The given problem states that the number of rushing yards in game 16 is an outlier in the x-direction. Hence, we can say that game 16 has a significant effect on the equation of the least-squares regression line.
We need to find out the effects that this game has on the correlation and on the equation of the least-squares regression line. We also need to calculate the correlation and equation of the least-squares regression line with and without this game to confirm our answers.
Effect on Correlation:
An outlier in the x-direction has no effect on the correlation coefficient(r). The correlation coefficient measures the strength and direction of a linear relationship between two variables. It is not influenced by the presence of an outlier in the independent variable. So, the correlation coefficient with or without this game will remain the same.
Effect on Equation of the Least-Squares Regression Line:
An outlier in the x-direction has a significant effect on the equation of the least-squares regression line. The least-squares regression line is a straight line that summarizes the relationship between the independent and dependent variables. This line is constructed by minimizing the sum of squared deviations between the observed and predicted values. If an outlier is present, it will pull the regression line closer to it. So, the equation of the least-squares regression line will be different with or without this game.
Calculation of Correlation and Equation of Least-Squares Regression Line:
Without game 16,
the correlation coefficient and equation of the least-squares regression line are:
Correlation Coefficient(r) = 0.94
The equation of the least-squares regression line:
y = 2.25x + 10.5 With game 16,
the correlation coefficient and equation of the least-squares regression line are:
Correlation Coefficient(r) = 0.93
The equation of the least-squares regression line:
y = 1.92x + 22.8
From the above calculations, we can see that the correlation coefficient has a negligible change with or without game 16. However, the equation of the least-squares regression line is quite different with and without game 16.
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I really need help a.s.a.p
The area of the semicircle that has a radius of 3 kilometers is calculated as: 14.13 square kilometers.
How to Find the Semicircle's Area?To find the area of a semicircle, you can follow these steps:
Recall that a semicircle is half of a circle. Therefore, the formula for the area of a circle can be modified to find the area of a semicircle by dividing the formula by 2.The formula for the area of a circle is A = πr^2, where A is the area, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.To find the area of a semicircle, divide the formula for the area of a circle by 2. Therefore, the formula for the area of a semicircle is A = 1/2(πr^2).The semicircle's area = 1/2(πr²) = 1/2 * (3.14 * 3²)
= 14.13 square kilometers.
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Ms. Maynard grates 23/30 of a block of cheese. Mr. Connor then eats another 3/30 of the cheese. What fraction of the cheese is left over?
Ms. Maynard grates 23/30 of a block of cheese, leaving the fraction of 7/30 of the cheese. Mr. Connor then eats 3/30 of the cheese, leaving the fraction of 4/30 of the cheese remaining.
Let us suppose the total block of cheese as 1.
If Ms. Maynard grates 23/30 of a block of cheese, then the fraction of cheese left is:
Remaining cheese = 1 - 23/30 = 7/30
After Mr. Connor eats 3/30 of the cheese, the fraction of cheese left is:
Remaining cheese = 7/30 - 3/30 = 4/30
Therefore, 4/30 of the cheese is left over after grating by Ms. Maynard and Mr. Connor respectively.
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a bookstore is deciding what price it should charge for a certain book. after research, the store finds that if the book's price is dollars (where ), then the number of books sold per month is . what price should the store charge to maximize its revenue?
To maximize the revenue, the bookstore should charge $13 for the book.
Given:
p = book's price in dollars, where
p is less than or equal to 26.
number of books sold per month = 130-5p
Price that maximizes revenue = ?
Revenue = Price × QuantityofUnitsSold
Revenue = p(130-5p)
Revenue = [tex]130p - 5p^2[/tex] , This is quadratic equation so, The vertex of the parabola, which gives the price that maximizes revenue, can be determined by calculating the value of x-coordinate of the vertex.
Let x = p
The formula for the x-coordinate of the vertex is [tex]-b/2a[/tex]
where,
a = -5
b = 130
c = 0
x = [tex]-b/2a=-130/-10 = 13[/tex]
So, to maximize the revenue, the bookstore should charge $13 for the book.
Maximum revenue will be:-
Revenue = Price × QuantityofUnitsSold
Revenue = p(130-5p)
where p = 13
Revenue = (13)(130-5(13))
Revenue = $845
The maximum revenue at (price = 13) will be $845.
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Evaluate 0.3y + y/z
When Y=10 and z=5.
Therefore, when y = 10 and z = 5, the value of the expression 0.3y + y/z is 5.
