,
Area of sector = 150/360 × 3.14 × 3²
Area of sector = 11.8 square meters rounded up to the nearest tenth.
The power P required to do a fixed amount of work varies inversely as the time t. If a power of 15 J/h is required to do a fixed amount of work in 2 hours, what is the power required to do the same work in 1 hour?
Answer: the power required to do the same work in 1 hour is 30 j/h
Step-by-step explanation:
If two variables vary inversely, an increase in one of the variables causes a decrease in the other variable and vice versa.
The power P required to do a fixed amount of work varies inversely as the time t. If we introduce a constant of variation, k, the expression would be
P = k/t
If a power of 15 J/h is required to do a fixed amount of work in 2 hours, it means that
15 = k/2
k = 15 × 2 = 30
The equation becomes
P = 30/t
Therefore, the power required to do the same work in 1 hour is
P = 30/1 = 30 j/h
Out of 30 states, the three most common insects are Monarch butterflies, honeybees, and ladybugs. The number of Of states that have monarch butterflies as their official insect is one more than the number of states that have ladybugs as their official insect. The number of states that have honeybees as their official insect is three times the number of states with ladybugs as their state insect minus one. How many states have each kind of insect as their state insect?
There are 7 states with Monarch butterflies, 17 states with honeybees, and 6 states with ladybugs as their official insect.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let us consider M, H, and L to represent the number of states with Monarch butterflies, honeybees, and ladybugs as their official insect, respectively.
We know that M + H + L = 30, since there are 30 states in total.
From the problem statement, we also know that:
M = L + 1 (1)
H = 3L - 1 (2)
We can use equations (1) and (2) to solve for M, H, and L:
M + H + L = 30
Substituting equation (1) and (2) into this equation:
(L + 1) + (3L - 1) + L = 30
5L = 30
L = 6
So there are 6 states with ladybugs as their official insect. Using equation (1) and (2), we can then find:
M = L + 1 = 7
H = 3L - 1 = 17
Hence, there are 7 states with Monarch butterflies, 17 states with honeybees, and 6 states with ladybugs as their official insect.
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Final answer:
To solve this problem, assign variables to represent the number of states that have each kind of insect. Use the given information to set up equations and solve simultaneously to find the values of 'm', 'h', and 'l'.
Explanation:
To solve this problem, let's assign variables to represent the number of states that have each kind of insect as their state insect. Let 'm' represent the number of states with Monarch butterflies, 'h' represent the number of states with honeybees, and 'l' represent the number of states with ladybugs as their official insect.
According to the problem, we have the following information:
'm' = 'l' + 1 (The number of states with Monarch butterflies is one more than the number of states with ladybugs)
'h' = 3('l') - 1 (The number of states with honeybees is three times the number of states with ladybugs minus one)
We also know that the total number of states is 30. So we can set up the following equation:
m + h + l = 30
Now, we can solve these equations simultaneously to find the values of 'm', 'h', and 'l'.
Using the first equation, we substitute 'l + 1' for 'm' in the second equation:
h = 3('l') - 1
h = 3(l + 1) - 1
h = 3l + 3 - 1
h = 3l + 2
Now, we substitute 'l + 1' for 'm' and '3l + 2' for 'h' in the third equation:
(l + 1) + (3l + 2) + l = 30
Simplifying the equation:
5l + 3 = 30
5l = 27
l = 5.4
Since 'l' represents the number of states with ladybugs, we can't have a fraction of a state. Therefore, we round 'l' down to the nearest whole number:
l = 5
Substituting this value back into the equations, we find that 'm' = 6 and 'h' = 14.
Therefore, there are 6 states with Monarch butterflies as their official insect, 14 states with honeybees, and 5 states with ladybugs.
In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority. True or false?
Answer:
False
Step-by-step explanation:
We are told that there is a 33% probability that physics students belong to ethnic minorities, therefore if the sample is 10 people, the amount would be given as follows:
10 * 33% = 3.3 people would be from ethnic minorities. What means of those 10 no more than 4 (to round the number) people belong to an ethnic minority.
Therefore, this statement is false, because it does not represent exactly the probability established in the university.
It is possible to clarify that what affirmation is true part because it fulfills what it says, because the probability says that 4 or less, and the affirmation says that 6 or less, however, the affirmation mentions that it corresponds to the probability of 33% and that if it is false, to correspond it should be between 51% and 60%.
You shuffle a standard 52 card deck of cards, so that any order of the cards is equally likely, than draw 4 cards. How many different ways are there to make that draw, where you care about the order
Answer:
270725 different ways
Step-by-step explanation:
The problem tells us that the order of the letters does not matter. Therefore, in the combination the order is NOT important and is signed as follows:
C (n, r) = n! / r! (n - r)!
We have to n = 52 and r = 4
C (52, 4) = 52! / 4! * (52-4)! = 52! / (4! * 48!) = 270725
Which means that there are 270725 different ways in total to make that raffle
An Olympic-size swimming pool is approximately 50 meters long by 25 meters wide. What distance will a swimmer travel if they swim from one corner to the opposite?
The swimmer will travel a distance of 55.92 meters when swimming from one corner to the opposite corner of an Olympic-size swimming pool.
Given, the length and width of the pool form the two sides of the right-angled triangle, and the distance the swimmer will travel is the hypotenuse.
Using the Pythagorean theorem, we can calculate the distance as follows:
Distance² = Length² + Width²
Distance² = 50² + 25²
Distance² = 2500 + 625
Distance² = 3125
Distance = √3125
Distance = 55.90 meters
Therefore, a swimmer will travel approximately 55.92 meters.
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Final answer:
To determine the distance a swimmer travels across an Olympic-sized pool from corner to opposite, the Pythagorean theorem is used, giving approximately 55.90 meters as the distance.
Explanation:
The student's question entails calculating distances and speeds in different swimming and water current scenarios, which is a classic physics problem involving kinematics and geometry. However, since it involves calculations and applying formulae, particularly the Pythagorean theorem, and rate, time, and distance relationships, it falls under the subject of Mathematics.
To Calculate the Distance Swum Across an Olympic-sized Pool
For an Olympic-sized pool that is 50 meters in length and 25 meters in width, a swimmer traveling from one corner to the opposite would traverse a diagonal. To calculate this diagonal distance, we use the Pythagorean theorem:
Diagonal2 = Length2 + Width2
Diagonal = √(Length2 + Width2)
Substitute the given values:
Diagonal = √(502 + 252) = √(2500 + 625)
Diagonal = √(3125) meters
The swimmer will travel approximately √(3125) meters, which is about 55.90 meters.
What is the result when the following code is run? double x = 1; double y = 1; int i = 0; do { y = x / 2; x = x + y; i = i + 1; } while (x < 2.5); System.out.print(i + " ");
Answer:
The answer is: 3
Step-by-step explanation:
1. At the begining of the program we start by declairing the variables:
double x=1, double y=1 and int i=0.
2. The structure do...while is used to defined the loop. x<2.5 is the finalization condition of the loop. i is the counter of the loop.
y=x/2 is the first calculation
x=x+y is the second one. Here is where the values of the variable x changes.
a) for the first iteration, the values of y and x are shown below:
[tex]\\\\x=1\\y=1\\y=1/2=0.5\\x=1+0.5=1.5\\i=1[/tex]
The variable x is minor to 2.5 so the loop will continue computing.
b) the second iteration, the values of y and x are shown below::
[tex]y=0.5\\x=1.5\\y=\frac{1.5}{2}=0.75\\ x=1.5+0.75=2.25\\i=2[/tex]
The variable x is still minor to 2.5 so the loop will continue computing.
c) third iteration:
[tex]y=0.75\\x=2.25\\y=\frac{2.25}{2} =1.1125\\x=2.25+1.125=3.375\\i=3[/tex]
The condition x<2.5 is not true so the loop ends.
3. System.out.print(i + " "); displays the value of the variable i wich value is 3.
Therefore the number 3 is display.
Which is the area between the x-axis and y=x from x=3 to x=6
63
45/2
27/2
81
Answer:
27/2
Step-by-step explanation:
2.2.15
Question Help
Number of Children Number of
under 5
Households
To predict future enrollment in a school district, fifty households within
the district were sampled, and asked to disclose the number of
children under the age of five living in the household. The results of
the survey are presented in the table. Complete parts (a) through (c)
below
(a) Construct a relative frequency distribution of the data.
Number of Relative
Children under 5 Frequency
0.34
0.28
0.28
0.06
0.04
(Type integers or decimals. Do not round.)
(b) What percentage of households has two children under the age of 5?