What is expression?In mathematics, an expression is a combination of numbers, variables, and operators that are grouped together to represent a mathematical quantity or relationship. Expressions can be simple, such as a single number or variable, or they can be more complex, involving multiple operations and variables. Expressions are often used in mathematics to represent relationships between variables, to evaluate quantities, and to solve equations.
Here,
Substituting y = 10 and z = 5 in the given expression, we get:
0.3y + y/z = 0.3(10) + 10/5
= 3 + 2
= 5
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which congruency theorem can be used to prove that △abd ≅ △dca?
a. SAS
b. Not enough information
c. SSS
d. AAS
the correct answer is a. SAS congruency theorem can be used to prove that ABD =DCA.
In this question we accept two angles is given that is:
two triangles ∠ABD and
In this, an angle is common that is,
AD = AD
AB = CD
∠A is equal = ∠A (which is given)
That is the reason the SAS rule is right.
SSS is a geometric term that stands for "side-side-side." It refers to a congruence condition in which three sides of one triangle are equal to three corresponding sides of another triangle, making the two triangles congruent. Congruent triangles have the same size and shape, so if two triangles are congruent, all corresponding angles and sides are equal.
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the complete question is:
Which congruency theorem can be used to prove
that ABD =DCA?
a. SAS
b. Not enough information
c. SSS
d. AAS
help pls with explanation maybe?
The domain of this function can be expressed as (-∞,0) U (0,∞).
The interval on which the function is decreasing is
(-∞,0) U (0,∞).
The interval on which the function is increasing is none.
The interval on which the function is constant is (0,0).
What is domain?The domain of a function is the set of all acceptable inputs for the function. In other words, it is the set of all values for which the function is defined.
The domain of the given function is all real numbers, excluding 0.
This can be seen by observing that the denominator in the fraction is the absolute value of t, which is always positive.
Therefore, the domain of the function is all real numbers except 0, which can be expressed as (-∞,0) U (0,∞).
The function is decreasing over all intervals in its domain since the negative sign preceding the fraction indicates that the value of the function is always negative.
Therefore, the interval on which the function is decreasing is
(-∞,0) U (0,∞).
The function is constant over the interval (0,0) since the absolute value of 0 is 0 and thus, the denominator in the fraction is equal to 0.
Therefore, the interval on which the function is constant is (0,0).
Finally, the function is not increasing over any interval in its domain since the negative sign preceding the fraction indicates that the value of the function is always negative.
Therefore, the interval on which the function is increasing is none.
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A town with a population of 80,250 people has 500 city blocks. Each block is one-tenth mile long by one-tenth mile wide. Find the population density of the town in the people per square mile.
Answer:
First, we need to find the area of one block:
Area of one block = length x width = (1/10) mile x (1/10) mile = 1/100 square mile
Since there are 500 blocks in the town, the total area of the town is:
Total area of town = 500 blocks x (1/100) square mile/block = 5 square miles
To find the population density, we divide the population by the total area:
Population density = population / total area
Population density = 80,250 / 5 = 16,050 people per square mile
Therefore, the population density of the town is 16,050 people per square mile.
Help don’t understand
Thank you geometry 10tg grade
The surface area of a cylinder is given by the formula:
A = 2πrh + 2π[tex]r^{2}[/tex]= 2*3.14*4.8*19.1= 575.504 square ft.
What is surface area?Surface area is the measure of the total area that the surface of an object occupies. It is the sum of all the areas of the individual faces or surfaces of the object. For example, if you have a cube, the surface area would be the sum of the areas of all six faces of the cube. The surface area is usually measured in square units, such as square meters, square centimeters, or square feet, depending on the system of measurement used. Surface area is an important concept in many fields of study, including mathematics, physics, chemistry, and engineering.
by the question.
The surfaces area of a cylinder is given by the formula:
[tex]A = 2πrh + 2πr^2[/tex]
where r is the radius of the circular base of the cylinder, and h is the height of the cylinder.
If a=9.6ft and b=19.1ft, we need to determine the values of r and h before we can calculate the surface area.
Since the cylinder has a circular base, we know that the diameter of the base is equal to b, or 19.1ft. Therefore, the radius of the base is half the diameter, or:
r = b/2 = 19.1/2 = 9.55ft
we know that the radius of the cylinder is = diameter/2
= 9.6/2
= 4.8
The surfaces area of a cylinder= [tex]A = 2πrh + 2πr^2[/tex]
A = 2πrh + 2π[tex]r^{2}[/tex]= 2*3.14*4.8*19.1= 575.504 square ft.
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What's the area of a regular triangle with a side length of 15? (Explanations step-by-step are appreciated!)
the area of the equilateral triangle with a side length of 15 is approximately 97.4279 square units.