Enter your answer in the answer box and then click Check Answer
Answer:
Step-by-step explanation:
a)
Number of children under 5 Number of household Relative frequency
0 17 17 / 50 = 0.34
1 14 14 / 50 = 0.28
2 14 14 / 50 = 0.28
3 3 3 / 50 = 0.06
4 2 2 / 50 = 0.04
50
Note,
Relative frequency = Class frequency / Total Frequency
b) Percentage of households has two children under the age of 5 ,
= [tex]\frac{14}{50}[/tex] x 100
= 0.28 x 100
= 28%
Final answer:
To calculate the percentage of households with two children under the age of 5, divide the frequency of 2 by the total number of households and multiply by 100.
Explanation:
To calculate the percentage of households with two children under the age of 5, we need to find the relative frequency of 2 in the given data. The relative frequency is calculated by dividing the frequency of 2 by the total number of households, which is 50 in this case. The frequency of 2 is 0.06, so the relative frequency of 2 is 0.06/50 = 0.0012. To convert it to percentage, we multiply by 100, so the percentage of households with two children under the age of 5 is 0.0012 * 100 = 0.12%.
A dolphin starts at an elevation of -16 3/4 feet. He kicks 5 times and increases his elevation by the same amount for each kick. He is now at an elevation of -5 1/4 feet. Which equation can be used to find x, the number of feet the dolphin traveled with each kick?
Answer:
[tex]x = 2\,\frac{4}{5}\,ft[/tex]
Step-by-step explanation:
The equation of elevation for the dolphin is:
[tex]-\frac{67}{4} + 5\cdot x = -\frac{21}{4}[/tex]
[tex]5\cdot x = \frac{56}{4}[/tex]
[tex]x = 2\,\frac{4}{5}\,ft[/tex]
Answer:
5x -16 3/4 = -5 1/4
Note: This is based off of Study Island's multiple choice answers
Step-by-step explanation:
We're trying to figure out how far the dolphin travels with each kick. The dolphin starts at an elevation of -16 3/4 feet and ends up at an elevation of -5 1/4 feet. In other words, what can we add to -16 3/4 to get -5 1/4?
The elevation is our variable (x). The dolphin kicks 5 times to get from point a to point b. So we should add 5x to -16 3/4 to get -5 1/4. This equation will solve for the length in feet traveled per kick. Our equation is now:
5x + -16 3/4 = -5 1/4
Adding a negative is the same thing as subtracting a positive, so our final equation is:
5x - 16 3/4 = -5 1/4
If we want to solve this:
5x - 16.75 = -5.25
5x = 11.5
x = 2.3 feet per kick
The prices (in dollars) of 50 randomly chosen types of shoes at 4 different stores are shown in the box plots. At which store would a person MOST LIKELY pay $60 for a pair of shoes?
Answer:
C
Step-by-step explanation:
I think you missed attaching the picture, so hope my photo fits your questions well!
We must consider the median of the data sets, it may represent the center of the dispersion measure. Then we see answer C is the most suitable one, this is because it's median is approximately to $60.
Members of a hospital advisory committee will be selected from 5 doctors and 4 nurses. The committee must have 2 doctors and 2 nurses.
How many possible combinations of doctors and nurses could be chosen for the committee?
Answer:
16 possible ways
Step-by-step explanation:
Using the formular Cp,k= p!/I! (P-k)!
Where k= number of selected committee members
P= available number that can sit in the committee
For doctors,there are 5 doctors
C= 5!/2!(3)!= 120/12 = 10ways
For nurses,there are 4
C= 4!/2!(2)! = 24/4 =6ways
Total possible ways=10 + 6 = 16 ways
Answer:
60
Step-by-step explanation:
(2 out of 5 doctors) * (2 out of 4 nurses)
What is the measure of angle x? 1) 10 2) 18 3) 20 4) 25
Answer:
what is the actual problem?
Step-by-step explanation:
A farmer has 90 feet of fence with which to make a corral. If he arranges it into a rectangle that is twice as long as it is wide, what are the dimensions
Answer:
W = 15 ft. and L = 30 ft.
Step-by-step explanation:
Perimeter = 90 ft.
Twice as long as it is wide: L=2W
P = 2(L + W) = 2(2W + W) = 6W
90 = 6W
W = 15 ft. and L = 30 ft.
Answer:
The dimensions are: Width= 15ft
Length=30ft
Step-by-step explanation:
Perimeter of fence=90feet
He wants to make a rectangle with dimensions length and with.