A regular triangle is also known as an equilateral triangle, which means all of its sides are equal in length. To find the area of an equilateral triangle with a side length of 15, we can use the following formula:
Area = (√(3) / 4) × side²
where "side" is the length of one side of the triangle.
Let's plug in the given value of side length, which is 15, into the formula:
Area = (√(3) / 4) × 15²
Area = (√(3) / 4) × 225
Area = 97.4279 (rounded to 4 decimal places)
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Numbers that are greater than 11 over 16 and less than 15 over 16
Any number that is strictly greater than 11/16 and strictly less than 15/16 belongs to this interval.
What is the inequalities?In mathematics, inequalities are statements that cοmpare twο values and indicate whether οne value is greater than, less than, οr equal tο the οther value.
Tο find the numbers that are greater than 11/16 and less than 15/16, we need tο cοnsider all numbers between these twο values, excluding the endpοints. That is,
11/16 < x < 15/16
where x represents the number we are looking for. We can also write this using interval notation as:
(11/16, 15/16)
Hence, any number that is strictly greater than 11/16 and strictly less than 15/16 belongs to this interval.
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A man in a lighthouse tower that is 30 ft. He spots a ship at sea at an angle of depression of 10°. How far is the ship from the base of the lighthouse?
Answer:
170.16 ft
Step-by-step explanation:
tan10° = 30/x
x = 30x/ tan 10° = 30/0.1763
=170.16 ft
In 2002 a company's sales revenue was $540,000 and its marketing expenses were $97,200. Marketing expenses are what percentage of total sales?
Answer:
18%
Step-by-step explanation:
first you divide 97,200 from 540,000= 0.18 x 100=18%
Find the volume of this composite shape.
16 ft
24 ft
Answer:
that question is incomplete
What is the image point of (4,8) after a translation right 1 unit and up 5 units?(Explain+Rules)
Answer:
(5, 13)
Step-by-step explanation:
Points (4, 8)
Translation right 1 unit. Meaning x + 1
(4, 8) → (5, 8)
Up 5 units. Meaning y + 5
(5, 8) → (5, 13)
So, the final point at (5, 13)
16) During a theater season, New York theatergoers bought 11.7 million tickets for $588.5 million. To the nearest dollar, what was the mean price for a theater ticket in New York???
mean price for a theatre ticket in New York is $ 50.299
Mean can be expressed as the total sum of observations for the total number of observations.
In other words its the sum by the count
It gives the average measure of each entity.
The mean Price is sometimes called Average Price.
Total number of Tickets = 11.7 million
Total Cost = $588.5 million
Mean Price = Total Cost / Total Number of Tickets
= 588.5 million / 11.7 million
= $ 50.299
mean price for a theatre ticket in New York is $ 50.299
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Circumference area of circle use 3.14 for pi
The required area and the circumference of the given circle are 19.63 ft² and 15.70 ft respectively.
What is a circle?Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.
The points of the circle are at a fixed distance from the center.
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the “center”.
So, the area would be:
= πr²
= 3.14*2.5*2.5
= 19.63495
= 19.63 ft²
The circumference would be:
= 2πr
= 2*3.14*2.5
= 15.70796
= 15.70 ft
Therefore, the required area and the circumference of the given circle are 19.63 ft² and 15.70 ft respectively.
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Eric rents a bounce house for his son's birthday. There is a rental fee of $85 and a fee of $8 per hour. Eric only has $125 to spend on the bounce house. Write an equation to find the number of h, hours, that Eric can rent the bounce house.
please help, I need an answer and fast!
Answer:
[tex]85 + 8h = 125[/tex]
tell whether the ratios form a proportion 4:14 and 12:40
Answer:
NO
Step-by-step explanation:
First, we should simplify both fractions to the most simple form.
4/14=2/7
12/40=6/20=3/10
A proportion means that it is equal. 2/7 does not equal 3/10, so the answer is no.
the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 22 minutes and a standard deviation of 6 minutes. find the probability that a randomly selected athlete uses a stairclimber for (a) less than 18 minutes, (b) between 22 and 31 minutes, and (c) more than 30 minutes.
The probability that a randomly selected athlete uses a stair climber for,
(a) P(X < 18) = 0.2514
(b) P(22 < X < 31) = 0.4332
(c) P(X > 30) = 0.0918
Let X be the amount of time an athlete uses a stair climber. Then, X ~ N(22, 6^2) represents a normal distribution with mean 22 and standard deviation 6.
(a) To find the probability that a randomly selected athlete uses a stair climber for less than 18 minutes, we need to calculate P(X < 18).
Z-score for 18 minutes = (18 - 22) / 6 = -0.67
Using a standard normal table or calculator, we find that P(Z < -0.67) = 0.2514.
Therefore, P(X < 18) = P(Z < -0.67) = 0.2514.
(b) To find the probability that a randomly selected athlete uses a stair climber for between 22 and 31 minutes, we need to calculate P(22 < X < 31).
Z-score for 22 minutes = (22 - 22) / 6 = 0
Z-score for 31 minutes = (31 - 22) / 6 = 1.5
Using a standard normal table or calculator, we find that P(0 < Z < 1.5) = 0.4332.
Therefore, P(22 < X < 31) = P(0 < Z < 1.5) = 0.4332.
(c) To find the probability that a randomly selected athlete uses a stair climber for more than 30 minutes, we need to calculate P(X > 30).
Z-score for 30 minutes = (30 - 22) / 6 = 1.33
Using a standard normal table or calculator, we find that P(Z > 1.33) = 0.0918.
Therefore, P(X > 30) = P(Z > 1.33) = 0.0918.
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8 and 1/32 are powers of what number
Answer:
2
Step-by-step explanation:
Both 8 and 1/32 are powers of 2.
2³ is 8, since 2*2*2=8.
2^-5 is 1/32.
2^5 is 2*2*2*2*2, and the negative sign in front of the 5 flips the answer to be 1/32
Construct a polynomial function of least degree possible using the given information.
Real roots: −1, 1, 3 and (2,
f(2)) = (2, 7)
The polynomial function of least degree possible using the given information is: f(x) = -7/3 (x+1)(x-1)(x-3)
What is polynomial function?
A polynomial function is a type of mathematical function that consists of one or more terms, each of which is a constant multiplied by a variable raised to a non-negative integer power.
To construct a polynomial function of least degree possible using the given information, we need to use the fact that the function has real roots at -1, 1, and 3. This means that the function can be factored as follows:
f(x) = a(x+1)(x-1)(x-3)
where a is a constant coefficient that we need to determine.
Next, we need to use the fact that the function passes through the point (2, 7) to determine the value of a. We substitute x=2 and f(x)=7 into the above equation and solve for a:
7 = a(2+1)(2-1)(2-3)
7 = -3a
a = -7/3
Therefore, the polynomial function of least degree possible using the given information is:
f(x) = -7/3 (x+1)(x-1)(x-3)
Note that this function has real roots at -1, 1, and 3, and passes through the point (2, 7).
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Please Answer Quickly I need help
In the given proof the blanks are ΔAED ≅ ΔABC using the AA criteria.
What is reflexive property?Every component of the set is connected to itself, according to the reflexive feature of sets. The reflexive property of congruence is known when the relation specified on a set is congruence, and the reflexive property of equality is known when the relation defined on a set of numbers is equality. When this occurs, the relation can be referred to as a reflexive relation or as a reflexive property being satisfied on that set. In the parts that follow, let's learn more about equality and congruence's reflexive attribute.
Given that angle A is congruent to angle A using the reflexive property.
Thus, ΔAED ≅ ΔABC using the AA criteria.
Hence, in the given proof the blanks are ΔAED ≅ ΔABC using the AA criteria.
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A new player joins the team and raises the mean to 22
A. The mean age of the team rounded to 1 decimal place is 20.9 years
B. The age of the new player is 23.1 years
A. How do i determine the mean age of the team?The mean age of the team can be obtained as illustrated below:
Age (x) = 19, 20, 21, 22, 23, Frequency (f) = 2, 3, 1, 4, 1Mean age =?Mean age = ∑fx / ∑f
Mean age = [(19 × 2) + (20 × 3) + (21 × 1) + (22 × 4) + (23 × 1)] / (2 + 3 + 1 + 4 + 1)
Mean age = 230 / 11
Mean age = 20.9 years
Thus, the mean age of the team is 20.9 years
B. How do i determine the age of the new player?The age of the new player can be obtained as follow:
Mean of previous player = 20.9 yearsNew mean = 22Age of new player =?New mean = (mean of previous + age of new player) / 2
22 = (20.9 + age of new player) / 2
Cross multiply
22 × 2 = 20.9 + age of new player
44 = 20.9 + age of new player
Collect like terms
44 - 20.9 = Age of new player
Age of new player = 23.1 years
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Complete question:
Pleas attached photo
I need help plsssssssssssssss
Answer:3.14sq^2
Step-by-step explanation:b x c x a = 3.14
John borrows R3000 from the bank .he must repay the loan after 3 years . the bank changes compound interest at 10% per annum .how much interest will John pay over the three years
Answer:
Step-by-step explanation:
10 percent of 3000 = 300
3000+300=3300
3300+300=3600
3600+300=3900
interest = 3900-3000
= R900
he will pay R900 interest over 3 years.
i think this is the answer.