The rectangle length is twice as long as the width= L= 2W
Perimeter of a rectangle = 2(L + W)
90= 2(2W +W)
90= 6W
90/6=W=15ft
L=2W= 2× 15=30ft
Please Help! A cylinder has a diameter of 5 m and a height of 10 m. What is its volume? Choose all that apply.?
A. π(2.5)^2 (10) m^3
B. π(5)^2 (10) m^3
C. 62.5π m^3
D. 250π m^3
Answer:
D
Step-by-step explanation:
Cause if you se it close you wil get it
Spinning a roulette wheel 6 times, keeping track of the occurrences of a winning number of "16".
a. Not binomial: there are more than two outcomes for each trial.
b. Procedure results in a binomial distribution.
c. Not binomial: the trials are not independent.
d. Not binomial: there are too many trials.
Answer:
Correct option is b. Procedure results in a binomial distribution.
Step-by-step explanation:
Consider that X is Binomial random variable. The properties that are satisfied by X are:
There are n independent trials.Each trial has only two outcomes: Success & Failure.Each trial has the same probability of success.Suppose a roulette wheel is spun and the number of times the ball lands on '16' is observed.
If the random variable X is defined as the number of times the ball lands on '16', then the random variable X follows a Binomial distribution.
Because,
Each spin is independent of each otherSuccess: The ball lands on '16'Failure: The ball does not lands on '16'The probability of the ball landing on '16' is [tex]\frac{1}{37}[/tex] for each trial.Thus, the correct option is b. Procedure results in a binomial distribution.
Which of the following regression models is used to model a nonlinear relationship between the independent and dependent variables by including the independent variable and the square of the independent variable in the model?
a. multiple regression model
b. a least squares regression model
c. quadratic regression model
d. a simple regression model
Answer:
Option C) Quadratic regression model
Step-by-step explanation:
Quadratic regression model
It is regression model in which states a non-linear relationship between the independent and dependent variables.It includes the dependent variable and the square of the independent variable.[tex]\hat{y}= b_0 + b_1x + b_2x^2[/tex]where x is the independent variable and [tex]\hat{y}[/tex] is the dependent variable.
It is also referred to as second-order polynomial model.It is used when the data shape resembles to a parabola.Thus, the correct answer is
Option C) Quadratic regression model
The (c) quadratic regression model is used to model a nonlinear relationship between the independent and dependent variables by including the independent variable and the square of the independent variable.
Explanation:The correct answer to this question is C. Quadratic regression model. In statistics, a quadratic regression model is used to model a nonlinear relationship between the independent and the dependent variables. This is achieved by including the independent variable and the square of the independent variable in the model. For example, if 'x' is the independent variable, the model would include both 'x' and 'x²'. The quadratic term allows for the model to fit simple curved relationships between the dependent and independent variable. The other models listed, such as multiple regression model, least squares regression model and a simple regression model, tend to represent linear relationships.
Here is a simple illustrative example: suppose you wanted to model the relation between the amount of fertilizer used (independent variable 'x') and the height of a plant (dependent variable 'y'). If the relation isn't linear (meaning more fertilizer does not always result in more growth, and growth rate declines after a certain point, forming a curved pattern in the data), you could use a quadratic regression model
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A school is putting on a play. On the first night of the play, twice as many adults attended the lay as students. Students tickets cost $3 and adults tickets cost $5. The total amount of money earned from tickets sales was $1,131. Write a system of equations that represent this situation.
Answer:
x+2x+$3+$5=$1131
Step-by-step explanation:
Take students to be x then the adults be 2x and the dollars being played and the total money.Then you will take the $3+$8 and subtract from $1131 dollars then you'll get x
Answer: The system of equations that represent this situation is
x = 2y
5x + 3y = 1131
Step-by-step explanation:
Let x represent the number of adult tickets sold on the first night of the play.
Let y represent the number of student tickets sold on the first night of the play.
On the first night of the play, twice as many adults attended the play as students. This means that
x = 2y
Students tickets cost $3 and adults tickets cost $5. The total amount of money earned from tickets sales was $1,131. This means that
5x + 3y = 1131- - - - - - - - - 1
Add a party there were four large submarine sandwiches all the same size during the party 2/3 of the chicken sandwich three force of a turn a sandwich 712s of the roast beef sandwich and 5/6 of the veggie sandwich or eat it which sandwich had the least amount
Answer:
Veggie
Step-by-step explanation:
I corrected your question for a better situation.
At a party there were four large submarine sandwiches all the same size . During the party 2/3 of the chicken sandwich three over 4 of the tuna sandwich 7/12 of the roast beef sandwich and 5/6 of the veggie sandwich were eating which sandwich had the least amount left
Here is my answer:
Chicken sandwich left: 1 - 2/3 =1/3 Tuna sandwich left = 1 - 3/4 = 1/4 Roast sandwich left = 1 -7/12 = 5/12 Veggie sandwich left = 1 - 5/6 = 1/6So the sandwich had the least amount is Veggie
In order for a film camera with a lens of fixed focal length F to focus on an object located a distance x from the lens, the film must be placed a distance y behind the lens. F, y, and x are related as follows: 1/F=1/X+ 1/Y. Now suppose a camera has a lens with focal length F = 65.1. Explain what happens to the focusing distance y as the object moves far away from the lens.2. Explain what happens to the focusing distance y as the object moves closer and closer to the lens.3. In general, why is it not possible to cross a vertical asymptote?
Answer:
y will increase if x is increased,
y will decrease if x is decreased.
Step-by-step explanation:
1/F=1/X+ 1/Y
1/F-1/X=1/Y
X-F/FX=1/Y
FX/X-F=Y
Rearranging, Y=FX/X-F
So this is the function in terms of X, and F is just a constant
Therefore, the function becomes Y=65X/X-65
Explanation:
y = focusing distance
x = distance from lens
Focusing distance y will increase if the object x moves far away from the lens i.e. x is increased,
Similarly, focusing distance y will decrease if the object x moves closer and closer to the lens i.e. x is decreased.
An asymptote is a function that mimics a curve f(x) as x approaches infinity.
A vertical asymptote, however, cannot be crossed in a function. Remember that a function cannot have multiple y values for a given x value, hence the vertical line test for a function. If a function crossed a vertical asymptote and then went back to it, then it would have to go back over itself as it becomes arbitrarily close to the asymptote. Therefore, it is not possible to cross a vertical asymptote.
The focal point, F, the object distance from the lens, X, and the image distance from the the lens, Y, vary according to the lens formula
1. The value of the focusing distance, Y, is negative and increases in
magnitude, when X < 65, and positive and decreasing in magnitude when
X > 65, the line X = 65 is a vertical asymptote.
2. When X > 65, the value of Y is positive and increasing as the object
moves closer to the lens. At X = 65, there is no image when 0 ≤ X < 65, the
value of Y is negative and increasing towards 0.
3. A vertical asymptote is a discontinuity, where the function is not defined
Reasons:
Known;
[tex]\dfrac{1}{F} = \dfrac{1}{X} + \dfrac{1}{Y}[/tex]
Where;
F = The focal length
X = Object distance from lens
Y = Location of film = Image distance from lens
(a) Given that F = 65, we have;
[tex]\dfrac{1}{65} = \dfrac{1}{X} + \dfrac{1}{Y}[/tex]
[tex]\dfrac{1}{65} - \dfrac{1}{X} = \dfrac{1}{Y}[/tex]
[tex]Y = \dfrac{65 \cdot X}{X - 65}[/tex]
Given that 65·X > X - 65 When X > [tex]-\dfrac{65}{64}[/tex], we have;
As X is increased, Y is decreases, with the rate of decrease reducing as the
value of X gets larger.
(b) As the object moves closer to the lens, when X > 65, the value of Y
increases, at X = 65, the value of Y is infinity, which is a vertical asymptote,
as the object moves closer, the value of Y becomes negative, with the
value increasing (becoming less negative) and when X = 0, Y = 0
3. It is not possible to cross the asymptote because the function has a
discontinuity at the asymptote, which represent the point where the image
is at infinity, such that giving that the distance of the image increases as X
approaches the asymptote, crossing the asymptote results in the image
located further than infinity (which is impossible).
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-2 -1 0 1 2 fx 1/8 1/4 1/2 1 2 what is the initial value of the exponential function represented by the table
Answer:
Step-by-step explanation:
The standard form of an exponential function is
[tex]y=a(b)^x[/tex] , where a is the initial value and b is the growth factor.