Tomorrow, Sunita and Sunil will get married according to Hindu ritual. In Sunil's house, four banana plants have to be fixed in four corners for 'Linga Chauka in such a way that consecutive banana plants should be fixed at equal distances and banana plants in diagonally opposite direction should also be at the equal distances. If the coordinates of any two opposite banana plants are (3, 4) and (7, 2), then find the equation of the line made by the rice flour joining the remaining two opposite banana plants.
The equation of the line made by the rice flour joining the remaining two opposite banana plants is y = 2x - 7.
How to find the equation of the line?We are given the coordinates of two opposite banana plants, (3, 4) and (7, 2). Since the consecutive plants are fixed at equal distances, the other two plants will lie on the perpendicular bisector of the line segment joining (3, 4) and (7, 2).
First, let's find the midpoint of the line segment joining (3, 4) and (7, 2):
Midpoint = ((x1 + x2)/2, (y1 + y2)/2) = ((3 + 7)/2, (4 + 2)/2) = (5, 3)
Find the slope of the line segment joining (3, 4) and (7, 2):
Slope = (y2 - y1)/(x2 - x1) = (2 - 4)/(7 - 3) = -2/4 = -1/2
Now, we can use the point-slope form of a linear equation to find the equation of the line made by the rice flour joining the remaining two opposite banana plants:
y - y1 = m(x - x1)
Here, m is the slope, and (x1, y1) is the midpoint (5, 3):
y - 3 = 2(x - 5)
y - 3 = 2x - 10
y = 2x - 7
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Solve each inequality given that the function f is increasing over its domain[tex]f(4x-3)\geq f(2-x^2), D_{f}=(-8, 4) \\g(3x^2-2x)\geq g(3x-2), D_{g}=All real numbers[/tex]
The values of the inequalities are -5 ≤ x ≤ 1 and 2/3 ≤ x ≤ 1
What are inequalities?
An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here, we have
Inequality 1: f(4x - 3) ≥ f(2 - x²), Df = (-8 , 4)
The function increases at (-8,4).
So, we have:
4x - 3 ≥ 2 - x²
Rewrite as:
x² + 4x - 2 - 3 ≥ 0
Evaluate the like terms
x² + 4x - 5 ≥ 0
Expand
x² + 5x - x - 5 ≥ 0
Factorize the expression
x(x + 5) - 1(x + 5) ≥ 0
Factor out x + 5
(x - 1)(x + 5) ≥ 0
Solve for x
x ≥ 1 or x ≥ -5
Rewrite as:
-5 ≤ x ≤ 1
Inequality 2: g(3x² - 2x) ≥ g(3x - 2), Dg = all real numbers
g(3x² - 2x) ≥ g(3x - 2)
(3x² - 2x) ≥ (3x - 2)
Evaluate the like terms
3x² - 2x -3x + 2 ≤ 0
3x² - 5x + 2 ≤ 0
3x² - 3x -2x + 2 ≤ 0
3x(x-1) -2(x-1) ≤ 0
Solve for x
x≤1 or x≤2/3
Hence, the values of the inequalities are -5 ≤ x ≤ 1 and 2/3 ≤ x ≤ 1
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Please help with graph problem. Thank you loads!!!
Answer:
a. 250,000
b. 450,000
Step-by-step explanation:
-6(3x - 9y-10) slove
Answer:
-18x + 54y + 60
Step-by-step explanation:
you get this answer by distributing the -6 to all 3 properties.
-6 x 3x = -18x
-6 x -9y = 54y
-6 x -10 = 60
fizzfizz soda comes in two flavors, regular and diet. if a researcher has 7 boxes of each, how many ways can he select 4 boxes, consisting of 2 boxes of regular and 2 boxes of diet, for a quality control test?
Number of ways that the researcher can select 4 boxes, consisting of 2 boxes of regular and 2 boxes of diet, for a quality control test is 441
To select 4 boxes consisting of 2 regular and 2 diet from 7 boxes of each, we need to use combinations.
The number of ways to select 2 regular boxes out of 7 is
C(7,2) = 21
Similarly, the number of ways to select 2 diet boxes out of 7 is also 21.
Now we need to choose 2 regular boxes out of 2 and 2 diet boxes out of 2, which can only be done in one way.
So the total number of ways to select 4 boxes consisting of 2 regular and 2 diet is
21 x 21 x 1 x 1 = 441
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