You will always find your initial value at the y value where x = 0. From your table where x = 0 and y = 1/2:
[tex]\frac{1}{2}=a(b)^0[/tex]
Any number or variable raised to the power of 0 = 1, therefore
[tex]\frac{1}{2}=a(1)[/tex] which gives us an initial value, a, of 1/2.
Amanda wants to attend Baylor University for her 4-year college. She is a National Merit Scholar and scores a 1500 on her SATs. This qualifies her for a yearly scholarship of $44,194. How much additional money does she need to have to attend Baylor for 4 years?
Answer:
$58,544
Step-by-step explanation:
Given that Baylor charges tuition fees at $41,194, Room at $13038 and Required fees at $4598 p.a. We also know that the scholarship pays $44194 p.a.
#The additional money for the four years is the total minus the scholarship multiplied by 4 yrs:
[tex]C_{p.a}=Tution+Room+Required\\\\=41194+13038+4598\\\\=58830\\\\Scholarship=44194\\\\\bigtriangleup p.a=58830-44194\\\\=14636[/tex]
The additional cost to attend the college for the next four years is:
[tex]\bigtriangleup p.a=14636\\\\\sum{\bigtriangleup p.a _i}=4\times 14636\\\\=58544[/tex]
Hence, Amanda needs an additional $58,544 to attend Baylor for the 4 years.
What is the center of the circle described by the equation
x^2+4x+y^2-6y=12
(4, -6)
(-4, 6)
(-2, 3)
(2, -3)
Answer:
The center of the circle is (-2 , 3) ⇒ 3rd answer
Step-by-step explanation:
The equation of a circle is (x - h)² + (y - k)² = r², where
(h , k) are the coordinates of its centerr is the radius of it∵ The equation of the circle is x² + 4x + y² - 6y = 12
- Lets make a completing square for x² + 4x
∵ x² = (x)(x)
∵ 4x ÷ 2 = 2x
- That means the second term of the bracket (x + ...)² is 2
∴ The bracket is (x + 2)
∵ (x + 2)² = x² + 4x + 4
∴ We must add 4 and subtract 4 in the equation of the circle
∴ (x² + 4x + 4) - 4 + y² - 6y = 12
Lets make a completing square for y² - 6y
∵ y² = (y)(y)
∵ -6y ÷ 2 = -3y
- That means the second term of the bracket (y + ....) is -3
∴ The bracket is (y - 3)
∵ (y - 3)² = y² - 6y + 9
∴ We must add 9 and subtract 9 in the equation of the circle
∴ (x² + 4x + 4) - 4 + (y² - 6y + 9) - 9= 12
Now lets simplify the equation
∵ (x + 2)² + (y - 3)² - 13 = 12
- Add 13 to both sides
∴ (x + 2)² + (y - 3)² = 25
- Compare it with the form of the equation of the circle to
find h and k
∵ (x - h)² + (y - k)² = r²
∴ h = -2 and k = 3
The center of the circle is (-2 , 3)
Statistics!! Please help, 10 points and brainliest!
1. You are comparing the heights of contemporary males and eighteenth-century males. The sample mean for a sample of 30 contemporary males is 70.1 inches with a sample standard deviation of 2.52 inches. The sample mean for eighteenth-century males was 65.2 inches with a sample standard deviation of 3.51 inches. Is there sufficient data to conclude that contemporary males are taller than eighteenth-century males?
A. The p-value is less than 0.00001. There is insufficient data to reject the null hypothesis.
B. The p-value is greater than 0.00001. There is sufficient data to reject the null hypothesis.
C. The p-value is greater than 0.00001. There is insufficient data to reject the null hypothesis.
D. The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.
Answer:
[tex]t=\frac{70.1-65.2}{\frac{2.52}{\sqrt{30}}}=10.65[/tex]
[tex]p_v =P(t_{(29)}>10.65)=7.76x10^{-12}[/tex]
And the best conclusion for this case would be:
D. The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.
Step-by-step explanation:
Data given and notation
[tex]\bar X=70.1[/tex] represent the sample mean
[tex]\sigma=2.52[/tex] represent the population standard deviation
[tex]n=30[/tex] sample size
[tex]\mu_o =65.2[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 65.2, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 65.2[/tex]
Alternative hypothesis:[tex]\mu > 65.2[/tex]
If we analyze the size for the sample is = 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{70.1-65.2}{\frac{2.52}{\sqrt{30}}}=10.65[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=30-1=29[/tex]
Since is a one side right tailed test the p value would be:
[tex]p_v =P(t_{(29)}>10.65)=7.76x10^{-12}[/tex]
And the best conclusion for this case would be:
D. The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.
The correct option is D. The p-value is less than [tex]0.00001.[/tex] There is sufficient data to reject the null hypothesis.
Hypotheses:
Null hypothesis [tex](\(H_0\)): \(\mu_1 = \mu_2\)[/tex] (the mean height of contemporary males is equal to the mean height of eighteenth-century males)
Alternative hypothesis [tex](\(H_1\)): \(\mu_1 > \mu_2\)[/tex] (the mean height of contemporary males is greater than the mean height of eighteenth-century males)
Given Data:
Sample mean for contemporary males [tex](\(\bar{x}_1\)) = 70.1 inches[/tex]
Sample standard deviation for contemporary males [tex](\(s_1\)) = 2.52 inches[/tex]
Sample size for contemporary males [tex](\(n_1\)) = 30[/tex]
Sample mean for eighteenth-century males [tex](\(\bar{x}_2\)) = 65.2 inches[/tex]
Sample standard deviation for eighteenth-century males [tex](\(s_2\)) = 3.51\ inches[/tex]
Sample size for eighteenth-century males [tex](\(n_2\)) = 30[/tex]
Test Statistic:
We use a two-sample t-test for the difference of means:
[tex]\[t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}\][/tex]
Substituting the given values:
[tex]\[t = \frac{70.1 - 65.2}{\sqrt{\frac{2.52^2}{30} + \frac{3.51^2}{30}}}\][/tex]
First, calculate the variances and their respective terms:
[tex]\[s_1^2 = 2.52^2 = 6.3504, \quad s_2^2 = 3.51^2 = 12.3201\][/tex]
[tex]\[\frac{s_1^2}{n_1} = \frac{6.3504}{30} = 0.21168, \quad \frac{s_2^2}{n_2} = \frac{12.3201}{30} = 0.41067\][/tex]
[tex]\[\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{0.21168 + 0.41067} = \sqrt{0.62235} = 0.7889\][/tex]
Now calculate the t-value:
[tex]\[t = \frac{70.1 - 65.2}{0.7889} = \frac{4.9}{0.7889} = 6.21\][/tex]
Degrees of Freedom:
Since the sample sizes are the same, we can use the following approximation for degrees of freedom [tex]df[/tex]
[tex]\[df = n_1 + n_2 - 2 = 30 + 30 - 2 = 58\][/tex]
P-value:
Using a t-distribution table or a calculator for a one-tailed test with [tex]58[/tex] degrees of freedom, we find that a t-value of [tex]6.21[/tex] corresponds to a p-value much less than [tex]0.00001.[/tex]
During the 2004 season, New York theater goers bought 11.3 million tickets for a total of $749.0 . Theater goers spent a total of 3.2% more than the year before. What was the totalamount spent during 2003?
Answer:
The total amount spent during 2003 was $725.78.
Step-by-step explanation:
Given:
During the 2004 season, New York theater goers bought 11.3 million tickets for a total of $749.0 . Theater goers spent a total of 3.2% more than the year before.
Now, to find the total amount that was spent during 2003.
Let the amount spent during 2003 be [tex]x.[/tex]
The amount spent during 2004 = $749.0.
As, given theater goers spent a total of 3.2% more than the year before.
So, we put equation to get the amount spent during 2003:
[tex]x+3.2\%\ of\ x=749[/tex]
[tex]x+\frac{3.2}{100} \times x=749[/tex]
[tex]x+\frac{3.2x}{100}=749[/tex]
[tex]\frac{100x+3.2x}{100} =749[/tex]
[tex]\frac{103.2x}{100} =749[/tex]
Multiplying both sides by 100 we get:
[tex]103.2x=74900[/tex]
Dividing both sides by 103.2 we get:
[tex]x=\$725.78[/tex]
Therefore, the total amount spent during 2003 was $725.78.
A set of computer science exam scores are normally distributed with a mean of 71.33 point, and a standard deviation of 3 points. What proportion of the exam scores are between 68 and 77.99 points?
Approximately 85.33% of the exam scores are between 68 and 77.99 points.
To find the proportion of exam scores between 68 and 77.99 points in a normally distributed set, we can use the Z-score formula:
[tex]\[ Z = \frac{X - \mu}{\sigma} \][/tex]
where X is the score, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.
Given:
- Mean [tex]\( \mu = 71.33 \)[/tex]
- Standard deviation [tex]\( \sigma = 3 \)[/tex]
- We need to find the proportion of scores between [tex]\( X_1 = 68 \)[/tex] and [tex]\( X_2 = 77.99 \)[/tex].
1. Calculate the Z-scores for [tex]\( X_1 = 68 \)[/tex]:
[tex]\[ Z_1 = \frac{68 - 71.33}{3} = \frac{-3.33}{3} = -1.11 \][/tex]
2. Calculate the Z-scores for [tex]\( X_2 = 77.99 \)[/tex]:
[tex]\[ Z_2 = \frac{77.99 - 71.33}{3} = \frac{6.66}{3} = 2.22 \][/tex]
Next, we look up these Z-scores in the standard normal distribution table or use a calculator to find the corresponding proportions:
- The proportion corresponding to [tex]\( Z_1 = -1.11 \)[/tex] is approximately 0.1335.
- The proportion corresponding to [tex]\( Z_2 = 2.22 \)[/tex] is approximately 0.9868.
The proportion of scores between [tex]\( X_1 = 68 \)[/tex] and [tex]\( X_2 = 77.99 \)[/tex] is the difference between these two proportions:
[tex]\[ P(68 < X < 77.99) = P(Z < 2.22) - P(Z < -1.11) \][/tex]
[tex]\[ P(68 < X < 77.99) = 0.9868 - 0.1335 = 0.8533 \][/tex]
I need help justifying why my classification is correct
Answer:
7) 6 is not a perfect square, sqrt(6) can't be written in a fraction form
8) 2 is not a perfect cube, cuberoot of 2 can't be written in a fraction form
9) 3/2 is already a fraction, so clearly rational
Marcos made a fruit salad. It contains 6 strawberries, 5 mango slices, 18 grapes, and 2 kiwis. What is the ratio of the number of strawberries to grapes? Express the ratio in simplest form.
3:9
3:1
1:3
9:3
Answer:
1 : 3
Step-by-step explanation:
The ratio of strawberries : grapes = 6 : 18 ( divide both values by 6 )
ratio = 1 : 3 ← in simplest form
Answer:
1 : 3
Step-by-step explanation:
The ratio of strawberries : grapes = 6 : 18 ( divide both values by 6 )
ratio = 1 : 3 ← in simplest form
Brinley is making headbands for her friends.Each headband needs 16 and a half inches of elastic and she has 132 inches of elastic.Use the guess,check,and revise strategy to solve the equation 16 and a half h = 132 to find h, the headbands Brinely can make.
Answer:
8 headbands can be made.
Step-by-step explanation:
dividing both sides by 16.5, the material needed for one, leaves the equation as h=8, because 132 divided by 16.5 equals 8
Brinley can make 8 hands from the elastic she has.
What is the unitary method?
The unitary method is a method in which you find the value of a unit and then the value of a required number of units. Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this case, the apples are the units, and the cost of the apples is the value.
Given here, A headband needs 16 and a half inches of elastic and Brinley has 132 inches of elastic
Therefore the number of headbands that she could make is
= 132/16.5
=8 Headbands.
Hence, Brinley can make 8 hands from the elastic she has.
Learn more about the unitary method here:
https://brainly.com/question/22056199
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Find the probability of winning second prize (that is, picking five of the six winning numbers) with a 6/44 lottery, as played in Connecticut, Missouri, Oregon, and Virginia. (Round the answer to five decimal places.)
Answer:
The answer to the question is
The probability of winning second prize (that is, picking five of the six winning numbers) with a 6/44 lottery, as played in Connecticut, Missouri, Oregon, and Virginia is 3.49905×10⁻⁵≡ 0.00003 to five decimal places.
Step-by-step explanation:
The probability of winning the second prize or picking five of the six winning numbers) with a 6/44 lottery is given by
Number of 5 sets of numbers in 44 = ₄₄C₅ = 1086008 ways
Number of 5 set of winning numbers in 44 = 1
Number of ways of picking the last number to make it 6 numbers is given by
44 - 5 lucky numbers - The 1 winning number = 38
Therefore, there are 38 ways from 1086008 of selecting the 5 second place winning numbers
Therefore the probability of picking the 5 second place winning numbers is [tex]\frac{38}{1086008}[/tex] = 3.49905×10⁻⁵